%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO520+1 : TPTP v9.0.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:06:27 AM UTC 2025
% Result : Theorem 0.52s 0.73s
% Output : Proof 0.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO520+1 : TPTP v9.0.0. Released v7.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 14:59:23 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.52/0.73 % SZS status Theorem
% 0.52/0.73 % SZS output start Proof
% 0.52/0.73 tff(f813_type, type, (
% 0.52/0.73 f813: ( $i * $i * $i * $i * $i ) > $i)).
% 0.52/0.73 tff(tptp_fun_Xc_2_type, type, (
% 0.52/0.73 tptp_fun_Xc_2: $i)).
% 0.52/0.73 tff(tptp_fun_Xb_0_type, type, (
% 0.52/0.73 tptp_fun_Xb_0: $i)).
% 0.52/0.73 tff(tptp_fun_Xq_3_type, type, (
% 0.52/0.73 tptp_fun_Xq_3: $i)).
% 0.52/0.73 tff(tptp_fun_Xp_4_type, type, (
% 0.52/0.73 tptp_fun_Xp_4: $i)).
% 0.52/0.73 tff(s_type, type, (
% 0.52/0.73 s: ( $i * $i ) > $i)).
% 0.52/0.73 tff(il_type, type, (
% 0.52/0.73 il: ( $i * $i * $i * $i ) > $i)).
% 0.52/0.73 tff(s_e_type, type, (
% 0.52/0.73 s_e: ( $i * $i * $i * $i ) > $o)).
% 0.52/0.73 tff(tptp_fun_Xa_1_type, type, (
% 0.52/0.73 tptp_fun_Xa_1: $i)).
% 0.52/0.73 tff(s_r_type, type, (
% 0.52/0.73 s_r: ( $i * $i * $i ) > $o)).
% 0.52/0.73 tff(perp_type, type, (
% 0.52/0.73 perp: ( $i * $i * $i * $i ) > $o)).
% 0.52/0.73 tff(s_col_type, type, (
% 0.52/0.73 s_col: ( $i * $i * $i ) > $o)).
% 0.52/0.73 tff(perpAt_type, type, (
% 0.52/0.73 perpAt: ( $i * $i * $i * $i * $i ) > $o)).
% 0.52/0.73 tff(g813_type, type, (
% 0.52/0.73 g813: ( $i * $i * $i * $i * $i ) > $i)).
% 0.52/0.73 tff(g811_type, type, (
% 0.52/0.73 g811: ( $i * $i * $i * $i * $i ) > $i)).
% 0.52/0.73 tff(f811_type, type, (
% 0.52/0.73 f811: ( $i * $i * $i * $i * $i ) > $i)).
% 0.52/0.73 tff(s_t_type, type, (
% 0.52/0.73 s_t: ( $i * $i * $i ) > $o)).
% 0.52/0.73 tff(1,plain,
% 0.52/0.73 (^[Xa: $i, Xb: $i, Xc: $i] : refl((~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))))) <=> (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))))))),
% 0.52/0.73 inference(bind,[status(th)],[])).
% 0.52/0.73 tff(2,plain,
% 0.52/0.73 (![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))),
% 0.52/0.73 inference(quant_intro,[status(thm)],[1])).
% 0.52/0.73 tff(3,plain,
% 0.52/0.73 (^[Xa: $i, Xb: $i, Xc: $i] : trans(monotonicity(rewrite((s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))) <=> (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))), ((((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))) <=> (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))))), rewrite((((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))) <=> (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))), ((((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))) <=> (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))))),
% 0.52/0.73 inference(bind,[status(th)],[])).
% 0.52/0.73 tff(4,plain,
% 0.52/0.73 (![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))),
% 0.52/0.73 inference(quant_intro,[status(thm)],[3])).
% 0.52/0.73 tff(5,plain,
% 0.52/0.73 (![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))),
% 0.52/0.73 inference(rewrite,[status(thm)],[])).
% 0.52/0.73 tff(6,axiom,(![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d_Defn8_1')).
% 0.52/0.73 tff(7,plain,
% 0.52/0.73 (![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))),
% 0.52/0.73 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.52/0.73 tff(8,plain,(
% 0.52/0.73 ![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))),
% 0.52/0.73 inference(skolemize,[status(sab)],[7])).
% 0.52/0.73 tff(9,plain,
% 0.52/0.73 (![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))),
% 0.52/0.73 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.52/0.73 tff(10,plain,
% 0.52/0.73 (![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))),
% 0.52/0.73 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.52/0.73 tff(11,plain,
% 0.52/0.73 ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))) | (~((~((~s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~(s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))))),
% 0.52/0.73 inference(quant_inst,[status(thm)],[])).
% 0.52/0.73 tff(12,plain,
% 0.52/0.73 (~((~((~s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~(s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.52/0.73 tff(13,plain,
% 0.52/0.73 (((~((~s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~(s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))) | ((~s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))),
% 0.52/0.73 inference(tautology,[status(thm)],[])).
% 0.52/0.73 tff(14,plain,
% 0.52/0.73 ((~s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.52/0.73 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.52/0.73 tff(15,plain,
% 0.52/0.73 (^[Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : refl((~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))))) <=> (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))))))),
% 0.52/0.73 inference(bind,[status(th)],[])).
% 0.52/0.73 tff(16,plain,
% 0.52/0.73 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))))) <=> ![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))),
% 0.52/0.73 inference(quant_intro,[status(thm)],[15])).
% 0.52/0.73 tff(17,plain,
% 0.52/0.73 (^[Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : trans(monotonicity(rewrite(((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) <=> ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))), rewrite(((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))) <=> ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))), ((((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))) <=> (((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))))), rewrite((((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))) <=> (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))), ((((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))) <=> (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))))),
% 0.52/0.73 inference(bind,[status(th)],[])).
% 0.52/0.73 tff(18,plain,
% 0.52/0.73 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))) <=> ![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))),
% 0.52/0.73 inference(quant_intro,[status(thm)],[17])).
% 0.52/0.73 tff(19,plain,
% 0.52/0.73 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))) <=> ![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))),
% 0.52/0.73 inference(rewrite,[status(thm)],[])).
% 0.52/0.73 tff(20,plain,
% 0.52/0.73 (^[Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : rewrite((((((((Xa = Xb) | (~s_col(Xa, Xb, Xp))) | (~s_col(Xa, Xb, Xq))) | (Xq = Xp)) | (~s_col(Xa, Xb, Xc))) | (~perp(Xa, Xb, Xc, Xp))) & ((((((Xa = Xb) | (~s_col(Xa, Xb, Xp))) | (~s_col(Xa, Xb, Xq))) | (Xq = Xp)) | s_r(Xc, Xp, Xq)) | (~perp(Xa, Xb, Xc, Xp)))) <=> (((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))))),
% 0.52/0.73 inference(bind,[status(th)],[])).
% 0.52/0.73 tff(21,plain,
% 0.52/0.73 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (((((((Xa = Xb) | (~s_col(Xa, Xb, Xp))) | (~s_col(Xa, Xb, Xq))) | (Xq = Xp)) | (~s_col(Xa, Xb, Xc))) | (~perp(Xa, Xb, Xc, Xp))) & ((((((Xa = Xb) | (~s_col(Xa, Xb, Xp))) | (~s_col(Xa, Xb, Xq))) | (Xq = Xp)) | s_r(Xc, Xp, Xq)) | (~perp(Xa, Xb, Xc, Xp)))) <=> ![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))),
% 0.52/0.73 inference(quant_intro,[status(thm)],[20])).
