Z3---4.15.1.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : GEO495+1 : TPTP v9.0.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n010.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 0.40s 0.57s
% Output   : Proof 0.55s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : GEO495+1 : TPTP v9.0.0. Released v7.0.0.
% 0.00/0.12  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n010.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % 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 14:57:41 EDT 2025
% 0.12/0.34  % CPUTime    : 
% 0.40/0.57  % SZS status Theorem
% 0.40/0.57  % SZS output start Proof
% 0.40/0.57  tff(s_e_type, type, (
% 0.40/0.57     s_e: ( $i * $i * $i * $i ) > $o)).
% 0.40/0.57  tff(tptp_fun_Xd_0_type, type, (
% 0.40/0.57     tptp_fun_Xd_0: $i)).
% 0.40/0.57  tff(ext_type, type, (
% 0.40/0.57     ext: ( $i * $i * $i * $i ) > $i)).
% 0.40/0.57  tff(tptp_fun_Xb_2_type, type, (
% 0.40/0.57     tptp_fun_Xb_2: $i)).
% 0.40/0.57  tff(tptp_fun_Xa_3_type, type, (
% 0.40/0.57     tptp_fun_Xa_3: $i)).
% 0.40/0.57  tff(tptp_fun_Xc_1_type, type, (
% 0.40/0.57     tptp_fun_Xc_1: $i)).
% 0.40/0.57  tff(gamma_type, type, (
% 0.40/0.57     gamma: $i)).
% 0.40/0.57  tff(alpha_type, type, (
% 0.40/0.57     alpha: $i)).
% 0.40/0.57  tff(insert_type, type, (
% 0.40/0.57     insert: ( $i * $i * $i * $i ) > $i)).
% 0.40/0.57  tff(ins_type, type, (
% 0.40/0.57     ins: ( $i * $i * $i * $i ) > $i)).
% 0.40/0.57  tff(s_t_type, type, (
% 0.40/0.57     s_t: ( $i * $i * $i ) > $o)).
% 0.40/0.57  tff(le_type, type, (
% 0.40/0.57     le: ( $i * $i * $i * $i ) > $o)).
% 0.40/0.57  tff(1,plain,
% 0.40/0.57      (^[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)))),
% 0.40/0.57      inference(bind,[status(th)],[])).
% 0.40/0.57  tff(2,plain,
% 0.40/0.57      (![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))),
% 0.40/0.57      inference(quant_intro,[status(thm)],[1])).
% 0.40/0.57  tff(3,plain,
% 0.40/0.57      (![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))),
% 0.40/0.57      inference(rewrite,[status(thm)],[])).
% 0.40/0.57  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/sandbox/benchmark/theBenchmark.p','d_insert')).
% 0.40/0.57  tff(5,plain,
% 0.40/0.57      (![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb))),
% 0.40/0.57      inference(modus_ponens,[status(thm)],[4, 3])).
% 0.40/0.57  tff(6,plain,(
% 0.40/0.57      ![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb))),
% 0.40/0.57      inference(skolemize,[status(sab)],[5])).
% 0.40/0.57  tff(7,plain,
% 0.40/0.57      (![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb))),
% 0.40/0.57      inference(modus_ponens,[status(thm)],[6, 2])).
% 0.40/0.57  tff(8,plain,
% 0.40/0.57      ((~![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb))) | (insert(Xa!3, Xb!2, Xc!1, Xd!0) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.40/0.57      inference(quant_inst,[status(thm)],[])).
% 0.40/0.57  tff(9,plain,
% 0.40/0.57      (insert(Xa!3, Xb!2, Xc!1, Xd!0) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)),
% 0.40/0.57      inference(unit_resolution,[status(thm)],[8, 7])).
% 0.40/0.57  tff(10,plain,
% 0.40/0.57      (ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2) = insert(Xa!3, Xb!2, Xc!1, Xd!0)),
% 0.40/0.57      inference(symmetry,[status(thm)],[9])).
% 0.40/0.57  tff(11,assumption,(Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)), introduced(assumption)).
% 0.40/0.57  tff(12,plain,
% 0.40/0.57      (Xd!0 = insert(Xa!3, Xb!2, Xc!1, Xd!0)),
% 0.40/0.57      inference(transitivity,[status(thm)],[11, 10])).
% 0.40/0.57  tff(13,plain,
% 0.40/0.57      (s_e(Xa!3, Xb!2, Xc!1, Xd!0) <=> s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.40/0.57      inference(monotonicity,[status(thm)],[12])).
% 0.40/0.57  tff(14,plain,
% 0.40/0.57      (s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)) <=> s_e(Xa!3, Xb!2, Xc!1, Xd!0)),
% 0.40/0.57      inference(symmetry,[status(thm)],[13])).
% 0.40/0.57  tff(15,plain,
% 0.40/0.57      (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : refl((~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))))) <=> (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))))))),
% 0.40/0.57      inference(bind,[status(th)],[])).
% 0.40/0.57  tff(16,plain,
% 0.40/0.57      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))),
% 0.40/0.57      inference(quant_intro,[status(thm)],[15])).
% 0.40/0.57  tff(17,plain,
% 0.40/0.57      (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : trans(monotonicity(rewrite(((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))) <=> ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))), ((((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))) <=> (((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))))), rewrite((((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))) <=> (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))), ((((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))) <=> (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))))),
% 0.40/0.57      inference(bind,[status(th)],[])).
% 0.40/0.57  tff(18,plain,
% 0.40/0.57      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))),
% 0.40/0.57      inference(quant_intro,[status(thm)],[17])).
% 0.40/0.57  tff(19,plain,
% 0.40/0.57      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))),
% 0.40/0.57      inference(rewrite,[status(thm)],[])).
% 0.40/0.57  tff(20,plain,
% 0.40/0.57      (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : trans(monotonicity(rewrite((((~s_t(Xc, Y, Xd)) | (~s_e(Xa, Xb, Xc, Y))) | le(Xa, Xb, Xc, Xd)) <=> ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))), (((((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) & (((~s_t(Xc, Y, Xd)) | (~s_e(Xa, Xb, Xc, Y))) | le(Xa, Xb, Xc, Xd))) <=> ((((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))))), rewrite(((((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))) <=> (((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))), (((((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) & (((~s_t(Xc, Y, Xd)) | (~s_e(Xa, Xb, Xc, Y))) | le(Xa, Xb, Xc, Xd))) <=> (((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))),
% 0.40/0.57      inference(bind,[status(th)],[])).
% 0.40/0.57  tff(21,plain,
% 0.40/0.57      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : ((((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) & (((~s_t(Xc, Y, Xd)) | (~s_e(Xa, Xb, Xc, Y))) | le(Xa, Xb, Xc, Xd))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))),
% 0.40/0.57      inference(quant_intro,[status(thm)],[20])).
% 0.40/0.57  tff(22,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : ((((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) & (((~s_t(Xc, Y, Xd)) | (~s_e(Xa, Xb, Xc, Y))) | le(Xa, Xb, Xc, Xd)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d_Defn5_4')).
% 0.40/0.57  tff(23,plain,
% 0.40/0.57      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))),
% 0.40/0.57      inference(modus_ponens,[status(thm)],[22, 21])).
% 0.40/0.57  tff(24,plain,
% 0.40/0.57      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))),
% 0.40/0.57      inference(modus_ponens,[status(thm)],[23, 19])).
% 0.40/0.57  tff(25,plain,(
% 0.40/0.57      ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))),
% 0.40/0.57      inference(skolemize,[status(sab)],[24])).
% 0.40/0.57  tff(26,plain,
% 0.40/0.57      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))),
% 0.40/0.57      inference(modus_ponens,[status(thm)],[25, 18])).
% 0.40/0.57  tff(27,plain,
% 0.40/0.57      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))),
% 0.40/0.57      inference(modus_ponens,[status(thm)],[26, 16])).
% 0.40/0.57  tff(28,plain,
% 0.40/0.57      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~(le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)) | (~s_t(Xc!1, Xd!0, Xd!0))))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~(le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)) | (~s_t(Xc!1, Xd!0, Xd!0)))))))),
% 0.40/0.57      inference(rewrite,[status(thm)],[])).
% 0.40/0.58  tff(29,plain,
% 0.40/0.58      ((~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~((~s_t(Xc!1, Xd!0, Xd!0)) | le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)))))) <=> (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~(le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)) | (~s_t(Xc!1, Xd!0, Xd!0))))))),
% 0.40/0.58      inference(rewrite,[status(thm)],[])).
% 0.40/0.58  tff(30,plain,
% 0.40/0.58      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~((~s_t(Xc!1, Xd!0, Xd!0)) | le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0))))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~(le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)) | (~s_t(Xc!1, Xd!0, Xd!0)))))))),
% 0.40/0.58      inference(monotonicity,[status(thm)],[29])).
% 0.40/0.58  tff(31,plain,
% 0.40/0.58      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~((~s_t(Xc!1, Xd!0, Xd!0)) | le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0))))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~(le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)) | (~s_t(Xc!1, Xd!0, Xd!0)))))))),
% 0.40/0.58      inference(transitivity,[status(thm)],[30, 28])).
% 0.40/0.58  tff(32,plain,
% 0.40/0.58      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~((~s_t(Xc!1, Xd!0, Xd!0)) | le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0))))))),
% 0.40/0.58      inference(quant_inst,[status(thm)],[])).
% 0.40/0.58  tff(33,plain,
% 0.40/0.58      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~(le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)) | (~s_t(Xc!1, Xd!0, Xd!0))))))),
% 0.40/0.58      inference(modus_ponens,[status(thm)],[32, 31])).
% 0.40/0.58  tff(34,plain,
% 0.40/0.58      (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~(le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)) | (~s_t(Xc!1, Xd!0, Xd!0)))))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[33, 27])).
% 0.40/0.58  tff(35,plain,
% 0.40/0.58      (((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~(le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)) | (~s_t(Xc!1, Xd!0, Xd!0))))) | ((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))),
% 0.40/0.58      inference(tautology,[status(thm)],[])).
% 0.40/0.58  tff(36,plain,
% 0.40/0.58      ((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[35, 34])).
% 0.40/0.58  tff(37,plain,
% 0.40/0.58      ((~(s_e(Xa!3, Xb!2, Xc!1, Xd!0) | (~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (~le(Xc!1, Xd!0, Xa!3, Xb!2)))) <=> (~(s_e(Xa!3, Xb!2, Xc!1, Xd!0) | (~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (~le(Xc!1, Xd!0, Xa!3, Xb!2))))),
% 0.40/0.58      inference(rewrite,[status(thm)],[])).
% 0.40/0.58  tff(38,plain,
% 0.40/0.58      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_e(Xa, Xb, Xc, Xd) | (~le(Xa, Xb, Xc, Xd)) | (~le(Xc, Xd, Xa, Xb)))) <=> (~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_e(Xa, Xb, Xc, Xd) | (~le(Xa, Xb, Xc, Xd)) | (~le(Xc, Xd, Xa, Xb))))),
% 0.40/0.58      inference(rewrite,[status(thm)],[])).
% 0.40/0.58  tff(39,plain,
% 0.40/0.58      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~le(Xa, Xb, Xc, Xd)) | (~le(Xc, Xd, Xa, Xb))) | s_e(Xa, Xb, Xc, Xd))) <=> (~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_e(Xa, Xb, Xc, Xd) | (~le(Xa, Xb, Xc, Xd)) | (~le(Xc, Xd, Xa, Xb))))),
% 0.40/0.58      inference(rewrite,[status(thm)],[])).
% 0.40/0.58  tff(40,axiom,(~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~le(Xa, Xb, Xc, Xd)) | (~le(Xc, Xd, Xa, Xb))) | s_e(Xa, Xb, Xc, Xd))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz5_9')).
% 0.40/0.58  tff(41,plain,
% 0.40/0.58      (~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_e(Xa, Xb, Xc, Xd) | (~le(Xa, Xb, Xc, Xd)) | (~le(Xc, Xd, Xa, Xb)))),
% 0.40/0.58      inference(modus_ponens,[status(thm)],[40, 39])).
