%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO528+1 : TPTP v9.0.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:06:27 AM UTC 2025
% Result : Theorem 0.21s 0.53s
% Output : Proof 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GEO528+1 : TPTP v9.0.0. Released v7.0.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 15:01:17 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.21/0.53 % SZS status Theorem
% 0.21/0.53 % SZS output start Proof
% 0.21/0.53 tff(sameside_type, type, (
% 0.21/0.53 sameside: ( $i * $i * $i ) > $o)).
% 0.21/0.53 tff(tptp_fun_Xp_0_type, type, (
% 0.21/0.53 tptp_fun_Xp_0: $i)).
% 0.21/0.53 tff(s_type, type, (
% 0.21/0.53 s: ( $i * $i ) > $i)).
% 0.21/0.53 tff(midpoint_type, type, (
% 0.21/0.53 midpoint: ( $i * $i ) > $i)).
% 0.21/0.53 tff(reflect_type, type, (
% 0.21/0.53 reflect: ( $i * $i * $i ) > $i)).
% 0.21/0.53 tff(tptp_fun_Xb_1_type, type, (
% 0.21/0.53 tptp_fun_Xb_1: $i)).
% 0.21/0.53 tff(tptp_fun_Xa_2_type, type, (
% 0.21/0.53 tptp_fun_Xa_2: $i)).
% 0.21/0.53 tff(s_t_type, type, (
% 0.21/0.53 s_t: ( $i * $i * $i ) > $o)).
% 0.21/0.53 tff(xb_type, type, (
% 0.21/0.53 xb: $i)).
% 0.21/0.53 tff(s_col_type, type, (
% 0.21/0.53 s_col: ( $i * $i * $i ) > $o)).
% 0.21/0.53 tff(s_m_type, type, (
% 0.21/0.53 s_m: ( $i * $i * $i ) > $o)).
% 0.21/0.53 tff(s_e_type, type, (
% 0.21/0.53 s_e: ( $i * $i * $i * $i ) > $o)).
% 0.21/0.53 tff(opposite_type, type, (
% 0.21/0.53 opposite: ( $i * $i * $i * $i ) > $o)).
% 0.21/0.53 tff(il_type, type, (
% 0.21/0.53 il: ( $i * $i * $i * $i ) > $i)).
% 0.21/0.53 tff(perp_type, type, (
% 0.21/0.53 perp: ( $i * $i * $i * $i ) > $o)).
% 0.21/0.53 tff(1,plain,
% 0.21/0.53 (^[Xa: $i, Xb: $i, Xc: $i] : refl((~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))))) <=> (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(2,plain,
% 0.21/0.53 (![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.53 tff(3,plain,
% 0.21/0.53 (^[Xa: $i, Xb: $i, Xc: $i] : trans(monotonicity(rewrite((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) <=> (s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))), rewrite((s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))) <=> (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))), (((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))))), rewrite(((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))), (((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(4,plain,
% 0.21/0.53 (![Xa: $i, Xb: $i, Xc: $i] : ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.53 tff(5,plain,
% 0.21/0.53 (![Xa: $i, Xb: $i, Xc: $i] : ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> ![Xa: $i, Xb: $i, Xc: $i] : ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(6,plain,
% 0.21/0.53 (^[Xa: $i, Xb: $i, Xc: $i] : trans(monotonicity(trans(monotonicity(rewrite((((((~s_col(Xa, Xb, Xc)) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) & (s_col(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xc)))) <=> ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)))), rewrite((s_col(Xa, Xb, Xc) | (~s_t(Xb, Xc, Xa))) <=> ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))), (((((((~s_col(Xa, Xb, Xc)) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) & (s_col(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xc)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xb, Xc, Xa)))) <=> (((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))))), rewrite((((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) <=> ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)))), (((((((~s_col(Xa, Xb, Xc)) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) & (s_col(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xc)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xb, Xc, Xa)))) <=> ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))))), rewrite((s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))) <=> (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))), ((((((((~s_col(Xa, Xb, Xc)) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) & (s_col(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xc)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xb, Xc, Xa)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> (((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))))), rewrite((((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))), ((((((((~s_col(Xa, Xb, Xc)) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) & (s_col(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xc)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xb, Xc, Xa)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(7,plain,
% 0.21/0.53 (![Xa: $i, Xb: $i, Xc: $i] : (((((((~s_col(Xa, Xb, Xc)) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) & (s_col(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xc)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xb, Xc, Xa)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> ![Xa: $i, Xb: $i, Xc: $i] : ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.54 tff(8,axiom,(![Xa: $i, Xb: $i, Xc: $i] : (((((((~s_col(Xa, Xb, Xc)) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) & (s_col(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xc)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xb, Xc, Xa)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d_Defn4_10')).
% 0.21/0.54 tff(9,plain,
% 0.21/0.54 (![Xa: $i, Xb: $i, Xc: $i] : ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.21/0.54 tff(10,plain,
% 0.21/0.54 (![Xa: $i, Xb: $i, Xc: $i] : ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.21/0.54 tff(11,plain,(
% 0.21/0.54 ![Xa: $i, Xb: $i, Xc: $i] : ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))),
% 0.21/0.54 inference(skolemize,[status(sab)],[10])).
% 0.21/0.54 tff(12,plain,
% 0.21/0.54 (![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.21/0.54 tff(13,plain,
% 0.21/0.54 (![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.21/0.54 tff(14,plain,
% 0.21/0.54 (((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~((~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~((~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~(s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~((~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~((~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~(s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(15,plain,
% 0.21/0.54 ((~((~(s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~((~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~(s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))))) <=> (~((~((~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~((~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~(s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(16,plain,
% 0.21/0.54 (((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~(s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~((~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~(s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~((~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~((~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~(s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))))))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[15])).
% 0.21/0.54 tff(17,plain,
% 0.21/0.54 (((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~(s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~((~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~(s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~((~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~((~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~(s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))))))),
% 0.21/0.55 inference(transitivity,[status(thm)],[16, 14])).
% 0.21/0.55 tff(18,plain,
% 0.21/0.55 ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~(s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~((~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~(s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(19,plain,
% 0.21/0.55 ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~((~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~((~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~(s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.55 tff(20,plain,
% 0.21/0.55 (~((~((~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~((~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~(s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.21/0.55 tff(21,plain,
% 0.21/0.55 (((~((~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~((~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~(s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | ((~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(22,plain,
% 0.21/0.55 ((~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.21/0.55 tff(23,plain,
% 0.21/0.55 (^[Xa: $i, Xb: $i] : refl(s_m(Xa, midpoint(Xa, Xb), Xb) <=> s_m(Xa, midpoint(Xa, Xb), Xb))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(24,plain,
% 0.21/0.55 (![Xa: $i, Xb: $i] : s_m(Xa, midpoint(Xa, Xb), Xb) <=> ![Xa: $i, Xb: $i] : s_m(Xa, midpoint(Xa, Xb), Xb)),
% 0.21/0.55 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.55 tff(25,plain,
% 0.21/0.55 (![Xa: $i, Xb: $i] : s_m(Xa, midpoint(Xa, Xb), Xb) <=> ![Xa: $i, Xb: $i] : s_m(Xa, midpoint(Xa, Xb), Xb)),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(26,axiom,(![Xa: $i, Xb: $i] : s_m(Xa, midpoint(Xa, Xb), Xb)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz8_22')).
% 0.21/0.55 tff(27,plain,
% 0.21/0.55 (![Xa: $i, Xb: $i] : s_m(Xa, midpoint(Xa, Xb), Xb)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.55 tff(28,plain,(
% 0.21/0.55 ![Xa: $i, Xb: $i] : s_m(Xa, midpoint(Xa, Xb), Xb)),
% 0.21/0.55 inference(skolemize,[status(sab)],[27])).
% 0.21/0.55 tff(29,plain,
% 0.21/0.55 (![Xa: $i, Xb: $i] : s_m(Xa, midpoint(Xa, Xb), Xb)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.21/0.55 tff(30,plain,
% 0.21/0.55 ((~![Xa: $i, Xb: $i] : s_m(Xa, midpoint(Xa, Xb), Xb)) | s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(31,plain,
% 0.21/0.55 (s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.21/0.55 tff(32,plain,
% 0.21/0.55 (^[Xp: $i, Xa: $i, Xq: $i] : refl(((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp))) <=> ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp))))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(33,plain,
% 0.21/0.55 (![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp))) <=> ![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.55 tff(34,plain,
% 0.21/0.55 (![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp))) <=> ![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(35,axiom,(![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz7_6')).