% 0.52/0.73 tff(22,axiom,(![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (((((((Xa = Xb) | (~s_col(Xa, Xb, Xp))) | (~s_col(Xa, Xb, Xq))) | (Xq = Xp)) | (~s_col(Xa, Xb, Xc))) | (~perp(Xa, Xb, Xc, Xp))) & ((((((Xa = Xb) | (~s_col(Xa, Xb, Xp))) | (~s_col(Xa, Xb, Xq))) | (Xq = Xp)) | s_r(Xc, Xp, Xq)) | (~perp(Xa, Xb, Xc, Xp))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz8_16a')).
% 0.52/0.73 tff(23,plain,
% 0.52/0.73 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))),
% 0.52/0.73 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.52/0.73 tff(24,plain,
% 0.52/0.73 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))),
% 0.52/0.73 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.52/0.73 tff(25,plain,(
% 0.52/0.73 ![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))),
% 0.52/0.73 inference(skolemize,[status(sab)],[24])).
% 0.52/0.73 tff(26,plain,
% 0.52/0.73 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))),
% 0.52/0.73 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.52/0.73 tff(27,plain,
% 0.52/0.73 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))),
% 0.52/0.73 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.52/0.73 tff(28,plain,
% 0.52/0.73 (((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))) <=> ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.52/0.73 inference(rewrite,[status(thm)],[])).
% 0.52/0.73 tff(29,plain,
% 0.52/0.73 ((~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))))) <=> (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))),
% 0.52/0.73 inference(rewrite,[status(thm)],[])).
% 0.52/0.73 tff(30,plain,
% 0.52/0.73 (((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2)))))))) <=> ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.52/0.73 inference(monotonicity,[status(thm)],[29])).
% 0.52/0.73 tff(31,plain,
% 0.52/0.73 (((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2)))))))) <=> ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.52/0.74 inference(transitivity,[status(thm)],[30, 28])).
% 0.52/0.74 tff(32,plain,
% 0.52/0.74 ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2)))))))),
% 0.52/0.74 inference(quant_inst,[status(thm)],[])).
% 0.52/0.74 tff(33,plain,
% 0.52/0.74 ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.52/0.74 tff(34,plain,
% 0.52/0.74 (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))),
% 0.52/0.74 inference(unit_resolution,[status(thm)],[33, 27])).
% 0.52/0.74 tff(35,plain,
% 0.52/0.74 (((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | ((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.52/0.74 inference(tautology,[status(thm)],[])).
% 0.52/0.74 tff(36,plain,
% 0.52/0.74 ((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.52/0.74 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.52/0.74 tff(37,plain,
% 0.52/0.74 ((~((Xp!4 = Xq!3) | s_col(Xc!2, Xa!1, Xb!0) | (Xa!1 = Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)))) <=> (~((Xp!4 = Xq!3) | s_col(Xc!2, Xa!1, Xb!0) | (Xa!1 = Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2))))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(38,plain,
% 0.52/0.74 ((~![Xp: $i, Xq: $i, Xc: $i, Xa: $i, Xb: $i] : ((Xp = Xq) | s_col(Xc, Xa, Xb) | (Xa = Xc) | (~perpAt(Xp, Xq, Xc, Xb, Xc)) | (~perpAt(Xp, Xq, Xc, Xa, Xc)))) <=> (~![Xp: $i, Xq: $i, Xc: $i, Xa: $i, Xb: $i] : ((Xp = Xq) | s_col(Xc, Xa, Xb) | (Xa = Xc) | (~perpAt(Xp, Xq, Xc, Xb, Xc)) | (~perpAt(Xp, Xq, Xc, Xa, Xc))))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(39,plain,
% 0.52/0.74 ((~![Xp: $i, Xq: $i, Xc: $i, Xa: $i, Xb: $i] : (((((Xp = Xq) | (~perpAt(Xp, Xq, Xc, Xa, Xc))) | (~perpAt(Xp, Xq, Xc, Xb, Xc))) | (Xa = Xc)) | s_col(Xc, Xa, Xb))) <=> (~![Xp: $i, Xq: $i, Xc: $i, Xa: $i, Xb: $i] : ((Xp = Xq) | s_col(Xc, Xa, Xb) | (Xa = Xc) | (~perpAt(Xp, Xq, Xc, Xb, Xc)) | (~perpAt(Xp, Xq, Xc, Xa, Xc))))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(40,axiom,(~![Xp: $i, Xq: $i, Xc: $i, Xa: $i, Xb: $i] : (((((Xp = Xq) | (~perpAt(Xp, Xq, Xc, Xa, Xc))) | (~perpAt(Xp, Xq, Xc, Xb, Xc))) | (Xa = Xc)) | s_col(Xc, Xa, Xb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aLemma9_13g')).
% 0.52/0.74 tff(41,plain,
% 0.52/0.74 (~![Xp: $i, Xq: $i, Xc: $i, Xa: $i, Xb: $i] : ((Xp = Xq) | s_col(Xc, Xa, Xb) | (Xa = Xc) | (~perpAt(Xp, Xq, Xc, Xb, Xc)) | (~perpAt(Xp, Xq, Xc, Xa, Xc)))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.52/0.74 tff(42,plain,
% 0.52/0.74 (~![Xp: $i, Xq: $i, Xc: $i, Xa: $i, Xb: $i] : ((Xp = Xq) | s_col(Xc, Xa, Xb) | (Xa = Xc) | (~perpAt(Xp, Xq, Xc, Xb, Xc)) | (~perpAt(Xp, Xq, Xc, Xa, Xc)))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[41, 38])).
% 0.52/0.74 tff(43,plain,
% 0.52/0.74 (~![Xp: $i, Xq: $i, Xc: $i, Xa: $i, Xb: $i] : ((Xp = Xq) | s_col(Xc, Xa, Xb) | (Xa = Xc) | (~perpAt(Xp, Xq, Xc, Xb, Xc)) | (~perpAt(Xp, Xq, Xc, Xa, Xc)))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.52/0.74 tff(44,plain,
% 0.52/0.74 (~![Xp: $i, Xq: $i, Xc: $i, Xa: $i, Xb: $i] : ((Xp = Xq) | s_col(Xc, Xa, Xb) | (Xa = Xc) | (~perpAt(Xp, Xq, Xc, Xb, Xc)) | (~perpAt(Xp, Xq, Xc, Xa, Xc)))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[43, 38])).
% 0.52/0.74 tff(45,plain,(
% 0.52/0.74 ~((Xp!4 = Xq!3) | s_col(Xc!2, Xa!1, Xb!0) | (Xa!1 = Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)))),
% 0.52/0.74 inference(skolemize,[status(sab)],[44])).
% 0.52/0.74 tff(46,plain,
% 0.52/0.74 (~((Xp!4 = Xq!3) | s_col(Xc!2, Xa!1, Xb!0) | (Xa!1 = Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[45, 37])).
% 0.52/0.74 tff(47,plain,
% 0.52/0.74 (perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)),
% 0.52/0.74 inference(or_elim,[status(thm)],[46])).
% 0.52/0.74 tff(48,plain,
% 0.52/0.74 (^[Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : refl(((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq))) <=> ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq))))),
% 0.52/0.74 inference(bind,[status(th)],[])).
% 0.52/0.74 tff(49,plain,
% 0.52/0.74 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))),
% 0.52/0.74 inference(quant_intro,[status(thm)],[48])).
% 0.52/0.74 tff(50,plain,
% 0.52/0.74 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(51,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz8_14c')).
% 0.52/0.74 tff(52,plain,
% 0.52/0.74 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.52/0.74 tff(53,plain,(
% 0.52/0.74 ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))),
% 0.52/0.74 inference(skolemize,[status(sab)],[52])).
