%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO497+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 05:06:25 AM UTC 2025
% Result : Theorem 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO497+1 : TPTP v9.0.0. Released v7.0.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.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 14:57:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(s_e_type, type, (
% 0.20/0.43 s_e: ( $i * $i * $i * $i ) > $o)).
% 0.20/0.43 tff(ext_type, type, (
% 0.20/0.43 ext: ( $i * $i * $i * $i ) > $i)).
% 0.20/0.43 tff(tptp_fun_Xc_0_type, type, (
% 0.20/0.43 tptp_fun_Xc_0: $i)).
% 0.20/0.43 tff(tptp_fun_Xb_1_type, type, (
% 0.20/0.43 tptp_fun_Xb_1: $i)).
% 0.20/0.43 tff(tptp_fun_Xa_2_type, type, (
% 0.20/0.43 tptp_fun_Xa_2: $i)).
% 0.20/0.43 tff(gamma_type, type, (
% 0.20/0.43 gamma: $i)).
% 0.20/0.43 tff(alpha_type, type, (
% 0.20/0.43 alpha: $i)).
% 0.20/0.43 tff(tptp_fun_Xr_3_type, type, (
% 0.20/0.43 tptp_fun_Xr_3: $i)).
% 0.20/0.43 tff(insert_type, type, (
% 0.20/0.43 insert: ( $i * $i * $i * $i ) > $i)).
% 0.20/0.43 tff(s_t_type, type, (
% 0.20/0.43 s_t: ( $i * $i * $i ) > $o)).
% 0.20/0.43 tff(sameside_type, type, (
% 0.20/0.43 sameside: ( $i * $i * $i ) > $o)).
% 0.20/0.43 tff(1,plain,
% 0.20/0.43 (^[Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : refl((insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb)) <=> (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(2,plain,
% 0.20/0.43 (![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb)) <=> ![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.43 tff(3,plain,
% 0.20/0.43 (![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb)) <=> ![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(4,axiom,(![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d_insert')).
% 0.20/0.43 tff(5,plain,
% 0.20/0.43 (![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.43 tff(6,plain,(
% 0.20/0.43 ![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb))),
% 0.20/0.43 inference(skolemize,[status(sab)],[5])).
% 0.20/0.43 tff(7,plain,
% 0.20/0.43 (![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.43 tff(8,plain,
% 0.20/0.43 ((~![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb))) | (insert(Xb!1, Xc!0, Xa!2, Xr!3) = ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(9,plain,
% 0.20/0.43 (insert(Xb!1, Xc!0, Xa!2, Xr!3) = ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.43 tff(10,plain,
% 0.20/0.43 (ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0) = insert(Xb!1, Xc!0, Xa!2, Xr!3)),
% 0.20/0.43 inference(symmetry,[status(thm)],[9])).
% 0.20/0.43 tff(11,plain,
% 0.20/0.43 (^[X: $i, Y: $i, W: $i, V: $i] : refl((~((~s_t(X, Y, ext(X, Y, W, V))) | (~s_e(Y, ext(X, Y, W, V), W, V)))) <=> (~((~s_t(X, Y, ext(X, Y, W, V))) | (~s_e(Y, ext(X, Y, W, V), W, V)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(12,plain,
% 0.20/0.43 (![X: $i, Y: $i, W: $i, V: $i] : (~((~s_t(X, Y, ext(X, Y, W, V))) | (~s_e(Y, ext(X, Y, W, V), W, V)))) <=> ![X: $i, Y: $i, W: $i, V: $i] : (~((~s_t(X, Y, ext(X, Y, W, V))) | (~s_e(Y, ext(X, Y, W, V), W, V))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.43 tff(13,plain,
% 0.20/0.43 (^[X: $i, Y: $i, W: $i, V: $i] : rewrite((s_t(X, Y, ext(X, Y, W, V)) & s_e(Y, ext(X, Y, W, V), W, V)) <=> (~((~s_t(X, Y, ext(X, Y, W, V))) | (~s_e(Y, ext(X, Y, W, V), W, V)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(14,plain,
% 0.20/0.43 (![X: $i, Y: $i, W: $i, V: $i] : (s_t(X, Y, ext(X, Y, W, V)) & s_e(Y, ext(X, Y, W, V), W, V)) <=> ![X: $i, Y: $i, W: $i, V: $i] : (~((~s_t(X, Y, ext(X, Y, W, V))) | (~s_e(Y, ext(X, Y, W, V), W, V))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.43 tff(15,plain,
% 0.20/0.43 (![X: $i, Y: $i, W: $i, V: $i] : (s_t(X, Y, ext(X, Y, W, V)) & s_e(Y, ext(X, Y, W, V), W, V)) <=> ![X: $i, Y: $i, W: $i, V: $i] : (s_t(X, Y, ext(X, Y, W, V)) & s_e(Y, ext(X, Y, W, V), W, V))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(16,axiom,(![X: $i, Y: $i, W: $i, V: $i] : (s_t(X, Y, ext(X, Y, W, V)) & s_e(Y, ext(X, Y, W, V), W, V))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO011+0.ax','aA4')).