% 0.21/0.55 tff(36,plain,
% 0.21/0.55 (![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.55 tff(37,plain,(
% 0.21/0.55 ![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.21/0.55 inference(skolemize,[status(sab)],[36])).
% 0.21/0.55 tff(38,plain,
% 0.21/0.55 (![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.21/0.55 tff(39,plain,
% 0.21/0.55 (((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | (reflect(Xa!2, Xb!1, Xp!0) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) <=> ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | (reflect(Xa!2, Xb!1, Xp!0) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(40,plain,
% 0.21/0.55 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | (reflect(Xa!2, Xb!1, Xp!0) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(41,plain,
% 0.21/0.55 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | (reflect(Xa!2, Xb!1, Xp!0) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.55 tff(42,plain,
% 0.21/0.55 (reflect(Xa!2, Xb!1, Xp!0) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[41, 38, 31])).
% 0.21/0.55 tff(43,plain,
% 0.21/0.55 (s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0) = reflect(Xa!2, Xb!1, Xp!0)),
% 0.21/0.55 inference(symmetry,[status(thm)],[42])).
% 0.21/0.55 tff(44,plain,
% 0.21/0.55 (s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) <=> s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[43])).
% 0.21/0.55 tff(45,plain,
% 0.21/0.55 (s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0)) <=> s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))),
% 0.21/0.55 inference(symmetry,[status(thm)],[44])).
% 0.21/0.55 tff(46,plain,
% 0.21/0.55 (^[Xa: $i, Xm: $i, Xb: $i] : refl((~((~((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb))) | (~((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb))) | (~((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb))))) <=> (~((~((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb))) | (~((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb))) | (~((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb))))))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(47,plain,
% 0.21/0.55 (![Xa: $i, Xm: $i, Xb: $i] : (~((~((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb))) | (~((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb))) | (~((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb))))) <=> ![Xa: $i, Xm: $i, Xb: $i] : (~((~((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb))) | (~((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb))) | (~((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb)))))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.55 tff(48,plain,
% 0.21/0.55 (^[Xa: $i, Xm: $i, Xb: $i] : rewrite((((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb)) & ((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb)) & ((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb))) <=> (~((~((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb))) | (~((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb))) | (~((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb))))))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(49,plain,
% 0.21/0.55 (![Xa: $i, Xm: $i, Xb: $i] : (((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb)) & ((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb)) & ((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb))) <=> ![Xa: $i, Xm: $i, Xb: $i] : (~((~((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb))) | (~((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb))) | (~((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb)))))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[48])).
% 0.21/0.55 tff(50,plain,
% 0.21/0.55 (![Xa: $i, Xm: $i, Xb: $i] : (((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb)) & ((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb)) & ((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb))) <=> ![Xa: $i, Xm: $i, Xb: $i] : (((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb)) & ((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb)) & ((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(51,plain,
% 0.21/0.55 (^[Xa: $i, Xm: $i, Xb: $i] : trans(monotonicity(rewrite((((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb))) | s_m(Xa, Xm, Xb)) <=> ((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb))), (((((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb)) & ((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb))) & (((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb))) | s_m(Xa, Xm, Xb))) <=> ((((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb)) & ((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb))) & ((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb))))), rewrite(((((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb)) & ((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb))) & ((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb))) <=> (((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb)) & ((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb)) & ((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb)))), (((((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb)) & ((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb))) & (((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb))) | s_m(Xa, Xm, Xb))) <=> (((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb)) & ((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb)) & ((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb)))))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(52,plain,
% 0.21/0.55 (![Xa: $i, Xm: $i, Xb: $i] : ((((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb)) & ((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb))) & (((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb))) | s_m(Xa, Xm, Xb))) <=> ![Xa: $i, Xm: $i, Xb: $i] : (((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb)) & ((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb)) & ((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb)))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.55 tff(53,axiom,(![Xa: $i, Xm: $i, Xb: $i] : ((((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb)) & ((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb))) & (((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb))) | s_m(Xa, Xm, Xb)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d_Defn7_1')).
% 0.21/0.55 tff(54,plain,
% 0.21/0.55 (![Xa: $i, Xm: $i, Xb: $i] : (((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb)) & ((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb)) & ((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.21/0.55 tff(55,plain,
% 0.21/0.55 (![Xa: $i, Xm: $i, Xb: $i] : (((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb)) & ((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb)) & ((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.21/0.55 tff(56,plain,(
% 0.21/0.55 ![Xa: $i, Xm: $i, Xb: $i] : (((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb)) & ((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb)) & ((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb)))),
% 0.21/0.55 inference(skolemize,[status(sab)],[55])).
% 0.21/0.55 tff(57,plain,
% 0.21/0.55 (![Xa: $i, Xm: $i, Xb: $i] : (~((~((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb))) | (~((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb))) | (~((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb)))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.21/0.55 tff(58,plain,
% 0.21/0.55 (![Xa: $i, Xm: $i, Xb: $i] : (~((~((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb))) | (~((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb))) | (~((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb)))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[57, 47])).
% 0.21/0.55 tff(59,plain,
% 0.21/0.55 ((~![Xa: $i, Xm: $i, Xb: $i] : (~((~((~s_m(Xa, Xm, Xb)) | s_t(Xa, Xm, Xb))) | (~((~s_m(Xa, Xm, Xb)) | s_e(Xm, Xa, Xm, Xb))) | (~((~s_t(Xa, Xm, Xb)) | (~s_e(Xm, Xa, Xm, Xb)) | s_m(Xa, Xm, Xb)))))) | (~((~((~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0)))) | (~((~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0)))) | (~((~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | (~s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(60,plain,
% 0.21/0.55 (~((~((~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0)))) | (~((~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0)))) | (~((~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | (~s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0)))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.21/0.55 tff(61,plain,
% 0.21/0.55 (((~((~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0)))) | (~((~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0)))) | (~((~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | (~s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))))) | ((~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0)))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(62,plain,
% 0.21/0.55 ((~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.21/0.55 tff(63,plain,
% 0.21/0.55 ((~((~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0)))) | (~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(64,plain,
% 0.21/0.55 ((~((~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0)))) | s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[63, 31])).
% 0.21/0.55 tff(65,plain,
% 0.21/0.55 (s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[64, 62])).
% 0.21/0.55 tff(66,plain,
% 0.21/0.55 (s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[65, 45])).
% 0.21/0.55 tff(67,plain,
% 0.21/0.55 ((~((~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.56 tff(68,plain,
% 0.21/0.56 (s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[67, 66, 22])).
% 0.21/0.56 tff(69,plain,
% 0.21/0.56 (s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) <=> s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[43])).
% 0.21/0.56 tff(70,plain,
% 0.21/0.56 (s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0)) <=> s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))),
% 0.21/0.56 inference(symmetry,[status(thm)],[69])).
% 0.21/0.56 tff(71,plain,
% 0.21/0.56 (((~((~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0)))) | (~((~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0)))) | (~((~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | (~s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))))) | ((~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0)))),
% 0.21/0.56 inference(tautology,[status(thm)],[])).
% 0.21/0.56 tff(72,plain,
% 0.21/0.56 ((~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[71, 60])).
% 0.21/0.56 tff(73,plain,
% 0.21/0.56 ((~((~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0)))) | (~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))),
% 0.21/0.56 inference(tautology,[status(thm)],[])).
% 0.21/0.56 tff(74,plain,
% 0.21/0.56 ((~((~s_m(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))) | s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0)))) | s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[73, 31])).
% 0.21/0.56 tff(75,plain,
% 0.21/0.56 (s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), reflect(Xa!2, Xb!1, Xp!0))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[74, 72])).
% 0.21/0.56 tff(76,plain,
% 0.21/0.56 (s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[75, 70])).
% 0.21/0.56 tff(77,plain,
% 0.21/0.56 ((Xp!0 = reflect(Xa!2, Xb!1, Xp!0)) <=> (reflect(Xa!2, Xb!1, Xp!0) = Xp!0)),
% 0.21/0.56 inference(commutativity,[status(thm)],[])).
% 0.21/0.56 tff(78,plain,
% 0.21/0.56 ((Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) <=> (Xp!0 = reflect(Xa!2, Xb!1, Xp!0))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[43])).
% 0.21/0.56 tff(79,plain,
% 0.21/0.56 ((Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) <=> (reflect(Xa!2, Xb!1, Xp!0) = Xp!0)),
% 0.21/0.56 inference(transitivity,[status(thm)],[78, 77])).
% 0.21/0.56 tff(80,plain,
% 0.21/0.56 ((reflect(Xa!2, Xb!1, Xp!0) = Xp!0) <=> (Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))),
% 0.21/0.56 inference(symmetry,[status(thm)],[79])).