% 0.52/0.74 tff(54,plain,
% 0.52/0.74 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.52/0.74 tff(55,plain,
% 0.52/0.74 (((~![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))) | ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (Xc!2 = il(Xp!4, Xq!3, Xb!0, Xc!2)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (Xc!2 = il(Xp!4, Xq!3, Xb!0, Xc!2)))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(56,plain,
% 0.52/0.74 ((~![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))) | ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (Xc!2 = il(Xp!4, Xq!3, Xb!0, Xc!2)))),
% 0.52/0.74 inference(quant_inst,[status(thm)],[])).
% 0.52/0.74 tff(57,plain,
% 0.52/0.74 ((~![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (Xc!2 = il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.52/0.74 tff(58,plain,
% 0.52/0.74 (Xc!2 = il(Xp!4, Xq!3, Xb!0, Xc!2)),
% 0.52/0.74 inference(unit_resolution,[status(thm)],[57, 54, 47])).
% 0.52/0.74 tff(59,plain,
% 0.52/0.74 (il(Xp!4, Xq!3, Xb!0, Xc!2) = Xc!2),
% 0.52/0.74 inference(symmetry,[status(thm)],[58])).
% 0.52/0.74 tff(60,plain,
% 0.52/0.74 (s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)) <=> s_col(Xp!4, Xq!3, Xc!2)),
% 0.52/0.74 inference(monotonicity,[status(thm)],[59])).
% 0.52/0.74 tff(61,plain,
% 0.52/0.74 (s_col(Xp!4, Xq!3, Xc!2) <=> s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.52/0.74 inference(symmetry,[status(thm)],[60])).
% 0.52/0.74 tff(62,plain,
% 0.52/0.74 (^[Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : refl((~((~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))))) <=> (~((~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))))))),
% 0.52/0.74 inference(bind,[status(th)],[])).
% 0.52/0.74 tff(63,plain,
% 0.52/0.74 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (~((~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (~((~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))))),
% 0.52/0.74 inference(quant_intro,[status(thm)],[62])).
% 0.52/0.74 tff(64,plain,
% 0.52/0.74 (^[Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : trans(monotonicity(rewrite(((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) <=> ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))), rewrite(((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) <=> ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))), ((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))))), rewrite((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))) <=> (~((~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))))), ((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))) <=> (~((~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))))))),
% 0.52/0.74 inference(bind,[status(th)],[])).
% 0.52/0.74 tff(65,plain,
% 0.52/0.74 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (~((~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))))),
% 0.52/0.74 inference(quant_intro,[status(thm)],[64])).
% 0.52/0.74 tff(66,plain,
% 0.52/0.74 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(67,plain,
% 0.52/0.74 (^[Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))))), (((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) <=> ((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))))), rewrite(((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)))), (((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))))), ((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) <=> ((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))))), rewrite(((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)))), ((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))))), (((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) <=> ((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))))), rewrite(((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))))), (((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))))), ((((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) <=> ((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))))), rewrite(((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))))), ((((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))))), (((((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) <=> ((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))))), rewrite(((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))))), (((((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))))), ((((((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) <=> ((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))))), rewrite(((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))))), ((((((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))))), (((((((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))) <=> ((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))))), rewrite(((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))), (((((((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))))),
% 0.59/0.75 inference(bind,[status(th)],[])).
% 0.59/0.75 tff(68,plain,
% 0.59/0.75 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((((((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))),
% 0.59/0.75 inference(quant_intro,[status(thm)],[67])).
% 0.59/0.75 tff(69,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((((((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz8_13a')).
% 0.59/0.75 tff(70,plain,
% 0.59/0.75 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.59/0.75 tff(71,plain,
% 0.59/0.75 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.59/0.75 tff(72,plain,(
% 0.59/0.75 ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))),
% 0.59/0.75 inference(skolemize,[status(sab)],[71])).
% 0.59/0.75 tff(73,plain,
% 0.59/0.75 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (~((~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.59/0.75 tff(74,plain,
% 0.59/0.75 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (~((~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[73, 63])).
% 0.59/0.75 tff(75,plain,
% 0.59/0.75 ((~![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (~((~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))))) | (~((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xb!0 = Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_r(f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))),
% 0.59/0.75 inference(quant_inst,[status(thm)],[])).
% 0.59/0.75 tff(76,plain,
% 0.59/0.75 (~((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xb!0 = Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_r(f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.59/0.75 tff(77,plain,
% 0.59/0.75 (((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xb!0 = Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_r(f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2))),
% 0.59/0.75 inference(tautology,[status(thm)],[])).
% 0.59/0.75 tff(78,plain,
% 0.59/0.75 ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.59/0.75 tff(79,plain,
% 0.59/0.75 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2))) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2)),
% 0.59/0.75 inference(tautology,[status(thm)],[])).
% 0.59/0.75 tff(80,plain,
% 0.59/0.75 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2))) | s_col(Xp!4, Xq!3, Xc!2)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[79, 47])).
% 0.59/0.75 tff(81,plain,
% 0.59/0.75 (s_col(Xp!4, Xq!3, Xc!2)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[80, 78])).
% 0.59/0.75 tff(82,plain,
% 0.59/0.75 (s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[81, 61])).
% 0.59/0.75 tff(83,plain,
% 0.59/0.75 (perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2)) <=> perp(Xp!4, Xq!3, Xa!1, Xc!2)),
% 0.59/0.75 inference(monotonicity,[status(thm)],[59])).
% 0.59/0.75 tff(84,plain,
% 0.59/0.75 (perp(Xp!4, Xq!3, Xa!1, Xc!2) <=> perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.59/0.75 inference(symmetry,[status(thm)],[83])).
% 0.59/0.75 tff(85,plain,
% 0.59/0.75 (^[Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : refl((~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1)))))) <=> (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1)))))))),
% 0.59/0.75 inference(bind,[status(th)],[])).
% 0.59/0.75 tff(86,plain,
% 0.59/0.75 (![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1)))))) <=> ![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))),
% 0.59/0.75 inference(quant_intro,[status(thm)],[85])).
% 0.59/0.75 tff(87,plain,
% 0.59/0.75 (^[Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : trans(monotonicity(rewrite((perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))) <=> (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1)))), ((((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1)) & (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1)))) <=> (((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1)) & (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1)))))), rewrite((((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1)) & (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1)))) <=> (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))), ((((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1)) & (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1)))) <=> (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))))),
% 0.59/0.75 inference(bind,[status(th)],[])).
% 0.59/0.75 tff(88,plain,
% 0.59/0.75 (![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1)) & (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1)))) <=> ![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))),
% 0.59/0.75 inference(quant_intro,[status(thm)],[87])).
% 0.59/0.75 tff(89,plain,
% 0.59/0.75 (![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1)) & (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1)))) <=> ![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1)) & (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(90,axiom,(![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1)) & (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d_Defn8_11b')).
% 0.59/0.75 tff(91,plain,
% 0.59/0.75 (![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1)) & (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.59/0.75 tff(92,plain,(
% 0.59/0.75 ![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1)) & (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))),
% 0.59/0.75 inference(skolemize,[status(sab)],[91])).
% 0.59/0.75 tff(93,plain,
% 0.59/0.75 (![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.59/0.75 tff(94,plain,
% 0.59/0.75 (![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.59/0.75 tff(95,plain,
% 0.59/0.75 (((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2)))))) <=> ((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2))))))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(96,plain,
% 0.59/0.75 ((~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~(perp(Xp!4, Xq!3, Xa!1, Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)))))) <=> (~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2)))))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(97,plain,
% 0.59/0.75 (((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~(perp(Xp!4, Xq!3, Xa!1, Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2))))))) <=> ((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2))))))),
% 0.59/0.75 inference(monotonicity,[status(thm)],[96])).