% 0.20/0.43 tff(17,plain,
% 0.20/0.43 (![X: $i, Y: $i, W: $i, V: $i] : (s_t(X, Y, ext(X, Y, W, V)) & s_e(Y, ext(X, Y, W, V), W, V))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.43 tff(18,plain,(
% 0.20/0.43 ![X: $i, Y: $i, W: $i, V: $i] : (s_t(X, Y, ext(X, Y, W, V)) & s_e(Y, ext(X, Y, W, V), W, V))),
% 0.20/0.43 inference(skolemize,[status(sab)],[17])).
% 0.20/0.43 tff(19,plain,
% 0.20/0.43 (![X: $i, Y: $i, W: $i, V: $i] : (~((~s_t(X, Y, ext(X, Y, W, V))) | (~s_e(Y, ext(X, Y, W, V), W, V))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 (![X: $i, Y: $i, W: $i, V: $i] : (~((~s_t(X, Y, ext(X, Y, W, V))) | (~s_e(Y, ext(X, Y, W, V), W, V))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 ((~![X: $i, Y: $i, W: $i, V: $i] : (~((~s_t(X, Y, ext(X, Y, W, V))) | (~s_e(Y, ext(X, Y, W, V), W, V))))) | (~((~s_t(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0))) | (~s_e(Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xb!1, Xc!0))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 (~((~s_t(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0))) | (~s_e(Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xb!1, Xc!0)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.20/0.43 tff(23,plain,
% 0.20/0.43 (((~s_t(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0))) | (~s_e(Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xb!1, Xc!0))) | s_t(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (s_t(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 (^[Xa: $i, Xb: $i, Xc: $i] : refl(((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa)) <=> ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(26,plain,
% 0.20/0.44 (![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa)) <=> ![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.44 tff(27,plain,
% 0.20/0.44 (![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa)) <=> ![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(28,axiom,(![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz3_2')).
% 0.20/0.44 tff(29,plain,
% 0.20/0.44 (![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.44 tff(30,plain,(
% 0.20/0.44 ![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))),
% 0.20/0.44 inference(skolemize,[status(sab)],[29])).
% 0.20/0.44 tff(31,plain,
% 0.20/0.44 (![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.44 tff(32,plain,
% 0.20/0.44 (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0))) | s_t(ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xa!2, ext(Xr!3, Xa!2, alpha, gamma)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0))) | s_t(ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xa!2, ext(Xr!3, Xa!2, alpha, gamma)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(33,plain,
% 0.20/0.44 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0))) | s_t(ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xa!2, ext(Xr!3, Xa!2, alpha, gamma)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(34,plain,
% 0.20/0.44 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0))) | s_t(ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xa!2, ext(Xr!3, Xa!2, alpha, gamma))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.44 tff(35,plain,
% 0.20/0.44 (s_t(ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xa!2, ext(Xr!3, Xa!2, alpha, gamma))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[34, 31, 24])).
% 0.20/0.44 tff(36,plain,
% 0.20/0.44 ((ext(Xr!3, Xa!2, alpha, gamma) = Xa!2) <=> (Xa!2 = ext(Xr!3, Xa!2, alpha, gamma))),
% 0.20/0.44 inference(commutativity,[status(thm)],[])).
% 0.20/0.44 tff(37,plain,
% 0.20/0.44 ((Xa!2 = ext(Xr!3, Xa!2, alpha, gamma)) <=> (ext(Xr!3, Xa!2, alpha, gamma) = Xa!2)),
% 0.20/0.44 inference(symmetry,[status(thm)],[36])).
% 0.20/0.44 tff(38,plain,
% 0.20/0.44 ((~(Xa!2 = ext(Xr!3, Xa!2, alpha, gamma))) <=> (~(ext(Xr!3, Xa!2, alpha, gamma) = Xa!2))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.44 tff(39,plain,
% 0.20/0.44 (^[Xb: $i, Xa: $i] : refl((~(Xb = ext(Xa, Xb, alpha, gamma))) <=> (~(Xb = ext(Xa, Xb, alpha, gamma))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(40,plain,
% 0.20/0.44 (![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma))) <=> ![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 (![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma))) <=> ![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(42,axiom,(![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz3_14b')).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 (![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.44 tff(44,plain,(
% 0.20/0.44 ![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[43])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 (![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 ((~![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma)))) | (~(Xa!2 = ext(Xr!3, Xa!2, alpha, gamma)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 (~(Xa!2 = ext(Xr!3, Xa!2, alpha, gamma))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 (~(ext(Xr!3, Xa!2, alpha, gamma) = Xa!2)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[47, 38])).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 (sameside(Xr!3, Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0)) <=> sameside(Xr!3, Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[10])).
