%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO512+1 : TPTP v9.0.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:06:26 AM UTC 2025
% Result : Theorem 0.23s 0.50s
% Output : Proof 0.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GEO512+1 : TPTP v9.0.0. Released v7.0.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Jun 19 14:58:38 EDT 2025
% 0.15/0.36 % CPUTime :
% 0.23/0.50 % SZS status Theorem
% 0.23/0.50 % SZS output start Proof
% 0.23/0.50 tff(f813_type, type, (
% 0.23/0.50 f813: ( $i * $i * $i * $i * $i ) > $i)).
% 0.23/0.50 tff(tptp_fun_Xr_2_type, type, (
% 0.23/0.50 tptp_fun_Xr_2: $i)).
% 0.23/0.50 tff(tptp_fun_Xd_0_type, type, (
% 0.23/0.50 tptp_fun_Xd_0: $i)).
% 0.23/0.50 tff(tptp_fun_Xc_1_type, type, (
% 0.23/0.50 tptp_fun_Xc_1: $i)).
% 0.23/0.50 tff(tptp_fun_Xq_3_type, type, (
% 0.23/0.50 tptp_fun_Xq_3: $i)).
% 0.23/0.50 tff(tptp_fun_Xp_4_type, type, (
% 0.23/0.50 tptp_fun_Xp_4: $i)).
% 0.23/0.50 tff(il_type, type, (
% 0.23/0.50 il: ( $i * $i * $i * $i ) > $i)).
% 0.23/0.50 tff(g813_type, type, (
% 0.23/0.50 g813: ( $i * $i * $i * $i * $i ) > $i)).
% 0.23/0.50 tff(perpAt_type, type, (
% 0.23/0.50 perpAt: ( $i * $i * $i * $i * $i ) > $o)).
% 0.23/0.50 tff(s_col_type, type, (
% 0.23/0.50 s_col: ( $i * $i * $i ) > $o)).
% 0.23/0.50 tff(tptp_fun_Xb_5_type, type, (
% 0.23/0.50 tptp_fun_Xb_5: $i)).
% 0.23/0.50 tff(tptp_fun_Xa_6_type, type, (
% 0.23/0.50 tptp_fun_Xa_6: $i)).
% 0.23/0.50 tff(s_r_type, type, (
% 0.23/0.50 s_r: ( $i * $i * $i ) > $o)).
% 0.23/0.50 tff(g811_type, type, (
% 0.23/0.50 g811: ( $i * $i * $i * $i * $i ) > $i)).
% 0.23/0.50 tff(f811_type, type, (
% 0.23/0.50 f811: ( $i * $i * $i * $i * $i ) > $i)).
% 0.23/0.50 tff(perp_type, type, (
% 0.23/0.50 perp: ( $i * $i * $i * $i ) > $o)).
% 0.23/0.50 tff(1,plain,
% 0.23/0.50 ((~((Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | perpAt(Xa!6, Xb!5, Xr!2, Xc!1, Xd!0) | (~s_col(Xa!6, Xb!5, Xq!3)) | (~s_col(Xa!6, Xb!5, Xp!4)))) <=> (~((Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | perpAt(Xa!6, Xb!5, Xr!2, Xc!1, Xd!0) | (~s_col(Xa!6, Xb!5, Xq!3)) | (~s_col(Xa!6, Xb!5, Xp!4))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(2,plain,
% 0.23/0.50 ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xr: $i, Xc: $i, Xd: $i] : ((Xp = Xq) | (Xa = Xb) | (~perpAt(Xp, Xq, Xr, Xc, Xd)) | perpAt(Xa, Xb, Xr, Xc, Xd) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xp)))) <=> (~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xr: $i, Xc: $i, Xd: $i] : ((Xp = Xq) | (Xa = Xb) | (~perpAt(Xp, Xq, Xr, Xc, Xd)) | perpAt(Xa, Xb, Xr, Xc, Xd) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xp))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(3,plain,
% 0.23/0.50 ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xr: $i, Xc: $i, Xd: $i] : ((((((~s_col(Xa, Xb, Xp)) | (~s_col(Xa, Xb, Xq))) | (Xp = Xq)) | (Xa = Xb)) | (~perpAt(Xp, Xq, Xr, Xc, Xd))) | perpAt(Xa, Xb, Xr, Xc, Xd))) <=> (~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xr: $i, Xc: $i, Xd: $i] : ((Xp = Xq) | (Xa = Xb) | (~perpAt(Xp, Xq, Xr, Xc, Xd)) | perpAt(Xa, Xb, Xr, Xc, Xd) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xp))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(4,axiom,(~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xr: $i, Xc: $i, Xd: $i] : ((((((~s_col(Xa, Xb, Xp)) | (~s_col(Xa, Xb, Xq))) | (Xp = Xq)) | (Xa = Xb)) | (~perpAt(Xp, Xq, Xr, Xc, Xd))) | perpAt(Xa, Xb, Xr, Xc, Xd))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aExtPerp')).
% 0.23/0.50 tff(5,plain,
% 0.23/0.50 (~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xr: $i, Xc: $i, Xd: $i] : ((Xp = Xq) | (Xa = Xb) | (~perpAt(Xp, Xq, Xr, Xc, Xd)) | perpAt(Xa, Xb, Xr, Xc, Xd) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xp)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.23/0.50 tff(6,plain,
% 0.23/0.50 (~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xr: $i, Xc: $i, Xd: $i] : ((Xp = Xq) | (Xa = Xb) | (~perpAt(Xp, Xq, Xr, Xc, Xd)) | perpAt(Xa, Xb, Xr, Xc, Xd) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xp)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.23/0.50 tff(7,plain,
% 0.23/0.50 (~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xr: $i, Xc: $i, Xd: $i] : ((Xp = Xq) | (Xa = Xb) | (~perpAt(Xp, Xq, Xr, Xc, Xd)) | perpAt(Xa, Xb, Xr, Xc, Xd) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xp)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.23/0.50 tff(8,plain,
% 0.23/0.50 (~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xr: $i, Xc: $i, Xd: $i] : ((Xp = Xq) | (Xa = Xb) | (~perpAt(Xp, Xq, Xr, Xc, Xd)) | perpAt(Xa, Xb, Xr, Xc, Xd) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xp)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.23/0.50 tff(9,plain,(
% 0.23/0.50 ~((Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | perpAt(Xa!6, Xb!5, Xr!2, Xc!1, Xd!0) | (~s_col(Xa!6, Xb!5, Xq!3)) | (~s_col(Xa!6, Xb!5, Xp!4)))),
% 0.23/0.50 inference(skolemize,[status(sab)],[8])).
% 0.23/0.50 tff(10,plain,
% 0.23/0.50 (~((Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | perpAt(Xa!6, Xb!5, Xr!2, Xc!1, Xd!0) | (~s_col(Xa!6, Xb!5, Xq!3)) | (~s_col(Xa!6, Xb!5, Xp!4)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.23/0.50 tff(11,plain,
% 0.23/0.50 (perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)),
% 0.23/0.50 inference(or_elim,[status(thm)],[10])).
% 0.23/0.50 tff(12,plain,
% 0.23/0.50 (^[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))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(13,plain,
% 0.23/0.50 (![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)))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[12])).