% 0.40/0.58  tff(42,plain,
% 0.40/0.58      (~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_e(Xa, Xb, Xc, Xd) | (~le(Xa, Xb, Xc, Xd)) | (~le(Xc, Xd, Xa, Xb)))),
% 0.40/0.58      inference(modus_ponens,[status(thm)],[41, 38])).
% 0.40/0.58  tff(43,plain,
% 0.40/0.58      (~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_e(Xa, Xb, Xc, Xd) | (~le(Xa, Xb, Xc, Xd)) | (~le(Xc, Xd, Xa, Xb)))),
% 0.40/0.58      inference(modus_ponens,[status(thm)],[42, 38])).
% 0.40/0.58  tff(44,plain,
% 0.40/0.58      (~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_e(Xa, Xb, Xc, Xd) | (~le(Xa, Xb, Xc, Xd)) | (~le(Xc, Xd, Xa, Xb)))),
% 0.40/0.58      inference(modus_ponens,[status(thm)],[43, 38])).
% 0.40/0.58  tff(45,plain,(
% 0.40/0.58      ~(s_e(Xa!3, Xb!2, Xc!1, Xd!0) | (~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (~le(Xc!1, Xd!0, Xa!3, Xb!2)))),
% 0.40/0.58      inference(skolemize,[status(sab)],[44])).
% 0.40/0.58  tff(46,plain,
% 0.40/0.58      (~(s_e(Xa!3, Xb!2, Xc!1, Xd!0) | (~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (~le(Xc!1, Xd!0, Xa!3, Xb!2)))),
% 0.40/0.58      inference(modus_ponens,[status(thm)],[45, 37])).
% 0.40/0.58  tff(47,plain,
% 0.40/0.58      (le(Xa!3, Xb!2, Xc!1, Xd!0)),
% 0.40/0.58      inference(or_elim,[status(thm)],[46])).
% 0.40/0.58  tff(48,plain,
% 0.40/0.58      ((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.40/0.58      inference(tautology,[status(thm)],[])).
% 0.40/0.58  tff(49,plain,
% 0.40/0.58      ((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[48, 47])).
% 0.40/0.58  tff(50,plain,
% 0.40/0.58      (s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[49, 36])).
% 0.40/0.58  tff(51,plain,
% 0.40/0.58      (s_e(Xa!3, Xb!2, Xc!1, Xd!0)),
% 0.40/0.58      inference(modus_ponens,[status(thm)],[50, 14])).
% 0.40/0.58  tff(52,plain,
% 0.40/0.58      (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)),
% 0.40/0.58      inference(or_elim,[status(thm)],[46])).
% 0.40/0.58  tff(53,plain,
% 0.40/0.58      ($false),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[52, 51])).
% 0.40/0.58  tff(54,plain,(~(Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.58  tff(55,plain,
% 0.42/0.58      (s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1) <=> s_t(Xd!0, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1)),
% 0.42/0.58      inference(monotonicity,[status(thm)],[10])).
% 0.42/0.58  tff(56,plain,
% 0.42/0.58      (s_t(Xd!0, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1) <=> s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)),
% 0.42/0.58      inference(symmetry,[status(thm)],[55])).
% 0.42/0.58  tff(57,plain,
% 0.42/0.58      (((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~(le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)) | (~s_t(Xc!1, Xd!0, Xd!0))))) | ((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.42/0.58      inference(tautology,[status(thm)],[])).
% 0.42/0.58  tff(58,plain,
% 0.42/0.58      ((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)),
% 0.42/0.58      inference(unit_resolution,[status(thm)],[57, 34])).
% 0.42/0.58  tff(59,plain,
% 0.42/0.58      ((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)),
% 0.42/0.58      inference(tautology,[status(thm)],[])).
% 0.42/0.58  tff(60,plain,
% 0.42/0.58      ((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)),
% 0.42/0.58      inference(unit_resolution,[status(thm)],[59, 47])).
% 0.42/0.58  tff(61,plain,
% 0.42/0.58      (s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)),
% 0.42/0.58      inference(unit_resolution,[status(thm)],[60, 58])).
% 0.42/0.58  tff(62,plain,
% 0.42/0.58      (^[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)))),
% 0.42/0.58      inference(bind,[status(th)],[])).
% 0.42/0.58  tff(63,plain,
% 0.42/0.58      (![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))),
% 0.42/0.58      inference(quant_intro,[status(thm)],[62])).
% 0.42/0.58  tff(64,plain,
% 0.42/0.58      (![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))),
% 0.42/0.58      inference(rewrite,[status(thm)],[])).
% 0.42/0.58  tff(65,axiom,(![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz3_2')).
% 0.42/0.58  tff(66,plain,
% 0.42/0.58      (![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))),
% 0.42/0.58      inference(modus_ponens,[status(thm)],[65, 64])).
% 0.42/0.58  tff(67,plain,(
% 0.42/0.58      ![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))),
% 0.42/0.58      inference(skolemize,[status(sab)],[66])).
% 0.42/0.58  tff(68,plain,
% 0.42/0.58      (![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))),
% 0.42/0.58      inference(modus_ponens,[status(thm)],[67, 63])).
% 0.42/0.58  tff(69,plain,
% 0.42/0.58      (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)) | s_t(Xd!0, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)) | s_t(Xd!0, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1))),
% 0.42/0.58      inference(rewrite,[status(thm)],[])).
% 0.42/0.58  tff(70,plain,
% 0.42/0.58      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)) | s_t(Xd!0, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1))),
% 0.42/0.58      inference(quant_inst,[status(thm)],[])).
% 0.42/0.58  tff(71,plain,
% 0.42/0.58      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)) | s_t(Xd!0, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1)),
% 0.42/0.58      inference(modus_ponens,[status(thm)],[70, 69])).
% 0.42/0.58  tff(72,plain,
% 0.42/0.58      (s_t(Xd!0, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1)),
% 0.42/0.58      inference(unit_resolution,[status(thm)],[71, 68, 61])).
% 0.42/0.58  tff(73,plain,
% 0.42/0.58      (s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)),
% 0.42/0.58      inference(modus_ponens,[status(thm)],[72, 56])).
% 0.42/0.58  tff(74,plain,
% 0.42/0.58      (^[Xa: $i, Xb: $i, Xc: $i] : refl(((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))) <=> ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))))),
% 0.42/0.58      inference(bind,[status(th)],[])).
% 0.42/0.58  tff(75,plain,
% 0.42/0.58      (![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))) <=> ![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))),
% 0.42/0.58      inference(quant_intro,[status(thm)],[74])).
% 0.42/0.58  tff(76,plain,
% 0.42/0.58      (![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))) <=> ![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))),
% 0.42/0.58      inference(rewrite,[status(thm)],[])).
% 0.42/0.58  tff(77,plain,
% 0.42/0.58      (^[Xa: $i, Xb: $i, Xc: $i] : trans(monotonicity(rewrite(((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))) <=> ((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))), ((((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))) | (Xa = Xb)) <=> (((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))) | (Xa = Xb)))), rewrite((((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))) | (Xa = Xb)) <=> ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))), ((((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))) | (Xa = Xb)) <=> ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))))),
% 0.42/0.58      inference(bind,[status(th)],[])).
% 0.42/0.58  tff(78,plain,
% 0.42/0.58      (![Xa: $i, Xb: $i, Xc: $i] : (((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))) | (Xa = Xb)) <=> ![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))),
% 0.42/0.58      inference(quant_intro,[status(thm)],[77])).
% 0.42/0.58  tff(79,axiom,(![Xa: $i, Xb: $i, Xc: $i] : (((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))) | (Xa = Xb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz3_4')).
% 0.42/0.58  tff(80,plain,
% 0.42/0.58      (![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))),
% 0.42/0.58      inference(modus_ponens,[status(thm)],[79, 78])).
% 0.42/0.58  tff(81,plain,
% 0.42/0.58      (![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))),
% 0.42/0.58      inference(modus_ponens,[status(thm)],[80, 76])).
% 0.42/0.58  tff(82,plain,(
% 0.42/0.58      ![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))),
% 0.42/0.58      inference(skolemize,[status(sab)],[81])).
% 0.42/0.58  tff(83,plain,
% 0.42/0.58      (![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))),
% 0.42/0.58      inference(modus_ponens,[status(thm)],[82, 75])).
% 0.42/0.58  tff(84,plain,
% 0.42/0.58      (((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | ((~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.42/0.58      inference(rewrite,[status(thm)],[])).
% 0.42/0.58  tff(85,plain,
% 0.42/0.58      (((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1))) <=> ((~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.42/0.58      inference(rewrite,[status(thm)],[])).
% 0.42/0.58  tff(86,plain,
% 0.42/0.58      (((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | ((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | ((~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))),
% 0.42/0.58      inference(monotonicity,[status(thm)],[85])).
% 0.42/0.58  tff(87,plain,
% 0.42/0.58      (((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | ((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.42/0.59      inference(transitivity,[status(thm)],[86, 84])).
% 0.42/0.59  tff(88,plain,
% 0.42/0.59      ((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | ((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)))),
% 0.42/0.59      inference(quant_inst,[status(thm)],[])).
% 0.42/0.59  tff(89,plain,
% 0.42/0.59      ((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.42/0.59      inference(modus_ponens,[status(thm)],[88, 87])).
% 0.42/0.59  tff(90,plain,
% 0.42/0.59      ((~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.42/0.59      inference(unit_resolution,[status(thm)],[89, 83])).
% 0.42/0.59  tff(91,plain,
% 0.42/0.59      ((~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.42/0.59      inference(unit_resolution,[status(thm)],[90, 73])).
% 0.42/0.59  tff(92,plain,
% 0.42/0.59      (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)),
% 0.42/0.59      inference(unit_resolution,[status(thm)],[91, 54])).
% 0.42/0.59  tff(93,plain,
% 0.42/0.59      (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1))),
% 0.42/0.59      inference(rewrite,[status(thm)],[])).
% 0.42/0.59  tff(94,plain,
% 0.42/0.59      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1))),
% 0.42/0.59      inference(quant_inst,[status(thm)],[])).
% 0.42/0.59  tff(95,plain,
% 0.42/0.59      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)),
% 0.42/0.59      inference(modus_ponens,[status(thm)],[94, 93])).
% 0.42/0.59  tff(96,plain,
% 0.42/0.59      (~s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.42/0.59      inference(unit_resolution,[status(thm)],[95, 68, 92])).
% 0.42/0.59  tff(97,plain,
% 0.42/0.59      (^[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)))))),
% 0.42/0.59      inference(bind,[status(th)],[])).
% 0.42/0.59  tff(98,plain,
% 0.42/0.59      (![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))))),
% 0.42/0.59      inference(quant_intro,[status(thm)],[97])).
% 0.42/0.59  tff(99,plain,
% 0.42/0.59      (^[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)))))),
% 0.42/0.59      inference(bind,[status(th)],[])).
% 0.42/0.59  tff(100,plain,
% 0.42/0.59      (![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))))),
% 0.42/0.59      inference(quant_intro,[status(thm)],[99])).
% 0.42/0.59  tff(101,plain,
% 0.42/0.59      (![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))),
% 0.42/0.59      inference(rewrite,[status(thm)],[])).
% 0.42/0.59  tff(102,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/sandbox/benchmark/Axioms/GEO011+0.ax','aA4')).
% 0.42/0.59  tff(103,plain,
% 0.42/0.59      (![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))),
% 0.42/0.59      inference(modus_ponens,[status(thm)],[102, 101])).
% 0.42/0.59  tff(104,plain,(
% 0.42/0.59      ![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))),
% 0.42/0.59      inference(skolemize,[status(sab)],[103])).
% 0.42/0.59  tff(105,plain,
% 0.42/0.59      (![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))))),
% 0.42/0.59      inference(modus_ponens,[status(thm)],[104, 100])).
% 0.42/0.59  tff(106,plain,
% 0.42/0.59      (![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))))),
% 0.42/0.59      inference(modus_ponens,[status(thm)],[105, 98])).
% 0.42/0.59  tff(107,plain,
% 0.42/0.59      ((~![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(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))),
% 0.42/0.59      inference(quant_inst,[status(thm)],[])).