% 0.20/0.44 tff(50,plain,
% 0.20/0.44 (sameside(Xr!3, Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3)) <=> sameside(Xr!3, Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0))),
% 0.20/0.44 inference(symmetry,[status(thm)],[49])).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 ((~sameside(Xr!3, Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3))) <=> (~sameside(Xr!3, Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[50])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 (s_e(Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xb!1, Xc!0) <=> s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[10])).
% 0.20/0.44 tff(53,plain,
% 0.20/0.44 (s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0) <=> s_e(Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xb!1, Xc!0)),
% 0.20/0.44 inference(symmetry,[status(thm)],[52])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 ((~s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0)) <=> (~s_e(Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xb!1, Xc!0))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[53])).
% 0.20/0.44 tff(55,assumption,(~s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0)), introduced(assumption)).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 (~s_e(Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xb!1, Xc!0)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.44 tff(57,plain,
% 0.20/0.44 (((~s_t(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0))) | (~s_e(Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xb!1, Xc!0))) | s_e(Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xb!1, Xc!0)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(58,plain,
% 0.20/0.44 (s_e(Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xb!1, Xc!0)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[57, 22])).
% 0.20/0.44 tff(59,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[58, 56])).
% 0.20/0.44 tff(60,plain,(s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 (((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0)) | (~s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(62,plain,
% 0.20/0.44 ((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.20/0.44 tff(63,plain,
% 0.20/0.44 ((~(~((~((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | sameside(insert(Xb!1, Xc!0, Xa!2, Xr!3), Xa!2, Xr!3))) | (~((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0)))))) <=> ((~((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | sameside(insert(Xb!1, Xc!0, Xa!2, Xr!3), Xa!2, Xr!3))) | (~((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 ((((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | sameside(insert(Xb!1, Xc!0, Xa!2, Xr!3), Xa!2, Xr!3)) & ((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0))) <=> (~((~((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | sameside(insert(Xb!1, Xc!0, Xa!2, Xr!3), Xa!2, Xr!3))) | (~((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(65,plain,
% 0.20/0.44 ((~(((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | sameside(insert(Xb!1, Xc!0, Xa!2, Xr!3), Xa!2, Xr!3)) & ((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0)))) <=> (~(~((~((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | sameside(insert(Xb!1, Xc!0, Xa!2, Xr!3), Xa!2, Xr!3))) | (~((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[64])).
% 0.20/0.44 tff(66,plain,
% 0.20/0.44 ((~(((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | sameside(insert(Xb!1, Xc!0, Xa!2, Xr!3), Xa!2, Xr!3)) & ((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0)))) <=> ((~((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | sameside(insert(Xb!1, Xc!0, Xa!2, Xr!3), Xa!2, Xr!3))) | (~((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[65, 63])).
% 0.20/0.44 tff(67,plain,
% 0.20/0.44 ((~![Xr: $i, Xa: $i, Xb: $i, Xc: $i] : (((Xb = Xc) | (Xr = Xa) | sameside(insert(Xb, Xc, Xa, Xr), Xa, Xr)) & ((Xb = Xc) | (Xr = Xa) | s_e(Xa, insert(Xb, Xc, Xa, Xr), Xb, Xc)))) <=> (~![Xr: $i, Xa: $i, Xb: $i, Xc: $i] : (((Xb = Xc) | (Xr = Xa) | sameside(insert(Xb, Xc, Xa, Xr), Xa, Xr)) & ((Xb = Xc) | (Xr = Xa) | s_e(Xa, insert(Xb, Xc, Xa, Xr), Xb, Xc))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(68,plain,
% 0.20/0.44 ((~![Xr: $i, Xa: $i, Xb: $i, Xc: $i] : ((((Xr = Xa) | (Xb = Xc)) | sameside(insert(Xb, Xc, Xa, Xr), Xa, Xr)) & (((Xr = Xa) | (Xb = Xc)) | s_e(Xa, insert(Xb, Xc, Xa, Xr), Xb, Xc)))) <=> (~![Xr: $i, Xa: $i, Xb: $i, Xc: $i] : (((Xb = Xc) | (Xr = Xa) | sameside(insert(Xb, Xc, Xa, Xr), Xa, Xr)) & ((Xb = Xc) | (Xr = Xa) | s_e(Xa, insert(Xb, Xc, Xa, Xr), Xb, Xc))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(69,axiom,(~![Xr: $i, Xa: $i, Xb: $i, Xc: $i] : ((((Xr = Xa) | (Xb = Xc)) | sameside(insert(Xb, Xc, Xa, Xr), Xa, Xr)) & (((Xr = Xa) | (Xb = Xc)) | s_e(Xa, insert(Xb, Xc, Xa, Xr), Xb, Xc)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz6_11a')).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 (~![Xr: $i, Xa: $i, Xb: $i, Xc: $i] : (((Xb = Xc) | (Xr = Xa) | sameside(insert(Xb, Xc, Xa, Xr), Xa, Xr)) & ((Xb = Xc) | (Xr = Xa) | s_e(Xa, insert(Xb, Xc, Xa, Xr), Xb, Xc)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.44 tff(71,plain,
% 0.20/0.44 (~![Xr: $i, Xa: $i, Xb: $i, Xc: $i] : (((Xb = Xc) | (Xr = Xa) | sameside(insert(Xb, Xc, Xa, Xr), Xa, Xr)) & ((Xb = Xc) | (Xr = Xa) | s_e(Xa, insert(Xb, Xc, Xa, Xr), Xb, Xc)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[70, 67])).
