%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO504+1 : TPTP v9.0.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:06:26 AM UTC 2025
% Result : Theorem 0.21s 0.47s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GEO504+1 : TPTP v9.0.0. Released v7.0.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 14:56:05 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 % SZS output start Proof
% 0.21/0.47 tff(s_e_type, type, (
% 0.21/0.47 s_e: ( $i * $i * $i * $i ) > $o)).
% 0.21/0.47 tff(s_type, type, (
% 0.21/0.47 s: ( $i * $i ) > $i)).
% 0.21/0.47 tff(tptp_fun_Xa_2_type, type, (
% 0.21/0.47 tptp_fun_Xa_2: $i)).
% 0.21/0.47 tff(tptp_fun_Xb_1_type, type, (
% 0.21/0.47 tptp_fun_Xb_1: $i)).
% 0.21/0.47 tff(tptp_fun_Xc_0_type, type, (
% 0.21/0.47 tptp_fun_Xc_0: $i)).
% 0.21/0.47 tff(isomidpoint_type, type, (
% 0.21/0.47 isomidpoint: ( $i * $i * $i ) > $i)).
% 0.21/0.47 tff(s_m_type, type, (
% 0.21/0.47 s_m: ( $i * $i * $i ) > $o)).
% 0.21/0.47 tff(s_r_type, type, (
% 0.21/0.47 s_r: ( $i * $i * $i ) > $o)).
% 0.21/0.47 tff(1,plain,
% 0.21/0.47 (^[Xa: $i, Xb: $i, Xc: $i] : refl((~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc))))) <=> (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(2,plain,
% 0.21/0.47 (![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc))))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.47 tff(3,plain,
% 0.21/0.47 (^[Xa: $i, Xb: $i, Xc: $i] : rewrite((((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & ((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc))) <=> (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(4,plain,
% 0.21/0.47 (![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & ((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.47 tff(5,plain,
% 0.21/0.47 (![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & ((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & ((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(6,plain,
% 0.21/0.47 (^[Xa: $i, Xb: $i, Xc: $i] : rewrite((((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))) <=> (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & ((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(7,plain,
% 0.21/0.47 (![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & ((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.47 tff(8,axiom,(![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d_Defn8_1')).
% 0.21/0.47 tff(9,plain,
% 0.21/0.47 (![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & ((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.21/0.47 tff(10,plain,
% 0.21/0.47 (![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & ((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.21/0.47 tff(11,plain,(
% 0.21/0.47 ![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & ((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[10])).
% 0.21/0.47 tff(12,plain,
% 0.21/0.47 (![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.21/0.47 tff(13,plain,
% 0.21/0.47 (![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.21/0.47 tff(14,plain,
% 0.21/0.47 ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))))) | (~((~((~s_r(Xa!2, Xb!1, Xc!0)) | s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0)))) | (~((~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_r(Xa!2, Xb!1, Xc!0)))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(15,plain,
% 0.21/0.48 (~((~((~s_r(Xa!2, Xb!1, Xc!0)) | s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0)))) | (~((~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_r(Xa!2, Xb!1, Xc!0))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.21/0.48 tff(16,plain,
% 0.21/0.48 (((~((~s_r(Xa!2, Xb!1, Xc!0)) | s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0)))) | (~((~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_r(Xa!2, Xb!1, Xc!0)))) | ((~s_r(Xa!2, Xb!1, Xc!0)) | s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(17,plain,
% 0.21/0.48 ((~s_r(Xa!2, Xb!1, Xc!0)) | s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.21/0.48 tff(18,plain,
% 0.21/0.48 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_r(Xa, Xb, Xc)) | s_r(Xc, Xb, Xa))) <=> (~![Xa: $i, Xb: $i, Xc: $i] : ((~s_r(Xa, Xb, Xc)) | s_r(Xc, Xb, Xa)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(19,axiom,(~![Xa: $i, Xb: $i, Xc: $i] : ((~s_r(Xa, Xb, Xc)) | s_r(Xc, Xb, Xa))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz8_2')).
% 0.21/0.48 tff(20,plain,
% 0.21/0.48 (~![Xa: $i, Xb: $i, Xc: $i] : ((~s_r(Xa, Xb, Xc)) | s_r(Xc, Xb, Xa))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.21/0.48 tff(21,plain,
% 0.21/0.48 (~![Xa: $i, Xb: $i, Xc: $i] : ((~s_r(Xa, Xb, Xc)) | s_r(Xc, Xb, Xa))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[20, 18])).