% 0.42/0.59  tff(108,plain,
% 0.42/0.59      (~((~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.42/0.59      inference(unit_resolution,[status(thm)],[107, 106])).
% 0.42/0.59  tff(109,plain,
% 0.42/0.59      (((~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.42/0.59      inference(tautology,[status(thm)],[])).
% 0.42/0.59  tff(110,plain,
% 0.42/0.59      (s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.42/0.59      inference(unit_resolution,[status(thm)],[109, 108])).
% 0.42/0.59  tff(111,plain,
% 0.42/0.59      (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : refl((s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))) <=> (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))))),
% 0.42/0.59      inference(bind,[status(th)],[])).
% 0.42/0.59  tff(112,plain,
% 0.42/0.59      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))),
% 0.42/0.59      inference(quant_intro,[status(thm)],[111])).
% 0.42/0.59  tff(113,plain,
% 0.42/0.59      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))),
% 0.42/0.59      inference(rewrite,[status(thm)],[])).
% 0.42/0.59  tff(114,plain,
% 0.42/0.59      (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : trans(monotonicity(rewrite(((~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))) <=> ((~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))), ((((~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xd)) <=> (((~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xd)))), rewrite((((~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xd)) <=> (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))), ((((~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xd)) <=> (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))))),
% 0.42/0.59      inference(bind,[status(th)],[])).
% 0.42/0.59  tff(115,plain,
% 0.42/0.59      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xd)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))),
% 0.42/0.59      inference(quant_intro,[status(thm)],[114])).
% 0.42/0.59  tff(116,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xd))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz3_6b')).
% 0.42/0.59  tff(117,plain,
% 0.42/0.59      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))),
% 0.42/0.59      inference(modus_ponens,[status(thm)],[116, 115])).
% 0.42/0.59  tff(118,plain,
% 0.42/0.59      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))),
% 0.42/0.59      inference(modus_ponens,[status(thm)],[117, 113])).
% 0.42/0.59  tff(119,plain,(
% 0.42/0.59      ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))),
% 0.42/0.59      inference(skolemize,[status(sab)],[118])).
% 0.42/0.59  tff(120,plain,
% 0.42/0.59      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))),
% 0.42/0.59      inference(modus_ponens,[status(thm)],[119, 112])).
% 0.42/0.59  tff(121,plain,
% 0.42/0.59      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))) | ((~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))) | (~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))),
% 0.42/0.59      inference(rewrite,[status(thm)],[])).
% 0.42/0.59  tff(122,plain,
% 0.42/0.59      ((s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))) <=> ((~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))),
% 0.42/0.59      inference(rewrite,[status(thm)],[])).
% 0.42/0.59  tff(123,plain,
% 0.42/0.59      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))) | (s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))) | ((~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))))),
% 0.42/0.59      inference(monotonicity,[status(thm)],[122])).
% 0.42/0.59  tff(124,plain,
% 0.42/0.59      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))) | (s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))) | (~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))),
% 0.42/0.59      inference(transitivity,[status(thm)],[123, 121])).
% 0.42/0.59  tff(125,plain,
% 0.42/0.59      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))) | (s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))),
% 0.42/0.59      inference(quant_inst,[status(thm)],[])).
% 0.42/0.59  tff(126,plain,
% 0.42/0.59      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))) | (~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.42/0.59      inference(modus_ponens,[status(thm)],[125, 124])).
% 0.42/0.59  tff(127,plain,
% 0.42/0.59      (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.42/0.59      inference(unit_resolution,[status(thm)],[126, 120, 110, 96])).
% 0.42/0.59  tff(128,plain,
% 0.42/0.59      (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)) | s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)) | s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.42/0.59      inference(rewrite,[status(thm)],[])).
% 0.42/0.59  tff(129,plain,
% 0.42/0.59      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)) | s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.42/0.59      inference(quant_inst,[status(thm)],[])).
% 0.42/0.59  tff(130,plain,
% 0.42/0.59      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)) | s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.42/0.59      inference(modus_ponens,[status(thm)],[129, 128])).
% 0.42/0.59  tff(131,plain,
% 0.42/0.59      (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)),
% 0.42/0.59      inference(unit_resolution,[status(thm)],[130, 68, 127])).
% 0.42/0.59  tff(132,plain,
% 0.42/0.59      (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : refl((~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb)))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd)))))) <=> (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb)))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd)))))))),
% 0.42/0.59      inference(bind,[status(th)],[])).
% 0.42/0.59  tff(133,plain,
% 0.42/0.59      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb)))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd)))))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb)))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))))),
% 0.42/0.59      inference(quant_intro,[status(thm)],[132])).
% 0.42/0.59  tff(134,plain,
% 0.42/0.59      (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : rewrite((((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd)) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd)))) <=> (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb)))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd)))))))),
% 0.42/0.60      inference(bind,[status(th)],[])).
% 0.42/0.60  tff(135,plain,
% 0.42/0.60      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd)) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd)))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb)))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))))),
% 0.42/0.60      inference(quant_intro,[status(thm)],[134])).
% 0.42/0.60  tff(136,plain,
% 0.42/0.60      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd)) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd)))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd)) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))),
% 0.42/0.60      inference(rewrite,[status(thm)],[])).
% 0.42/0.60  tff(137,plain,
% 0.42/0.60      (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : rewrite(((((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd)))) <=> (((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd)) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd)))))),
% 0.42/0.60      inference(bind,[status(th)],[])).
% 0.42/0.60  tff(138,plain,
% 0.42/0.60      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd)))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd)) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))),
% 0.42/0.60      inference(quant_intro,[status(thm)],[137])).
% 0.42/0.60  tff(139,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz5_5a')).
% 0.42/0.60  tff(140,plain,
% 0.42/0.60      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd)) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))),
% 0.42/0.60      inference(modus_ponens,[status(thm)],[139, 138])).
% 0.42/0.60  tff(141,plain,
% 0.42/0.60      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd)) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))),
% 0.42/0.60      inference(modus_ponens,[status(thm)],[140, 136])).
% 0.42/0.60  tff(142,plain,(
% 0.42/0.60      ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd)) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))),
% 0.42/0.60      inference(skolemize,[status(sab)],[141])).
% 0.42/0.60  tff(143,plain,
% 0.42/0.60      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb)))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))))),
% 0.42/0.60      inference(modus_ponens,[status(thm)],[142, 135])).
% 0.42/0.60  tff(144,plain,
% 0.42/0.60      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb)))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))))),
% 0.42/0.60      inference(modus_ponens,[status(thm)],[143, 133])).
% 0.42/0.60  tff(145,plain,
% 0.42/0.60      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb)))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))))) | (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))))),
% 0.42/0.60      inference(quant_inst,[status(thm)],[])).
% 0.42/0.60  tff(146,plain,
% 0.42/0.60      (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))))),
% 0.42/0.60      inference(unit_resolution,[status(thm)],[145, 144])).
% 0.42/0.60  tff(147,plain,
% 0.42/0.60      (((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))) | ((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.42/0.60      inference(tautology,[status(thm)],[])).
% 0.42/0.60  tff(148,plain,
% 0.42/0.60      ((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.42/0.60      inference(unit_resolution,[status(thm)],[147, 146])).
% 0.42/0.60  tff(149,plain,
% 0.42/0.60      (le(Xc!1, Xd!0, Xa!3, Xb!2)),
% 0.42/0.60      inference(or_elim,[status(thm)],[46])).
% 0.42/0.60  tff(150,plain,
% 0.42/0.60      ((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))) | (~le(Xc!1, Xd!0, Xa!3, Xb!2)) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.42/0.60      inference(tautology,[status(thm)],[])).
% 0.42/0.60  tff(151,plain,
% 0.42/0.60      ((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.42/0.60      inference(unit_resolution,[status(thm)],[150, 149])).
% 0.42/0.60  tff(152,plain,
% 0.42/0.60      (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.42/0.60      inference(unit_resolution,[status(thm)],[151, 148])).
% 0.42/0.60  tff(153,plain,
% 0.42/0.60      (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ins(Xa!3, Xb!2, Xc!1, Xd!0)),
% 0.42/0.60      inference(symmetry,[status(thm)],[152])).
% 0.42/0.60  tff(154,plain,
% 0.42/0.60      (^[Xa: $i, Xb: $i] : refl(s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma)) <=> s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma)))),
% 0.42/0.60      inference(bind,[status(th)],[])).
% 0.42/0.60  tff(155,plain,
% 0.42/0.60      (![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))),
% 0.42/0.60      inference(quant_intro,[status(thm)],[154])).
% 0.42/0.60  tff(156,plain,
% 0.42/0.60      (![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))),
% 0.42/0.60      inference(rewrite,[status(thm)],[])).
% 0.42/0.60  tff(157,axiom,(![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz3_14a')).
% 0.42/0.60  tff(158,plain,
% 0.42/0.60      (![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma))),
% 0.42/0.60      inference(modus_ponens,[status(thm)],[157, 156])).
% 0.42/0.60  tff(159,plain,(
% 0.42/0.60      ![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma))),
% 0.42/0.60      inference(skolemize,[status(sab)],[158])).
% 0.42/0.60  tff(160,plain,
% 0.42/0.60      (![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma))),
% 0.42/0.60      inference(modus_ponens,[status(thm)],[159, 155])).
% 0.42/0.60  tff(161,plain,
% 0.42/0.60      ((~![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma))) | s_t(Xd!0, Xc!1, ext(Xd!0, Xc!1, alpha, gamma))),
% 0.42/0.60      inference(quant_inst,[status(thm)],[])).
% 0.42/0.60  tff(162,plain,
% 0.42/0.60      (s_t(Xd!0, Xc!1, ext(Xd!0, Xc!1, alpha, gamma))),
% 0.42/0.60      inference(unit_resolution,[status(thm)],[161, 160])).
% 0.42/0.60  tff(163,plain,
% 0.42/0.60      (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xd!0, Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xd!0, Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0))),
% 0.42/0.60      inference(rewrite,[status(thm)],[])).
% 0.42/0.60  tff(164,plain,
% 0.42/0.60      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xd!0, Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0))),
% 0.42/0.60      inference(quant_inst,[status(thm)],[])).
% 0.42/0.60  tff(165,plain,
% 0.42/0.60      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xd!0, Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0)),
% 0.42/0.60      inference(modus_ponens,[status(thm)],[164, 163])).
% 0.42/0.60  tff(166,plain,
% 0.42/0.60      (s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0)),
% 0.42/0.60      inference(unit_resolution,[status(thm)],[165, 68, 162])).
% 0.42/0.60  tff(167,plain,
% 0.42/0.60      (s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) <=> s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)),
% 0.42/0.60      inference(monotonicity,[status(thm)],[10])).
% 0.42/0.60  tff(168,plain,
% 0.42/0.60      (s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0) <=> s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)),
% 0.42/0.60      inference(symmetry,[status(thm)],[167])).
% 0.42/0.60  tff(169,plain,
% 0.42/0.60      (s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)),
% 0.42/0.60      inference(modus_ponens,[status(thm)],[61, 168])).
% 0.42/0.60  tff(170,plain,
% 0.42/0.60      (^[Xa: $i, Xb: $i, Xd: $i, Xc: $i] : refl(((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd)) <=> ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd)))),
% 0.42/0.60      inference(bind,[status(th)],[])).
% 0.42/0.60  tff(171,plain,
% 0.42/0.60      (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd)) <=> ![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))),
% 0.42/0.60      inference(quant_intro,[status(thm)],[170])).
% 0.42/0.60  tff(172,plain,
% 0.42/0.60      (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd)) <=> ![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))),
% 0.42/0.60      inference(rewrite,[status(thm)],[])).
% 0.42/0.60  tff(173,plain,
% 0.42/0.60      (^[Xa: $i, Xb: $i, Xd: $i, Xc: $i] : trans(monotonicity(rewrite(((~s_t(Xa, Xb, Xd)) | (~s_t(Xb, Xc, Xd))) <=> ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)))), ((((~s_t(Xa, Xb, Xd)) | (~s_t(Xb, Xc, Xd))) | s_t(Xa, Xc, Xd)) <=> (((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd))) | s_t(Xa, Xc, Xd)))), rewrite((((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd))) | s_t(Xa, Xc, Xd)) <=> ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))), ((((~s_t(Xa, Xb, Xd)) | (~s_t(Xb, Xc, Xd))) | s_t(Xa, Xc, Xd)) <=> ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))))),
% 0.42/0.60      inference(bind,[status(th)],[])).