% 0.20/0.45 tff(72,plain,
% 0.20/0.45 (~![Xr: $i, Xa: $i, Xb: $i, Xc: $i] : (((Xb = Xc) | (Xr = Xa) | sameside(insert(Xb, Xc, Xa, Xr), Xa, Xr)) & ((Xb = Xc) | (Xr = Xa) | s_e(Xa, insert(Xb, Xc, Xa, Xr), Xb, Xc)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.20/0.45 tff(73,plain,
% 0.20/0.45 (~![Xr: $i, Xa: $i, Xb: $i, Xc: $i] : (((Xb = Xc) | (Xr = Xa) | sameside(insert(Xb, Xc, Xa, Xr), Xa, Xr)) & ((Xb = Xc) | (Xr = Xa) | s_e(Xa, insert(Xb, Xc, Xa, Xr), Xb, Xc)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[72, 67])).
% 0.20/0.45 tff(74,plain,(
% 0.20/0.45 ~(((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | sameside(insert(Xb!1, Xc!0, Xa!2, Xr!3), Xa!2, Xr!3)) & ((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[73])).
% 0.20/0.45 tff(75,plain,
% 0.20/0.45 ((~((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | sameside(insert(Xb!1, Xc!0, Xa!2, Xr!3), Xa!2, Xr!3))) | (~((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[74, 66])).
% 0.20/0.45 tff(76,plain,
% 0.20/0.45 (~((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | sameside(insert(Xb!1, Xc!0, Xa!2, Xr!3), Xa!2, Xr!3))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[75, 62])).
% 0.20/0.45 tff(77,plain,
% 0.20/0.45 (((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | sameside(insert(Xb!1, Xc!0, Xa!2, Xr!3), Xa!2, Xr!3)) | (~sameside(insert(Xb!1, Xc!0, Xa!2, Xr!3), Xa!2, Xr!3))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(78,plain,
% 0.20/0.45 (~sameside(insert(Xb!1, Xc!0, Xa!2, Xr!3), Xa!2, Xr!3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.20/0.45 tff(79,plain,
% 0.20/0.45 (^[Xa: $i, Xp: $i, Xb: $i] : refl(((~sameside(Xa, Xp, Xb)) | sameside(Xb, Xp, Xa)) <=> ((~sameside(Xa, Xp, Xb)) | sameside(Xb, Xp, Xa)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(80,plain,
% 0.20/0.45 (![Xa: $i, Xp: $i, Xb: $i] : ((~sameside(Xa, Xp, Xb)) | sameside(Xb, Xp, Xa)) <=> ![Xa: $i, Xp: $i, Xb: $i] : ((~sameside(Xa, Xp, Xb)) | sameside(Xb, Xp, Xa))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.45 tff(81,plain,
% 0.20/0.45 (![Xa: $i, Xp: $i, Xb: $i] : ((~sameside(Xa, Xp, Xb)) | sameside(Xb, Xp, Xa)) <=> ![Xa: $i, Xp: $i, Xb: $i] : ((~sameside(Xa, Xp, Xb)) | sameside(Xb, Xp, Xa))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(82,axiom,(![Xa: $i, Xp: $i, Xb: $i] : ((~sameside(Xa, Xp, Xb)) | sameside(Xb, Xp, Xa))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz6_6')).
% 0.20/0.45 tff(83,plain,
% 0.20/0.45 (![Xa: $i, Xp: $i, Xb: $i] : ((~sameside(Xa, Xp, Xb)) | sameside(Xb, Xp, Xa))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.45 tff(84,plain,(
% 0.20/0.45 ![Xa: $i, Xp: $i, Xb: $i] : ((~sameside(Xa, Xp, Xb)) | sameside(Xb, Xp, Xa))),
% 0.20/0.45 inference(skolemize,[status(sab)],[83])).