% 0.21/0.56 tff(81,plain,
% 0.21/0.56 ((~(reflect(Xa!2, Xb!1, Xp!0) = Xp!0)) <=> (~(Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[80])).
% 0.21/0.56 tff(82,plain,
% 0.21/0.56 ((~![Xa: $i, Xb: $i, Xp: $i] : ((Xa = Xb) | s_col(Xa, Xb, Xp) | opposite(Xp, Xa, Xb, reflect(Xa, Xb, Xp)))) <=> (~![Xa: $i, Xb: $i, Xp: $i] : ((Xa = Xb) | s_col(Xa, Xb, Xp) | opposite(Xp, Xa, Xb, reflect(Xa, Xb, Xp))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(83,plain,
% 0.21/0.56 ((~![Xa: $i, Xb: $i, Xp: $i, Xp1: $i] : ((((Xa = Xb) | (~(reflect(Xa, Xb, Xp) = Xp1))) | s_col(Xa, Xb, Xp)) | opposite(Xp, Xa, Xb, Xp1))) <=> (~![Xa: $i, Xb: $i, Xp: $i] : ((Xa = Xb) | s_col(Xa, Xb, Xp) | opposite(Xp, Xa, Xb, reflect(Xa, Xb, Xp))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(84,axiom,(~![Xa: $i, Xb: $i, Xp: $i, Xp1: $i] : ((((Xa = Xb) | (~(reflect(Xa, Xb, Xp) = Xp1))) | s_col(Xa, Xb, Xp)) | opposite(Xp, Xa, Xb, Xp1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz10_14')).
% 0.21/0.56 tff(85,plain,
% 0.21/0.56 (~![Xa: $i, Xb: $i, Xp: $i] : ((Xa = Xb) | s_col(Xa, Xb, Xp) | opposite(Xp, Xa, Xb, reflect(Xa, Xb, Xp)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.21/0.56 tff(86,plain,
% 0.21/0.56 (~![Xa: $i, Xb: $i, Xp: $i] : ((Xa = Xb) | s_col(Xa, Xb, Xp) | opposite(Xp, Xa, Xb, reflect(Xa, Xb, Xp)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[85, 82])).
% 0.21/0.56 tff(87,plain,
% 0.21/0.56 (~![Xa: $i, Xb: $i, Xp: $i] : ((Xa = Xb) | s_col(Xa, Xb, Xp) | opposite(Xp, Xa, Xb, reflect(Xa, Xb, Xp)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.21/0.56 tff(88,plain,
% 0.21/0.56 (~![Xa: $i, Xb: $i, Xp: $i] : ((Xa = Xb) | s_col(Xa, Xb, Xp) | opposite(Xp, Xa, Xb, reflect(Xa, Xb, Xp)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[87, 82])).
% 0.21/0.56 tff(89,plain,(
% 0.21/0.56 ~((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | opposite(Xp!0, Xa!2, Xb!1, reflect(Xa!2, Xb!1, Xp!0)))),
% 0.21/0.56 inference(skolemize,[status(sab)],[88])).
% 0.21/0.56 tff(90,plain,
% 0.21/0.56 (~s_col(Xa!2, Xb!1, Xp!0)),
% 0.21/0.56 inference(or_elim,[status(thm)],[89])).
% 0.21/0.56 tff(91,plain,
% 0.21/0.56 (~(Xa!2 = Xb!1)),
% 0.21/0.56 inference(or_elim,[status(thm)],[89])).
% 0.21/0.56 tff(92,plain,
% 0.21/0.56 (^[Xa: $i, Xb: $i, Xp: $i] : refl(((Xa = Xb) | s_col(Xa, Xb, Xp) | (~(reflect(Xa, Xb, Xp) = Xp))) <=> ((Xa = Xb) | s_col(Xa, Xb, Xp) | (~(reflect(Xa, Xb, Xp) = Xp))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(93,plain,
% 0.21/0.56 (![Xa: $i, Xb: $i, Xp: $i] : ((Xa = Xb) | s_col(Xa, Xb, Xp) | (~(reflect(Xa, Xb, Xp) = Xp))) <=> ![Xa: $i, Xb: $i, Xp: $i] : ((Xa = Xb) | s_col(Xa, Xb, Xp) | (~(reflect(Xa, Xb, Xp) = Xp)))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[92])).
% 0.21/0.56 tff(94,plain,
% 0.21/0.56 (![Xa: $i, Xb: $i, Xp: $i] : ((Xa = Xb) | s_col(Xa, Xb, Xp) | (~(reflect(Xa, Xb, Xp) = Xp))) <=> ![Xa: $i, Xb: $i, Xp: $i] : ((Xa = Xb) | s_col(Xa, Xb, Xp) | (~(reflect(Xa, Xb, Xp) = Xp)))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(95,plain,
% 0.21/0.56 (^[Xa: $i, Xb: $i, Xp: $i] : trans(monotonicity(rewrite(((Xa = Xb) | (~(reflect(Xa, Xb, Xp) = Xp))) <=> ((Xa = Xb) | (~(reflect(Xa, Xb, Xp) = Xp)))), ((((Xa = Xb) | (~(reflect(Xa, Xb, Xp) = Xp))) | s_col(Xa, Xb, Xp)) <=> (((Xa = Xb) | (~(reflect(Xa, Xb, Xp) = Xp))) | s_col(Xa, Xb, Xp)))), rewrite((((Xa = Xb) | (~(reflect(Xa, Xb, Xp) = Xp))) | s_col(Xa, Xb, Xp)) <=> ((Xa = Xb) | s_col(Xa, Xb, Xp) | (~(reflect(Xa, Xb, Xp) = Xp)))), ((((Xa = Xb) | (~(reflect(Xa, Xb, Xp) = Xp))) | s_col(Xa, Xb, Xp)) <=> ((Xa = Xb) | s_col(Xa, Xb, Xp) | (~(reflect(Xa, Xb, Xp) = Xp)))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(96,plain,
% 0.21/0.56 (![Xa: $i, Xb: $i, Xp: $i] : (((Xa = Xb) | (~(reflect(Xa, Xb, Xp) = Xp))) | s_col(Xa, Xb, Xp)) <=> ![Xa: $i, Xb: $i, Xp: $i] : ((Xa = Xb) | s_col(Xa, Xb, Xp) | (~(reflect(Xa, Xb, Xp) = Xp)))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[95])).
% 0.21/0.56 tff(97,axiom,(![Xa: $i, Xb: $i, Xp: $i] : (((Xa = Xb) | (~(reflect(Xa, Xb, Xp) = Xp))) | s_col(Xa, Xb, Xp))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz10_8a')).
% 0.21/0.56 tff(98,plain,
% 0.21/0.56 (![Xa: $i, Xb: $i, Xp: $i] : ((Xa = Xb) | s_col(Xa, Xb, Xp) | (~(reflect(Xa, Xb, Xp) = Xp)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.21/0.56 tff(99,plain,
% 0.21/0.56 (![Xa: $i, Xb: $i, Xp: $i] : ((Xa = Xb) | s_col(Xa, Xb, Xp) | (~(reflect(Xa, Xb, Xp) = Xp)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.21/0.56 tff(100,plain,(
% 0.21/0.56 ![Xa: $i, Xb: $i, Xp: $i] : ((Xa = Xb) | s_col(Xa, Xb, Xp) | (~(reflect(Xa, Xb, Xp) = Xp)))),
% 0.21/0.56 inference(skolemize,[status(sab)],[99])).
% 0.21/0.56 tff(101,plain,
% 0.21/0.56 (![Xa: $i, Xb: $i, Xp: $i] : ((Xa = Xb) | s_col(Xa, Xb, Xp) | (~(reflect(Xa, Xb, Xp) = Xp)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.21/0.56 tff(102,plain,
% 0.21/0.56 (((~![Xa: $i, Xb: $i, Xp: $i] : ((Xa = Xb) | s_col(Xa, Xb, Xp) | (~(reflect(Xa, Xb, Xp) = Xp)))) | ((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~(reflect(Xa!2, Xb!1, Xp!0) = Xp!0)))) <=> ((~![Xa: $i, Xb: $i, Xp: $i] : ((Xa = Xb) | s_col(Xa, Xb, Xp) | (~(reflect(Xa, Xb, Xp) = Xp)))) | (Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~(reflect(Xa!2, Xb!1, Xp!0) = Xp!0)))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(103,plain,
% 0.21/0.56 ((~![Xa: $i, Xb: $i, Xp: $i] : ((Xa = Xb) | s_col(Xa, Xb, Xp) | (~(reflect(Xa, Xb, Xp) = Xp)))) | ((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~(reflect(Xa!2, Xb!1, Xp!0) = Xp!0)))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(104,plain,
% 0.21/0.56 ((~![Xa: $i, Xb: $i, Xp: $i] : ((Xa = Xb) | s_col(Xa, Xb, Xp) | (~(reflect(Xa, Xb, Xp) = Xp)))) | (Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~(reflect(Xa!2, Xb!1, Xp!0) = Xp!0))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.21/0.56 tff(105,plain,
% 0.21/0.56 (~(reflect(Xa!2, Xb!1, Xp!0) = Xp!0)),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[104, 101, 91, 90])).