% 0.42/0.60  tff(174,plain,
% 0.42/0.60      (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (((~s_t(Xa, Xb, Xd)) | (~s_t(Xb, Xc, Xd))) | s_t(Xa, Xc, Xd)) <=> ![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))),
% 0.42/0.60      inference(quant_intro,[status(thm)],[173])).
% 0.42/0.60  tff(175,axiom,(![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (((~s_t(Xa, Xb, Xd)) | (~s_t(Xb, Xc, Xd))) | s_t(Xa, Xc, Xd))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz3_5b')).
% 0.42/0.60  tff(176,plain,
% 0.42/0.60      (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))),
% 0.42/0.60      inference(modus_ponens,[status(thm)],[175, 174])).
% 0.42/0.60  tff(177,plain,
% 0.42/0.60      (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))),
% 0.42/0.60      inference(modus_ponens,[status(thm)],[176, 172])).
% 0.42/0.60  tff(178,plain,(
% 0.42/0.60      ![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))),
% 0.42/0.60      inference(skolemize,[status(sab)],[177])).
% 0.42/0.60  tff(179,plain,
% 0.42/0.60      (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))),
% 0.42/0.60      inference(modus_ponens,[status(thm)],[178, 171])).
% 0.42/0.60  tff(180,plain,
% 0.42/0.60      (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0)))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | (~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0)))),
% 0.42/0.60      inference(rewrite,[status(thm)],[])).
% 0.42/0.60  tff(181,plain,
% 0.42/0.60      (((~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0)) | s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) <=> ((~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0)))),
% 0.42/0.60      inference(rewrite,[status(thm)],[])).
% 0.42/0.60  tff(182,plain,
% 0.42/0.60      (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0)) | s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0))))),
% 0.42/0.60      inference(monotonicity,[status(thm)],[181])).
% 0.42/0.60  tff(183,plain,
% 0.42/0.60      (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0)) | s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | (~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0)))),
% 0.42/0.60      inference(transitivity,[status(thm)],[182, 180])).
% 0.42/0.60  tff(184,plain,
% 0.42/0.60      ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0)) | s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0))),
% 0.42/0.60      inference(quant_inst,[status(thm)],[])).
% 0.42/0.60  tff(185,plain,
% 0.42/0.60      ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | (~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0))),
% 0.42/0.60      inference(modus_ponens,[status(thm)],[184, 183])).
% 0.42/0.60  tff(186,plain,
% 0.42/0.60      (s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)),
% 0.42/0.60      inference(unit_resolution,[status(thm)],[185, 179, 169, 166])).
% 0.42/0.60  tff(187,plain,
% 0.42/0.60      (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.42/0.61      inference(rewrite,[status(thm)],[])).
% 0.42/0.61  tff(188,plain,
% 0.42/0.61      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.42/0.61      inference(quant_inst,[status(thm)],[])).
% 0.42/0.61  tff(189,plain,
% 0.42/0.61      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))),
% 0.42/0.61      inference(modus_ponens,[status(thm)],[188, 187])).
% 0.42/0.61  tff(190,plain,
% 0.42/0.61      (s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))),
% 0.42/0.61      inference(unit_resolution,[status(thm)],[189, 68, 186])).
% 0.42/0.61  tff(191,assumption,(~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)), introduced(assumption)).
% 0.42/0.61  tff(192,assumption,(~(Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))), introduced(assumption)).
% 0.42/0.61  tff(193,assumption,(~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))), introduced(assumption)).
% 0.42/0.61  tff(194,plain,
% 0.42/0.61      (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : refl((s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd))) <=> (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd))))),
% 0.42/0.61      inference(bind,[status(th)],[])).
% 0.42/0.61  tff(195,plain,
% 0.42/0.61      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))),
% 0.42/0.61      inference(quant_intro,[status(thm)],[194])).
% 0.42/0.61  tff(196,plain,
% 0.42/0.61      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))),
% 0.42/0.61      inference(rewrite,[status(thm)],[])).
% 0.42/0.61  tff(197,plain,
% 0.42/0.61      (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((Xa = Xb) | (~s_t(Xa, Xb, Xc))) <=> ((~s_t(Xa, Xb, Xc)) | (Xa = Xb))), ((((Xa = Xb) | (~s_t(Xa, Xb, Xc))) | (~s_t(Xa, Xb, Xd))) <=> (((~s_t(Xa, Xb, Xc)) | (Xa = Xb)) | (~s_t(Xa, Xb, Xd))))), rewrite((((~s_t(Xa, Xb, Xc)) | (Xa = Xb)) | (~s_t(Xa, Xb, Xd))) <=> ((~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))), ((((Xa = Xb) | (~s_t(Xa, Xb, Xc))) | (~s_t(Xa, Xb, Xd))) <=> ((~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd))))), (((((Xa = Xb) | (~s_t(Xa, Xb, Xc))) | (~s_t(Xa, Xb, Xd))) | s_t(Xb, Xc, Xd)) <=> (((~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd))) | s_t(Xb, Xc, Xd)))), rewrite((((~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd))) | s_t(Xb, Xc, Xd)) <=> (s_t(Xb, Xc, Xd) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))), (((((Xa = Xb) | (~s_t(Xa, Xb, Xc))) | (~s_t(Xa, Xb, Xd))) | s_t(Xb, Xc, Xd)) <=> (s_t(Xb, Xc, Xd) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd))))), ((((((Xa = Xb) | (~s_t(Xa, Xb, Xc))) | (~s_t(Xa, Xb, Xd))) | s_t(Xb, Xc, Xd)) | s_t(Xb, Xd, Xc)) <=> ((s_t(Xb, Xc, Xd) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd))) | s_t(Xb, Xd, Xc)))), rewrite(((s_t(Xb, Xc, Xd) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd))) | s_t(Xb, Xd, Xc)) <=> (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))), ((((((Xa = Xb) | (~s_t(Xa, Xb, Xc))) | (~s_t(Xa, Xb, Xd))) | s_t(Xb, Xc, Xd)) | s_t(Xb, Xd, Xc)) <=> (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))))),
% 0.42/0.61      inference(bind,[status(th)],[])).
% 0.42/0.61  tff(198,plain,
% 0.42/0.61      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((((Xa = Xb) | (~s_t(Xa, Xb, Xc))) | (~s_t(Xa, Xb, Xd))) | s_t(Xb, Xc, Xd)) | s_t(Xb, Xd, Xc)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))),
% 0.42/0.61      inference(quant_intro,[status(thm)],[197])).
% 0.42/0.61  tff(199,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((((Xa = Xb) | (~s_t(Xa, Xb, Xc))) | (~s_t(Xa, Xb, Xd))) | s_t(Xb, Xc, Xd)) | s_t(Xb, Xd, Xc))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz5_2')).
% 0.42/0.61  tff(200,plain,
% 0.42/0.61      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))),
% 0.42/0.61      inference(modus_ponens,[status(thm)],[199, 198])).
% 0.42/0.61  tff(201,plain,
% 0.42/0.61      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))),
% 0.42/0.61      inference(modus_ponens,[status(thm)],[200, 196])).
% 0.42/0.61  tff(202,plain,(
% 0.42/0.61      ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))),
% 0.42/0.61      inference(skolemize,[status(sab)],[201])).
% 0.42/0.61  tff(203,plain,
% 0.42/0.61      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))),
% 0.42/0.61      inference(modus_ponens,[status(thm)],[202, 195])).
% 0.42/0.61  tff(204,plain,
% 0.42/0.61      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))) | ((~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))),
% 0.42/0.61      inference(rewrite,[status(thm)],[])).
% 0.42/0.61  tff(205,plain,
% 0.42/0.61      ((s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))) <=> ((~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))),
% 0.42/0.61      inference(rewrite,[status(thm)],[])).
% 0.42/0.61  tff(206,plain,
% 0.42/0.61      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))) | (s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))) | ((~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))))),
% 0.42/0.61      inference(monotonicity,[status(thm)],[205])).
% 0.42/0.61  tff(207,plain,
% 0.42/0.61      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))) | (s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))),
% 0.42/0.61      inference(transitivity,[status(thm)],[206, 204])).
% 0.42/0.61  tff(208,plain,
% 0.42/0.61      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))) | (s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))),
% 0.42/0.61      inference(quant_inst,[status(thm)],[])).
% 0.42/0.61  tff(209,plain,
% 0.42/0.61      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.42/0.61      inference(modus_ponens,[status(thm)],[208, 207])).
% 0.42/0.62  tff(210,plain,
% 0.42/0.62      ((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.42/0.62      inference(unit_resolution,[status(thm)],[209, 203, 73, 193])).
% 0.42/0.62  tff(211,plain,
% 0.42/0.62      (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.42/0.62      inference(unit_resolution,[status(thm)],[210, 192, 191])).
% 0.42/0.62  tff(212,plain,
% 0.42/0.62      (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.42/0.62      inference(rewrite,[status(thm)],[])).
% 0.42/0.62  tff(213,plain,
% 0.42/0.62      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.42/0.62      inference(quant_inst,[status(thm)],[])).
% 0.42/0.62  tff(214,plain,
% 0.42/0.62      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.42/0.62      inference(modus_ponens,[status(thm)],[213, 212])).
% 0.42/0.62  tff(215,plain,
% 0.42/0.62      (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)),
% 0.42/0.62      inference(unit_resolution,[status(thm)],[214, 68, 211])).
% 0.42/0.62  tff(216,plain,
% 0.42/0.62      (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1))),
% 0.42/0.62      inference(rewrite,[status(thm)],[])).
% 0.42/0.62  tff(217,plain,
% 0.42/0.62      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1))),
% 0.42/0.62      inference(quant_inst,[status(thm)],[])).
% 0.42/0.62  tff(218,plain,
% 0.42/0.62      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)),
% 0.42/0.62      inference(modus_ponens,[status(thm)],[217, 216])).
% 0.42/0.62  tff(219,plain,
% 0.42/0.62      ((~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)),
% 0.42/0.62      inference(unit_resolution,[status(thm)],[218, 68])).
% 0.42/0.62  tff(220,plain,
% 0.42/0.62      (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)),
% 0.42/0.62      inference(unit_resolution,[status(thm)],[219, 110])).
% 0.42/0.62  tff(221,plain,
% 0.42/0.62      (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1))),
% 0.42/0.62      inference(rewrite,[status(thm)],[])).
% 0.42/0.62  tff(222,plain,
% 0.42/0.62      ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1))),
% 0.42/0.62      inference(quant_inst,[status(thm)],[])).
% 0.42/0.62  tff(223,plain,
% 0.42/0.62      ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)),
% 0.42/0.62      inference(modus_ponens,[status(thm)],[222, 221])).
% 0.42/0.62  tff(224,plain,
% 0.42/0.62      ((~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)),
% 0.42/0.62      inference(unit_resolution,[status(thm)],[223, 179, 220])).
% 0.42/0.62  tff(225,plain,
% 0.42/0.62      (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)),
% 0.42/0.62      inference(unit_resolution,[status(thm)],[224, 73])).
% 0.42/0.62  tff(226,plain,
% 0.42/0.62      (^[Xa: $i, Xb: $i, Xd: $i, Xc: $i] : refl((s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd))) <=> (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd))))),
% 0.42/0.62      inference(bind,[status(th)],[])).
% 0.42/0.62  tff(227,plain,
% 0.42/0.62      (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd))) <=> ![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))),
% 0.42/0.62      inference(quant_intro,[status(thm)],[226])).
% 0.42/0.62  tff(228,plain,
% 0.42/0.62      (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd))) <=> ![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))),
% 0.42/0.62      inference(rewrite,[status(thm)],[])).