% 0.23/0.50 tff(14,plain,
% 0.23/0.50 (![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)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(15,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')).
% 0.23/0.50 tff(16,plain,
% 0.23/0.50 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.23/0.50 tff(17,plain,(
% 0.23/0.50 ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))),
% 0.23/0.50 inference(skolemize,[status(sab)],[16])).
% 0.23/0.50 tff(18,plain,
% 0.23/0.50 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.23/0.50 tff(19,plain,
% 0.23/0.50 (((~![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, Xr!2, Xc!1, Xd!0)) | (Xr!2 = il(Xp!4, Xq!3, Xc!1, Xd!0)))) <=> ((~![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, Xr!2, Xc!1, Xd!0)) | (Xr!2 = il(Xp!4, Xq!3, Xc!1, Xd!0)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(20,plain,
% 0.23/0.50 ((~![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, Xr!2, Xc!1, Xd!0)) | (Xr!2 = il(Xp!4, Xq!3, Xc!1, Xd!0)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(21,plain,
% 0.23/0.50 ((~![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, Xr!2, Xc!1, Xd!0)) | (Xr!2 = il(Xp!4, Xq!3, Xc!1, Xd!0))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.23/0.50 tff(22,plain,
% 0.23/0.50 (Xr!2 = il(Xp!4, Xq!3, Xc!1, Xd!0)),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 0.23/0.50 tff(23,plain,
% 0.23/0.50 (il(Xp!4, Xq!3, Xc!1, Xd!0) = Xr!2),
% 0.23/0.50 inference(symmetry,[status(thm)],[22])).
% 0.23/0.50 tff(24,plain,
% 0.23/0.50 ((il(Xp!4, Xq!3, Xc!1, Xd!0) = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) <=> (Xr!2 = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[23])).
% 0.23/0.50 tff(25,plain,
% 0.23/0.50 ((Xr!2 = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) <=> (il(Xp!4, Xq!3, Xc!1, Xd!0) = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.23/0.50 inference(symmetry,[status(thm)],[24])).
% 0.23/0.50 tff(26,plain,
% 0.23/0.50 ((~(Xr!2 = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) <=> (~(il(Xp!4, Xq!3, Xc!1, Xd!0) = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[25])).
% 0.23/0.50 tff(27,plain,
% 0.23/0.50 (^[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)))))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(28,plain,
% 0.23/0.50 (![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))))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[27])).
% 0.23/0.50 tff(29,plain,
% 0.23/0.50 (^[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))))))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(30,plain,
% 0.23/0.50 (![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))))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[29])).
% 0.23/0.50 tff(31,plain,
% 0.23/0.50 (![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))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(32,plain,
% 0.23/0.50 (^[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))))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(33,plain,
% 0.23/0.50 (![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))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[32])).
% 0.23/0.50 tff(34,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')).
% 0.23/0.50 tff(35,plain,
% 0.23/0.50 (![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))))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.23/0.50 tff(36,plain,
% 0.23/0.50 (![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))))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.23/0.50 tff(37,plain,(
% 0.23/0.50 ![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))))),
% 0.23/0.50 inference(skolemize,[status(sab)],[36])).
% 0.23/0.50 tff(38,plain,
% 0.23/0.50 (![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))))))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.23/0.50 tff(39,plain,
% 0.23/0.50 (![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))))))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.23/0.50 tff(40,plain,
% 0.23/0.50 ((~![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, Xr!2, Xc!1, Xd!0)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, Xr!2))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, Xr!2))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), Xr!2, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(41,plain,
% 0.23/0.50 (~((~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, Xr!2))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, Xr!2))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), Xr!2, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.23/0.51 tff(42,plain,
% 0.23/0.51 (((~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, Xr!2))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, Xr!2))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), Xr!2, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | ((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(43,plain,
% 0.23/0.51 ((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.23/0.51 tff(44,plain,
% 0.23/0.51 ((~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | (~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(45,plain,
% 0.23/0.51 ((~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | (~(Xr!2 = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[44, 11])).
% 0.23/0.51 tff(46,plain,
% 0.23/0.51 (~(Xr!2 = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[45, 43])).
% 0.23/0.51 tff(47,plain,
% 0.23/0.51 (~(il(Xp!4, Xq!3, Xc!1, Xd!0) = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[46, 26])).
% 0.23/0.51 tff(48,plain,
% 0.23/0.51 (s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), il(Xp!4, Xq!3, Xc!1, Xd!0), g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) <=> s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), Xr!2, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[23])).
% 0.23/0.51 tff(49,plain,
% 0.23/0.51 (s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), Xr!2, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) <=> s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), il(Xp!4, Xq!3, Xc!1, Xd!0), g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.23/0.51 inference(symmetry,[status(thm)],[48])).
% 0.23/0.51 tff(50,plain,
% 0.23/0.51 (((~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, Xr!2))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, Xr!2))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), Xr!2, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | ((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), Xr!2, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(51,plain,
% 0.23/0.51 ((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), Xr!2, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[50, 41])).
% 0.23/0.51 tff(52,plain,
% 0.23/0.51 ((~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), Xr!2, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | (~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), Xr!2, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(53,plain,
% 0.23/0.51 ((~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), Xr!2, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), Xr!2, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[52, 11])).
% 0.23/0.51 tff(54,plain,
% 0.23/0.51 (s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), Xr!2, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[53, 51])).
% 0.23/0.51 tff(55,plain,
% 0.23/0.51 (s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), il(Xp!4, Xq!3, Xc!1, Xd!0), g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[54, 49])).
% 0.23/0.51 tff(56,plain,
% 0.23/0.51 (((~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, Xr!2))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, Xr!2))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), Xr!2, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | ((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(57,plain,
% 0.23/0.51 ((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[56, 41])).
% 0.23/0.51 tff(58,plain,
% 0.23/0.51 ((~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | (~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(59,plain,
% 0.23/0.51 ((~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[58, 11])).
% 0.23/0.51 tff(60,plain,
% 0.23/0.51 (s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[59, 57])).
% 0.23/0.51 tff(61,plain,
% 0.23/0.51 (s_col(Xa!6, Xb!5, Xp!4)),
% 0.23/0.51 inference(or_elim,[status(thm)],[10])).
% 0.23/0.51 tff(62,plain,
% 0.23/0.51 (s_col(Xa!6, Xb!5, Xq!3)),
% 0.23/0.51 inference(or_elim,[status(thm)],[10])).
% 0.23/0.51 tff(63,plain,
% 0.23/0.51 (~(Xa!6 = Xb!5)),
% 0.23/0.51 inference(or_elim,[status(thm)],[10])).
% 0.23/0.51 tff(64,plain,
% 0.23/0.51 (~(Xp!4 = Xq!3)),
% 0.23/0.51 inference(or_elim,[status(thm)],[10])).
% 0.23/0.51 tff(65,plain,
% 0.23/0.51 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : refl(((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd))) <=> ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd))))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(66,plain,
% 0.23/0.51 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[65])).