% 0.59/0.75 tff(98,plain,
% 0.59/0.75 (((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~(perp(Xp!4, Xq!3, Xa!1, Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2))))))) <=> ((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2))))))),
% 0.59/0.76 inference(transitivity,[status(thm)],[97, 95])).
% 0.59/0.76 tff(99,plain,
% 0.59/0.76 ((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~(perp(Xp!4, Xq!3, Xa!1, Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2))))))),
% 0.59/0.76 inference(quant_inst,[status(thm)],[])).
% 0.59/0.76 tff(100,plain,
% 0.59/0.76 ((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2)))))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.59/0.76 tff(101,plain,
% 0.59/0.76 (~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2))))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[100, 94])).
% 0.59/0.76 tff(102,plain,
% 0.59/0.76 (((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2)))) | ((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2))),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(103,plain,
% 0.59/0.76 ((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2)),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.59/0.76 tff(104,plain,
% 0.59/0.76 (perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)),
% 0.59/0.76 inference(or_elim,[status(thm)],[46])).
% 0.59/0.76 tff(105,plain,
% 0.59/0.76 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2))) | (~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2)),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(106,plain,
% 0.59/0.76 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2))) | perp(Xp!4, Xq!3, Xa!1, Xc!2)),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.59/0.76 tff(107,plain,
% 0.59/0.76 (perp(Xp!4, Xq!3, Xa!1, Xc!2)),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[106, 103])).
% 0.59/0.76 tff(108,plain,
% 0.59/0.76 (perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[107, 84])).
% 0.59/0.76 tff(109,plain,
% 0.59/0.76 ((f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = Xc!2) <=> (Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.59/0.76 inference(commutativity,[status(thm)],[])).
% 0.59/0.76 tff(110,plain,
% 0.59/0.76 ((f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) <=> (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = Xc!2)),
% 0.59/0.76 inference(monotonicity,[status(thm)],[59])).
% 0.59/0.76 tff(111,plain,
% 0.59/0.76 ((f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) <=> (Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.59/0.76 inference(transitivity,[status(thm)],[110, 109])).
% 0.59/0.76 tff(112,plain,
% 0.59/0.76 ((Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) <=> (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.59/0.76 inference(symmetry,[status(thm)],[111])).
% 0.59/0.76 tff(113,plain,
% 0.59/0.76 ((~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) <=> (~(f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)))),
% 0.59/0.76 inference(monotonicity,[status(thm)],[112])).
% 0.59/0.76 tff(114,plain,
% 0.59/0.76 (((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xb!0 = Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_r(f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(115,plain,
% 0.59/0.76 ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[114, 76])).
% 0.59/0.76 tff(116,plain,
% 0.59/0.76 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(117,plain,
% 0.59/0.76 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[116, 47])).
% 0.59/0.76 tff(118,plain,
% 0.59/0.76 (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[117, 115])).
% 0.59/0.76 tff(119,plain,
% 0.59/0.76 (~(f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[118, 113])).
% 0.59/0.76 tff(120,plain,
% 0.59/0.76 (((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xb!0 = Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_r(f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(121,plain,
% 0.59/0.76 ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[120, 76])).
% 0.59/0.76 tff(122,plain,
% 0.59/0.76 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(123,plain,
% 0.59/0.76 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[122, 47])).
% 0.59/0.76 tff(124,plain,
% 0.59/0.76 (s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[123, 121])).
% 0.59/0.76 tff(125,plain,
% 0.59/0.76 (~(Xp!4 = Xq!3)),
% 0.59/0.76 inference(or_elim,[status(thm)],[46])).
% 0.59/0.76 tff(126,plain,
% 0.59/0.76 ((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(127,plain,
% 0.59/0.76 ((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[126, 125, 124])).
% 0.59/0.76 tff(128,plain,
% 0.59/0.76 (s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[127, 119, 108, 82, 36])).
% 0.59/0.76 tff(129,plain,
% 0.59/0.76 ((~((~s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(130,plain,
% 0.59/0.76 ((~((~s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.59/0.76 tff(131,plain,
% 0.59/0.76 (s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[130, 14])).
% 0.59/0.76 tff(132,plain,
% 0.59/0.76 ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))) | (~((~((~s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~(s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))))),
% 0.59/0.76 inference(quant_inst,[status(thm)],[])).
% 0.59/0.76 tff(133,plain,
% 0.59/0.76 (~((~((~s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~(s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[132, 10])).
% 0.59/0.76 tff(134,plain,
% 0.59/0.76 (((~((~s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~(s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))) | ((~s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(135,plain,
% 0.59/0.76 ((~s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.59/0.76 tff(136,plain,
% 0.59/0.76 (((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))) <=> ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(137,plain,
% 0.61/0.77 ((~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))))) <=> (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(138,plain,
% 0.61/0.77 (((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)))))))) <=> ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[137])).
% 0.61/0.77 tff(139,plain,
% 0.61/0.77 (((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)))))))) <=> ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.61/0.77 inference(transitivity,[status(thm)],[138, 136])).
% 0.61/0.77 tff(140,plain,
% 0.61/0.77 ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)))))))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(141,plain,
% 0.61/0.77 ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.61/0.77 tff(142,plain,
% 0.61/0.77 (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[141, 27])).
% 0.61/0.77 tff(143,plain,
% 0.61/0.77 (((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | ((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.61/0.77 inference(tautology,[status(thm)],[])).
% 0.61/0.77 tff(144,plain,
% 0.61/0.77 ((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.61/0.77 tff(145,plain,
% 0.61/0.77 (perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) <=> perp(Xp!4, Xq!3, Xb!0, Xc!2)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[59])).
% 0.61/0.77 tff(146,plain,
% 0.61/0.77 (perp(Xp!4, Xq!3, Xb!0, Xc!2) <=> perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.61/0.77 inference(symmetry,[status(thm)],[145])).
% 0.61/0.77 tff(147,plain,
% 0.61/0.77 (((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2)))))) <=> ((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2))))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(148,plain,
% 0.61/0.77 ((~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~(perp(Xp!4, Xq!3, Xb!0, Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)))))) <=> (~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2)))))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(149,plain,
% 0.61/0.78 (((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~(perp(Xp!4, Xq!3, Xb!0, Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2))))))) <=> ((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2))))))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[148])).
% 0.61/0.78 tff(150,plain,
% 0.61/0.78 (((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~(perp(Xp!4, Xq!3, Xb!0, Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2))))))) <=> ((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2))))))),
% 0.61/0.78 inference(transitivity,[status(thm)],[149, 147])).
% 0.61/0.78 tff(151,plain,
% 0.61/0.78 ((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~(perp(Xp!4, Xq!3, Xb!0, Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2))))))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(152,plain,
% 0.61/0.78 ((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2)))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.61/0.78 tff(153,plain,
% 0.61/0.78 (~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2))))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[152, 94])).
% 0.61/0.78 tff(154,plain,
% 0.61/0.78 (((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2)))) | ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.61/0.78 inference(tautology,[status(thm)],[])).
% 0.61/0.78 tff(155,plain,
% 0.61/0.78 ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.61/0.78 tff(156,plain,
% 0.61/0.78 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2))) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2)),
% 0.61/0.78 inference(tautology,[status(thm)],[])).
% 0.61/0.78 tff(157,plain,
% 0.61/0.78 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2))) | perp(Xp!4, Xq!3, Xb!0, Xc!2)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[156, 47])).
% 0.61/0.78 tff(158,plain,
% 0.61/0.78 (perp(Xp!4, Xq!3, Xb!0, Xc!2)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[157, 155])).
% 0.61/0.78 tff(159,plain,
% 0.61/0.78 (perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[158, 146])).
% 0.61/0.78 tff(160,plain,
% 0.61/0.78 ((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.61/0.78 inference(tautology,[status(thm)],[])).