% 0.21/0.56 tff(106,plain,
% 0.21/0.56 (~(Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[105, 81])).
% 0.21/0.56 tff(107,plain,
% 0.21/0.56 (^[Xa: $i, Xb: $i, Xc: $i] : refl(((~s_t(Xa, Xb, Xc)) | (Xc = Xb) | (~s_e(Xa, Xc, Xa, Xb))) <=> ((~s_t(Xa, Xb, Xc)) | (Xc = Xb) | (~s_e(Xa, Xc, Xa, Xb))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(108,plain,
% 0.21/0.56 (![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | (Xc = Xb) | (~s_e(Xa, Xc, Xa, Xb))) <=> ![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | (Xc = Xb) | (~s_e(Xa, Xc, Xa, Xb)))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[107])).
% 0.21/0.56 tff(109,plain,
% 0.21/0.56 (![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | (Xc = Xb) | (~s_e(Xa, Xc, Xa, Xb))) <=> ![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | (Xc = Xb) | (~s_e(Xa, Xc, Xa, Xb)))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(110,plain,
% 0.21/0.56 (^[Xa: $i, Xb: $i, Xc: $i] : rewrite((((~s_t(Xa, Xb, Xc)) | (~s_e(Xa, Xc, Xa, Xb))) | (Xc = Xb)) <=> ((~s_t(Xa, Xb, Xc)) | (Xc = Xb) | (~s_e(Xa, Xc, Xa, Xb))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(111,plain,
% 0.21/0.56 (![Xa: $i, Xb: $i, Xc: $i] : (((~s_t(Xa, Xb, Xc)) | (~s_e(Xa, Xc, Xa, Xb))) | (Xc = Xb)) <=> ![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | (Xc = Xb) | (~s_e(Xa, Xc, Xa, Xb)))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[110])).
% 0.21/0.56 tff(112,axiom,(![Xa: $i, Xb: $i, Xc: $i] : (((~s_t(Xa, Xb, Xc)) | (~s_e(Xa, Xc, Xa, Xb))) | (Xc = Xb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aNarbouxLemma1')).
% 0.21/0.56 tff(113,plain,
% 0.21/0.56 (![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | (Xc = Xb) | (~s_e(Xa, Xc, Xa, Xb)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.56 tff(114,plain,
% 0.21/0.56 (![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | (Xc = Xb) | (~s_e(Xa, Xc, Xa, Xb)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.21/0.56 tff(115,plain,(
% 0.21/0.56 ![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | (Xc = Xb) | (~s_e(Xa, Xc, Xa, Xb)))),
% 0.21/0.56 inference(skolemize,[status(sab)],[114])).
% 0.21/0.56 tff(116,plain,
% 0.21/0.56 (![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | (Xc = Xb) | (~s_e(Xa, Xc, Xa, Xb)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.21/0.56 tff(117,plain,
% 0.21/0.56 (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | (Xc = Xb) | (~s_e(Xa, Xc, Xa, Xb)))) | ((Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (~s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | (Xc = Xb) | (~s_e(Xa, Xc, Xa, Xb)))) | (Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (~s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(118,plain,
% 0.21/0.56 (((~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) <=> ((Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (~s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(119,plain,
% 0.21/0.56 (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | (Xc = Xb) | (~s_e(Xa, Xc, Xa, Xb)))) | ((~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | (Xc = Xb) | (~s_e(Xa, Xc, Xa, Xb)))) | ((Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (~s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[118])).
% 0.21/0.56 tff(120,plain,
% 0.21/0.56 (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | (Xc = Xb) | (~s_e(Xa, Xc, Xa, Xb)))) | ((~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | (Xc = Xb) | (~s_e(Xa, Xc, Xa, Xb)))) | (Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (~s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))),
% 0.21/0.56 inference(transitivity,[status(thm)],[119, 117])).
% 0.21/0.56 tff(121,plain,
% 0.21/0.56 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | (Xc = Xb) | (~s_e(Xa, Xc, Xa, Xb)))) | ((~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(122,plain,
% 0.21/0.56 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | (Xc = Xb) | (~s_e(Xa, Xc, Xa, Xb)))) | (Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (~s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.21/0.56 tff(123,plain,
% 0.21/0.56 ((Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (~s_e(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[122, 116])).
% 0.21/0.56 tff(124,plain,
% 0.21/0.56 (~s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[123, 106, 76])).
% 0.21/0.56 tff(125,plain,
% 0.21/0.56 (^[Xa: $i, Xp: $i, Xb: $i] : refl((s_t(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb)) | sameside(Xa, Xp, Xb)) <=> (s_t(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb)) | sameside(Xa, Xp, Xb)))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(126,plain,
% 0.21/0.56 (![Xa: $i, Xp: $i, Xb: $i] : (s_t(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb)) | sameside(Xa, Xp, Xb)) <=> ![Xa: $i, Xp: $i, Xb: $i] : (s_t(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb)) | sameside(Xa, Xp, Xb))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[125])).
% 0.21/0.56 tff(127,plain,
% 0.21/0.56 (![Xa: $i, Xp: $i, Xb: $i] : (s_t(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb)) | sameside(Xa, Xp, Xb)) <=> ![Xa: $i, Xp: $i, Xb: $i] : (s_t(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb)) | sameside(Xa, Xp, Xb))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(128,plain,
% 0.21/0.56 (^[Xa: $i, Xp: $i, Xb: $i] : trans(monotonicity(rewrite((sameside(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb))) <=> ((~s_col(Xa, Xp, Xb)) | sameside(Xa, Xp, Xb))), (((sameside(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb))) | s_t(Xa, Xp, Xb)) <=> (((~s_col(Xa, Xp, Xb)) | sameside(Xa, Xp, Xb)) | s_t(Xa, Xp, Xb)))), rewrite((((~s_col(Xa, Xp, Xb)) | sameside(Xa, Xp, Xb)) | s_t(Xa, Xp, Xb)) <=> (s_t(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb)) | sameside(Xa, Xp, Xb))), (((sameside(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb))) | s_t(Xa, Xp, Xb)) <=> (s_t(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb)) | sameside(Xa, Xp, Xb))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(129,plain,
% 0.21/0.56 (![Xa: $i, Xp: $i, Xb: $i] : ((sameside(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb))) | s_t(Xa, Xp, Xb)) <=> ![Xa: $i, Xp: $i, Xb: $i] : (s_t(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb)) | sameside(Xa, Xp, Xb))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[128])).
% 0.21/0.56 tff(130,axiom,(![Xa: $i, Xp: $i, Xb: $i] : ((sameside(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb))) | s_t(Xa, Xp, Xb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz6_4b')).
% 0.21/0.56 tff(131,plain,
% 0.21/0.56 (![Xa: $i, Xp: $i, Xb: $i] : (s_t(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb)) | sameside(Xa, Xp, Xb))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.56 tff(132,plain,
% 0.21/0.56 (![Xa: $i, Xp: $i, Xb: $i] : (s_t(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb)) | sameside(Xa, Xp, Xb))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.21/0.56 tff(133,plain,(
% 0.21/0.56 ![Xa: $i, Xp: $i, Xb: $i] : (s_t(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb)) | sameside(Xa, Xp, Xb))),
% 0.21/0.56 inference(skolemize,[status(sab)],[132])).
% 0.21/0.56 tff(134,plain,
% 0.21/0.56 (![Xa: $i, Xp: $i, Xb: $i] : (s_t(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb)) | sameside(Xa, Xp, Xb))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.21/0.56 tff(135,plain,
% 0.21/0.56 (((~![Xa: $i, Xp: $i, Xb: $i] : (s_t(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb)) | sameside(Xa, Xp, Xb))) | (s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))) <=> ((~![Xa: $i, Xp: $i, Xb: $i] : (s_t(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb)) | sameside(Xa, Xp, Xb))) | s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(136,plain,
% 0.21/0.56 ((~![Xa: $i, Xp: $i, Xb: $i] : (s_t(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb)) | sameside(Xa, Xp, Xb))) | (s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))),
% 0.21/0.57 inference(quant_inst,[status(thm)],[])).