% 0.23/0.51 tff(67,plain,
% 0.23/0.51 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(68,plain,
% 0.23/0.51 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((Xa = Xb) | (Xc = Xd)) <=> ((Xc = Xd) | (Xa = Xb))), ((((Xa = Xb) | (Xc = Xd)) | (~s_col(Xa, Xb, Xc))) <=> (((Xc = Xd) | (Xa = Xb)) | (~s_col(Xa, Xb, Xc))))), rewrite((((Xc = Xd) | (Xa = Xb)) | (~s_col(Xa, Xb, Xc))) <=> ((Xc = Xd) | (Xa = Xb) | (~s_col(Xa, Xb, Xc)))), ((((Xa = Xb) | (Xc = Xd)) | (~s_col(Xa, Xb, Xc))) <=> ((Xc = Xd) | (Xa = Xb) | (~s_col(Xa, Xb, Xc))))), (((((Xa = Xb) | (Xc = Xd)) | (~s_col(Xa, Xb, Xc))) | (~s_col(Xa, Xb, Xd))) <=> (((Xc = Xd) | (Xa = Xb) | (~s_col(Xa, Xb, Xc))) | (~s_col(Xa, Xb, Xd))))), rewrite((((Xc = Xd) | (Xa = Xb) | (~s_col(Xa, Xb, Xc))) | (~s_col(Xa, Xb, Xd))) <=> ((Xc = Xd) | (Xa = Xb) | (~s_col(Xa, Xb, Xc)) | (~s_col(Xa, Xb, Xd)))), (((((Xa = Xb) | (Xc = Xd)) | (~s_col(Xa, Xb, Xc))) | (~s_col(Xa, Xb, Xd))) <=> ((Xc = Xd) | (Xa = Xb) | (~s_col(Xa, Xb, Xc)) | (~s_col(Xa, Xb, Xd))))), ((((((Xa = Xb) | (Xc = Xd)) | (~s_col(Xa, Xb, Xc))) | (~s_col(Xa, Xb, Xd))) | (~s_col(Xc, Xd, Xp))) <=> (((Xc = Xd) | (Xa = Xb) | (~s_col(Xa, Xb, Xc)) | (~s_col(Xa, Xb, Xd))) | (~s_col(Xc, Xd, Xp))))), rewrite((((Xc = Xd) | (Xa = Xb) | (~s_col(Xa, Xb, Xc)) | (~s_col(Xa, Xb, Xd))) | (~s_col(Xc, Xd, Xp))) <=> ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | (~s_col(Xa, Xb, Xd)))), ((((((Xa = Xb) | (Xc = Xd)) | (~s_col(Xa, Xb, Xc))) | (~s_col(Xa, Xb, Xd))) | (~s_col(Xc, Xd, Xp))) <=> ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | (~s_col(Xa, Xb, Xd))))), (((((((Xa = Xb) | (Xc = Xd)) | (~s_col(Xa, Xb, Xc))) | (~s_col(Xa, Xb, Xd))) | (~s_col(Xc, Xd, Xp))) | s_col(Xa, Xb, Xp)) <=> (((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | (~s_col(Xa, Xb, Xd))) | s_col(Xa, Xb, Xp)))), rewrite((((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | (~s_col(Xa, Xb, Xd))) | s_col(Xa, Xb, Xp)) <=> ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))), (((((((Xa = Xb) | (Xc = Xd)) | (~s_col(Xa, Xb, Xc))) | (~s_col(Xa, Xb, Xd))) | (~s_col(Xc, Xd, Xp))) | s_col(Xa, Xb, Xp)) <=> ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(69,plain,
% 0.23/0.51 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((((((Xa = Xb) | (Xc = Xd)) | (~s_col(Xa, Xb, Xc))) | (~s_col(Xa, Xb, Xd))) | (~s_col(Xc, Xd, Xp))) | s_col(Xa, Xb, Xp)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[68])).
% 0.23/0.51 tff(70,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((((((Xa = Xb) | (Xc = Xd)) | (~s_col(Xa, Xb, Xc))) | (~s_col(Xa, Xb, Xd))) | (~s_col(Xc, Xd, Xp))) | s_col(Xa, Xb, Xp))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aExtCol2')).
% 0.23/0.51 tff(71,plain,
% 0.23/0.51 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.23/0.51 tff(72,plain,
% 0.23/0.51 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.23/0.51 tff(73,plain,(
% 0.23/0.51 ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))),
% 0.23/0.51 inference(skolemize,[status(sab)],[72])).
% 0.23/0.51 tff(74,plain,
% 0.23/0.51 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.23/0.51 tff(75,plain,
% 0.23/0.51 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))) | ((Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~s_col(Xa!6, Xb!5, Xq!3)) | (~s_col(Xa!6, Xb!5, Xp!4)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | s_col(Xa!6, Xb!5, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))) | (Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~s_col(Xa!6, Xb!5, Xq!3)) | (~s_col(Xa!6, Xb!5, Xp!4)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | s_col(Xa!6, Xb!5, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(76,plain,
% 0.23/0.51 (((Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (~s_col(Xa!6, Xb!5, Xp!4)) | s_col(Xa!6, Xb!5, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) | (~s_col(Xa!6, Xb!5, Xq!3))) <=> ((Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~s_col(Xa!6, Xb!5, Xq!3)) | (~s_col(Xa!6, Xb!5, Xp!4)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | s_col(Xa!6, Xb!5, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(77,plain,
% 0.23/0.51 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))) | ((Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (~s_col(Xa!6, Xb!5, Xp!4)) | s_col(Xa!6, Xb!5, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) | (~s_col(Xa!6, Xb!5, Xq!3)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))) | ((Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~s_col(Xa!6, Xb!5, Xq!3)) | (~s_col(Xa!6, Xb!5, Xp!4)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | s_col(Xa!6, Xb!5, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[76])).
% 0.23/0.51 tff(78,plain,
% 0.23/0.51 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))) | ((Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (~s_col(Xa!6, Xb!5, Xp!4)) | s_col(Xa!6, Xb!5, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) | (~s_col(Xa!6, Xb!5, Xq!3)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))) | (Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~s_col(Xa!6, Xb!5, Xq!3)) | (~s_col(Xa!6, Xb!5, Xp!4)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | s_col(Xa!6, Xb!5, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))),
% 0.23/0.51 inference(transitivity,[status(thm)],[77, 75])).
% 0.23/0.51 tff(79,plain,
% 0.23/0.51 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))) | ((Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (~s_col(Xa!6, Xb!5, Xp!4)) | s_col(Xa!6, Xb!5, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) | (~s_col(Xa!6, Xb!5, Xq!3)))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(80,plain,
% 0.23/0.51 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))) | (Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~s_col(Xa!6, Xb!5, Xq!3)) | (~s_col(Xa!6, Xb!5, Xp!4)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | s_col(Xa!6, Xb!5, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.23/0.51 tff(81,plain,
% 0.23/0.51 (s_col(Xa!6, Xb!5, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[80, 74, 64, 63, 62, 61, 60])).
% 0.23/0.51 tff(82,plain,
% 0.23/0.51 (perpAt(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) <=> perpAt(Xa!6, Xb!5, Xr!2, Xc!1, Xd!0)),
% 0.23/0.51 inference(monotonicity,[status(thm)],[23])).