% 0.20/0.45 tff(85,plain,
% 0.20/0.45 (![Xa: $i, Xp: $i, Xb: $i] : ((~sameside(Xa, Xp, Xb)) | sameside(Xb, Xp, Xa))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.20/0.45 tff(86,plain,
% 0.20/0.45 (((~![Xa: $i, Xp: $i, Xb: $i] : ((~sameside(Xa, Xp, Xb)) | sameside(Xb, Xp, Xa))) | ((~sameside(Xr!3, Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3))) | sameside(insert(Xb!1, Xc!0, Xa!2, Xr!3), Xa!2, Xr!3))) <=> ((~![Xa: $i, Xp: $i, Xb: $i] : ((~sameside(Xa, Xp, Xb)) | sameside(Xb, Xp, Xa))) | (~sameside(Xr!3, Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3))) | sameside(insert(Xb!1, Xc!0, Xa!2, Xr!3), Xa!2, Xr!3))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(87,plain,
% 0.20/0.45 ((~![Xa: $i, Xp: $i, Xb: $i] : ((~sameside(Xa, Xp, Xb)) | sameside(Xb, Xp, Xa))) | ((~sameside(Xr!3, Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3))) | sameside(insert(Xb!1, Xc!0, Xa!2, Xr!3), Xa!2, Xr!3))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(88,plain,
% 0.20/0.45 ((~![Xa: $i, Xp: $i, Xb: $i] : ((~sameside(Xa, Xp, Xb)) | sameside(Xb, Xp, Xa))) | (~sameside(Xr!3, Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3))) | sameside(insert(Xb!1, Xc!0, Xa!2, Xr!3), Xa!2, Xr!3)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.45 tff(89,plain,
% 0.20/0.45 (~sameside(Xr!3, Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[88, 85, 78])).
% 0.20/0.45 tff(90,plain,
% 0.20/0.45 (~sameside(Xr!3, Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[89, 51])).
% 0.20/0.45 tff(91,plain,
% 0.20/0.45 (^[Xa: $i, Xb: $i] : refl(s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma)) <=> s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(92,plain,
% 0.20/0.45 (![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma)) <=> ![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[91])).
% 0.20/0.45 tff(93,plain,
% 0.20/0.45 (![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma)) <=> ![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(94,axiom,(![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz3_14a')).
% 0.20/0.45 tff(95,plain,
% 0.20/0.45 (![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.45 tff(96,plain,(
% 0.20/0.45 ![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma))),
% 0.20/0.45 inference(skolemize,[status(sab)],[95])).
% 0.20/0.45 tff(97,plain,
% 0.20/0.45 (![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.20/0.45 tff(98,plain,
% 0.20/0.45 ((~![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma))) | s_t(Xr!3, Xa!2, ext(Xr!3, Xa!2, alpha, gamma))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(99,plain,
% 0.20/0.45 (s_t(Xr!3, Xa!2, ext(Xr!3, Xa!2, alpha, gamma))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.20/0.45 tff(100,plain,
% 0.20/0.45 (((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | sameside(insert(Xb!1, Xc!0, Xa!2, Xr!3), Xa!2, Xr!3)) | (~(Xr!3 = Xa!2))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(101,plain,
% 0.20/0.45 (~(Xr!3 = Xa!2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[100, 76])).
% 0.20/0.45 tff(102,plain,
% 0.20/0.45 (^[Xa: $i, Xp: $i, Xb: $i, Xc: $i] : refl(((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | sameside(Xa, Xp, Xb) | (Xc = Xp) | (Xb = Xp)) <=> ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | sameside(Xa, Xp, Xb) | (Xc = Xp) | (Xb = Xp)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(103,plain,
% 0.20/0.45 (![Xa: $i, Xp: $i, Xb: $i, Xc: $i] : ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | sameside(Xa, Xp, Xb) | (Xc = Xp) | (Xb = Xp)) <=> ![Xa: $i, Xp: $i, Xb: $i, Xc: $i] : ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | sameside(Xa, Xp, Xb) | (Xc = Xp) | (Xb = Xp))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[102])).