% 0.21/0.48 tff(22,plain,
% 0.21/0.48 (~![Xa: $i, Xb: $i, Xc: $i] : ((~s_r(Xa, Xb, Xc)) | s_r(Xc, Xb, Xa))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.21/0.48 tff(23,plain,
% 0.21/0.48 (~![Xa: $i, Xb: $i, Xc: $i] : ((~s_r(Xa, Xb, Xc)) | s_r(Xc, Xb, Xa))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.21/0.48 tff(24,plain,(
% 0.21/0.48 ~((~s_r(Xa!2, Xb!1, Xc!0)) | s_r(Xc!0, Xb!1, Xa!2))),
% 0.21/0.48 inference(skolemize,[status(sab)],[23])).
% 0.21/0.48 tff(25,plain,
% 0.21/0.48 (s_r(Xa!2, Xb!1, Xc!0)),
% 0.21/0.48 inference(or_elim,[status(thm)],[24])).
% 0.21/0.48 tff(26,plain,
% 0.21/0.48 ((~((~s_r(Xa!2, Xb!1, Xc!0)) | s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0)))) | (~s_r(Xa!2, Xb!1, Xc!0)) | s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(27,plain,
% 0.21/0.48 ((~((~s_r(Xa!2, Xb!1, Xc!0)) | s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0)))) | s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.21/0.48 tff(28,plain,
% 0.21/0.48 (s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[27, 17])).
% 0.21/0.48 tff(29,plain,
% 0.21/0.48 (^[Xc: $i, Xa: $i, Xb: $i] : refl(((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb)) <=> ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(30,plain,
% 0.21/0.48 (![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb)) <=> ![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[29])).
% 0.21/0.48 tff(31,plain,
% 0.21/0.48 (![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb)) <=> ![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(32,axiom,(![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz7_25')).
% 0.21/0.48 tff(33,plain,
% 0.21/0.48 (![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.48 tff(34,plain,(
% 0.21/0.48 ![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))),
% 0.21/0.48 inference(skolemize,[status(sab)],[33])).
% 0.21/0.48 tff(35,plain,
% 0.21/0.48 (![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.21/0.48 tff(36,plain,
% 0.21/0.48 (((~![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))) | ((~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_m(Xc!0, isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), s(Xb!1, Xc!0)))) <=> ((~![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))) | (~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_m(Xc!0, isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), s(Xb!1, Xc!0)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(37,plain,
% 0.21/0.48 ((~![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))) | ((~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_m(Xc!0, isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), s(Xb!1, Xc!0)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(38,plain,
% 0.21/0.48 ((~![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))) | (~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_m(Xc!0, isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), s(Xb!1, Xc!0))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.48 tff(39,plain,
% 0.21/0.48 (s_m(Xc!0, isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), s(Xb!1, Xc!0))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[38, 35, 28])).
% 0.21/0.48 tff(40,plain,
% 0.21/0.48 (^[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))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(41,plain,
% 0.21/0.48 (![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)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[40])).
% 0.21/0.48 tff(42,plain,
% 0.21/0.48 (![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)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(43,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')).
% 0.21/0.48 tff(44,plain,
% 0.21/0.48 (![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.21/0.48 tff(45,plain,(
% 0.21/0.48 ![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[44])).
% 0.21/0.48 tff(46,plain,
% 0.21/0.48 (![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.21/0.48 tff(47,plain,
% 0.21/0.48 (((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(Xc!0, isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), s(Xb!1, Xc!0))) | (s(Xb!1, Xc!0) = s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)))) <=> ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(Xc!0, isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), s(Xb!1, Xc!0))) | (s(Xb!1, Xc!0) = s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(48,plain,
% 0.21/0.48 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(Xc!0, isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), s(Xb!1, Xc!0))) | (s(Xb!1, Xc!0) = s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(49,plain,
% 0.21/0.48 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(Xc!0, isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), s(Xb!1, Xc!0))) | (s(Xb!1, Xc!0) = s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.21/0.48 tff(50,plain,
% 0.21/0.48 (s(Xb!1, Xc!0) = s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[49, 46, 39])).