% 0.61/0.78 tff(161,plain,
% 0.61/0.78 ((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[160, 125, 124])).
% 0.61/0.78 tff(162,plain,
% 0.61/0.78 (s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[161, 119, 159, 82, 144])).
% 0.61/0.78 tff(163,plain,
% 0.61/0.78 ((~((~s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.61/0.78 inference(tautology,[status(thm)],[])).
% 0.61/0.78 tff(164,plain,
% 0.61/0.78 ((~((~s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.61/0.78 tff(165,plain,
% 0.61/0.78 (s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[164, 135])).
% 0.61/0.78 tff(166,plain,
% 0.61/0.78 ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))) | (~((~((~s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~(s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(167,plain,
% 0.61/0.78 (~((~((~s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~(s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[166, 10])).
% 0.61/0.78 tff(168,plain,
% 0.61/0.78 (((~((~s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~(s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))) | ((~s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))),
% 0.61/0.78 inference(tautology,[status(thm)],[])).
% 0.61/0.78 tff(169,plain,
% 0.61/0.78 ((~s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.61/0.78 tff(170,plain,
% 0.61/0.78 (^[Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : refl((~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))))) <=> (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(171,plain,
% 0.61/0.78 (![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))))) <=> ![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[170])).
% 0.61/0.78 tff(172,plain,
% 0.61/0.78 (^[Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : trans(monotonicity(rewrite(((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) <=> ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))), rewrite(((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) <=> ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))), rewrite(((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) <=> ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))), rewrite(((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))), rewrite(((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))), rewrite(((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))), ((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))))), rewrite((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))) <=> (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))), ((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))) <=> (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(173,plain,
% 0.61/0.78 (![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))) <=> ![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[172])).
% 0.61/0.78 tff(174,plain,
% 0.61/0.78 (![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))) <=> ![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(175,plain,
% 0.61/0.78 (^[Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) <=> ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))), (((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) <=> ((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))))), rewrite(((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))))), (((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))))), rewrite(((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) <=> ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))), ((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) <=> ((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))))), rewrite(((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))))), ((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))))), trans(monotonicity(trans(monotonicity(rewrite(((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) <=> ((~s_col(Y, Z, U)) | (~perpAt(Y, Z, X, Y1, Z1)))), ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) <=> (((~s_col(Y, Z, U)) | (~perpAt(Y, Z, X, Y1, Z1))) | (~s_col(Y1, Z1, V))))), rewrite((((~s_col(Y, Z, U)) | (~perpAt(Y, Z, X, Y1, Z1))) | (~s_col(Y1, Z1, V))) <=> ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | (~perpAt(Y, Z, X, Y1, Z1)))), ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) <=> ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | (~perpAt(Y, Z, X, Y1, Z1))))), (((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V)) <=> (((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | (~perpAt(Y, Z, X, Y1, Z1))) | s_r(U, X, V)))), rewrite((((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | (~perpAt(Y, Z, X, Y1, Z1))) | s_r(U, X, V)) <=> ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))), (((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V)) <=> ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))))), (((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V))) <=> ((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))))), rewrite(((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))))), (((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) <=> ((Y = Z) | perpAt(Y, Z, X, Y1, Z1))), (((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) <=> (((Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (Y1 = Z1)))), rewrite((((Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (Y1 = Z1)) <=> ((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1))), (((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) <=> ((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1)))), ((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) <=> (((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, X))))), rewrite((((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1))), ((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1)))), (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) <=> (((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y1, Z1, X))))), rewrite((((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))), (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))), ((((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) <=> (((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))))), rewrite((((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))), ((((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))))), ((((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) <=> ((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))))), rewrite(((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))))), ((((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) <=> ((Y = Z) | perpAt(Y, Z, X, Y1, Z1))), (((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) <=> (((Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (Y1 = Z1)))), rewrite((((Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (Y1 = Z1)) <=> ((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1))), (((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) <=> ((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1)))), ((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) <=> (((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, X))))), rewrite((((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1))), ((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1)))), (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) <=> (((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y1, Z1, X))))), rewrite((((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))), (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))), ((((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) <=> (((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))))), rewrite((((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))), ((((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))))), (((((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) <=> ((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))))), rewrite(((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))))), (((((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) <=> ((Y = Z) | perpAt(Y, Z, X, Y1, Z1))), (((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) <=> (((Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (Y1 = Z1)))), rewrite((((Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (Y1 = Z1)) <=> ((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1))), (((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) <=> ((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1)))), ((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) <=> (((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, X))))), rewrite((((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1))), ((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1)))), (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) <=> (((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y1, Z1, X))))), rewrite((((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))), (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))), ((((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X)))) <=> (((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X)))))), rewrite((((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X)))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))), ((((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X)))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))), ((((((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))))) <=> ((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))))), rewrite(((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))), ((((((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(176,plain,
% 0.61/0.79 (![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (((((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))))) <=> ![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[175])).
% 0.61/0.79 tff(177,axiom,(![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (((((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d_Defn8_11a')).
% 0.61/0.79 tff(178,plain,
% 0.61/0.79 (![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.61/0.79 tff(179,plain,
% 0.61/0.79 (![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[178, 174])).
% 0.61/0.79 tff(180,plain,(
% 0.61/0.79 ![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))),
% 0.61/0.79 inference(skolemize,[status(sab)],[179])).
% 0.61/0.79 tff(181,plain,
% 0.61/0.79 (![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[180, 173])).
% 0.61/0.79 tff(182,plain,
% 0.61/0.79 (![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[181, 171])).
% 0.61/0.79 tff(183,plain,
% 0.61/0.79 (((~![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))) | (~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))) <=> ((~![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))) | (~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(184,plain,
% 0.61/0.79 ((~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~(Xp!4 = Xq!3)))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3))))) <=> (~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(185,plain,
% 0.61/0.80 (((~![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))) | (~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~(Xp!4 = Xq!3)))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))))) <=> ((~![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))) | (~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[184])).
% 0.61/0.80 tff(186,plain,
% 0.61/0.80 (((~![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))) | (~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~(Xp!4 = Xq!3)))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))))) <=> ((~![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))) | (~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.61/0.80 inference(transitivity,[status(thm)],[185, 183])).
% 0.61/0.80 tff(187,plain,
% 0.61/0.80 ((~![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))) | (~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~(Xp!4 = Xq!3)))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))))),
% 0.61/0.81 inference(quant_inst,[status(thm)],[])).
% 0.61/0.81 tff(188,plain,
% 0.61/0.81 ((~![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))) | (~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.61/0.81 tff(189,plain,
% 0.61/0.81 (~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[188, 182])).
% 0.61/0.81 tff(190,plain,
% 0.61/0.81 (((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | ((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.61/0.81 inference(tautology,[status(thm)],[])).
% 0.61/0.81 tff(191,plain,
% 0.61/0.81 ((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.61/0.81 tff(192,plain,
% 0.61/0.81 (perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) <=> perpAt(Xb!0, Xc!2, Xc!2, Xp!4, Xq!3)),
% 0.61/0.81 inference(monotonicity,[status(thm)],[59, 59])).
% 0.61/0.81 tff(193,plain,
% 0.61/0.81 (perpAt(Xb!0, Xc!2, Xc!2, Xp!4, Xq!3) <=> perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)),
% 0.61/0.81 inference(symmetry,[status(thm)],[192])).
% 0.61/0.81 tff(194,plain,
% 0.61/0.81 (^[Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : refl(((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb)) <=> ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb)))),
% 0.61/0.81 inference(bind,[status(th)],[])).
% 0.61/0.81 tff(195,plain,
% 0.61/0.81 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb))),
% 0.61/0.81 inference(quant_intro,[status(thm)],[194])).