% 0.21/0.57 tff(137,plain,
% 0.21/0.57 ((~![Xa: $i, Xp: $i, Xb: $i] : (s_t(Xa, Xp, Xb) | (~s_col(Xa, Xp, Xb)) | sameside(Xa, Xp, Xb))) | s_t(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.21/0.57 tff(138,plain,
% 0.21/0.57 (sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[137, 134, 124, 68])).
% 0.21/0.57 tff(139,plain,
% 0.21/0.57 (^[Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : refl((~((~((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb))) | (~((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq)))))) <=> (~((~((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb))) | (~((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq)))))))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(140,plain,
% 0.21/0.57 (![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : (~((~((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb))) | (~((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq)))))) <=> ![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : (~((~((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb))) | (~((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[139])).
% 0.21/0.57 tff(141,plain,
% 0.21/0.57 (^[Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : trans(monotonicity(rewrite(((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) <=> ((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb))), ((((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq)))) <=> (((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq)))))), rewrite((((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq)))) <=> (~((~((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb))) | (~((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))))), ((((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq)))) <=> (~((~((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb))) | (~((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))))))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(142,plain,
% 0.21/0.57 (![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : (((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq)))) <=> ![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : (~((~((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb))) | (~((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[141])).
% 0.21/0.57 tff(143,plain,
% 0.21/0.57 (![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : (((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq)))) <=> ![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : (((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(144,plain,
% 0.21/0.57 (^[Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((((((Xp = Xq) | s_col(Xp, Xq, Xa)) | s_col(Xp, Xq, Xb)) | (~s_t(Xa, Xt, Xb))) | (~s_col(Xp, Xq, Xt))) | opposite(Xa, Xp, Xq, Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | (~s_col(Xp, Xq, Xa)))) <=> (((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))))), rewrite(((~opposite(Xa, Xp, Xq, Xb)) | (~s_col(Xp, Xq, Xb))) <=> ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))), (((((((((Xp = Xq) | s_col(Xp, Xq, Xa)) | s_col(Xp, Xq, Xb)) | (~s_t(Xa, Xt, Xb))) | (~s_col(Xp, Xq, Xt))) | opposite(Xa, Xp, Xq, Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | (~s_col(Xp, Xq, Xa)))) & ((~opposite(Xa, Xp, Xq, Xb)) | (~s_col(Xp, Xq, Xb)))) <=> ((((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb)))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))))), rewrite(((((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb)))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))) <=> (((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb))))), (((((((((Xp = Xq) | s_col(Xp, Xq, Xa)) | s_col(Xp, Xq, Xb)) | (~s_t(Xa, Xt, Xb))) | (~s_col(Xp, Xq, Xt))) | opposite(Xa, Xp, Xq, Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | (~s_col(Xp, Xq, Xa)))) & ((~opposite(Xa, Xp, Xq, Xb)) | (~s_col(Xp, Xq, Xb)))) <=> (((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))))), ((((((((((Xp = Xq) | s_col(Xp, Xq, Xa)) | s_col(Xp, Xq, Xb)) | (~s_t(Xa, Xt, Xb))) | (~s_col(Xp, Xq, Xt))) | opposite(Xa, Xp, Xq, Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | (~s_col(Xp, Xq, Xa)))) & ((~opposite(Xa, Xp, Xq, Xb)) | (~s_col(Xp, Xq, Xb)))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) <=> ((((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))))), rewrite(((((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) <=> (((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb)))), ((((((((((Xp = Xq) | s_col(Xp, Xq, Xa)) | s_col(Xp, Xq, Xb)) | (~s_t(Xa, Xt, Xb))) | (~s_col(Xp, Xq, Xt))) | opposite(Xa, Xp, Xq, Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | (~s_col(Xp, Xq, Xa)))) & ((~opposite(Xa, Xp, Xq, Xb)) | (~s_col(Xp, Xq, Xb)))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) <=> (((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))))), (((((((((((Xp = Xq) | s_col(Xp, Xq, Xa)) | s_col(Xp, Xq, Xb)) | (~s_t(Xa, Xt, Xb))) | (~s_col(Xp, Xq, Xt))) | opposite(Xa, Xp, Xq, Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | (~s_col(Xp, Xq, Xa)))) & ((~opposite(Xa, Xp, Xq, Xb)) | (~s_col(Xp, Xq, Xb)))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq)))) <=> ((((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq)))))), rewrite(((((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq)))) <=> (((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))), (((((((((((Xp = Xq) | s_col(Xp, Xq, Xa)) | s_col(Xp, Xq, Xb)) | (~s_t(Xa, Xt, Xb))) | (~s_col(Xp, Xq, Xt))) | opposite(Xa, Xp, Xq, Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | (~s_col(Xp, Xq, Xa)))) & ((~opposite(Xa, Xp, Xq, Xb)) | (~s_col(Xp, Xq, Xb)))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq)))) <=> (((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(145,plain,
% 0.21/0.57 (![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : ((((((((((Xp = Xq) | s_col(Xp, Xq, Xa)) | s_col(Xp, Xq, Xb)) | (~s_t(Xa, Xt, Xb))) | (~s_col(Xp, Xq, Xt))) | opposite(Xa, Xp, Xq, Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | (~s_col(Xp, Xq, Xa)))) & ((~opposite(Xa, Xp, Xq, Xb)) | (~s_col(Xp, Xq, Xb)))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq)))) <=> ![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : (((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[144])).
% 0.21/0.57 tff(146,axiom,(![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : ((((((((((Xp = Xq) | s_col(Xp, Xq, Xa)) | s_col(Xp, Xq, Xb)) | (~s_t(Xa, Xt, Xb))) | (~s_col(Xp, Xq, Xt))) | opposite(Xa, Xp, Xq, Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | (~s_col(Xp, Xq, Xa)))) & ((~opposite(Xa, Xp, Xq, Xb)) | (~s_col(Xp, Xq, Xb)))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d_Defn9_1')).
% 0.21/0.57 tff(147,plain,
% 0.21/0.57 (![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : (((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.21/0.57 tff(148,plain,
% 0.21/0.57 (![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : (((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.21/0.57 tff(149,plain,(
% 0.21/0.57 ![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : (((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb)) & ((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb))) & ((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb)) & ((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))),
% 0.21/0.57 inference(skolemize,[status(sab)],[148])).
% 0.21/0.57 tff(150,plain,
% 0.21/0.57 (![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : (~((~((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb))) | (~((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[149, 142])).
% 0.21/0.57 tff(151,plain,
% 0.21/0.57 (![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : (~((~((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb))) | (~((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[150, 140])).
% 0.21/0.57 tff(152,plain,
% 0.21/0.57 (((~![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : (~((~((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb))) | (~((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))))) | (~((~((~s_col(Xa!2, Xb!1, Xp!0)) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_t(Xp!0, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(Xa!2, Xb!1, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1)))) | (~((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))))) <=> ((~![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : (~((~((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb))) | (~((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))))) | (~((~((~s_col(Xa!2, Xb!1, Xp!0)) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_t(Xp!0, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(Xa!2, Xb!1, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1)))) | (~((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))))))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(153,plain,
% 0.21/0.57 ((~((~((Xa!2 = Xb!1) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(Xa!2, Xb!1, Xp!0) | s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((~s_col(Xa!2, Xb!1, Xp!0)) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_t(Xp!0, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(Xa!2, Xb!1, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1)))))) <=> (~((~((~s_col(Xa!2, Xb!1, Xp!0)) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_t(Xp!0, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(Xa!2, Xb!1, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1)))) | (~((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(154,plain,
% 0.21/0.57 (((~![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : (~((~((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb))) | (~((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))))) | (~((~((Xa!2 = Xb!1) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(Xa!2, Xb!1, Xp!0) | s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((~s_col(Xa!2, Xb!1, Xp!0)) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_t(Xp!0, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(Xa!2, Xb!1, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1))))))) <=> ((~![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : (~((~((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb))) | (~((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))))) | (~((~((~s_col(Xa!2, Xb!1, Xp!0)) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_t(Xp!0, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(Xa!2, Xb!1, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1)))) | (~((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))))))),
% 0.21/0.58 inference(monotonicity,[status(thm)],[153])).