% 0.21/0.48 tff(51,plain,
% 0.21/0.48 (s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0) = s(Xb!1, Xc!0)),
% 0.21/0.48 inference(symmetry,[status(thm)],[50])).
% 0.21/0.48 tff(52,plain,
% 0.21/0.48 (s_m(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xb!1, Xc!0) <=> s_m(s(Xb!1, Xc!0), Xb!1, Xc!0)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[51])).
% 0.21/0.48 tff(53,plain,
% 0.21/0.48 (s_m(s(Xb!1, Xc!0), Xb!1, Xc!0) <=> s_m(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xb!1, Xc!0)),
% 0.21/0.48 inference(symmetry,[status(thm)],[52])).
% 0.21/0.48 tff(54,plain,
% 0.21/0.48 (^[Xp: $i, Xa: $i] : refl(s_m(Xp, Xa, s(Xa, Xp)) <=> s_m(Xp, Xa, s(Xa, Xp)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(55,plain,
% 0.21/0.48 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp)) <=> ![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[54])).
% 0.21/0.48 tff(56,plain,
% 0.21/0.48 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp)) <=> ![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(57,axiom,(![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz7_4a')).
% 0.21/0.48 tff(58,plain,
% 0.21/0.48 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.48 tff(59,plain,(
% 0.21/0.48 ![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.21/0.48 inference(skolemize,[status(sab)],[58])).
% 0.21/0.48 tff(60,plain,
% 0.21/0.48 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.21/0.48 tff(61,plain,
% 0.21/0.48 ((~![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))) | s_m(Xc!0, Xb!1, s(Xb!1, Xc!0))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(62,plain,
% 0.21/0.48 (s_m(Xc!0, Xb!1, s(Xb!1, Xc!0))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.21/0.48 tff(63,plain,
% 0.21/0.48 (^[Xa: $i, Xm: $i, Xb: $i] : refl(((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa)) <=> ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(64,plain,
% 0.21/0.48 (![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa)) <=> ![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.48 tff(65,plain,
% 0.21/0.48 (![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa)) <=> ![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(66,axiom,(![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz7_2')).
% 0.21/0.48 tff(67,plain,
% 0.21/0.48 (![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.21/0.48 tff(68,plain,(
% 0.21/0.48 ![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.21/0.48 inference(skolemize,[status(sab)],[67])).
% 0.21/0.48 tff(69,plain,
% 0.21/0.48 (![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.21/0.48 tff(70,plain,
% 0.21/0.48 (((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | ((~s_m(Xc!0, Xb!1, s(Xb!1, Xc!0))) | s_m(s(Xb!1, Xc!0), Xb!1, Xc!0))) <=> ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | (~s_m(Xc!0, Xb!1, s(Xb!1, Xc!0))) | s_m(s(Xb!1, Xc!0), Xb!1, Xc!0))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(71,plain,
% 0.21/0.48 ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | ((~s_m(Xc!0, Xb!1, s(Xb!1, Xc!0))) | s_m(s(Xb!1, Xc!0), Xb!1, Xc!0))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(72,plain,
% 0.21/0.48 ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | (~s_m(Xc!0, Xb!1, s(Xb!1, Xc!0))) | s_m(s(Xb!1, Xc!0), Xb!1, Xc!0)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.48 tff(73,plain,
% 0.21/0.48 (s_m(s(Xb!1, Xc!0), Xb!1, Xc!0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[72, 69, 62])).
% 0.21/0.48 tff(74,plain,
% 0.21/0.48 (s_m(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xb!1, Xc!0)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[73, 53])).
% 0.21/0.48 tff(75,plain,
% 0.21/0.48 (((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xb!1, Xc!0)) | (Xc!0 = s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0))))) <=> ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xb!1, Xc!0)) | (Xc!0 = s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(76,plain,
% 0.21/0.48 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xb!1, Xc!0)) | (Xc!0 = s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(77,plain,
% 0.21/0.48 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xb!1, Xc!0)) | (Xc!0 = s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.21/0.48 tff(78,plain,
% 0.21/0.48 ((~s_m(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xb!1, Xc!0)) | (Xc!0 = s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[77, 46])).
% 0.21/0.48 tff(79,plain,
% 0.21/0.48 (Xc!0 = s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[78, 74])).