% 0.61/0.81 tff(196,plain,
% 0.61/0.81 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(197,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz8_12a')).
% 0.61/0.81 tff(198,plain,
% 0.61/0.81 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.61/0.81 tff(199,plain,(
% 0.61/0.81 ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb))),
% 0.61/0.81 inference(skolemize,[status(sab)],[198])).
% 0.61/0.81 tff(200,plain,
% 0.61/0.81 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[199, 195])).
% 0.61/0.81 tff(201,plain,
% 0.61/0.81 (((~![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb))) | ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perpAt(Xb!0, Xc!2, Xc!2, Xp!4, Xq!3))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb))) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perpAt(Xb!0, Xc!2, Xc!2, Xp!4, Xq!3))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(202,plain,
% 0.61/0.81 ((~![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb))) | ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perpAt(Xb!0, Xc!2, Xc!2, Xp!4, Xq!3))),
% 0.61/0.81 inference(quant_inst,[status(thm)],[])).
% 0.61/0.81 tff(203,plain,
% 0.61/0.81 ((~![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb))) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perpAt(Xb!0, Xc!2, Xc!2, Xp!4, Xq!3)),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.61/0.81 tff(204,plain,
% 0.61/0.81 (perpAt(Xb!0, Xc!2, Xc!2, Xp!4, Xq!3)),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[203, 200, 47])).
% 0.61/0.81 tff(205,plain,
% 0.61/0.81 (perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[204, 193])).
% 0.61/0.81 tff(206,plain,
% 0.61/0.81 (s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)) <=> s_col(Xb!0, Xc!2, Xc!2)),
% 0.66/0.81 inference(monotonicity,[status(thm)],[59, 59])).
% 0.66/0.81 tff(207,plain,
% 0.66/0.81 (s_col(Xb!0, Xc!2, Xc!2) <=> s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.66/0.81 inference(symmetry,[status(thm)],[206])).
% 0.66/0.81 tff(208,plain,
% 0.66/0.81 (((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xb!0 = Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_r(f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2))),
% 0.66/0.81 inference(tautology,[status(thm)],[])).
% 0.66/0.81 tff(209,plain,
% 0.66/0.81 ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2)),
% 0.66/0.81 inference(unit_resolution,[status(thm)],[208, 76])).
% 0.66/0.81 tff(210,plain,
% 0.66/0.81 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2))) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2)),
% 0.66/0.81 inference(tautology,[status(thm)],[])).
% 0.66/0.81 tff(211,plain,
% 0.66/0.81 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2))) | s_col(Xb!0, Xc!2, Xc!2)),
% 0.66/0.81 inference(unit_resolution,[status(thm)],[210, 47])).
% 0.66/0.81 tff(212,plain,
% 0.66/0.81 (s_col(Xb!0, Xc!2, Xc!2)),
% 0.66/0.81 inference(unit_resolution,[status(thm)],[211, 209])).
% 0.66/0.81 tff(213,plain,
% 0.66/0.81 (s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.66/0.81 inference(modus_ponens,[status(thm)],[212, 207])).
% 0.66/0.81 tff(214,plain,
% 0.66/0.81 ((~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.66/0.81 inference(tautology,[status(thm)],[])).
% 0.66/0.81 tff(215,plain,
% 0.66/0.81 ((~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.66/0.82 inference(unit_resolution,[status(thm)],[214, 124])).
% 0.66/0.82 tff(216,plain,
% 0.66/0.82 (s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.66/0.82 inference(unit_resolution,[status(thm)],[215, 213, 205, 191])).
% 0.66/0.82 tff(217,plain,
% 0.66/0.82 ((~((~s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.66/0.82 inference(tautology,[status(thm)],[])).
% 0.66/0.82 tff(218,plain,
% 0.66/0.82 ((~((~s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.66/0.82 inference(unit_resolution,[status(thm)],[217, 216])).
% 0.66/0.82 tff(219,plain,
% 0.66/0.82 (s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.66/0.82 inference(unit_resolution,[status(thm)],[218, 169])).
% 0.66/0.82 tff(220,plain,
% 0.66/0.82 (s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) <=> s_t(Xb!0, Xc!2, Xa!1)),
% 0.66/0.82 inference(monotonicity,[status(thm)],[59])).
% 0.66/0.82 tff(221,plain,
% 0.66/0.82 (s_t(Xb!0, Xc!2, Xa!1) <=> s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1)),
% 0.66/0.82 inference(symmetry,[status(thm)],[220])).
% 0.66/0.82 tff(222,plain,
% 0.66/0.82 ((~s_t(Xb!0, Xc!2, Xa!1)) <=> (~s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1))),
% 0.66/0.82 inference(monotonicity,[status(thm)],[221])).
% 0.66/0.82 tff(223,plain,
% 0.66/0.82 (^[Xa: $i, Xb: $i, Xc: $i] : refl((~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))))) <=> (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))))))),
% 0.66/0.82 inference(bind,[status(th)],[])).
% 0.66/0.82 tff(224,plain,
% 0.66/0.82 (![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))),
% 0.66/0.82 inference(quant_intro,[status(thm)],[223])).
% 0.66/0.82 tff(225,plain,
% 0.66/0.82 (^[Xa: $i, Xb: $i, Xc: $i] : trans(monotonicity(rewrite((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) <=> (s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))), rewrite((s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))) <=> (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))), (((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))))), rewrite(((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))), (((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))))),
% 0.66/0.82 inference(bind,[status(th)],[])).
% 0.66/0.82 tff(226,plain,
% 0.66/0.82 (![Xa: $i, Xb: $i, Xc: $i] : ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))),
% 0.66/0.82 inference(quant_intro,[status(thm)],[225])).
% 0.66/0.82 tff(227,plain,
% 0.66/0.82 (![Xa: $i, Xb: $i, Xc: $i] : ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> ![Xa: $i, Xb: $i, Xc: $i] : ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))),
% 0.66/0.82 inference(rewrite,[status(thm)],[])).
% 0.66/0.82 tff(228,plain,
% 0.66/0.82 (^[Xa: $i, Xb: $i, Xc: $i] : trans(monotonicity(trans(monotonicity(rewrite((((((~s_col(Xa, Xb, Xc)) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) & (s_col(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xc)))) <=> ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)))), rewrite((s_col(Xa, Xb, Xc) | (~s_t(Xb, Xc, Xa))) <=> ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))), (((((((~s_col(Xa, Xb, Xc)) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) & (s_col(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xc)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xb, Xc, Xa)))) <=> (((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))))), rewrite((((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) <=> ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)))), (((((((~s_col(Xa, Xb, Xc)) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) & (s_col(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xc)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xb, Xc, Xa)))) <=> ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))))), rewrite((s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))) <=> (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))), ((((((((~s_col(Xa, Xb, Xc)) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) & (s_col(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xc)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xb, Xc, Xa)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> (((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))))), rewrite((((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))), ((((((((~s_col(Xa, Xb, Xc)) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) & (s_col(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xc)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xb, Xc, Xa)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))),
% 0.66/0.82 inference(bind,[status(th)],[])).
% 0.66/0.82 tff(229,plain,
% 0.66/0.82 (![Xa: $i, Xb: $i, Xc: $i] : (((((((~s_col(Xa, Xb, Xc)) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) & (s_col(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xc)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xb, Xc, Xa)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> ![Xa: $i, Xb: $i, Xc: $i] : ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))),
% 0.66/0.82 inference(quant_intro,[status(thm)],[228])).
% 0.66/0.82 tff(230,axiom,(![Xa: $i, Xb: $i, Xc: $i] : (((((((~s_col(Xa, Xb, Xc)) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) & (s_col(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xc)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xb, Xc, Xa)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d_Defn4_10')).