% 0.23/0.51 tff(83,plain,
% 0.23/0.51 (perpAt(Xa!6, Xb!5, Xr!2, Xc!1, Xd!0) <=> perpAt(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)),
% 0.23/0.51 inference(symmetry,[status(thm)],[82])).
% 0.23/0.51 tff(84,plain,
% 0.23/0.51 ((~perpAt(Xa!6, Xb!5, Xr!2, Xc!1, Xd!0)) <=> (~perpAt(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[83])).
% 0.23/0.51 tff(85,plain,
% 0.23/0.51 (~perpAt(Xa!6, Xb!5, Xr!2, Xc!1, Xd!0)),
% 0.23/0.51 inference(or_elim,[status(thm)],[10])).
% 0.23/0.51 tff(86,plain,
% 0.23/0.51 (~perpAt(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.23/0.52 tff(87,plain,
% 0.23/0.52 (^[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))))))),
% 0.23/0.52 inference(bind,[status(th)],[])).
% 0.23/0.52 tff(88,plain,
% 0.23/0.52 (![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)))))),
% 0.23/0.52 inference(quant_intro,[status(thm)],[87])).
% 0.23/0.52 tff(89,plain,
% 0.23/0.52 (^[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)))))))),
% 0.23/0.52 inference(bind,[status(th)],[])).
% 0.23/0.52 tff(90,plain,
% 0.23/0.52 (![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)))))),
% 0.23/0.52 inference(quant_intro,[status(thm)],[89])).
% 0.23/0.52 tff(91,plain,
% 0.23/0.52 (![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)))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(92,plain,
% 0.23/0.52 (^[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)))))),
% 0.23/0.52 inference(bind,[status(th)],[])).
% 0.23/0.52 tff(93,plain,
% 0.23/0.52 (![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)))),
% 0.23/0.52 inference(quant_intro,[status(thm)],[92])).
% 0.23/0.52 tff(94,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')).
% 0.23/0.52 tff(95,plain,
% 0.23/0.52 (![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)))),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.23/0.52 tff(96,plain,
% 0.23/0.52 (![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)))),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.23/0.52 tff(97,plain,(
% 0.23/0.52 ![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)))),
% 0.23/0.52 inference(skolemize,[status(sab)],[96])).
% 0.23/0.52 tff(98,plain,
% 0.23/0.52 (![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)))))),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.23/0.52 tff(99,plain,
% 0.23/0.52 (![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)))))),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[98, 88])).
% 0.23/0.52 tff(100,plain,
% 0.23/0.52 (((~![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(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_r(il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xp!4, Xq!3, f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xc!1, Xd!0, g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_r(f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)), il(Xp!4, Xq!3, Xc!1, Xd!0), g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))))))) <=> ((~![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(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_r(il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xp!4, Xq!3, f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xc!1, Xd!0, g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_r(f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)), il(Xp!4, Xq!3, Xc!1, Xd!0), g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))))))))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(101,plain,
% 0.23/0.53 ((~((~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~((~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_r(il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0)) | (~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)))) | (~((Xc!1 = Xd!0) | (Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | s_col(Xp!4, Xq!3, f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xc!1 = Xd!0) | (Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | s_col(Xc!1, Xd!0, g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xc!1 = Xd!0) | (Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_r(f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)), il(Xp!4, Xq!3, Xc!1, Xd!0), g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0))))) <=> (~((~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_r(il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xp!4, Xq!3, f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xc!1, Xd!0, g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_r(f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)), il(Xp!4, Xq!3, Xc!1, Xd!0), g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))))))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(102,plain,
% 0.23/0.53 (((~![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(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~((~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_r(il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0)) | (~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)))) | (~((Xc!1 = Xd!0) | (Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | s_col(Xp!4, Xq!3, f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xc!1 = Xd!0) | (Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | s_col(Xc!1, Xd!0, g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xc!1 = Xd!0) | (Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_r(f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)), il(Xp!4, Xq!3, Xc!1, Xd!0), g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)))))) <=> ((~![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(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_r(il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xp!4, Xq!3, f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xc!1, Xd!0, g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_r(f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)), il(Xp!4, Xq!3, Xc!1, Xd!0), g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))))))))),
% 0.23/0.53 inference(monotonicity,[status(thm)],[101])).
% 0.23/0.53 tff(103,plain,
% 0.23/0.53 (((~![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(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~((~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_r(il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0)) | (~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)))) | (~((Xc!1 = Xd!0) | (Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | s_col(Xp!4, Xq!3, f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xc!1 = Xd!0) | (Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | s_col(Xc!1, Xd!0, g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xc!1 = Xd!0) | (Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_r(f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)), il(Xp!4, Xq!3, Xc!1, Xd!0), g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)))))) <=> ((~![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(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_r(il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xp!4, Xq!3, f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xc!1, Xd!0, g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_r(f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)), il(Xp!4, Xq!3, Xc!1, Xd!0), g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))))))))),
% 0.23/0.54 inference(transitivity,[status(thm)],[102, 100])).
% 0.23/0.54 tff(104,plain,
% 0.23/0.54 ((~![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(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~((~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_r(il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0)) | (~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)))) | (~((Xc!1 = Xd!0) | (Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | s_col(Xp!4, Xq!3, f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xc!1 = Xd!0) | (Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | s_col(Xc!1, Xd!0, g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xc!1 = Xd!0) | (Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_r(f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)), il(Xp!4, Xq!3, Xc!1, Xd!0), g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)))))),
% 0.23/0.54 inference(quant_inst,[status(thm)],[])).
% 0.23/0.54 tff(105,plain,
% 0.23/0.54 ((~![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(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_r(il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xp!4, Xq!3, f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xc!1, Xd!0, g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_r(f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)), il(Xp!4, Xq!3, Xc!1, Xd!0), g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))))))),
% 0.23/0.54 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.23/0.54 tff(106,plain,
% 0.23/0.54 (~((~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_r(il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xp!4, Xq!3, f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xc!1, Xd!0, g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_r(f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)), il(Xp!4, Xq!3, Xc!1, Xd!0), g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))))))),
% 0.23/0.54 inference(unit_resolution,[status(thm)],[105, 99])).
% 0.23/0.54 tff(107,plain,
% 0.23/0.54 (((~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_r(il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xp!4, Xq!3, f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xc!1, Xd!0, g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_r(f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)), il(Xp!4, Xq!3, Xc!1, Xd!0), g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))))) | ((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0)))),
% 0.40/0.54 inference(tautology,[status(thm)],[])).
% 0.40/0.54 tff(108,plain,
% 0.40/0.54 ((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))),
% 0.40/0.54 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.40/0.54 tff(109,plain,
% 0.40/0.54 (^[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)))))))),
% 0.40/0.54 inference(bind,[status(th)],[])).
% 0.40/0.54 tff(110,plain,
% 0.40/0.54 (![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))))))),
% 0.40/0.54 inference(quant_intro,[status(thm)],[109])).
% 0.40/0.54 tff(111,plain,
% 0.40/0.54 (^[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))))))))),
% 0.40/0.54 inference(bind,[status(th)],[])).
% 0.40/0.54 tff(112,plain,
% 0.40/0.54 (![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))))))),
% 0.40/0.54 inference(quant_intro,[status(thm)],[111])).