% 0.21/0.48 tff(80,plain,
% 0.21/0.48 (s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)) = Xc!0),
% 0.21/0.48 inference(symmetry,[status(thm)],[79])).
% 0.21/0.48 tff(81,plain,
% 0.21/0.48 (s_e(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xa!2, s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)), s(Xb!1, Xa!2)) <=> s_e(s(Xb!1, Xc!0), Xa!2, Xc!0, s(Xb!1, Xa!2))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[51, 80])).
% 0.21/0.48 tff(82,plain,
% 0.21/0.48 (s_e(s(Xb!1, Xc!0), Xa!2, Xc!0, s(Xb!1, Xa!2)) <=> s_e(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xa!2, s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)), s(Xb!1, Xa!2))),
% 0.21/0.48 inference(symmetry,[status(thm)],[81])).
% 0.21/0.48 tff(83,plain,
% 0.21/0.48 ((~s_e(s(Xb!1, Xc!0), Xa!2, Xc!0, s(Xb!1, Xa!2))) <=> (~s_e(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xa!2, s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)), s(Xb!1, Xa!2)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[82])).
% 0.21/0.48 tff(84,plain,
% 0.21/0.48 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : refl(((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc)) <=> ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(85,plain,
% 0.21/0.48 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[84])).
% 0.21/0.48 tff(86,plain,
% 0.21/0.48 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(87,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz2_14')).
% 0.21/0.48 tff(88,plain,
% 0.21/0.48 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.48 tff(89,plain,(
% 0.21/0.48 ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))),
% 0.21/0.48 inference(skolemize,[status(sab)],[88])).
% 0.21/0.48 tff(90,plain,
% 0.21/0.48 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.21/0.48 tff(91,plain,
% 0.21/0.48 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | ((~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_e(Xc!0, Xa!2, s(Xb!1, Xc!0), Xa!2))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | (~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_e(Xc!0, Xa!2, s(Xb!1, Xc!0), Xa!2))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(92,plain,
% 0.21/0.48 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | ((~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_e(Xc!0, Xa!2, s(Xb!1, Xc!0), Xa!2))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(93,plain,
% 0.21/0.48 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | (~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_e(Xc!0, Xa!2, s(Xb!1, Xc!0), Xa!2)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.48 tff(94,plain,
% 0.21/0.48 (s_e(Xc!0, Xa!2, s(Xb!1, Xc!0), Xa!2)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[93, 90, 28])).
% 0.21/0.48 tff(95,plain,
% 0.21/0.48 ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))))) | (~((~((~s_r(Xc!0, Xb!1, Xa!2)) | s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2)))) | (~((~s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2))) | s_r(Xc!0, Xb!1, Xa!2)))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(96,plain,
% 0.21/0.48 (~((~((~s_r(Xc!0, Xb!1, Xa!2)) | s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2)))) | (~((~s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2))) | s_r(Xc!0, Xb!1, Xa!2))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[95, 13])).
% 0.21/0.48 tff(97,plain,
% 0.21/0.48 (((~((~s_r(Xc!0, Xb!1, Xa!2)) | s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2)))) | (~((~s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2))) | s_r(Xc!0, Xb!1, Xa!2)))) | ((~s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2))) | s_r(Xc!0, Xb!1, Xa!2))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(98,plain,
% 0.21/0.48 ((~s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2))) | s_r(Xc!0, Xb!1, Xa!2)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.21/0.48 tff(99,plain,
% 0.21/0.48 (~s_r(Xc!0, Xb!1, Xa!2)),
% 0.21/0.48 inference(or_elim,[status(thm)],[24])).
% 0.21/0.48 tff(100,plain,
% 0.21/0.48 ((~((~s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2))) | s_r(Xc!0, Xb!1, Xa!2))) | (~s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2))) | s_r(Xc!0, Xb!1, Xa!2)),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(101,plain,
% 0.21/0.48 ((~((~s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2))) | s_r(Xc!0, Xb!1, Xa!2))) | (~s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.21/0.49 tff(102,plain,
% 0.21/0.49 (~s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[101, 98])).
% 0.21/0.49 tff(103,plain,
% 0.21/0.49 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : refl((s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))) <=> (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(104,plain,
% 0.21/0.49 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[103])).