% 0.21/0.58 tff(155,plain,
% 0.21/0.58 (((~![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : (~((~((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb))) | (~((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))))) | (~((~((Xa!2 = Xb!1) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(Xa!2, Xb!1, Xp!0) | s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((~s_col(Xa!2, Xb!1, Xp!0)) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_t(Xp!0, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(Xa!2, Xb!1, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1))))))) <=> ((~![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : (~((~((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb))) | (~((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))))) | (~((~((~s_col(Xa!2, Xb!1, Xp!0)) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_t(Xp!0, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(Xa!2, Xb!1, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1)))) | (~((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))))))),
% 0.21/0.58 inference(transitivity,[status(thm)],[154, 152])).
% 0.21/0.58 tff(156,plain,
% 0.21/0.58 ((~![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : (~((~((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb))) | (~((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))))) | (~((~((Xa!2 = Xb!1) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(Xa!2, Xb!1, Xp!0) | s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((~s_col(Xa!2, Xb!1, Xp!0)) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_t(Xp!0, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(Xa!2, Xb!1, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1))))))),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(157,plain,
% 0.21/0.58 ((~![Xp: $i, Xq: $i, Xa: $i, Xb: $i, Xt: $i] : (~((~((Xp = Xq) | (~s_t(Xa, Xt, Xb)) | s_col(Xp, Xq, Xa) | s_col(Xp, Xq, Xb) | (~s_col(Xp, Xq, Xt)) | opposite(Xa, Xp, Xq, Xb))) | (~((~s_col(Xp, Xq, Xa)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~s_col(Xp, Xq, Xb)) | (~opposite(Xa, Xp, Xq, Xb)))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_t(Xa, il(Xa, Xb, Xp, Xq), Xb))) | (~((~opposite(Xa, Xp, Xq, Xb)) | s_col(Xp, Xq, il(Xa, Xb, Xp, Xq))))))) | (~((~((~s_col(Xa!2, Xb!1, Xp!0)) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_t(Xp!0, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(Xa!2, Xb!1, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1)))) | (~((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.21/0.58 tff(158,plain,
% 0.21/0.58 (~((~((~s_col(Xa!2, Xb!1, Xp!0)) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_t(Xp!0, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(Xa!2, Xb!1, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1)))) | (~((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[157, 151])).
% 0.21/0.58 tff(159,plain,
% 0.21/0.58 (((~((~s_col(Xa!2, Xb!1, Xp!0)) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_t(Xp!0, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | s_col(Xa!2, Xb!1, il(Xp!0, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xa!2, Xb!1)))) | (~((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | ((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))),
% 0.21/0.58 inference(tautology,[status(thm)],[])).
% 0.21/0.58 tff(160,plain,
% 0.21/0.58 ((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.21/0.58 tff(161,plain,
% 0.21/0.58 (opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) <=> opposite(Xp!0, Xa!2, Xb!1, reflect(Xa!2, Xb!1, Xp!0))),
% 0.21/0.58 inference(monotonicity,[status(thm)],[43])).
% 0.21/0.58 tff(162,plain,
% 0.21/0.58 (opposite(Xp!0, Xa!2, Xb!1, reflect(Xa!2, Xb!1, Xp!0)) <=> opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))),
% 0.21/0.58 inference(symmetry,[status(thm)],[161])).
% 0.21/0.58 tff(163,plain,
% 0.21/0.58 ((~opposite(Xp!0, Xa!2, Xb!1, reflect(Xa!2, Xb!1, Xp!0))) <=> (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))),
% 0.21/0.58 inference(monotonicity,[status(thm)],[162])).
% 0.21/0.58 tff(164,plain,
% 0.21/0.58 (~opposite(Xp!0, Xa!2, Xb!1, reflect(Xa!2, Xb!1, Xp!0))),
% 0.21/0.58 inference(or_elim,[status(thm)],[89])).
% 0.21/0.58 tff(165,plain,
% 0.21/0.58 (~opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.21/0.58 tff(166,plain,
% 0.21/0.58 (^[Xa: $i, Xb: $i, Xp: $i] : refl((~((~((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp))))) | (~((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp)))))) <=> (~((~((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp))))) | (~((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp)))))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(167,plain,
% 0.21/0.58 (![Xa: $i, Xb: $i, Xp: $i] : (~((~((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp))))) | (~((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp)))))) <=> ![Xa: $i, Xb: $i, Xp: $i] : (~((~((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp))))) | (~((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp))))))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[166])).
% 0.21/0.58 tff(168,plain,
% 0.21/0.58 (^[Xa: $i, Xb: $i, Xp: $i] : trans(monotonicity(rewrite(((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp))) <=> ((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp)))), ((((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp)))) & ((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp)))) <=> (((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp)))) & ((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp)))))), rewrite((((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp)))) & ((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp)))) <=> (~((~((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp))))) | (~((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp))))))), ((((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp)))) & ((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp)))) <=> (~((~((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp))))) | (~((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp))))))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(169,plain,
% 0.21/0.58 (![Xa: $i, Xb: $i, Xp: $i] : (((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp)))) & ((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp)))) <=> ![Xa: $i, Xb: $i, Xp: $i] : (~((~((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp))))) | (~((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp))))))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[168])).
% 0.21/0.58 tff(170,plain,
% 0.21/0.58 (![Xa: $i, Xb: $i, Xp: $i] : (((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp)))) & ((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp)))) <=> ![Xa: $i, Xb: $i, Xp: $i] : (((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp)))) & ((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp))))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(171,plain,
% 0.21/0.58 (^[Xa: $i, Xb: $i, Xp: $i] : rewrite((((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp)))) & (((Xa = Xb) | (Xp = reflect(Xa, Xb, Xp))) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)))) <=> (((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp)))) & ((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp)))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(172,plain,
% 0.21/0.58 (![Xa: $i, Xb: $i, Xp: $i] : (((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp)))) & (((Xa = Xb) | (Xp = reflect(Xa, Xb, Xp))) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)))) <=> ![Xa: $i, Xb: $i, Xp: $i] : (((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp)))) & ((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp))))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[171])).
% 0.21/0.58 tff(173,axiom,(![Xa: $i, Xb: $i, Xp: $i] : (((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp)))) & (((Xa = Xb) | (Xp = reflect(Xa, Xb, Xp))) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz10_2a')).
% 0.21/0.58 tff(174,plain,
% 0.21/0.58 (![Xa: $i, Xb: $i, Xp: $i] : (((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp)))) & ((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp))))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.21/0.58 tff(175,plain,
% 0.21/0.58 (![Xa: $i, Xb: $i, Xp: $i] : (((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp)))) & ((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp))))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.21/0.58 tff(176,plain,(
% 0.21/0.58 ![Xa: $i, Xb: $i, Xp: $i] : (((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp)))) & ((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp))))),
% 0.21/0.58 inference(skolemize,[status(sab)],[175])).
% 0.21/0.58 tff(177,plain,
% 0.21/0.58 (![Xa: $i, Xb: $i, Xp: $i] : (~((~((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp))))) | (~((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp))))))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[176, 169])).
% 0.21/0.58 tff(178,plain,
% 0.21/0.58 (![Xa: $i, Xb: $i, Xp: $i] : (~((~((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp))))) | (~((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp))))))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[177, 167])).
% 0.21/0.58 tff(179,plain,
% 0.21/0.58 ((~![Xa: $i, Xb: $i, Xp: $i] : (~((~((Xa = Xb) | s_col(Xa, Xb, midpoint(Xp, reflect(Xa, Xb, Xp))))) | (~((Xa = Xb) | perp(Xa, Xb, Xp, reflect(Xa, Xb, Xp)) | (Xp = reflect(Xa, Xb, Xp))))))) | (~((~((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))))) | (~((Xa!2 = Xb!1) | perp(Xa!2, Xb!1, Xp!0, reflect(Xa!2, Xb!1, Xp!0)) | (Xp!0 = reflect(Xa!2, Xb!1, Xp!0))))))),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(180,plain,
% 0.21/0.58 (~((~((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))))) | (~((Xa!2 = Xb!1) | perp(Xa!2, Xb!1, Xp!0, reflect(Xa!2, Xb!1, Xp!0)) | (Xp!0 = reflect(Xa!2, Xb!1, Xp!0)))))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.21/0.58 tff(181,plain,
% 0.21/0.58 (((~((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))))) | (~((Xa!2 = Xb!1) | perp(Xa!2, Xb!1, Xp!0, reflect(Xa!2, Xb!1, Xp!0)) | (Xp!0 = reflect(Xa!2, Xb!1, Xp!0))))) | ((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))))),
% 0.21/0.58 inference(tautology,[status(thm)],[])).