% 0.40/0.55 tff(113,plain,
% 0.40/0.55 (![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))))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(114,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')).
% 0.40/0.55 tff(115,plain,
% 0.40/0.55 (![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))))),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.40/0.55 tff(116,plain,(
% 0.40/0.55 ![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))))),
% 0.40/0.55 inference(skolemize,[status(sab)],[115])).
% 0.40/0.55 tff(117,plain,
% 0.40/0.55 (![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))))))),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.40/0.55 tff(118,plain,
% 0.40/0.55 (![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))))))),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.40/0.55 tff(119,plain,
% 0.40/0.55 (((~![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, Xc!1, Xd!0)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | perp(Xp!4, Xq!3, Xc!1, Xd!0)))))) <=> ((~![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, Xc!1, Xd!0)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | perp(Xp!4, Xq!3, Xc!1, Xd!0))))))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(120,plain,
% 0.40/0.55 ((~((~((~perp(Xp!4, Xq!3, Xc!1, Xd!0)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0))) | (~(perp(Xp!4, Xq!3, Xc!1, Xd!0) | (~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)))))) <=> (~((~((~perp(Xp!4, Xq!3, Xc!1, Xd!0)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | perp(Xp!4, Xq!3, Xc!1, Xd!0)))))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(121,plain,
% 0.40/0.55 (((~![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, Xc!1, Xd!0)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0))) | (~(perp(Xp!4, Xq!3, Xc!1, Xd!0) | (~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0))))))) <=> ((~![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, Xc!1, Xd!0)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | perp(Xp!4, Xq!3, Xc!1, Xd!0))))))),
% 0.40/0.55 inference(monotonicity,[status(thm)],[120])).
% 0.40/0.55 tff(122,plain,
% 0.40/0.55 (((~![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, Xc!1, Xd!0)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0))) | (~(perp(Xp!4, Xq!3, Xc!1, Xd!0) | (~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0))))))) <=> ((~![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, Xc!1, Xd!0)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | perp(Xp!4, Xq!3, Xc!1, Xd!0))))))),
% 0.40/0.55 inference(transitivity,[status(thm)],[121, 119])).
% 0.40/0.55 tff(123,plain,
% 0.40/0.55 ((~![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, Xc!1, Xd!0)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0))) | (~(perp(Xp!4, Xq!3, Xc!1, Xd!0) | (~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0))))))),
% 0.40/0.55 inference(quant_inst,[status(thm)],[])).
% 0.40/0.55 tff(124,plain,
% 0.40/0.55 ((~![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, Xc!1, Xd!0)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | perp(Xp!4, Xq!3, Xc!1, Xd!0)))))),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.40/0.55 tff(125,plain,
% 0.40/0.55 (~((~((~perp(Xp!4, Xq!3, Xc!1, Xd!0)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | perp(Xp!4, Xq!3, Xc!1, Xd!0))))),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[124, 118])).
% 0.40/0.55 tff(126,plain,
% 0.40/0.55 (((~((~perp(Xp!4, Xq!3, Xc!1, Xd!0)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | perp(Xp!4, Xq!3, Xc!1, Xd!0)))) | ((~perp(Xp!4, Xq!3, Xc!1, Xd!0)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0))),
% 0.40/0.55 inference(tautology,[status(thm)],[])).
% 0.40/0.55 tff(127,plain,
% 0.40/0.55 ((~perp(Xp!4, Xq!3, Xc!1, Xd!0)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.40/0.55 tff(128,plain,
% 0.40/0.55 (((~((~perp(Xp!4, Xq!3, Xc!1, Xd!0)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | perp(Xp!4, Xq!3, Xc!1, Xd!0)))) | ((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | perp(Xp!4, Xq!3, Xc!1, Xd!0))),
% 0.40/0.55 inference(tautology,[status(thm)],[])).
% 0.40/0.55 tff(129,plain,
% 0.40/0.55 ((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | perp(Xp!4, Xq!3, Xc!1, Xd!0)),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[128, 125])).
% 0.40/0.55 tff(130,plain,
% 0.40/0.55 ((~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | perp(Xp!4, Xq!3, Xc!1, Xd!0))) | (~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | perp(Xp!4, Xq!3, Xc!1, Xd!0)),
% 0.40/0.55 inference(tautology,[status(thm)],[])).
% 0.40/0.55 tff(131,plain,
% 0.40/0.55 ((~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | perp(Xp!4, Xq!3, Xc!1, Xd!0))) | perp(Xp!4, Xq!3, Xc!1, Xd!0)),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[130, 11])).
% 0.40/0.55 tff(132,plain,
% 0.40/0.55 (perp(Xp!4, Xq!3, Xc!1, Xd!0)),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[131, 129])).
% 0.40/0.55 tff(133,plain,
% 0.40/0.55 ((~((~perp(Xp!4, Xq!3, Xc!1, Xd!0)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0))) | (~perp(Xp!4, Xq!3, Xc!1, Xd!0)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)),
% 0.40/0.55 inference(tautology,[status(thm)],[])).
% 0.40/0.55 tff(134,plain,
% 0.40/0.55 (perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[133, 132, 127])).
% 0.40/0.55 tff(135,plain,
% 0.40/0.55 ((~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))),
% 0.40/0.55 inference(tautology,[status(thm)],[])).
% 0.40/0.55 tff(136,plain,
% 0.40/0.55 ((~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.40/0.55 tff(137,plain,
% 0.40/0.55 (s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[136, 108])).
% 0.40/0.55 tff(138,plain,
% 0.40/0.55 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))) | ((Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~s_col(Xa!6, Xb!5, Xq!3)) | (~s_col(Xa!6, Xb!5, Xp!4)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))) | (Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~s_col(Xa!6, Xb!5, Xq!3)) | (~s_col(Xa!6, Xb!5, Xp!4)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0)))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(139,plain,
% 0.40/0.55 (((Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xa!6, Xb!5, Xp!4)) | s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0)) | (~s_col(Xa!6, Xb!5, Xq!3))) <=> ((Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~s_col(Xa!6, Xb!5, Xq!3)) | (~s_col(Xa!6, Xb!5, Xp!4)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0)))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(140,plain,
% 0.40/0.55 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))) | ((Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xa!6, Xb!5, Xp!4)) | s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0)) | (~s_col(Xa!6, Xb!5, Xq!3)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))) | ((Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~s_col(Xa!6, Xb!5, Xq!3)) | (~s_col(Xa!6, Xb!5, Xp!4)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0))))),
% 0.40/0.55 inference(monotonicity,[status(thm)],[139])).
% 0.40/0.55 tff(141,plain,
% 0.40/0.55 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))) | ((Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xa!6, Xb!5, Xp!4)) | s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0)) | (~s_col(Xa!6, Xb!5, Xq!3)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))) | (Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~s_col(Xa!6, Xb!5, Xq!3)) | (~s_col(Xa!6, Xb!5, Xp!4)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0)))),
% 0.40/0.55 inference(transitivity,[status(thm)],[140, 138])).
% 0.40/0.55 tff(142,plain,
% 0.40/0.55 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))) | ((Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xa!6, Xb!5, Xp!4)) | s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0)) | (~s_col(Xa!6, Xb!5, Xq!3)))),
% 0.40/0.55 inference(quant_inst,[status(thm)],[])).