% 0.20/0.45 tff(104,plain,
% 0.20/0.45 (![Xa: $i, Xp: $i, Xb: $i, Xc: $i] : ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | sameside(Xa, Xp, Xb) | (Xc = Xp) | (Xb = Xp)) <=> ![Xa: $i, Xp: $i, Xb: $i, Xc: $i] : ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | sameside(Xa, Xp, Xb) | (Xc = Xp) | (Xb = Xp))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(105,plain,
% 0.20/0.45 (^[Xa: $i, Xp: $i, Xb: $i, Xc: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((Xa = Xp) | (Xb = Xp)) <=> ((Xa = Xp) | (Xb = Xp))), ((((Xa = Xp) | (Xb = Xp)) | (Xc = Xp)) <=> (((Xa = Xp) | (Xb = Xp)) | (Xc = Xp)))), rewrite((((Xa = Xp) | (Xb = Xp)) | (Xc = Xp)) <=> ((Xa = Xp) | (Xc = Xp) | (Xb = Xp))), ((((Xa = Xp) | (Xb = Xp)) | (Xc = Xp)) <=> ((Xa = Xp) | (Xc = Xp) | (Xb = Xp)))), (((((Xa = Xp) | (Xb = Xp)) | (Xc = Xp)) | (~s_t(Xa, Xp, Xc))) <=> (((Xa = Xp) | (Xc = Xp) | (Xb = Xp)) | (~s_t(Xa, Xp, Xc))))), rewrite((((Xa = Xp) | (Xc = Xp) | (Xb = Xp)) | (~s_t(Xa, Xp, Xc))) <=> ((Xa = Xp) | (~s_t(Xa, Xp, Xc)) | (Xc = Xp) | (Xb = Xp))), (((((Xa = Xp) | (Xb = Xp)) | (Xc = Xp)) | (~s_t(Xa, Xp, Xc))) <=> ((Xa = Xp) | (~s_t(Xa, Xp, Xc)) | (Xc = Xp) | (Xb = Xp)))), ((((((Xa = Xp) | (Xb = Xp)) | (Xc = Xp)) | (~s_t(Xa, Xp, Xc))) | (~s_t(Xb, Xp, Xc))) <=> (((Xa = Xp) | (~s_t(Xa, Xp, Xc)) | (Xc = Xp) | (Xb = Xp)) | (~s_t(Xb, Xp, Xc))))), rewrite((((Xa = Xp) | (~s_t(Xa, Xp, Xc)) | (Xc = Xp) | (Xb = Xp)) | (~s_t(Xb, Xp, Xc))) <=> ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | (Xc = Xp) | (Xb = Xp))), ((((((Xa = Xp) | (Xb = Xp)) | (Xc = Xp)) | (~s_t(Xa, Xp, Xc))) | (~s_t(Xb, Xp, Xc))) <=> ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | (Xc = Xp) | (Xb = Xp)))), (((((((Xa = Xp) | (Xb = Xp)) | (Xc = Xp)) | (~s_t(Xa, Xp, Xc))) | (~s_t(Xb, Xp, Xc))) | sameside(Xa, Xp, Xb)) <=> (((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | (Xc = Xp) | (Xb = Xp)) | sameside(Xa, Xp, Xb)))), rewrite((((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | (Xc = Xp) | (Xb = Xp)) | sameside(Xa, Xp, Xb)) <=> ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | sameside(Xa, Xp, Xb) | (Xc = Xp) | (Xb = Xp))), (((((((Xa = Xp) | (Xb = Xp)) | (Xc = Xp)) | (~s_t(Xa, Xp, Xc))) | (~s_t(Xb, Xp, Xc))) | sameside(Xa, Xp, Xb)) <=> ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | sameside(Xa, Xp, Xb) | (Xc = Xp) | (Xb = Xp))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(106,plain,
% 0.20/0.45 (![Xa: $i, Xp: $i, Xb: $i, Xc: $i] : ((((((Xa = Xp) | (Xb = Xp)) | (Xc = Xp)) | (~s_t(Xa, Xp, Xc))) | (~s_t(Xb, Xp, Xc))) | sameside(Xa, Xp, Xb)) <=> ![Xa: $i, Xp: $i, Xb: $i, Xc: $i] : ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | sameside(Xa, Xp, Xb) | (Xc = Xp) | (Xb = Xp))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[105])).
% 0.20/0.45 tff(107,axiom,(![Xa: $i, Xp: $i, Xb: $i, Xc: $i] : ((((((Xa = Xp) | (Xb = Xp)) | (Xc = Xp)) | (~s_t(Xa, Xp, Xc))) | (~s_t(Xb, Xp, Xc))) | sameside(Xa, Xp, Xb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz6_2a')).
% 0.20/0.45 tff(108,plain,
% 0.20/0.45 (![Xa: $i, Xp: $i, Xb: $i, Xc: $i] : ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | sameside(Xa, Xp, Xb) | (Xc = Xp) | (Xb = Xp))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.45 tff(109,plain,
% 0.20/0.45 (![Xa: $i, Xp: $i, Xb: $i, Xc: $i] : ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | sameside(Xa, Xp, Xb) | (Xc = Xp) | (Xb = Xp))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.20/0.45 tff(110,plain,(
% 0.20/0.45 ![Xa: $i, Xp: $i, Xb: $i, Xc: $i] : ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | sameside(Xa, Xp, Xb) | (Xc = Xp) | (Xb = Xp))),
% 0.20/0.45 inference(skolemize,[status(sab)],[109])).