% 0.42/0.62  tff(229,plain,
% 0.42/0.62      (^[Xa: $i, Xb: $i, Xd: $i, Xc: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) <=> ((~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd)))), ((((~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xc)) <=> (((~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xc)))), rewrite((((~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xc)) <=> (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd)))), ((((~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xc)) <=> (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))))), (((((~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xb)) <=> ((s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xc, Xb)))), rewrite(((s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xc, Xb)) <=> (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))), (((((~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xb)) <=> (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))))),
% 0.42/0.62      inference(bind,[status(th)],[])).
% 0.42/0.62  tff(230,plain,
% 0.42/0.62      (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((((~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xb)) <=> ![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))),
% 0.42/0.62      inference(quant_intro,[status(thm)],[229])).
% 0.42/0.62  tff(231,axiom,(![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((((~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz5_3')).
% 0.42/0.62  tff(232,plain,
% 0.42/0.62      (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))),
% 0.42/0.62      inference(modus_ponens,[status(thm)],[231, 230])).
% 0.42/0.62  tff(233,plain,
% 0.42/0.62      (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))),
% 0.42/0.62      inference(modus_ponens,[status(thm)],[232, 228])).
% 0.42/0.62  tff(234,plain,(
% 0.42/0.62      ![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))),
% 0.42/0.62      inference(skolemize,[status(sab)],[233])).
% 0.42/0.62  tff(235,plain,
% 0.42/0.62      (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))),
% 0.42/0.62      inference(modus_ponens,[status(thm)],[234, 227])).
% 0.42/0.62  tff(236,plain,
% 0.42/0.62      (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))) | ((~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.42/0.62      inference(rewrite,[status(thm)],[])).
% 0.42/0.62  tff(237,plain,
% 0.42/0.62      ((s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1))) <=> ((~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.42/0.62      inference(rewrite,[status(thm)],[])).
% 0.42/0.62  tff(238,plain,
% 0.42/0.62      (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))) | (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))) | ((~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))),
% 0.42/0.62      inference(monotonicity,[status(thm)],[237])).
% 0.42/0.62  tff(239,plain,
% 0.42/0.62      (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))) | (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.42/0.62      inference(transitivity,[status(thm)],[238, 236])).
% 0.42/0.62  tff(240,plain,
% 0.42/0.62      ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))) | (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)))),
% 0.42/0.62      inference(quant_inst,[status(thm)],[])).
% 0.42/0.62  tff(241,plain,
% 0.42/0.62      ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.42/0.62      inference(modus_ponens,[status(thm)],[240, 239])).
% 0.42/0.62  tff(242,plain,
% 0.42/0.62      (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.42/0.62      inference(unit_resolution,[status(thm)],[241, 235, 220, 225, 215])).
% 0.42/0.62  tff(243,plain,
% 0.42/0.62      (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : refl(((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd)) <=> ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd)))),
% 0.42/0.62      inference(bind,[status(th)],[])).
% 0.42/0.62  tff(244,plain,
% 0.42/0.62      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))),
% 0.42/0.62      inference(quant_intro,[status(thm)],[243])).
% 0.42/0.62  tff(245,plain,
% 0.42/0.62      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))),
% 0.42/0.62      inference(rewrite,[status(thm)],[])).
% 0.42/0.62  tff(246,plain,
% 0.42/0.62      (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xc, Xd))) <=> ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)))), ((((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xc, Xd))) | (Xb = Xc)) <=> (((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc))) | (Xb = Xc)))), rewrite((((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc))) | (Xb = Xc)) <=> ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)))), ((((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xc, Xd))) | (Xb = Xc)) <=> ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc))))), (((((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xc, Xd))) | (Xb = Xc)) | s_t(Xa, Xc, Xd)) <=> (((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc))) | s_t(Xa, Xc, Xd)))), rewrite((((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc))) | s_t(Xa, Xc, Xd)) <=> ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))), (((((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xc, Xd))) | (Xb = Xc)) | s_t(Xa, Xc, Xd)) <=> ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))))),
% 0.42/0.63      inference(bind,[status(th)],[])).
% 0.42/0.63  tff(247,plain,
% 0.42/0.63      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xc, Xd))) | (Xb = Xc)) | s_t(Xa, Xc, Xd)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))),
% 0.42/0.63      inference(quant_intro,[status(thm)],[246])).
% 0.42/0.63  tff(248,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xc, Xd))) | (Xb = Xc)) | s_t(Xa, Xc, Xd))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz3_7a')).
% 0.42/0.63  tff(249,plain,
% 0.42/0.63      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))),
% 0.42/0.63      inference(modus_ponens,[status(thm)],[248, 247])).
% 0.42/0.63  tff(250,plain,
% 0.42/0.63      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))),
% 0.42/0.63      inference(modus_ponens,[status(thm)],[249, 245])).
% 0.42/0.63  tff(251,plain,(
% 0.42/0.63      ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))),
% 0.42/0.63      inference(skolemize,[status(sab)],[250])).
% 0.42/0.63  tff(252,plain,
% 0.42/0.63      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))),
% 0.42/0.63      inference(modus_ponens,[status(thm)],[251, 244])).
% 0.42/0.63  tff(253,plain,
% 0.42/0.63      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))) | ((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.42/0.63      inference(rewrite,[status(thm)],[])).
% 0.42/0.63  tff(254,plain,
% 0.42/0.63      (((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) <=> ((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.42/0.63      inference(rewrite,[status(thm)],[])).
% 0.42/0.63  tff(255,plain,
% 0.47/0.63      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))) | ((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))) | ((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))))),
% 0.47/0.63      inference(monotonicity,[status(thm)],[254])).
% 0.47/0.63  tff(256,plain,
% 0.47/0.63      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))) | ((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.47/0.63      inference(transitivity,[status(thm)],[255, 253])).
% 0.47/0.63  tff(257,plain,
% 0.47/0.63      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))) | ((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.47/0.63      inference(quant_inst,[status(thm)],[])).
% 0.47/0.63  tff(258,plain,
% 0.47/0.63      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))),
% 0.47/0.63      inference(modus_ponens,[status(thm)],[257, 256])).
% 0.47/0.63  tff(259,plain,
% 0.47/0.63      (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))),
% 0.47/0.63      inference(unit_resolution,[status(thm)],[258, 252, 192, 242, 190])).
% 0.47/0.63  tff(260,plain,
% 0.47/0.63      ((~![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(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (~s_e(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xa!3, Xb!2))))),
% 0.47/0.63      inference(quant_inst,[status(thm)],[])).
% 0.47/0.63  tff(261,plain,
% 0.47/0.63      (~((~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (~s_e(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xa!3, Xb!2)))),
% 0.47/0.63      inference(unit_resolution,[status(thm)],[260, 106])).
% 0.47/0.63  tff(262,plain,
% 0.47/0.63      (((~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (~s_e(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xa!3, Xb!2))) | s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.47/0.63      inference(tautology,[status(thm)],[])).
% 0.47/0.63  tff(263,plain,
% 0.47/0.63      (s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.47/0.63      inference(unit_resolution,[status(thm)],[262, 261])).
% 0.47/0.63  tff(264,plain,
% 0.47/0.63      (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.47/0.63      inference(rewrite,[status(thm)],[])).
% 0.47/0.63  tff(265,plain,
% 0.47/0.63      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.47/0.63      inference(quant_inst,[status(thm)],[])).
% 0.47/0.63  tff(266,plain,
% 0.47/0.63      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))),
% 0.47/0.63      inference(modus_ponens,[status(thm)],[265, 264])).
% 0.47/0.63  tff(267,plain,
% 0.47/0.63      (s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))),
% 0.47/0.63      inference(unit_resolution,[status(thm)],[266, 68, 263])).
% 0.47/0.63  tff(268,plain,
% 0.47/0.63      (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))))),
% 0.47/0.63      inference(rewrite,[status(thm)],[])).
% 0.47/0.63  tff(269,plain,
% 0.47/0.63      (((~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) <=> (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))))),
% 0.47/0.63      inference(rewrite,[status(thm)],[])).
% 0.47/0.63  tff(270,plain,
% 0.47/0.63      (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))))),
% 0.47/0.64      inference(monotonicity,[status(thm)],[269])).
% 0.47/0.64  tff(271,plain,
% 0.47/0.64      (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))))),
% 0.47/0.64      inference(transitivity,[status(thm)],[270, 268])).
% 0.47/0.64  tff(272,plain,
% 0.47/0.64      ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.47/0.64      inference(quant_inst,[status(thm)],[])).
% 0.47/0.64  tff(273,plain,
% 0.47/0.64      ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.47/0.64      inference(modus_ponens,[status(thm)],[272, 271])).
% 0.47/0.64  tff(274,plain,
% 0.47/0.64      (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))),
% 0.47/0.64      inference(unit_resolution,[status(thm)],[273, 179, 267, 259])).
% 0.47/0.64  tff(275,plain,
% 0.47/0.64      (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.47/0.64      inference(rewrite,[status(thm)],[])).
% 0.47/0.64  tff(276,plain,
% 0.47/0.64      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.47/0.64      inference(quant_inst,[status(thm)],[])).
% 0.47/0.64  tff(277,plain,
% 0.47/0.64      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.47/0.64      inference(modus_ponens,[status(thm)],[276, 275])).
% 0.47/0.64  tff(278,plain,
% 0.47/0.64      (s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.47/0.64      inference(unit_resolution,[status(thm)],[277, 68, 274])).
% 0.47/0.64  tff(279,plain,
% 0.47/0.64      ((Xc!1 = ext(Xd!0, Xc!1, alpha, gamma)) <=> (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1)),
% 0.47/0.64      inference(commutativity,[status(thm)],[])).
% 0.47/0.64  tff(280,plain,
% 0.47/0.64      ((~(Xc!1 = ext(Xd!0, Xc!1, alpha, gamma))) <=> (~(ext(Xd!0, Xc!1, alpha, gamma) = Xc!1))),
% 0.47/0.64      inference(monotonicity,[status(thm)],[279])).
% 0.47/0.64  tff(281,plain,
% 0.47/0.64      (^[Xb: $i, Xa: $i] : refl((~(Xb = ext(Xa, Xb, alpha, gamma))) <=> (~(Xb = ext(Xa, Xb, alpha, gamma))))),
% 0.47/0.64      inference(bind,[status(th)],[])).
% 0.47/0.64  tff(282,plain,
% 0.47/0.64      (![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma))) <=> ![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma)))),
% 0.47/0.64      inference(quant_intro,[status(thm)],[281])).
% 0.47/0.64  tff(283,plain,
% 0.47/0.64      (![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma))) <=> ![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma)))),
% 0.47/0.64      inference(rewrite,[status(thm)],[])).
% 0.47/0.64  tff(284,axiom,(![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz3_14b')).
% 0.47/0.64  tff(285,plain,
% 0.47/0.64      (![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma)))),
% 0.47/0.64      inference(modus_ponens,[status(thm)],[284, 283])).
% 0.47/0.64  tff(286,plain,(
% 0.47/0.64      ![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma)))),
% 0.47/0.64      inference(skolemize,[status(sab)],[285])).
% 0.47/0.64  tff(287,plain,
% 0.47/0.64      (![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma)))),
% 0.47/0.64      inference(modus_ponens,[status(thm)],[286, 282])).
% 0.47/0.64  tff(288,plain,
% 0.47/0.64      ((~![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma)))) | (~(Xc!1 = ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.47/0.64      inference(quant_inst,[status(thm)],[])).
% 0.47/0.64  tff(289,plain,
% 0.47/0.64      (~(Xc!1 = ext(Xd!0, Xc!1, alpha, gamma))),
% 0.47/0.64      inference(unit_resolution,[status(thm)],[288, 287])).
% 0.47/0.64  tff(290,plain,
% 0.47/0.64      (~(ext(Xd!0, Xc!1, alpha, gamma) = Xc!1)),
% 0.47/0.64      inference(modus_ponens,[status(thm)],[289, 280])).
% 0.47/0.64  tff(291,plain,
% 0.47/0.64      (s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2) <=> s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2)),
% 0.47/0.64      inference(monotonicity,[status(thm)],[153])).
% 0.47/0.64  tff(292,plain,
% 0.47/0.64      (s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2) <=> s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)),
% 0.47/0.64      inference(symmetry,[status(thm)],[291])).