% 0.40/0.55 tff(143,plain,
% 0.40/0.55 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xp: $i] : ((Xc = Xd) | (Xa = Xb) | (~s_col(Xc, Xd, Xp)) | (~s_col(Xa, Xb, Xc)) | s_col(Xa, Xb, Xp) | (~s_col(Xa, Xb, Xd)))) | (Xp!4 = Xq!3) | (Xa!6 = Xb!5) | (~s_col(Xa!6, Xb!5, Xq!3)) | (~s_col(Xa!6, Xb!5, Xp!4)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0))),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.40/0.55 tff(144,plain,
% 0.40/0.55 ((~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0))),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[143, 74, 64, 63, 62, 61])).
% 0.40/0.55 tff(145,plain,
% 0.40/0.55 (s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[144, 137])).
% 0.40/0.56 tff(146,plain,
% 0.40/0.56 (((~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_r(il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0), il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xp!4, Xq!3, f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | s_col(Xc!1, Xd!0, g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))) | (~((Xp!4 = Xq!3) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (Xc!1 = Xd!0) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_r(f811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)), il(Xp!4, Xq!3, Xc!1, Xd!0), g811(Xp!4, Xq!3, Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))))))) | ((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))),
% 0.40/0.56 inference(tautology,[status(thm)],[])).
% 0.40/0.56 tff(147,plain,
% 0.40/0.56 ((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[146, 106])).
% 0.40/0.56 tff(148,plain,
% 0.40/0.56 ((~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | (~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))),
% 0.40/0.56 inference(tautology,[status(thm)],[])).
% 0.40/0.56 tff(149,plain,
% 0.40/0.56 ((~((~perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0)))) | s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[148, 134])).
% 0.40/0.56 tff(150,plain,
% 0.40/0.56 (s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[149, 147])).
% 0.40/0.56 tff(151,plain,
% 0.40/0.56 (((~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, Xr!2))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, Xr!2))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), Xr!2, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | ((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))),
% 0.40/0.56 inference(tautology,[status(thm)],[])).
% 0.40/0.56 tff(152,plain,
% 0.40/0.56 ((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[151, 41])).
% 0.40/0.56 tff(153,plain,
% 0.40/0.56 ((~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | (~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.40/0.56 inference(tautology,[status(thm)],[])).
% 0.40/0.56 tff(154,plain,
% 0.40/0.56 ((~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[153, 11])).
% 0.40/0.56 tff(155,plain,
% 0.40/0.56 (s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[154, 152])).
% 0.40/0.56 tff(156,plain,
% 0.40/0.56 (((~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, Xr!2))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, Xr!2))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), Xr!2, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | ((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))),
% 0.40/0.56 inference(tautology,[status(thm)],[])).
% 0.40/0.56 tff(157,plain,
% 0.40/0.56 ((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xc!1 = Xd!0))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[156, 41])).
% 0.40/0.56 tff(158,plain,
% 0.40/0.56 ((~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xc!1 = Xd!0))),
% 0.40/0.56 inference(tautology,[status(thm)],[])).
% 0.40/0.56 tff(159,plain,
% 0.40/0.56 ((~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~(Xc!1 = Xd!0))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[158, 11])).
% 0.40/0.56 tff(160,plain,
% 0.40/0.56 (~(Xc!1 = Xd!0)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[159, 157])).
% 0.40/0.56 tff(161,plain,
% 0.40/0.56 (^[Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xcx: $i, U: $i, V: $i] : refl(((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | perpAt(Xa, Xb, Xcx, Xp, Xq) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V))) <=> ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | perpAt(Xa, Xb, Xcx, Xp, Xq) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V))))),
% 0.40/0.56 inference(bind,[status(th)],[])).
% 0.40/0.56 tff(162,plain,
% 0.40/0.56 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xcx: $i, U: $i, V: $i] : ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | perpAt(Xa, Xb, Xcx, Xp, Xq) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V))) <=> ![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xcx: $i, U: $i, V: $i] : ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | perpAt(Xa, Xb, Xcx, Xp, Xq) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V)))),
% 0.40/0.56 inference(quant_intro,[status(thm)],[161])).
% 0.40/0.56 tff(163,plain,
% 0.40/0.56 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xcx: $i, U: $i, V: $i] : ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | perpAt(Xa, Xb, Xcx, Xp, Xq) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V))) <=> ![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xcx: $i, U: $i, V: $i] : ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | perpAt(Xa, Xb, Xcx, Xp, Xq) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(164,plain,
% 0.40/0.56 (^[Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xcx: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((Xa = Xb) | (Xp = Xq)) <=> ((Xp = Xq) | (Xa = Xb))), ((((Xa = Xb) | (Xp = Xq)) | (~s_col(Xp, Xq, Xcx))) <=> (((Xp = Xq) | (Xa = Xb)) | (~s_col(Xp, Xq, Xcx))))), rewrite((((Xp = Xq) | (Xa = Xb)) | (~s_col(Xp, Xq, Xcx))) <=> ((Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xa = Xb))), ((((Xa = Xb) | (Xp = Xq)) | (~s_col(Xp, Xq, Xcx))) <=> ((Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xa = Xb)))), (((((Xa = Xb) | (Xp = Xq)) | (~s_col(Xp, Xq, Xcx))) | (~s_col(Xa, Xb, Xcx))) <=> (((Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xa = Xb)) | (~s_col(Xa, Xb, Xcx))))), rewrite((((Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xa = Xb)) | (~s_col(Xa, Xb, Xcx))) <=> ((Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb))), (((((Xa = Xb) | (Xp = Xq)) | (~s_col(Xp, Xq, Xcx))) | (~s_col(Xa, Xb, Xcx))) <=> ((Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb)))), ((((((Xa = Xb) | (Xp = Xq)) | (~s_col(Xp, Xq, Xcx))) | (~s_col(Xa, Xb, Xcx))) | (~s_col(Xa, Xb, U))) <=> (((Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb)) | (~s_col(Xa, Xb, U))))), rewrite((((Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb)) | (~s_col(Xa, Xb, U))) <=> ((Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb))), ((((((Xa = Xb) | (Xp = Xq)) | (~s_col(Xp, Xq, Xcx))) | (~s_col(Xa, Xb, Xcx))) | (~s_col(Xa, Xb, U))) <=> ((Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb)))), (((((((Xa = Xb) | (Xp = Xq)) | (~s_col(Xp, Xq, Xcx))) | (~s_col(Xa, Xb, Xcx))) | (~s_col(Xa, Xb, U))) | (~s_col(Xp, Xq, V))) <=> (((Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb)) | (~s_col(Xp, Xq, V))))), rewrite((((Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb)) | (~s_col(Xp, Xq, V))) <=> ((Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | (~s_col(Xp, Xq, V)))), (((((((Xa = Xb) | (Xp = Xq)) | (~s_col(Xp, Xq, Xcx))) | (~s_col(Xa, Xb, Xcx))) | (~s_col(Xa, Xb, U))) | (~s_col(Xp, Xq, V))) <=> ((Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | (~s_col(Xp, Xq, V))))), ((((((((Xa = Xb) | (Xp = Xq)) | (~s_col(Xp, Xq, Xcx))) | (~s_col(Xa, Xb, Xcx))) | (~s_col(Xa, Xb, U))) | (~s_col(Xp, Xq, V))) | (Xcx = U)) <=> (((Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | (~s_col(Xp, Xq, V))) | (Xcx = U)))), rewrite((((Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | (~s_col(Xp, Xq, V))) | (Xcx = U)) <=> ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | (~s_col(Xp, Xq, V)))), ((((((((Xa = Xb) | (Xp = Xq)) | (~s_col(Xp, Xq, Xcx))) | (~s_col(Xa, Xb, Xcx))) | (~s_col(Xa, Xb, U))) | (~s_col(Xp, Xq, V))) | (Xcx = U)) <=> ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | (~s_col(Xp, Xq, V))))), (((((((((Xa = Xb) | (Xp = Xq)) | (~s_col(Xp, Xq, Xcx))) | (~s_col(Xa, Xb, Xcx))) | (~s_col(Xa, Xb, U))) | (~s_col(Xp, Xq, V))) | (Xcx = U)) | (Xcx = V)) <=> (((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | (~s_col(Xp, Xq, V))) | (Xcx = V)))), rewrite((((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | (~s_col(Xp, Xq, V))) | (Xcx = V)) <=> ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | (~s_col(Xp, Xq, V)))), (((((((((Xa = Xb) | (Xp = Xq)) | (~s_col(Xp, Xq, Xcx))) | (~s_col(Xa, Xb, Xcx))) | (~s_col(Xa, Xb, U))) | (~s_col(Xp, Xq, V))) | (Xcx = U)) | (Xcx = V)) <=> ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | (~s_col(Xp, Xq, V))))), ((((((((((Xa = Xb) | (Xp = Xq)) | (~s_col(Xp, Xq, Xcx))) | (~s_col(Xa, Xb, Xcx))) | (~s_col(Xa, Xb, U))) | (~s_col(Xp, Xq, V))) | (Xcx = U)) | (Xcx = V)) | (~s_r(U, Xcx, V))) <=> (((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | (~s_col(Xp, Xq, V))) | (~s_r(U, Xcx, V))))), rewrite((((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | (~s_col(Xp, Xq, V))) | (~s_r(U, Xcx, V))) <=> ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V)))), ((((((((((Xa = Xb) | (Xp = Xq)) | (~s_col(Xp, Xq, Xcx))) | (~s_col(Xa, Xb, Xcx))) | (~s_col(Xa, Xb, U))) | (~s_col(Xp, Xq, V))) | (Xcx = U)) | (Xcx = V)) | (~s_r(U, Xcx, V))) <=> ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V))))), (((((((((((Xa = Xb) | (Xp = Xq)) | (~s_col(Xp, Xq, Xcx))) | (~s_col(Xa, Xb, Xcx))) | (~s_col(Xa, Xb, U))) | (~s_col(Xp, Xq, V))) | (Xcx = U)) | (Xcx = V)) | (~s_r(U, Xcx, V))) | perpAt(Xa, Xb, Xcx, Xp, Xq)) <=> (((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V))) | perpAt(Xa, Xb, Xcx, Xp, Xq)))), rewrite((((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V))) | perpAt(Xa, Xb, Xcx, Xp, Xq)) <=> ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | perpAt(Xa, Xb, Xcx, Xp, Xq) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V)))), (((((((((((Xa = Xb) | (Xp = Xq)) | (~s_col(Xp, Xq, Xcx))) | (~s_col(Xa, Xb, Xcx))) | (~s_col(Xa, Xb, U))) | (~s_col(Xp, Xq, V))) | (Xcx = U)) | (Xcx = V)) | (~s_r(U, Xcx, V))) | perpAt(Xa, Xb, Xcx, Xp, Xq)) <=> ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | perpAt(Xa, Xb, Xcx, Xp, Xq) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V)))))),
% 0.40/0.56 inference(bind,[status(th)],[])).
% 0.40/0.56 tff(165,plain,
% 0.40/0.56 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xcx: $i, U: $i, V: $i] : ((((((((((Xa = Xb) | (Xp = Xq)) | (~s_col(Xp, Xq, Xcx))) | (~s_col(Xa, Xb, Xcx))) | (~s_col(Xa, Xb, U))) | (~s_col(Xp, Xq, V))) | (Xcx = U)) | (Xcx = V)) | (~s_r(U, Xcx, V))) | perpAt(Xa, Xb, Xcx, Xp, Xq)) <=> ![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xcx: $i, U: $i, V: $i] : ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | perpAt(Xa, Xb, Xcx, Xp, Xq) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V)))),
% 0.40/0.56 inference(quant_intro,[status(thm)],[164])).
% 0.40/0.56 tff(166,axiom,(![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xcx: $i, U: $i, V: $i] : ((((((((((Xa = Xb) | (Xp = Xq)) | (~s_col(Xp, Xq, Xcx))) | (~s_col(Xa, Xb, Xcx))) | (~s_col(Xa, Xb, U))) | (~s_col(Xp, Xq, V))) | (Xcx = U)) | (Xcx = V)) | (~s_r(U, Xcx, V))) | perpAt(Xa, Xb, Xcx, Xp, Xq))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz8_13b')).
% 0.40/0.56 tff(167,plain,
% 0.40/0.56 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xcx: $i, U: $i, V: $i] : ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | perpAt(Xa, Xb, Xcx, Xp, Xq) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V)))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.40/0.56 tff(168,plain,
% 0.40/0.56 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xcx: $i, U: $i, V: $i] : ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | perpAt(Xa, Xb, Xcx, Xp, Xq) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V)))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.40/0.56 tff(169,plain,(
% 0.40/0.56 ![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xcx: $i, U: $i, V: $i] : ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | perpAt(Xa, Xb, Xcx, Xp, Xq) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V)))),
% 0.40/0.56 inference(skolemize,[status(sab)],[168])).
% 0.40/0.56 tff(170,plain,
% 0.40/0.56 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xcx: $i, U: $i, V: $i] : ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | perpAt(Xa, Xb, Xcx, Xp, Xq) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V)))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.40/0.56 tff(171,plain,
% 0.40/0.56 (((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xcx: $i, U: $i, V: $i] : ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | perpAt(Xa, Xb, Xcx, Xp, Xq) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V)))) | ((Xa!6 = Xb!5) | (Xc!1 = Xd!0) | (~s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0))) | perpAt(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (~s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), il(Xp!4, Xq!3, Xc!1, Xd!0), g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (il(Xp!4, Xq!3, Xc!1, Xd!0) = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) | (~s_col(Xa!6, Xb!5, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (il(Xp!4, Xq!3, Xc!1, Xd!0) = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) <=> ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xcx: $i, U: $i, V: $i] : ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | perpAt(Xa, Xb, Xcx, Xp, Xq) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V)))) | (Xa!6 = Xb!5) | (Xc!1 = Xd!0) | (~s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0))) | perpAt(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (~s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), il(Xp!4, Xq!3, Xc!1, Xd!0), g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (il(Xp!4, Xq!3, Xc!1, Xd!0) = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) | (~s_col(Xa!6, Xb!5, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (il(Xp!4, Xq!3, Xc!1, Xd!0) = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))),
% 0.42/0.56 inference(rewrite,[status(thm)],[])).