% 0.21/0.49 tff(105,plain,
% 0.21/0.49 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(106,plain,
% 0.21/0.49 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : trans(monotonicity(rewrite(((~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))) <=> ((~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))), ((((~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))) | s_e(Xa, Xb, Xe, Xf)) <=> (((~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))) | s_e(Xa, Xb, Xe, Xf)))), rewrite((((~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))) | s_e(Xa, Xb, Xe, Xf)) <=> (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))), ((((~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))) | s_e(Xa, Xb, Xe, Xf)) <=> (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(107,plain,
% 0.21/0.49 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (((~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))) | s_e(Xa, Xb, Xe, Xf)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[106])).
% 0.21/0.49 tff(108,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (((~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))) | s_e(Xa, Xb, Xe, Xf))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz2_3')).
% 0.21/0.49 tff(109,plain,
% 0.21/0.49 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.21/0.49 tff(110,plain,
% 0.21/0.49 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.21/0.49 tff(111,plain,(
% 0.21/0.49 ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[110])).
% 0.21/0.49 tff(112,plain,
% 0.21/0.49 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.21/0.49 tff(113,plain,
% 0.21/0.49 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))) | (s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2)) | (~s_e(Xc!0, Xa!2, s(Xb!1, Xc!0), Xa!2)) | (~s_e(s(Xb!1, Xc!0), Xa!2, Xc!0, s(Xb!1, Xa!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))) | s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2)) | (~s_e(Xc!0, Xa!2, s(Xb!1, Xc!0), Xa!2)) | (~s_e(s(Xb!1, Xc!0), Xa!2, Xc!0, s(Xb!1, Xa!2))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(114,plain,
% 0.21/0.49 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))) | (s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2)) | (~s_e(Xc!0, Xa!2, s(Xb!1, Xc!0), Xa!2)) | (~s_e(s(Xb!1, Xc!0), Xa!2, Xc!0, s(Xb!1, Xa!2))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(115,plain,
% 0.21/0.49 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))) | s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2)) | (~s_e(Xc!0, Xa!2, s(Xb!1, Xc!0), Xa!2)) | (~s_e(s(Xb!1, Xc!0), Xa!2, Xc!0, s(Xb!1, Xa!2)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.21/0.49 tff(116,plain,
% 0.21/0.49 (~s_e(s(Xb!1, Xc!0), Xa!2, Xc!0, s(Xb!1, Xa!2))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[115, 112, 102, 94])).
% 0.21/0.49 tff(117,plain,
% 0.21/0.49 (~s_e(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xa!2, s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)), s(Xb!1, Xa!2))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[116, 83])).
% 0.21/0.49 tff(118,plain,
% 0.21/0.49 (^[Xp: $i, Xq: $i, Xa: $i] : refl(s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq)) <=> s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(119,plain,
% 0.21/0.49 (![Xp: $i, Xq: $i, Xa: $i] : s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq)) <=> ![Xp: $i, Xq: $i, Xa: $i] : s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[118])).
% 0.21/0.49 tff(120,plain,
% 0.21/0.49 (![Xp: $i, Xq: $i, Xa: $i] : s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq)) <=> ![Xp: $i, Xq: $i, Xa: $i] : s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(121,axiom,(![Xp: $i, Xq: $i, Xa: $i] : s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz7_13')).
% 0.21/0.49 tff(122,plain,
% 0.21/0.49 (![Xp: $i, Xq: $i, Xa: $i] : s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.21/0.49 tff(123,plain,(
% 0.21/0.49 ![Xp: $i, Xq: $i, Xa: $i] : s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq))),
% 0.21/0.49 inference(skolemize,[status(sab)],[122])).
% 0.21/0.49 tff(124,plain,
% 0.21/0.49 (![Xp: $i, Xq: $i, Xa: $i] : s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.21/0.49 tff(125,plain,
% 0.21/0.49 ((~![Xp: $i, Xq: $i, Xa: $i] : s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq))) | s_e(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xa!2, s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)), s(Xb!1, Xa!2))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(126,plain,
% 0.21/0.49 (s_e(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xa!2, s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)), s(Xb!1, Xa!2))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.21/0.49 tff(127,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[126, 117])).
% 0.21/0.49 % SZS output end Proof
% 0.21/0.50 % E exiting
%------------------------------------------------------------------------------