% 0.21/0.58 tff(182,plain,
% 0.21/0.58 ((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.21/0.58 tff(183,plain,
% 0.21/0.58 ((~((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))))) | (Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))),
% 0.21/0.58 inference(tautology,[status(thm)],[])).
% 0.21/0.58 tff(184,plain,
% 0.21/0.58 ((~((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))))) | s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[183, 91])).
% 0.21/0.58 tff(185,plain,
% 0.21/0.58 (s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[184, 182])).
% 0.21/0.58 tff(186,plain,
% 0.21/0.58 ((~((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))),
% 0.21/0.58 inference(tautology,[status(thm)],[])).
% 0.21/0.58 tff(187,plain,
% 0.21/0.58 ((~((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | opposite(Xp!0, Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[186, 91, 90, 185])).
% 0.21/0.58 tff(188,plain,
% 0.21/0.58 (s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[187, 165, 66, 160])).
% 0.21/0.58 tff(189,plain,
% 0.21/0.58 (^[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))))),
% 0.21/0.59 inference(bind,[status(th)],[])).
% 0.21/0.59 tff(190,plain,
% 0.21/0.59 (![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)))),
% 0.21/0.59 inference(quant_intro,[status(thm)],[189])).
% 0.21/0.59 tff(191,plain,
% 0.21/0.59 (![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)))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(192,plain,
% 0.21/0.59 (^[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)))))),
% 0.21/0.59 inference(bind,[status(th)],[])).
% 0.21/0.59 tff(193,plain,
% 0.21/0.59 (![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)))),
% 0.21/0.59 inference(quant_intro,[status(thm)],[192])).
% 0.21/0.59 tff(194,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')).
% 0.21/0.59 tff(195,plain,
% 0.21/0.59 (![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)))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.21/0.59 tff(196,plain,
% 0.21/0.59 (![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)))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[195, 191])).
% 0.21/0.59 tff(197,plain,(
% 0.21/0.59 ![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)))),
% 0.21/0.59 inference(skolemize,[status(sab)],[196])).
% 0.21/0.59 tff(198,plain,
% 0.21/0.59 (![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)))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[197, 190])).
% 0.21/0.59 tff(199,plain,
% 0.21/0.59 (((~![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!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | (midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!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)))) | (Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | (midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(200,plain,
% 0.21/0.59 (((midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (Xa!2 = Xb!1) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) <=> ((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | (midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(201,plain,
% 0.21/0.59 (((~![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)))) | ((midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (Xa!2 = Xb!1) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!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)))) | ((Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | (midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))))),
% 0.21/0.59 inference(monotonicity,[status(thm)],[200])).
% 0.21/0.59 tff(202,plain,
% 0.21/0.59 (((~![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)))) | ((midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (Xa!2 = Xb!1) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!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)))) | (Xa!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | (midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))),
% 0.21/0.59 inference(transitivity,[status(thm)],[201, 199])).
% 0.21/0.59 tff(203,plain,
% 0.21/0.59 ((~![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)))) | ((midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (Xa!2 = Xb!1) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))),
% 0.21/0.59 inference(quant_inst,[status(thm)],[])).
% 0.21/0.59 tff(204,plain,
% 0.21/0.59 ((~![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!2 = Xb!1) | s_col(Xa!2, Xb!1, Xp!0) | (~s_col(Xa!2, Xb!1, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | (midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_col(Xa!2, Xb!1, s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~s_col(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.21/0.59 tff(205,plain,
% 0.21/0.59 (midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[204, 198, 91, 90, 185, 188, 68])).
% 0.21/0.59 tff(206,plain,
% 0.21/0.59 ((~((~(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))),
% 0.21/0.59 inference(tautology,[status(thm)],[])).
% 0.21/0.59 tff(207,plain,
% 0.21/0.59 (~((~(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[206, 205, 138])).
% 0.21/0.59 tff(208,plain,
% 0.21/0.59 (((~((~(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~(Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~(s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0) | s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (xb = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | ((~(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))),
% 0.21/0.59 inference(tautology,[status(thm)],[])).
% 0.21/0.59 tff(209,plain,
% 0.21/0.59 ((~((~(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~(Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~(s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0) | s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (xb = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[208, 207])).
% 0.21/0.59 tff(210,plain,
% 0.21/0.59 (^[Xa: $i, Xp: $i, Xb: $i] : refl((~((~((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp)))) | (~((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) | (~(s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))) | (~((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))) | (~((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb))))) <=> (~((~((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp)))) | (~((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) | (~(s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))) | (~((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))) | (~((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb))))))),
% 0.21/0.59 inference(bind,[status(th)],[])).
% 0.21/0.59 tff(211,plain,
% 0.21/0.59 (![Xa: $i, Xp: $i, Xb: $i] : (~((~((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp)))) | (~((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) | (~(s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))) | (~((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))) | (~((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb))))) <=> ![Xa: $i, Xp: $i, Xb: $i] : (~((~((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp)))) | (~((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) | (~(s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))) | (~((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))) | (~((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))))),
% 0.21/0.59 inference(quant_intro,[status(thm)],[210])).
% 0.21/0.59 tff(212,plain,
% 0.21/0.59 (^[Xa: $i, Xp: $i, Xb: $i] : trans(monotonicity(rewrite(((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) <=> ((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp)))), rewrite(((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) <=> ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))), rewrite((s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb))) <=> (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))), rewrite(((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp)) <=> ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))), rewrite(((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)) <=> ((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb))), ((((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb))) & ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp)) & ((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb))) <=> (((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb))) & ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp)) & ((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb))))), rewrite((((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb))) & ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp)) & ((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb))) <=> (~((~((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp)))) | (~((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) | (~(s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))) | (~((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))) | (~((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))))), ((((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb))) & ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp)) & ((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb))) <=> (~((~((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp)))) | (~((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) | (~(s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))) | (~((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))) | (~((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))))))),
% 0.21/0.59 inference(bind,[status(th)],[])).
% 0.21/0.59 tff(213,plain,
% 0.21/0.59 (![Xa: $i, Xp: $i, Xb: $i] : (((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb))) & ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp)) & ((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb))) <=> ![Xa: $i, Xp: $i, Xb: $i] : (~((~((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp)))) | (~((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) | (~(s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))) | (~((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))) | (~((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))))),
% 0.21/0.59 inference(quant_intro,[status(thm)],[212])).
% 0.21/0.59 tff(214,plain,
% 0.21/0.59 (![Xa: $i, Xp: $i, Xb: $i] : (((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb))) & ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp)) & ((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb))) <=> ![Xa: $i, Xp: $i, Xb: $i] : (((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb))) & ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp)) & ((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(215,plain,
% 0.21/0.59 (^[Xa: $i, Xp: $i, Xb: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) <=> (((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))))), rewrite((((~sameside(Xa, Xp, Xb)) | s_t(Xp, Xa, Xb)) | s_t(Xp, Xb, Xa)) <=> (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))), (((((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) & (((~sameside(Xa, Xp, Xb)) | s_t(Xp, Xa, Xb)) | s_t(Xp, Xb, Xa))) <=> ((((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))))), rewrite(((((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))) <=> (((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb))))), (((((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) & (((~sameside(Xa, Xp, Xb)) | s_t(Xp, Xa, Xb)) | s_t(Xp, Xb, Xa))) <=> (((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))))), trans(monotonicity(rewrite((((~s_t(Xp, Xa, Xb)) | (Xa = Xp)) | (xb = Xp)) <=> ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | (xb = Xp))), (((((~s_t(Xp, Xa, Xb)) | (Xa = Xp)) | (xb = Xp)) | sameside(Xa, Xp, Xb)) <=> (((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | (xb = Xp)) | sameside(Xa, Xp, Xb)))), rewrite((((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | (xb = Xp)) | sameside(Xa, Xp, Xb)) <=> ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))), (((((~s_t(Xp, Xa, Xb)) | (Xa = Xp)) | (xb = Xp)) | sameside(Xa, Xp, Xb)) <=> ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp)))), ((((((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) & (((~sameside(Xa, Xp, Xb)) | s_t(Xp, Xa, Xb)) | s_t(Xp, Xb, Xa))) & ((((~s_t(Xp, Xa, Xb)) | (Xa = Xp)) | (xb = Xp)) | sameside(Xa, Xp, Xb))) <=> ((((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))) & ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))))), rewrite(((((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))) & ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))) <=> (((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb))) & ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp)))), ((((((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) & (((~sameside(Xa, Xp, Xb)) | s_t(Xp, Xa, Xb)) | s_t(Xp, Xb, Xa))) & ((((~s_t(Xp, Xa, Xb)) | (Xa = Xp)) | (xb = Xp)) | sameside(Xa, Xp, Xb))) <=> (((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb))) & ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))))), trans(monotonicity(rewrite((((~s_t(Xp, Xb, Xa)) | (Xa = Xp)) | (Xb = Xp)) <=> ((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp))), (((((~s_t(Xp, Xb, Xa)) | (Xa = Xp)) | (Xb = Xp)) | sameside(Xa, Xp, Xb)) <=> (((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp)) | sameside(Xa, Xp, Xb)))), rewrite((((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp)) | sameside(Xa, Xp, Xb)) <=> ((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb))), (((((~s_t(Xp, Xb, Xa)) | (Xa = Xp)) | (Xb = Xp)) | sameside(Xa, Xp, Xb)) <=> ((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))), (((((((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) & (((~sameside(Xa, Xp, Xb)) | s_t(Xp, Xa, Xb)) | s_t(Xp, Xb, Xa))) & ((((~s_t(Xp, Xa, Xb)) | (Xa = Xp)) | (xb = Xp)) | sameside(Xa, Xp, Xb))) & ((((~s_t(Xp, Xb, Xa)) | (Xa = Xp)) | (Xb = Xp)) | sameside(Xa, Xp, Xb))) <=> ((((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb))) & ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))) & ((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb))))), rewrite(((((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb))) & ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))) & ((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb))) <=> (((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb))) & ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp)) & ((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))), (((((((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) & (((~sameside(Xa, Xp, Xb)) | s_t(Xp, Xa, Xb)) | s_t(Xp, Xb, Xa))) & ((((~s_t(Xp, Xa, Xb)) | (Xa = Xp)) | (xb = Xp)) | sameside(Xa, Xp, Xb))) & ((((~s_t(Xp, Xb, Xa)) | (Xa = Xp)) | (Xb = Xp)) | sameside(Xa, Xp, Xb))) <=> (((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb))) & ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp)) & ((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))))),
% 0.21/0.60 inference(bind,[status(th)],[])).