% 0.66/0.82 tff(231,plain,
% 0.66/0.82 (![Xa: $i, Xb: $i, Xc: $i] : ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))),
% 0.66/0.82 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.66/0.82 tff(232,plain,
% 0.66/0.82 (![Xa: $i, Xb: $i, Xc: $i] : ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))),
% 0.66/0.82 inference(modus_ponens,[status(thm)],[231, 227])).
% 0.66/0.82 tff(233,plain,(
% 0.66/0.82 ![Xa: $i, Xb: $i, Xc: $i] : ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))),
% 0.66/0.82 inference(skolemize,[status(sab)],[232])).
% 0.66/0.82 tff(234,plain,
% 0.66/0.82 (![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))),
% 0.66/0.82 inference(modus_ponens,[status(thm)],[233, 226])).
% 0.66/0.82 tff(235,plain,
% 0.66/0.82 (![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))),
% 0.66/0.82 inference(modus_ponens,[status(thm)],[234, 224])).
% 0.66/0.82 tff(236,plain,
% 0.66/0.82 (((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~((~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | s_t(Xb!0, Xc!2, Xa!1)))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~((~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | s_t(Xb!0, Xc!2, Xa!1))))))),
% 0.66/0.82 inference(rewrite,[status(thm)],[])).
% 0.66/0.82 tff(237,plain,
% 0.66/0.82 ((~((~(s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | (~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xb!0, Xc!2, Xa!1))) | (~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))))) <=> (~((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~((~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | s_t(Xb!0, Xc!2, Xa!1)))))),
% 0.66/0.82 inference(rewrite,[status(thm)],[])).
% 0.66/0.82 tff(238,plain,
% 0.66/0.82 (((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~(s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | (~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xb!0, Xc!2, Xa!1))) | (~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1))))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~((~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | s_t(Xb!0, Xc!2, Xa!1))))))),
% 0.66/0.82 inference(monotonicity,[status(thm)],[237])).
% 0.66/0.82 tff(239,plain,
% 0.66/0.82 (((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~(s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | (~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xb!0, Xc!2, Xa!1))) | (~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1))))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~((~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | s_t(Xb!0, Xc!2, Xa!1))))))),
% 0.66/0.82 inference(transitivity,[status(thm)],[238, 236])).
% 0.66/0.82 tff(240,plain,
% 0.66/0.82 ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~(s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | (~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xb!0, Xc!2, Xa!1))) | (~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1))))))),
% 0.66/0.82 inference(quant_inst,[status(thm)],[])).
% 0.66/0.82 tff(241,plain,
% 0.66/0.82 ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~((~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | s_t(Xb!0, Xc!2, Xa!1)))))),
% 0.66/0.82 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.66/0.82 tff(242,plain,
% 0.66/0.82 (~((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~((~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | s_t(Xb!0, Xc!2, Xa!1))))),
% 0.66/0.82 inference(unit_resolution,[status(thm)],[241, 235])).
% 0.66/0.82 tff(243,plain,
% 0.66/0.82 (((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~((~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | s_t(Xb!0, Xc!2, Xa!1)))) | (s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))),
% 0.66/0.82 inference(tautology,[status(thm)],[])).
% 0.66/0.82 tff(244,plain,
% 0.66/0.82 (s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1))),
% 0.66/0.82 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.66/0.82 tff(245,plain,
% 0.66/0.82 (~s_col(Xc!2, Xa!1, Xb!0)),
% 0.66/0.82 inference(or_elim,[status(thm)],[46])).
% 0.66/0.82 tff(246,plain,
% 0.66/0.82 ((~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1))),
% 0.66/0.82 inference(tautology,[status(thm)],[])).
% 0.66/0.82 tff(247,plain,
% 0.66/0.82 ((~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~s_t(Xb!0, Xc!2, Xa!1))),
% 0.66/0.82 inference(unit_resolution,[status(thm)],[246, 245])).
% 0.66/0.82 tff(248,plain,
% 0.66/0.82 (~s_t(Xb!0, Xc!2, Xa!1)),
% 0.66/0.82 inference(unit_resolution,[status(thm)],[247, 244])).
% 0.66/0.82 tff(249,plain,
% 0.66/0.82 (~s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1)),
% 0.66/0.82 inference(modus_ponens,[status(thm)],[248, 222])).
% 0.66/0.82 tff(250,plain,
% 0.66/0.82 (s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) <=> s_t(Xa!1, Xb!0, Xc!2)),
% 0.66/0.82 inference(monotonicity,[status(thm)],[59])).
% 0.66/0.82 tff(251,plain,
% 0.66/0.82 (s_t(Xa!1, Xb!0, Xc!2) <=> s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.66/0.82 inference(symmetry,[status(thm)],[250])).
% 0.66/0.82 tff(252,plain,
% 0.66/0.82 ((~s_t(Xa!1, Xb!0, Xc!2)) <=> (~s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)))),
% 0.66/0.82 inference(monotonicity,[status(thm)],[251])).
% 0.66/0.82 tff(253,plain,
% 0.66/0.82 (((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~((~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | s_t(Xb!0, Xc!2, Xa!1)))) | ((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))),
% 0.66/0.82 inference(tautology,[status(thm)],[])).
% 0.66/0.82 tff(254,plain,
% 0.66/0.82 ((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0)),
% 0.66/0.82 inference(unit_resolution,[status(thm)],[253, 242])).
% 0.66/0.82 tff(255,plain,
% 0.66/0.82 ((~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0)),
% 0.66/0.82 inference(tautology,[status(thm)],[])).
% 0.66/0.82 tff(256,plain,
% 0.66/0.82 ((~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~s_t(Xa!1, Xb!0, Xc!2))),
% 0.66/0.82 inference(unit_resolution,[status(thm)],[255, 245])).
% 0.66/0.82 tff(257,plain,
% 0.66/0.82 (~s_t(Xa!1, Xb!0, Xc!2)),
% 0.66/0.82 inference(unit_resolution,[status(thm)],[256, 254])).
% 0.66/0.82 tff(258,plain,
% 0.66/0.82 (~s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.66/0.82 inference(modus_ponens,[status(thm)],[257, 252])).
% 0.66/0.82 tff(259,plain,
% 0.66/0.82 (s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) <=> s_t(Xc!2, Xa!1, Xb!0)),
% 0.66/0.82 inference(monotonicity,[status(thm)],[59])).
% 0.66/0.82 tff(260,plain,
% 0.66/0.82 (s_t(Xc!2, Xa!1, Xb!0) <=> s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0)),
% 0.66/0.82 inference(symmetry,[status(thm)],[259])).
% 0.66/0.82 tff(261,plain,
% 0.66/0.82 ((~s_t(Xc!2, Xa!1, Xb!0)) <=> (~s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0))),
% 0.66/0.82 inference(monotonicity,[status(thm)],[260])).
% 0.66/0.82 tff(262,plain,
% 0.66/0.82 (((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~((~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | s_t(Xb!0, Xc!2, Xa!1)))) | ((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))),
% 0.66/0.82 inference(tautology,[status(thm)],[])).
% 0.66/0.82 tff(263,plain,
% 0.66/0.82 ((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0)),
% 0.66/0.82 inference(unit_resolution,[status(thm)],[262, 242])).
% 0.66/0.82 tff(264,plain,
% 0.66/0.82 ((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0)),
% 0.66/0.82 inference(tautology,[status(thm)],[])).
% 0.66/0.82 tff(265,plain,
% 0.66/0.82 ((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~s_t(Xc!2, Xa!1, Xb!0))),
% 0.66/0.82 inference(unit_resolution,[status(thm)],[264, 245])).