% 0.20/0.45 tff(111,plain,
% 0.20/0.45 (![Xa: $i, Xp: $i, Xb: $i, Xc: $i] : ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | sameside(Xa, Xp, Xb) | (Xc = Xp) | (Xb = Xp))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.20/0.45 tff(112,plain,
% 0.20/0.45 (((~![Xa: $i, Xp: $i, Xb: $i, Xc: $i] : ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | sameside(Xa, Xp, Xb) | (Xc = Xp) | (Xb = Xp))) | ((Xr!3 = Xa!2) | (~s_t(Xr!3, Xa!2, ext(Xr!3, Xa!2, alpha, gamma))) | sameside(Xr!3, Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0)) | (ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0) = Xa!2) | (ext(Xr!3, Xa!2, alpha, gamma) = Xa!2) | (~s_t(ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xa!2, ext(Xr!3, Xa!2, alpha, gamma))))) <=> ((~![Xa: $i, Xp: $i, Xb: $i, Xc: $i] : ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | sameside(Xa, Xp, Xb) | (Xc = Xp) | (Xb = Xp))) | (Xr!3 = Xa!2) | (~s_t(Xr!3, Xa!2, ext(Xr!3, Xa!2, alpha, gamma))) | sameside(Xr!3, Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0)) | (ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0) = Xa!2) | (ext(Xr!3, Xa!2, alpha, gamma) = Xa!2) | (~s_t(ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xa!2, ext(Xr!3, Xa!2, alpha, gamma))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(113,plain,
% 0.20/0.45 (((~s_t(ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xa!2, ext(Xr!3, Xa!2, alpha, gamma))) | (Xr!3 = Xa!2) | (~s_t(Xr!3, Xa!2, ext(Xr!3, Xa!2, alpha, gamma))) | sameside(Xr!3, Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0)) | (ext(Xr!3, Xa!2, alpha, gamma) = Xa!2) | (ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0) = Xa!2)) <=> ((Xr!3 = Xa!2) | (~s_t(Xr!3, Xa!2, ext(Xr!3, Xa!2, alpha, gamma))) | sameside(Xr!3, Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0)) | (ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0) = Xa!2) | (ext(Xr!3, Xa!2, alpha, gamma) = Xa!2) | (~s_t(ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xa!2, ext(Xr!3, Xa!2, alpha, gamma))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(114,plain,
% 0.20/0.45 (((~![Xa: $i, Xp: $i, Xb: $i, Xc: $i] : ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | sameside(Xa, Xp, Xb) | (Xc = Xp) | (Xb = Xp))) | ((~s_t(ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xa!2, ext(Xr!3, Xa!2, alpha, gamma))) | (Xr!3 = Xa!2) | (~s_t(Xr!3, Xa!2, ext(Xr!3, Xa!2, alpha, gamma))) | sameside(Xr!3, Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0)) | (ext(Xr!3, Xa!2, alpha, gamma) = Xa!2) | (ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0) = Xa!2))) <=> ((~![Xa: $i, Xp: $i, Xb: $i, Xc: $i] : ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | sameside(Xa, Xp, Xb) | (Xc = Xp) | (Xb = Xp))) | ((Xr!3 = Xa!2) | (~s_t(Xr!3, Xa!2, ext(Xr!3, Xa!2, alpha, gamma))) | sameside(Xr!3, Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0)) | (ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0) = Xa!2) | (ext(Xr!3, Xa!2, alpha, gamma) = Xa!2) | (~s_t(ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xa!2, ext(Xr!3, Xa!2, alpha, gamma)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[113])).
% 0.20/0.46 tff(115,plain,
% 0.20/0.46 (((~![Xa: $i, Xp: $i, Xb: $i, Xc: $i] : ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | sameside(Xa, Xp, Xb) | (Xc = Xp) | (Xb = Xp))) | ((~s_t(ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xa!2, ext(Xr!3, Xa!2, alpha, gamma))) | (Xr!3 = Xa!2) | (~s_t(Xr!3, Xa!2, ext(Xr!3, Xa!2, alpha, gamma))) | sameside(Xr!3, Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0)) | (ext(Xr!3, Xa!2, alpha, gamma) = Xa!2) | (ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0) = Xa!2))) <=> ((~![Xa: $i, Xp: $i, Xb: $i, Xc: $i] : ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | sameside(Xa, Xp, Xb) | (Xc = Xp) | (Xb = Xp))) | (Xr!3 = Xa!2) | (~s_t(Xr!3, Xa!2, ext(Xr!3, Xa!2, alpha, gamma))) | sameside(Xr!3, Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0)) | (ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0) = Xa!2) | (ext(Xr!3, Xa!2, alpha, gamma) = Xa!2) | (~s_t(ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xa!2, ext(Xr!3, Xa!2, alpha, gamma))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[114, 112])).