% 0.47/0.64  tff(293,plain,
% 0.47/0.64      (((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))) | ((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2))),
% 0.47/0.64      inference(tautology,[status(thm)],[])).
% 0.47/0.64  tff(294,plain,
% 0.47/0.64      ((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2)),
% 0.47/0.64      inference(unit_resolution,[status(thm)],[293, 146])).
% 0.47/0.64  tff(295,plain,
% 0.47/0.64      ((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2))) | (~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2)),
% 0.47/0.64      inference(tautology,[status(thm)],[])).
% 0.47/0.64  tff(296,plain,
% 0.47/0.64      ((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2))) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2)),
% 0.47/0.64      inference(unit_resolution,[status(thm)],[295, 149])).
% 0.47/0.64  tff(297,plain,
% 0.47/0.64      (s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2)),
% 0.47/0.64      inference(unit_resolution,[status(thm)],[296, 294])).
% 0.47/0.64  tff(298,plain,
% 0.47/0.64      (s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)),
% 0.47/0.64      inference(modus_ponens,[status(thm)],[297, 292])).
% 0.47/0.64  tff(299,plain,
% 0.47/0.64      (^[Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : refl(((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa)) <=> ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa)))),
% 0.47/0.64      inference(bind,[status(th)],[])).
% 0.47/0.64  tff(300,plain,
% 0.47/0.64      (![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa)) <=> ![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))),
% 0.47/0.64      inference(quant_intro,[status(thm)],[299])).
% 0.47/0.64  tff(301,plain,
% 0.47/0.64      (![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa)) <=> ![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))),
% 0.47/0.64      inference(rewrite,[status(thm)],[])).
% 0.47/0.64  tff(302,plain,
% 0.47/0.64      (^[Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : trans(monotonicity(trans(monotonicity(rewrite(((Xq = Xa) | (~s_t(Xq, Xa, Xd))) <=> ((~s_t(Xq, Xa, Xd)) | (Xq = Xa))), ((((Xq = Xa) | (~s_t(Xq, Xa, Xd))) | (~s_e(Xa, Xd, Xb, Xc))) <=> (((~s_t(Xq, Xa, Xd)) | (Xq = Xa)) | (~s_e(Xa, Xd, Xb, Xc))))), rewrite((((~s_t(Xq, Xa, Xd)) | (Xq = Xa)) | (~s_e(Xa, Xd, Xb, Xc))) <=> ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xq = Xa))), ((((Xq = Xa) | (~s_t(Xq, Xa, Xd))) | (~s_e(Xa, Xd, Xb, Xc))) <=> ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xq = Xa)))), (((((Xq = Xa) | (~s_t(Xq, Xa, Xd))) | (~s_e(Xa, Xd, Xb, Xc))) | (Xd = ext(Xq, Xa, Xb, Xc))) <=> (((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xq = Xa)) | (Xd = ext(Xq, Xa, Xb, Xc))))), rewrite((((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xq = Xa)) | (Xd = ext(Xq, Xa, Xb, Xc))) <=> ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))), (((((Xq = Xa) | (~s_t(Xq, Xa, Xd))) | (~s_e(Xa, Xd, Xb, Xc))) | (Xd = ext(Xq, Xa, Xb, Xc))) <=> ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))))),
% 0.47/0.64      inference(bind,[status(th)],[])).
% 0.47/0.64  tff(303,plain,
% 0.47/0.64      (![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((((Xq = Xa) | (~s_t(Xq, Xa, Xd))) | (~s_e(Xa, Xd, Xb, Xc))) | (Xd = ext(Xq, Xa, Xb, Xc))) <=> ![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))),
% 0.47/0.64      inference(quant_intro,[status(thm)],[302])).
% 0.47/0.64  tff(304,axiom,(![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((((Xq = Xa) | (~s_t(Xq, Xa, Xd))) | (~s_e(Xa, Xd, Xb, Xc))) | (Xd = ext(Xq, Xa, Xb, Xc)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz2_12')).
% 0.47/0.64  tff(305,plain,
% 0.47/0.64      (![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))),
% 0.47/0.64      inference(modus_ponens,[status(thm)],[304, 303])).
% 0.47/0.64  tff(306,plain,
% 0.47/0.64      (![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))),
% 0.47/0.64      inference(modus_ponens,[status(thm)],[305, 301])).
% 0.47/0.64  tff(307,plain,(
% 0.47/0.64      ![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))),
% 0.47/0.64      inference(skolemize,[status(sab)],[306])).
% 0.47/0.64  tff(308,plain,
% 0.47/0.64      (![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))),
% 0.47/0.64      inference(modus_ponens,[status(thm)],[307, 300])).
% 0.47/0.64  tff(309,plain,
% 0.47/0.64      (((~![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))) | ((~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1))) <=> ((~![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1))),
% 0.48/0.65      inference(rewrite,[status(thm)],[])).
% 0.48/0.65  tff(310,plain,
% 0.48/0.65      (((~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1)) <=> ((~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1))),
% 0.48/0.65      inference(rewrite,[status(thm)],[])).
% 0.48/0.65  tff(311,plain,
% 0.48/0.65      (((~![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))) | ((~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1))) <=> ((~![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))) | ((~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1)))),
% 0.48/0.65      inference(monotonicity,[status(thm)],[310])).
% 0.48/0.65  tff(312,plain,
% 0.48/0.65      (((~![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))) | ((~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1))) <=> ((~![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1))),
% 0.48/0.65      inference(transitivity,[status(thm)],[311, 309])).
% 0.48/0.65  tff(313,plain,
% 0.48/0.65      ((~![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))) | ((~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1))),
% 0.48/0.65      inference(quant_inst,[status(thm)],[])).
% 0.48/0.65  tff(314,plain,
% 0.48/0.65      ((~![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1)),
% 0.48/0.65      inference(modus_ponens,[status(thm)],[313, 312])).
% 0.48/0.65  tff(315,plain,
% 0.48/0.65      ((~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1)),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[314, 308, 298])).
% 0.48/0.65  tff(316,plain,
% 0.48/0.65      ((~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[315, 290])).
% 0.48/0.65  tff(317,plain,
% 0.48/0.65      (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[316, 278])).
% 0.48/0.65  tff(318,plain,
% 0.48/0.65      (ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.48/0.65      inference(symmetry,[status(thm)],[317])).
% 0.48/0.65  tff(319,plain,
% 0.48/0.65      (ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2) = ins(Xa!3, Xb!2, Xc!1, Xd!0)),
% 0.48/0.65      inference(transitivity,[status(thm)],[318, 153])).
% 0.48/0.65  tff(320,plain,
% 0.48/0.65      (s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) <=> s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.48/0.65      inference(monotonicity,[status(thm)],[319])).
% 0.48/0.65  tff(321,plain,
% 0.48/0.65      (s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0)) <=> s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.48/0.65      inference(symmetry,[status(thm)],[320])).
% 0.48/0.65  tff(322,plain,
% 0.48/0.65      (((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))) | ((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0)))),
% 0.48/0.65      inference(tautology,[status(thm)],[])).
% 0.48/0.65  tff(323,plain,
% 0.48/0.65      ((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[322, 146])).
% 0.48/0.65  tff(324,plain,
% 0.48/0.65      ((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.48/0.65      inference(tautology,[status(thm)],[])).
% 0.48/0.65  tff(325,plain,
% 0.48/0.65      ((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0)))) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[324, 149])).
% 0.48/0.65  tff(326,plain,
% 0.48/0.65      (s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[325, 323])).
% 0.48/0.65  tff(327,plain,
% 0.48/0.65      (s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.48/0.65      inference(modus_ponens,[status(thm)],[326, 321])).
% 0.48/0.65  tff(328,plain,
% 0.48/0.65      (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[91, 192])).
% 0.48/0.65  tff(329,plain,
% 0.48/0.65      (~s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[95, 68, 328])).
% 0.48/0.65  tff(330,plain,
% 0.48/0.65      ($false),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[329, 327])).
% 0.48/0.65  tff(331,plain,((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.65  tff(332,plain,
% 0.48/0.65      (s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[331, 131, 54])).
% 0.48/0.65  tff(333,plain,
% 0.48/0.65      (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.48/0.65      inference(rewrite,[status(thm)],[])).
% 0.48/0.65  tff(334,plain,
% 0.48/0.65      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.48/0.65      inference(quant_inst,[status(thm)],[])).
% 0.48/0.65  tff(335,plain,
% 0.48/0.65      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.48/0.65      inference(modus_ponens,[status(thm)],[334, 333])).
% 0.48/0.65  tff(336,plain,
% 0.48/0.65      (s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[335, 68, 225])).
% 0.48/0.65  tff(337,plain,
% 0.48/0.65      (((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | ((ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2) = Xc!1) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | (ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2) = Xc!1) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))),
% 0.48/0.65      inference(rewrite,[status(thm)],[])).
% 0.48/0.65  tff(338,plain,
% 0.48/0.65      ((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | ((ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2) = Xc!1) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))),
% 0.48/0.65      inference(quant_inst,[status(thm)],[])).
% 0.48/0.65  tff(339,plain,
% 0.48/0.65      ((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | (ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2) = Xc!1) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.48/0.65      inference(modus_ponens,[status(thm)],[338, 337])).
% 0.48/0.65  tff(340,plain,
% 0.48/0.65      ((ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2) = Xc!1) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[339, 83, 336])).
% 0.48/0.65  tff(341,plain,
% 0.48/0.65      (ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2) = Xc!1),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[340, 332])).
% 0.48/0.65  tff(342,plain,
% 0.48/0.65      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb)))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))))) | (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xa!3, Xb!2, ins(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))))))),
% 0.48/0.66      inference(quant_inst,[status(thm)],[])).
% 0.48/0.66  tff(343,plain,
% 0.48/0.66      (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xa!3, Xb!2, ins(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)))))),
% 0.48/0.66      inference(unit_resolution,[status(thm)],[342, 144])).
% 0.48/0.66  tff(344,plain,
% 0.48/0.66      (((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xa!3, Xb!2, ins(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))))) | ((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)))),
% 0.48/0.66      inference(tautology,[status(thm)],[])).
% 0.48/0.66  tff(345,plain,
% 0.48/0.66      ((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.48/0.66      inference(unit_resolution,[status(thm)],[344, 343])).
% 0.48/0.66  tff(346,plain,
% 0.48/0.66      ((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)))) | (~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.48/0.66      inference(tautology,[status(thm)],[])).
% 0.48/0.66  tff(347,plain,
% 0.48/0.66      ((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)))) | (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.48/0.66      inference(unit_resolution,[status(thm)],[346, 47])).
% 0.48/0.66  tff(348,plain,
% 0.48/0.66      (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)),
% 0.48/0.66      inference(unit_resolution,[status(thm)],[347, 345])).
% 0.48/0.66  tff(349,plain,
% 0.48/0.66      (ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0) = ins(Xc!1, Xd!0, Xa!3, Xb!2)),
% 0.48/0.66      inference(symmetry,[status(thm)],[348])).
% 0.48/0.66  tff(350,plain,
% 0.48/0.66      (s_e(Xb!2, Xa!3, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) <=> s_e(Xb!2, Xa!3, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1)),
% 0.48/0.66      inference(monotonicity,[status(thm)],[10, 341])).
% 0.48/0.66  tff(351,plain,
% 0.48/0.66      (s_e(Xb!2, Xa!3, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1) <=> s_e(Xb!2, Xa!3, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.48/0.66      inference(symmetry,[status(thm)],[350])).
% 0.48/0.66  tff(352,plain,
% 0.48/0.66      (^[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)))),
% 0.48/0.66      inference(bind,[status(th)],[])).
% 0.48/0.66  tff(353,plain,
% 0.48/0.66      (![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))),
% 0.48/0.66      inference(quant_intro,[status(thm)],[352])).
% 0.48/0.66  tff(354,plain,
% 0.48/0.66      (![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))),
% 0.48/0.66      inference(rewrite,[status(thm)],[])).
% 0.48/0.66  tff(355,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')).
% 0.48/0.66  tff(356,plain,
% 0.48/0.66      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))),
% 0.48/0.66      inference(modus_ponens,[status(thm)],[355, 354])).