% 0.42/0.56 tff(172,plain,
% 0.42/0.56 (((il(Xp!4, Xq!3, Xc!1, Xd!0) = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) | (Xc!1 = Xd!0) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (il(Xp!4, Xq!3, Xc!1, Xd!0) = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) | (~s_col(Xa!6, Xb!5, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (~s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (Xa!6 = Xb!5) | perpAt(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (~s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), il(Xp!4, Xq!3, Xc!1, Xd!0), g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (~s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) <=> ((Xa!6 = Xb!5) | (Xc!1 = Xd!0) | (~s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0))) | perpAt(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (~s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), il(Xp!4, Xq!3, Xc!1, Xd!0), g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (il(Xp!4, Xq!3, Xc!1, Xd!0) = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) | (~s_col(Xa!6, Xb!5, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (il(Xp!4, Xq!3, Xc!1, Xd!0) = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))),
% 0.42/0.56 inference(rewrite,[status(thm)],[])).
% 0.42/0.56 tff(173,plain,
% 0.42/0.56 (((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xcx: $i, U: $i, V: $i] : ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | perpAt(Xa, Xb, Xcx, Xp, Xq) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V)))) | ((il(Xp!4, Xq!3, Xc!1, Xd!0) = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) | (Xc!1 = Xd!0) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (il(Xp!4, Xq!3, Xc!1, Xd!0) = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) | (~s_col(Xa!6, Xb!5, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (~s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (Xa!6 = Xb!5) | perpAt(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (~s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), il(Xp!4, Xq!3, Xc!1, Xd!0), g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (~s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) <=> ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xcx: $i, U: $i, V: $i] : ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | perpAt(Xa, Xb, Xcx, Xp, Xq) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V)))) | ((Xa!6 = Xb!5) | (Xc!1 = Xd!0) | (~s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0))) | perpAt(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (~s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), il(Xp!4, Xq!3, Xc!1, Xd!0), g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (il(Xp!4, Xq!3, Xc!1, Xd!0) = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) | (~s_col(Xa!6, Xb!5, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (il(Xp!4, Xq!3, Xc!1, Xd!0) = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))),
% 0.42/0.57 inference(monotonicity,[status(thm)],[172])).
% 0.42/0.57 tff(174,plain,
% 0.42/0.57 (((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xcx: $i, U: $i, V: $i] : ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | perpAt(Xa, Xb, Xcx, Xp, Xq) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V)))) | ((il(Xp!4, Xq!3, Xc!1, Xd!0) = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) | (Xc!1 = Xd!0) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (il(Xp!4, Xq!3, Xc!1, Xd!0) = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) | (~s_col(Xa!6, Xb!5, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (~s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (Xa!6 = Xb!5) | perpAt(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (~s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), il(Xp!4, Xq!3, Xc!1, Xd!0), g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (~s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) <=> ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xcx: $i, U: $i, V: $i] : ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | perpAt(Xa, Xb, Xcx, Xp, Xq) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V)))) | (Xa!6 = Xb!5) | (Xc!1 = Xd!0) | (~s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0))) | perpAt(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (~s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), il(Xp!4, Xq!3, Xc!1, Xd!0), g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (il(Xp!4, Xq!3, Xc!1, Xd!0) = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) | (~s_col(Xa!6, Xb!5, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (il(Xp!4, Xq!3, Xc!1, Xd!0) = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))),
% 0.42/0.57 inference(transitivity,[status(thm)],[173, 171])).
% 0.42/0.57 tff(175,plain,
% 0.42/0.57 ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xcx: $i, U: $i, V: $i] : ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | perpAt(Xa, Xb, Xcx, Xp, Xq) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V)))) | ((il(Xp!4, Xq!3, Xc!1, Xd!0) = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) | (Xc!1 = Xd!0) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (il(Xp!4, Xq!3, Xc!1, Xd!0) = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) | (~s_col(Xa!6, Xb!5, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (~s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (Xa!6 = Xb!5) | perpAt(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (~s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), il(Xp!4, Xq!3, Xc!1, Xd!0), g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (~s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))),
% 0.42/0.57 inference(quant_inst,[status(thm)],[])).
% 0.42/0.57 tff(176,plain,
% 0.42/0.57 ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xcx: $i, U: $i, V: $i] : ((Xcx = U) | (Xp = Xq) | (~s_col(Xp, Xq, Xcx)) | (Xcx = V) | (~s_col(Xa, Xb, U)) | (~s_col(Xa, Xb, Xcx)) | (Xa = Xb) | perpAt(Xa, Xb, Xcx, Xp, Xq) | (~s_r(U, Xcx, V)) | (~s_col(Xp, Xq, V)))) | (Xa!6 = Xb!5) | (Xc!1 = Xd!0) | (~s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (~s_col(Xc!1, Xd!0, il(Xp!4, Xq!3, Xc!1, Xd!0))) | (~s_col(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0))) | perpAt(Xa!6, Xb!5, il(Xp!4, Xq!3, Xc!1, Xd!0), Xc!1, Xd!0) | (~s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), il(Xp!4, Xq!3, Xc!1, Xd!0), g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (il(Xp!4, Xq!3, Xc!1, Xd!0) = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)) | (~s_col(Xa!6, Xb!5, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))) | (il(Xp!4, Xq!3, Xc!1, Xd!0) = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.42/0.57 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.42/0.57 tff(177,plain,
% 0.42/0.57 (il(Xp!4, Xq!3, Xc!1, Xd!0) = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)),
% 0.42/0.57 inference(unit_resolution,[status(thm)],[176, 170, 63, 160, 155, 150, 145, 86, 81, 55, 47])).
% 0.42/0.58 tff(178,plain,
% 0.42/0.58 (Xr!2 = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)),
% 0.42/0.58 inference(transitivity,[status(thm)],[22, 177])).
% 0.42/0.58 tff(179,plain,
% 0.42/0.58 (((~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xc!1 = Xd!0)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, Xr!2))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, Xr!2))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_col(Xc!1, Xd!0, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | (~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | s_r(f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2), Xr!2, g813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | ((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))),
% 0.42/0.58 inference(tautology,[status(thm)],[])).
% 0.42/0.58 tff(180,plain,
% 0.42/0.58 ((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[179, 41])).
% 0.42/0.58 tff(181,plain,
% 0.42/0.58 ((~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | (~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))),
% 0.42/0.58 inference(tautology,[status(thm)],[])).
% 0.42/0.58 tff(182,plain,
% 0.42/0.58 ((~((~perpAt(Xp!4, Xq!3, Xr!2, Xc!1, Xd!0)) | (~(Xr!2 = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))))) | (~(Xr!2 = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2)))),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[181, 11])).
% 0.42/0.58 tff(183,plain,
% 0.42/0.58 (~(Xr!2 = f813(Xp!4, Xq!3, Xc!1, Xd!0, Xr!2))),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[182, 180])).
% 0.42/0.58 tff(184,plain,
% 0.42/0.58 ($false),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[183, 178])).
% 0.42/0.58 % SZS output end Proof
% 0.42/0.58 % E exiting
%------------------------------------------------------------------------------