% 0.20/0.46 tff(116,plain,
% 0.20/0.46 ((~![Xa: $i, Xp: $i, Xb: $i, Xc: $i] : ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | sameside(Xa, Xp, Xb) | (Xc = Xp) | (Xb = Xp))) | ((~s_t(ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xa!2, ext(Xr!3, Xa!2, alpha, gamma))) | (Xr!3 = Xa!2) | (~s_t(Xr!3, Xa!2, ext(Xr!3, Xa!2, alpha, gamma))) | sameside(Xr!3, Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0)) | (ext(Xr!3, Xa!2, alpha, gamma) = Xa!2) | (ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0) = Xa!2))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(117,plain,
% 0.20/0.46 ((~![Xa: $i, Xp: $i, Xb: $i, Xc: $i] : ((~s_t(Xb, Xp, Xc)) | (Xa = Xp) | (~s_t(Xa, Xp, Xc)) | sameside(Xa, Xp, Xb) | (Xc = Xp) | (Xb = Xp))) | (Xr!3 = Xa!2) | (~s_t(Xr!3, Xa!2, ext(Xr!3, Xa!2, alpha, gamma))) | sameside(Xr!3, Xa!2, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0)) | (ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0) = Xa!2) | (ext(Xr!3, Xa!2, alpha, gamma) = Xa!2) | (~s_t(ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), Xa!2, ext(Xr!3, Xa!2, alpha, gamma)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.46 tff(118,plain,
% 0.20/0.46 (ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0) = Xa!2),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[117, 111, 101, 99, 90, 48, 35])).
% 0.20/0.46 tff(119,plain,
% 0.20/0.46 (s_e(Xb!1, Xc!0, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0)) <=> s_e(Xb!1, Xc!0, Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[118, 10])).
% 0.20/0.46 tff(120,plain,
% 0.20/0.46 (s_e(Xb!1, Xc!0, Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3)) <=> s_e(Xb!1, Xc!0, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0))),
% 0.20/0.46 inference(symmetry,[status(thm)],[119])).
% 0.20/0.46 tff(121,plain,
% 0.20/0.46 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : refl(((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb)) <=> ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(122,plain,
% 0.20/0.46 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[121])).
% 0.20/0.46 tff(123,plain,
% 0.20/0.46 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(124,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz2_2')).
% 0.20/0.46 tff(125,plain,
% 0.20/0.46 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.46 tff(126,plain,(
% 0.20/0.46 ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))),
% 0.20/0.46 inference(skolemize,[status(sab)],[125])).
% 0.20/0.46 tff(127,plain,
% 0.20/0.46 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.20/0.46 tff(128,plain,
% 0.20/0.46 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | ((~s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0)) | s_e(Xb!1, Xc!0, Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | (~s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0)) | s_e(Xb!1, Xc!0, Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(129,plain,
% 0.20/0.46 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | ((~s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0)) | s_e(Xb!1, Xc!0, Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(130,plain,
% 0.20/0.46 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | (~s_e(Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3), Xb!1, Xc!0)) | s_e(Xb!1, Xc!0, Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.20/0.46 tff(131,plain,
% 0.20/0.46 (s_e(Xb!1, Xc!0, Xa!2, insert(Xb!1, Xc!0, Xa!2, Xr!3))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[130, 127, 60])).
% 0.20/0.46 tff(132,plain,
% 0.20/0.46 (s_e(Xb!1, Xc!0, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[131, 120])).
% 0.20/0.46 tff(133,plain,
% 0.20/0.46 (((Xb!1 = Xc!0) | (Xr!3 = Xa!2) | sameside(insert(Xb!1, Xc!0, Xa!2, Xr!3), Xa!2, Xr!3)) | (~(Xb!1 = Xc!0))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(134,plain,
% 0.20/0.46 (~(Xb!1 = Xc!0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[133, 76])).
% 0.20/0.46 tff(135,plain,
% 0.20/0.46 (^[Xb: $i, Xc: $i, Xa: $i] : refl(((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc)) <=> ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(136,plain,
% 0.20/0.46 (![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc)) <=> ![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[135])).
% 0.20/0.46 tff(137,plain,
% 0.20/0.46 (![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc)) <=> ![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(138,axiom,(![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz2_13')).
% 0.20/0.46 tff(139,plain,
% 0.20/0.46 (![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.46 tff(140,plain,(
% 0.20/0.46 ![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))),
% 0.20/0.46 inference(skolemize,[status(sab)],[139])).
% 0.20/0.46 tff(141,plain,
% 0.20/0.46 (![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.20/0.46 tff(142,plain,
% 0.20/0.46 (((~![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))) | ((~s_e(Xb!1, Xc!0, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0))) | (Xb!1 = Xc!0))) <=> ((~![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))) | (~s_e(Xb!1, Xc!0, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0))) | (Xb!1 = Xc!0))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(143,plain,
% 0.20/0.47 ((~![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))) | ((~s_e(Xb!1, Xc!0, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0))) | (Xb!1 = Xc!0))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 ((~![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))) | (~s_e(Xb!1, Xc!0, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0))) | (Xb!1 = Xc!0)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.20/0.47 tff(145,plain,
% 0.20/0.47 (~s_e(Xb!1, Xc!0, ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0), ext(ext(Xr!3, Xa!2, alpha, gamma), Xa!2, Xb!1, Xc!0))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[144, 141, 134])).
% 0.20/0.47 tff(146,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[145, 132])).
% 0.20/0.47 % SZS output end Proof
% 0.20/0.47 % E exiting
%------------------------------------------------------------------------------