% 0.48/0.66  tff(357,plain,(
% 0.48/0.66      ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))),
% 0.48/0.66      inference(skolemize,[status(sab)],[356])).
% 0.48/0.66  tff(358,plain,
% 0.48/0.66      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))),
% 0.48/0.66      inference(modus_ponens,[status(thm)],[357, 353])).
% 0.48/0.66  tff(359,plain,
% 0.48/0.66      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | ((~s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))) | s_e(Xb!2, Xa!3, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | (~s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))) | s_e(Xb!2, Xa!3, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1))),
% 0.48/0.66      inference(rewrite,[status(thm)],[])).
% 0.48/0.66  tff(360,plain,
% 0.48/0.66      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | ((~s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))) | s_e(Xb!2, Xa!3, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1))),
% 0.48/0.66      inference(quant_inst,[status(thm)],[])).
% 0.48/0.66  tff(361,plain,
% 0.48/0.66      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | (~s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))) | s_e(Xb!2, Xa!3, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1)),
% 0.48/0.66      inference(modus_ponens,[status(thm)],[360, 359])).
% 0.48/0.66  tff(362,plain,
% 0.48/0.66      (s_e(Xb!2, Xa!3, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1)),
% 0.48/0.66      inference(unit_resolution,[status(thm)],[361, 358, 50])).
% 0.48/0.66  tff(363,plain,
% 0.48/0.66      (s_e(Xb!2, Xa!3, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.48/0.66      inference(modus_ponens,[status(thm)],[362, 351])).
% 0.48/0.66  tff(364,plain,
% 0.48/0.66      (^[Xb: $i, Xc: $i, Xa: $i] : refl(((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc)) <=> ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc)))),
% 0.48/0.66      inference(bind,[status(th)],[])).
% 0.48/0.66  tff(365,plain,
% 0.48/0.66      (![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))),
% 0.48/0.66      inference(quant_intro,[status(thm)],[364])).
% 0.48/0.66  tff(366,plain,
% 0.48/0.66      (![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))),
% 0.48/0.66      inference(rewrite,[status(thm)],[])).
% 0.48/0.66  tff(367,axiom,(![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz2_13')).
% 0.48/0.66  tff(368,plain,
% 0.48/0.66      (![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))),
% 0.48/0.66      inference(modus_ponens,[status(thm)],[367, 366])).
% 0.48/0.66  tff(369,plain,(
% 0.48/0.66      ![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))),
% 0.48/0.66      inference(skolemize,[status(sab)],[368])).
% 0.48/0.66  tff(370,plain,
% 0.48/0.66      (![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))),
% 0.48/0.66      inference(modus_ponens,[status(thm)],[369, 365])).
% 0.48/0.66  tff(371,plain,
% 0.48/0.66      (((~![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))) | ((~s_e(Xb!2, Xa!3, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (Xb!2 = Xa!3))) <=> ((~![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))) | (~s_e(Xb!2, Xa!3, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (Xb!2 = Xa!3))),
% 0.48/0.66      inference(rewrite,[status(thm)],[])).
% 0.48/0.66  tff(372,plain,
% 0.48/0.66      ((~![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))) | ((~s_e(Xb!2, Xa!3, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (Xb!2 = Xa!3))),
% 0.48/0.66      inference(quant_inst,[status(thm)],[])).
% 0.48/0.66  tff(373,plain,
% 0.48/0.66      ((~![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))) | (~s_e(Xb!2, Xa!3, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (Xb!2 = Xa!3)),
% 0.48/0.66      inference(modus_ponens,[status(thm)],[372, 371])).
% 0.48/0.66  tff(374,plain,
% 0.48/0.66      ((~s_e(Xb!2, Xa!3, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (Xb!2 = Xa!3)),
% 0.48/0.66      inference(unit_resolution,[status(thm)],[373, 370])).
% 0.48/0.66  tff(375,plain,
% 0.48/0.66      (Xb!2 = Xa!3),
% 0.48/0.66      inference(unit_resolution,[status(thm)],[374, 363])).
% 0.48/0.66  tff(376,plain,
% 0.48/0.66      (Xa!3 = Xb!2),
% 0.48/0.66      inference(symmetry,[status(thm)],[375])).
% 0.48/0.66  tff(377,plain,
% 0.48/0.66      ((~![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb))) | (insert(Xc!1, Xd!0, Xa!3, Xb!2) = ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0))),
% 0.48/0.66      inference(quant_inst,[status(thm)],[])).
% 0.48/0.66  tff(378,plain,
% 0.48/0.66      (insert(Xc!1, Xd!0, Xa!3, Xb!2) = ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0)),
% 0.48/0.66      inference(unit_resolution,[status(thm)],[377, 7])).
% 0.48/0.66  tff(379,plain,
% 0.48/0.66      (ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0) = insert(Xc!1, Xd!0, Xa!3, Xb!2)),
% 0.48/0.66      inference(symmetry,[status(thm)],[378])).
% 0.48/0.66  tff(380,plain,
% 0.48/0.66      (s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3) <=> s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.48/0.66      inference(monotonicity,[status(thm)],[379, 376])).
% 0.48/0.66  tff(381,plain,
% 0.48/0.66      (s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) <=> s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)),
% 0.48/0.66      inference(symmetry,[status(thm)],[380])).
% 0.48/0.66  tff(382,plain,
% 0.48/0.66      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~(le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2)) | (~s_t(Xa!3, Xb!2, Xb!2))))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~(le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2)) | (~s_t(Xa!3, Xb!2, Xb!2)))))))),
% 0.48/0.66      inference(rewrite,[status(thm)],[])).
% 0.48/0.66  tff(383,plain,
% 0.48/0.66      ((~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~((~s_t(Xa!3, Xb!2, Xb!2)) | le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2)))))) <=> (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~(le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2)) | (~s_t(Xa!3, Xb!2, Xb!2))))))),
% 0.48/0.66      inference(rewrite,[status(thm)],[])).
% 0.48/0.66  tff(384,plain,
% 0.48/0.66      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~((~s_t(Xa!3, Xb!2, Xb!2)) | le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2))))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~(le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2)) | (~s_t(Xa!3, Xb!2, Xb!2)))))))),
% 0.48/0.66      inference(monotonicity,[status(thm)],[383])).
% 0.48/0.66  tff(385,plain,
% 0.48/0.66      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~((~s_t(Xa!3, Xb!2, Xb!2)) | le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2))))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~(le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2)) | (~s_t(Xa!3, Xb!2, Xb!2)))))))),
% 0.48/0.66      inference(transitivity,[status(thm)],[384, 382])).
% 0.48/0.66  tff(386,plain,
% 0.48/0.66      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~((~s_t(Xa!3, Xb!2, Xb!2)) | le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2))))))),
% 0.48/0.66      inference(quant_inst,[status(thm)],[])).
% 0.48/0.66  tff(387,plain,
% 0.48/0.66      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~(le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2)) | (~s_t(Xa!3, Xb!2, Xb!2))))))),
% 0.48/0.66      inference(modus_ponens,[status(thm)],[386, 385])).
% 0.48/0.66  tff(388,plain,
% 0.48/0.66      (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~(le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2)) | (~s_t(Xa!3, Xb!2, Xb!2)))))),
% 0.48/0.66      inference(unit_resolution,[status(thm)],[387, 27])).
% 0.48/0.66  tff(389,plain,
% 0.48/0.66      (((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~(le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2)) | (~s_t(Xa!3, Xb!2, Xb!2))))) | ((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.48/0.66      inference(tautology,[status(thm)],[])).
% 0.48/0.66  tff(390,plain,
% 0.48/0.66      ((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.48/0.66      inference(unit_resolution,[status(thm)],[389, 388])).
% 0.48/0.66  tff(391,plain,
% 0.48/0.66      ((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.48/0.66      inference(tautology,[status(thm)],[])).
% 0.48/0.66  tff(392,plain,
% 0.48/0.66      ((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.48/0.66      inference(unit_resolution,[status(thm)],[391, 149])).
% 0.48/0.66  tff(393,plain,
% 0.48/0.66      (s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.48/0.66      inference(unit_resolution,[status(thm)],[392, 390])).
% 0.48/0.66  tff(394,plain,
% 0.48/0.66      (s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)),
% 0.48/0.66      inference(modus_ponens,[status(thm)],[393, 381])).
% 0.48/0.66  tff(395,plain,
% 0.48/0.66      (^[X: $i, Y: $i] : refl(((~s_t(X, Y, X)) | (X = Y)) <=> ((~s_t(X, Y, X)) | (X = Y)))),
% 0.48/0.66      inference(bind,[status(th)],[])).
% 0.48/0.66  tff(396,plain,
% 0.48/0.66      (![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y)) <=> ![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y))),
% 0.48/0.66      inference(quant_intro,[status(thm)],[395])).
% 0.48/0.66  tff(397,plain,
% 0.48/0.67      (![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y)) <=> ![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y))),
% 0.48/0.67      inference(rewrite,[status(thm)],[])).
% 0.48/0.67  tff(398,axiom,(![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO011+0.ax','aA6')).
% 0.48/0.67  tff(399,plain,
% 0.48/0.67      (![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y))),
% 0.48/0.67      inference(modus_ponens,[status(thm)],[398, 397])).
% 0.48/0.67  tff(400,plain,(
% 0.48/0.67      ![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y))),
% 0.48/0.67      inference(skolemize,[status(sab)],[399])).
% 0.48/0.67  tff(401,plain,
% 0.48/0.67      (![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y))),
% 0.48/0.67      inference(modus_ponens,[status(thm)],[400, 396])).
% 0.48/0.67  tff(402,plain,
% 0.48/0.67      (((~![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y))) | ((~s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | (Xa!3 = ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0)))) <=> ((~![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y))) | (~s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | (Xa!3 = ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0)))),
% 0.48/0.67      inference(rewrite,[status(thm)],[])).
% 0.48/0.67  tff(403,plain,
% 0.48/0.67      ((~![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y))) | ((~s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | (Xa!3 = ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0)))),
% 0.48/0.67      inference(quant_inst,[status(thm)],[])).
% 0.48/0.67  tff(404,plain,
% 0.48/0.67      ((~![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y))) | (~s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | (Xa!3 = ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0))),
% 0.48/0.67      inference(modus_ponens,[status(thm)],[403, 402])).
% 0.48/0.67  tff(405,plain,
% 0.48/0.67      (Xa!3 = ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0)),
% 0.48/0.67      inference(unit_resolution,[status(thm)],[404, 401, 394])).
% 0.48/0.67  tff(406,plain,
% 0.48/0.67      (ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0) = Xa!3),
% 0.48/0.67      inference(symmetry,[status(thm)],[405])).
% 0.48/0.67  tff(407,plain,
% 0.48/0.67      (s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) <=> s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0)),
% 0.48/0.67      inference(monotonicity,[status(thm)],[406, 349, 341])).
% 0.48/0.67  tff(408,plain,
% 0.48/0.67      (s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0) <=> s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)),
% 0.48/0.67      inference(symmetry,[status(thm)],[407])).
% 0.48/0.67  tff(409,plain,
% 0.48/0.67      (((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xa!3, Xb!2, ins(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))))) | ((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0))),
% 0.48/0.67      inference(tautology,[status(thm)],[])).
% 0.48/0.67  tff(410,plain,
% 0.48/0.67      ((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0)),
% 0.48/0.67      inference(unit_resolution,[status(thm)],[409, 343])).
% 0.48/0.67  tff(411,plain,
% 0.48/0.67      ((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0))) | (~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0)),
% 0.48/0.67      inference(tautology,[status(thm)],[])).
% 0.48/0.67  tff(412,plain,
% 0.48/0.67      ((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0))) | s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0)),
% 0.48/0.67      inference(unit_resolution,[status(thm)],[411, 47])).
% 0.48/0.67  tff(413,plain,
% 0.48/0.67      (s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0)),
% 0.48/0.67      inference(unit_resolution,[status(thm)],[412, 410])).
% 0.48/0.67  tff(414,plain,
% 0.48/0.67      (s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)),
% 0.48/0.67      inference(modus_ponens,[status(thm)],[413, 408])).