% 0.21/0.60 tff(216,plain,
% 0.21/0.60 (![Xa: $i, Xp: $i, Xb: $i] : ((((((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) & (((~sameside(Xa, Xp, Xb)) | s_t(Xp, Xa, Xb)) | s_t(Xp, Xb, Xa))) & ((((~s_t(Xp, Xa, Xb)) | (Xa = Xp)) | (xb = Xp)) | sameside(Xa, Xp, Xb))) & ((((~s_t(Xp, Xb, Xa)) | (Xa = Xp)) | (Xb = Xp)) | sameside(Xa, Xp, Xb))) <=> ![Xa: $i, Xp: $i, Xb: $i] : (((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb))) & ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp)) & ((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))),
% 0.21/0.60 inference(quant_intro,[status(thm)],[215])).
% 0.21/0.60 tff(217,axiom,(![Xa: $i, Xp: $i, Xb: $i] : ((((((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) & (((~sameside(Xa, Xp, Xb)) | s_t(Xp, Xa, Xb)) | s_t(Xp, Xb, Xa))) & ((((~s_t(Xp, Xa, Xb)) | (Xa = Xp)) | (xb = Xp)) | sameside(Xa, Xp, Xb))) & ((((~s_t(Xp, Xb, Xa)) | (Xa = Xp)) | (Xb = Xp)) | sameside(Xa, Xp, Xb)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d_Defn6_1')).
% 0.21/0.60 tff(218,plain,
% 0.21/0.60 (![Xa: $i, Xp: $i, Xb: $i] : (((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb))) & ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp)) & ((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.21/0.60 tff(219,plain,
% 0.21/0.60 (![Xa: $i, Xp: $i, Xb: $i] : (((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb))) & ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp)) & ((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[218, 214])).
% 0.21/0.60 tff(220,plain,(
% 0.21/0.60 ![Xa: $i, Xp: $i, Xb: $i] : (((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp))) & ((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp))) & (s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb))) & ((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp)) & ((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))),
% 0.21/0.60 inference(skolemize,[status(sab)],[219])).
% 0.21/0.60 tff(221,plain,
% 0.21/0.60 (![Xa: $i, Xp: $i, Xb: $i] : (~((~((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp)))) | (~((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) | (~(s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))) | (~((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))) | (~((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))))),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[220, 213])).
% 0.21/0.60 tff(222,plain,
% 0.21/0.60 (![Xa: $i, Xp: $i, Xb: $i] : (~((~((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp)))) | (~((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) | (~(s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))) | (~((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))) | (~((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))))),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[221, 211])).
% 0.21/0.60 tff(223,plain,
% 0.21/0.60 (((~![Xa: $i, Xp: $i, Xb: $i] : (~((~((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp)))) | (~((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) | (~(s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))) | (~((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))) | (~((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))))) | (~((~((~(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~(Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~(s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0) | s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (xb = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))))) <=> ((~![Xa: $i, Xp: $i, Xb: $i] : (~((~((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp)))) | (~((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) | (~(s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))) | (~((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))) | (~((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))))) | (~((~((~(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~(Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~(s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0) | s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (xb = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))))))),
% 0.21/0.60 inference(rewrite,[status(thm)],[])).
% 0.21/0.60 tff(224,plain,
% 0.21/0.60 ((~((~((~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (~(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (~(Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~(s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (xb = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | (Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))))) <=> (~((~((~(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~(Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~(s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0) | s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (xb = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))))),
% 0.21/0.60 inference(rewrite,[status(thm)],[])).
% 0.21/0.60 tff(225,plain,
% 0.21/0.60 (((~![Xa: $i, Xp: $i, Xb: $i] : (~((~((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp)))) | (~((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) | (~(s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))) | (~((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))) | (~((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))))) | (~((~((~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (~(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (~(Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~(s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (xb = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | (Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))))) <=> ((~![Xa: $i, Xp: $i, Xb: $i] : (~((~((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp)))) | (~((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) | (~(s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))) | (~((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))) | (~((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))))) | (~((~((~(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~(Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~(s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0) | s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (xb = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))))))),
% 0.21/0.61 inference(monotonicity,[status(thm)],[224])).
% 0.21/0.61 tff(226,plain,
% 0.21/0.61 (((~![Xa: $i, Xp: $i, Xb: $i] : (~((~((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp)))) | (~((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) | (~(s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))) | (~((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))) | (~((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))))) | (~((~((~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (~(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (~(Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~(s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (xb = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | (Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))))) <=> ((~![Xa: $i, Xp: $i, Xb: $i] : (~((~((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp)))) | (~((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) | (~(s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))) | (~((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))) | (~((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))))) | (~((~((~(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~(Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~(s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0) | s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (xb = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0))))))),
% 0.21/0.61 inference(transitivity,[status(thm)],[225, 223])).
% 0.21/0.61 tff(227,plain,
% 0.21/0.61 ((~![Xa: $i, Xp: $i, Xb: $i] : (~((~((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp)))) | (~((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) | (~(s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))) | (~((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))) | (~((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))))) | (~((~((~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (~(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~((~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)) | (~(Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))))) | (~(s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (xb = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | (Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))))),
% 0.44/0.62 inference(quant_inst,[status(thm)],[])).
% 0.44/0.62 tff(228,plain,
% 0.44/0.62 ((~![Xa: $i, Xp: $i, Xb: $i] : (~((~((~sameside(Xa, Xp, Xb)) | (~(Xa = Xp)))) | (~((~sameside(Xa, Xp, Xb)) | (~(Xb = Xp)))) | (~(s_t(Xp, Xb, Xa) | s_t(Xp, Xa, Xb) | (~sameside(Xa, Xp, Xb)))) | (~((Xa = Xp) | (~s_t(Xp, Xa, Xb)) | sameside(Xa, Xp, Xb) | (xb = Xp))) | (~((Xa = Xp) | (~s_t(Xp, Xb, Xa)) | (Xb = Xp) | sameside(Xa, Xp, Xb)))))) | (~((~((~(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~(Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~(s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0) | s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0))) | (~sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))) | (~((~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0) | (xb = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)))) | (~((midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)) = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (Xp!0 = s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0)) | (~s_t(s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0, midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)))) | sameside(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), s(midpoint(Xp!0, reflect(Xa!2, Xb!1, Xp!0)), Xp!0), Xp!0)))))),
% 0.44/0.62 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.44/0.62 tff(229,plain,
% 0.44/0.62 ($false),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[228, 222, 209])).
% 0.44/0.62 % SZS output end Proof
% 0.44/0.63 % E exiting
%------------------------------------------------------------------------------