% 0.66/0.82 tff(266,plain,
% 0.66/0.82 (~s_t(Xc!2, Xa!1, Xb!0)),
% 0.66/0.82 inference(unit_resolution,[status(thm)],[265, 263])).
% 0.66/0.82 tff(267,plain,
% 0.66/0.82 (~s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0)),
% 0.66/0.82 inference(modus_ponens,[status(thm)],[266, 261])).
% 0.66/0.82 tff(268,plain,
% 0.66/0.82 (^[Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : refl((s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) <=> (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)))),
% 0.66/0.82 inference(bind,[status(th)],[])).
% 0.66/0.82 tff(269,plain,
% 0.66/0.82 (![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) <=> ![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))),
% 0.66/0.82 inference(quant_intro,[status(thm)],[268])).
% 0.66/0.82 tff(270,plain,
% 0.66/0.82 (![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) <=> ![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))),
% 0.66/0.82 inference(rewrite,[status(thm)],[])).
% 0.66/0.82 tff(271,plain,
% 0.66/0.82 (^[Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) <=> ((~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))), ((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) <=> (((~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) | (~s_e(Xb, Xp, Xb, Xq))))), rewrite((((~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) | (~s_e(Xb, Xp, Xb, Xq))) <=> ((~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))), ((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) <=> ((~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)))), (((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) | (~s_e(Xc, Xp, Xc, Xq))) <=> (((~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) | (~s_e(Xc, Xp, Xc, Xq))))), rewrite((((~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) | (~s_e(Xc, Xp, Xc, Xq))) <=> ((~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))), (((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) | (~s_e(Xc, Xp, Xc, Xq))) <=> ((~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)))), ((((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) | (~s_e(Xc, Xp, Xc, Xq))) | s_t(Xa, Xb, Xc)) <=> (((~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) | s_t(Xa, Xb, Xc)))), rewrite((((~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) | s_t(Xa, Xb, Xc)) <=> (s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))), ((((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) | (~s_e(Xc, Xp, Xc, Xq))) | s_t(Xa, Xb, Xc)) <=> (s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)))), (((((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) | (~s_e(Xc, Xp, Xc, Xq))) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) <=> ((s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) | s_t(Xb, Xc, Xa)))), rewrite(((s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) | s_t(Xb, Xc, Xa)) <=> (s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))), (((((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) | (~s_e(Xc, Xp, Xc, Xq))) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) <=> (s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)))), ((((((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) | (~s_e(Xc, Xp, Xc, Xq))) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) <=> ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) | s_t(Xc, Xa, Xb)))), rewrite(((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) | s_t(Xc, Xa, Xb)) <=> (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))), ((((((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) | (~s_e(Xc, Xp, Xc, Xq))) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) <=> (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))))),
% 0.66/0.82 inference(bind,[status(th)],[])).
% 0.66/0.82 tff(272,plain,
% 0.66/0.82 (![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (((((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) | (~s_e(Xc, Xp, Xc, Xq))) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) <=> ![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))),
% 0.66/0.82 inference(quant_intro,[status(thm)],[271])).
% 0.66/0.82 tff(273,axiom,(![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (((((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) | (~s_e(Xc, Xp, Xc, Xq))) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aA9')).
% 0.66/0.82 tff(274,plain,
% 0.66/0.82 (![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))),
% 0.66/0.82 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.66/0.82 tff(275,plain,
% 0.66/0.82 (![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))),
% 0.66/0.82 inference(modus_ponens,[status(thm)],[274, 270])).
% 0.66/0.82 tff(276,plain,(
% 0.66/0.82 ![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))),
% 0.66/0.82 inference(skolemize,[status(sab)],[275])).
% 0.66/0.82 tff(277,plain,
% 0.66/0.82 (![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))),
% 0.66/0.82 inference(modus_ponens,[status(thm)],[276, 269])).
% 0.66/0.82 tff(278,plain,
% 0.66/0.82 (((~![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))) | (s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) | s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) | s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) <=> ((~![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))) | s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) | s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) | s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))),
% 0.66/0.83 inference(rewrite,[status(thm)],[])).
% 0.66/0.83 tff(279,plain,
% 0.66/0.83 ((s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) | s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) | s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) <=> (s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) | s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) | s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))),
% 0.66/0.83 inference(rewrite,[status(thm)],[])).
% 0.66/0.83 tff(280,plain,
% 0.66/0.83 (((~![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))) | (s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) | s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) | s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) <=> ((~![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))) | (s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) | s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) | s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))),
% 0.66/0.83 inference(monotonicity,[status(thm)],[279])).
% 0.66/0.83 tff(281,plain,
% 0.66/0.83 (((~![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))) | (s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) | s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) | s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) <=> ((~![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))) | s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) | s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) | s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))),
% 0.66/0.83 inference(transitivity,[status(thm)],[280, 278])).
% 0.66/0.83 tff(282,plain,
% 0.66/0.83 ((~![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))) | (s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) | s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) | s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))),
% 0.66/0.83 inference(quant_inst,[status(thm)],[])).
% 0.66/0.83 tff(283,plain,
% 0.66/0.83 ((~![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))) | s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) | s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) | s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.66/0.83 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.66/0.83 tff(284,plain,
% 0.66/0.83 (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.66/0.83 inference(unit_resolution,[status(thm)],[283, 277, 267, 258, 249, 219, 165, 131])).
% 0.66/0.83 tff(285,plain,
% 0.66/0.83 (s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)),
% 0.66/0.83 inference(symmetry,[status(thm)],[284])).
% 0.66/0.83 tff(286,plain,
% 0.66/0.83 (^[Xa: $i, Xp: $i] : refl(((~(s(Xa, Xp) = Xp)) | (Xp = Xa)) <=> ((~(s(Xa, Xp) = Xp)) | (Xp = Xa)))),
% 0.66/0.83 inference(bind,[status(th)],[])).
% 0.66/0.83 tff(287,plain,
% 0.66/0.83 (![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa)) <=> ![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa))),
% 0.66/0.83 inference(quant_intro,[status(thm)],[286])).
% 0.66/0.83 tff(288,plain,
% 0.66/0.83 (![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa)) <=> ![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa))),
% 0.66/0.83 inference(rewrite,[status(thm)],[])).
% 0.66/0.83 tff(289,axiom,(![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz7_10a')).
% 0.66/0.84 tff(290,plain,
% 0.66/0.84 (![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa))),
% 0.66/0.84 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.66/0.84 tff(291,plain,(
% 0.66/0.84 ![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa))),
% 0.66/0.84 inference(skolemize,[status(sab)],[290])).
% 0.66/0.84 tff(292,plain,
% 0.66/0.84 (![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa))),
% 0.66/0.84 inference(modus_ponens,[status(thm)],[291, 287])).
% 0.66/0.84 tff(293,plain,
% 0.66/0.84 (((~![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa))) | ((~(s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)))) <=> ((~![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa))) | (~(s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)))),
% 0.66/0.84 inference(rewrite,[status(thm)],[])).
% 0.66/0.84 tff(294,plain,
% 0.66/0.84 ((~![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa))) | ((~(s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)))),
% 0.66/0.84 inference(quant_inst,[status(thm)],[])).
% 0.66/0.84 tff(295,plain,
% 0.66/0.84 ((~![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa))) | (~(s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.66/0.84 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.66/0.84 tff(296,plain,
% 0.66/0.84 (~(s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.66/0.84 inference(unit_resolution,[status(thm)],[295, 292, 119])).
% 0.66/0.84 tff(297,plain,
% 0.66/0.84 ($false),
% 0.66/0.84 inference(unit_resolution,[status(thm)],[296, 285])).
% 0.66/0.84 % SZS output end Proof
% 0.66/0.84 % E exiting
%------------------------------------------------------------------------------