% 0.48/0.67  tff(415,plain,
% 0.48/0.67      (s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) <=> s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.48/0.67      inference(monotonicity,[status(thm)],[341, 153])).
% 0.48/0.67  tff(416,plain,
% 0.48/0.67      (s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0)) <=> s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.48/0.67      inference(symmetry,[status(thm)],[415])).
% 0.48/0.67  tff(417,plain,
% 0.48/0.67      (s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.48/0.67      inference(modus_ponens,[status(thm)],[326, 416])).
% 0.48/0.67  tff(418,plain,
% 0.48/0.67      (s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)) <=> s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.48/0.67      inference(monotonicity,[status(thm)],[375])).
% 0.48/0.67  tff(419,plain,
% 0.48/0.67      (s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)) <=> s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.48/0.67      inference(symmetry,[status(thm)],[418])).
% 0.48/0.67  tff(420,plain,
% 0.48/0.67      (s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2) <=> s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.48/0.67      inference(monotonicity,[status(thm)],[379])).
% 0.48/0.67  tff(421,plain,
% 0.48/0.67      (s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) <=> s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)),
% 0.48/0.67      inference(symmetry,[status(thm)],[420])).
% 0.48/0.67  tff(422,plain,
% 0.48/0.67      (s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)),
% 0.48/0.67      inference(modus_ponens,[status(thm)],[393, 421])).
% 0.48/0.67  tff(423,plain,
% 0.48/0.67      (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)) | s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)) | s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3))),
% 0.48/0.67      inference(rewrite,[status(thm)],[])).
% 0.48/0.67  tff(424,plain,
% 0.48/0.67      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)) | s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3))),
% 0.48/0.67      inference(quant_inst,[status(thm)],[])).
% 0.48/0.67  tff(425,plain,
% 0.48/0.67      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)) | s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)),
% 0.48/0.67      inference(modus_ponens,[status(thm)],[424, 423])).
% 0.48/0.67  tff(426,plain,
% 0.48/0.67      ((~s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)) | s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)),
% 0.48/0.67      inference(unit_resolution,[status(thm)],[425, 68])).
% 0.48/0.67  tff(427,plain,
% 0.48/0.67      (s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)),
% 0.48/0.67      inference(unit_resolution,[status(thm)],[426, 422])).
% 0.48/0.67  tff(428,plain,
% 0.48/0.67      ((~![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(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))))),
% 0.48/0.67      inference(quant_inst,[status(thm)],[])).
% 0.48/0.67  tff(429,plain,
% 0.48/0.67      (~((~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)))),
% 0.48/0.67      inference(unit_resolution,[status(thm)],[428, 106])).
% 0.48/0.67  tff(430,plain,
% 0.48/0.67      (((~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.48/0.67      inference(tautology,[status(thm)],[])).
% 0.48/0.67  tff(431,plain,
% 0.48/0.67      (s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.48/0.67      inference(unit_resolution,[status(thm)],[430, 429])).
% 0.48/0.67  tff(432,plain,
% 0.48/0.67      (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xb!2, Xa!3))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xb!2, Xa!3))),
% 0.48/0.67      inference(rewrite,[status(thm)],[])).
% 0.48/0.67  tff(433,plain,
% 0.48/0.67      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xb!2, Xa!3))),
% 0.48/0.67      inference(quant_inst,[status(thm)],[])).
% 0.48/0.67  tff(434,plain,
% 0.48/0.67      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xb!2, Xa!3)),
% 0.48/0.67      inference(modus_ponens,[status(thm)],[433, 432])).
% 0.48/0.67  tff(435,plain,
% 0.48/0.67      ((~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xb!2, Xa!3)),
% 0.48/0.67      inference(unit_resolution,[status(thm)],[434, 68])).
% 0.48/0.67  tff(436,plain,
% 0.48/0.67      (s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xb!2, Xa!3)),
% 0.48/0.67      inference(unit_resolution,[status(thm)],[435, 431])).
% 0.48/0.67  tff(437,plain,
% 0.48/0.67      (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | (~s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xb!2, Xa!3)) | s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | (~s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xb!2, Xa!3)) | s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3))),
% 0.48/0.67      inference(rewrite,[status(thm)],[])).
% 0.48/0.67  tff(438,plain,
% 0.48/0.67      ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | (~s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xb!2, Xa!3)) | s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3))),
% 0.48/0.67      inference(quant_inst,[status(thm)],[])).
% 0.48/0.67  tff(439,plain,
% 0.48/0.67      ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | (~s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xb!2, Xa!3)) | s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)),
% 0.48/0.67      inference(modus_ponens,[status(thm)],[438, 437])).
% 0.48/0.67  tff(440,plain,
% 0.48/0.67      (s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)),
% 0.48/0.67      inference(unit_resolution,[status(thm)],[439, 179, 436, 427])).
% 0.48/0.67  tff(441,plain,
% 0.48/0.67      (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)))),
% 0.48/0.68      inference(rewrite,[status(thm)],[])).
% 0.48/0.68  tff(442,plain,
% 0.48/0.68      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)))),
% 0.48/0.68      inference(quant_inst,[status(thm)],[])).
% 0.48/0.68  tff(443,plain,
% 0.48/0.68      ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.48/0.68      inference(modus_ponens,[status(thm)],[442, 441])).
% 0.48/0.68  tff(444,plain,
% 0.48/0.68      (s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.48/0.68      inference(unit_resolution,[status(thm)],[443, 68, 440])).
% 0.48/0.68  tff(445,plain,
% 0.48/0.68      (s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.48/0.68      inference(modus_ponens,[status(thm)],[444, 419])).
% 0.48/0.68  tff(446,plain,
% 0.48/0.68      (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : refl(((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc)) <=> ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc)))),
% 0.48/0.68      inference(bind,[status(th)],[])).
% 0.48/0.68  tff(447,plain,
% 0.48/0.68      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))),
% 0.48/0.68      inference(quant_intro,[status(thm)],[446])).
% 0.48/0.68  tff(448,plain,
% 0.48/0.68      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))),
% 0.48/0.68      inference(rewrite,[status(thm)],[])).
% 0.48/0.68  tff(449,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz2_5')).
% 0.48/0.68  tff(450,plain,
% 0.48/0.68      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))),
% 0.48/0.68      inference(modus_ponens,[status(thm)],[449, 448])).
% 0.48/0.68  tff(451,plain,(
% 0.48/0.68      ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))),
% 0.48/0.68      inference(skolemize,[status(sab)],[450])).
% 0.48/0.68  tff(452,plain,
% 0.48/0.68      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))),
% 0.48/0.68      inference(modus_ponens,[status(thm)],[451, 447])).
% 0.48/0.68  tff(453,plain,
% 0.48/0.68      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | ((~s_e(Xa!3, Xb!2, Xd!0, Xc!1)) | s_e(Xa!3, Xb!2, Xc!1, Xd!0))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | (~s_e(Xa!3, Xb!2, Xd!0, Xc!1)) | s_e(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.48/0.68      inference(rewrite,[status(thm)],[])).
% 0.48/0.68  tff(454,plain,
% 0.48/0.68      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | ((~s_e(Xa!3, Xb!2, Xd!0, Xc!1)) | s_e(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.48/0.68      inference(quant_inst,[status(thm)],[])).
% 0.48/0.68  tff(455,plain,
% 0.48/0.68      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | (~s_e(Xa!3, Xb!2, Xd!0, Xc!1)) | s_e(Xa!3, Xb!2, Xc!1, Xd!0)),
% 0.48/0.68      inference(modus_ponens,[status(thm)],[454, 453])).
% 0.48/0.68  tff(456,plain,
% 0.48/0.68      (~s_e(Xa!3, Xb!2, Xd!0, Xc!1)),
% 0.48/0.68      inference(unit_resolution,[status(thm)],[455, 452, 52])).
% 0.48/0.68  tff(457,plain,
% 0.48/0.68      (^[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)))),
% 0.48/0.68      inference(bind,[status(th)],[])).
% 0.48/0.68  tff(458,plain,
% 0.48/0.68      (![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))),
% 0.48/0.68      inference(quant_intro,[status(thm)],[457])).
% 0.48/0.68  tff(459,plain,
% 0.48/0.68      (![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))),
% 0.48/0.68      inference(rewrite,[status(thm)],[])).
% 0.48/0.68  tff(460,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz2_2')).
% 0.48/0.68  tff(461,plain,
% 0.48/0.68      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))),
% 0.48/0.68      inference(modus_ponens,[status(thm)],[460, 459])).
% 0.48/0.68  tff(462,plain,(
% 0.48/0.68      ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))),
% 0.48/0.68      inference(skolemize,[status(sab)],[461])).
% 0.48/0.68  tff(463,plain,
% 0.48/0.68      (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))),
% 0.48/0.68      inference(modus_ponens,[status(thm)],[462, 458])).
% 0.48/0.68  tff(464,plain,
% 0.48/0.68      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | ((~s_e(Xd!0, Xc!1, Xa!3, Xb!2)) | s_e(Xa!3, Xb!2, Xd!0, Xc!1))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | (~s_e(Xd!0, Xc!1, Xa!3, Xb!2)) | s_e(Xa!3, Xb!2, Xd!0, Xc!1))),
% 0.48/0.68      inference(rewrite,[status(thm)],[])).
% 0.48/0.68  tff(465,plain,
% 0.48/0.68      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | ((~s_e(Xd!0, Xc!1, Xa!3, Xb!2)) | s_e(Xa!3, Xb!2, Xd!0, Xc!1))),
% 0.48/0.68      inference(quant_inst,[status(thm)],[])).
% 0.48/0.68  tff(466,plain,
% 0.48/0.68      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | (~s_e(Xd!0, Xc!1, Xa!3, Xb!2)) | s_e(Xa!3, Xb!2, Xd!0, Xc!1)),
% 0.48/0.68      inference(modus_ponens,[status(thm)],[465, 464])).
% 0.48/0.68  tff(467,plain,
% 0.48/0.68      (~s_e(Xd!0, Xc!1, Xa!3, Xb!2)),
% 0.48/0.68      inference(unit_resolution,[status(thm)],[466, 463, 456])).
% 0.48/0.68  tff(468,plain,
% 0.48/0.68      (^[X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : refl((s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V))) <=> (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V))))),
% 0.48/0.68      inference(bind,[status(th)],[])).
% 0.48/0.68  tff(469,plain,
% 0.48/0.68      (![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V))) <=> ![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))),
% 0.48/0.68      inference(quant_intro,[status(thm)],[468])).
% 0.48/0.68  tff(470,plain,
% 0.48/0.68      (![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V))) <=> ![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))),
% 0.48/0.68      inference(rewrite,[status(thm)],[])).
% 0.48/0.68  tff(471,plain,
% 0.48/0.68      (^[X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : trans(monotonicity(rewrite(((~s_e(X, Y, Z, V)) | (~s_e(X, Y, Z2, V2))) <=> ((~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))), ((((~s_e(X, Y, Z, V)) | (~s_e(X, Y, Z2, V2))) | s_e(Z, V, Z2, V2)) <=> (((~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V))) | s_e(Z, V, Z2, V2)))), rewrite((((~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V))) | s_e(Z, V, Z2, V2)) <=> (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))), ((((~s_e(X, Y, Z, V)) | (~s_e(X, Y, Z2, V2))) | s_e(Z, V, Z2, V2)) <=> (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))))),
% 0.48/0.68      inference(bind,[status(th)],[])).
% 0.48/0.68  tff(472,plain,
% 0.48/0.68      (![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (((~s_e(X, Y, Z, V)) | (~s_e(X, Y, Z2, V2))) | s_e(Z, V, Z2, V2)) <=> ![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))),
% 0.48/0.68      inference(quant_intro,[status(thm)],[471])).
% 0.48/0.68  tff(473,axiom,(![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (((~s_e(X, Y, Z, V)) | (~s_e(X, Y, Z2, V2))) | s_e(Z, V, Z2, V2))), file('/export/starexec/sandbox/benchmark/Axioms/GEO011+0.ax','aA2')).
% 0.48/0.68  tff(474,plain,
% 0.48/0.68      (![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))),
% 0.48/0.68      inference(modus_ponens,[status(thm)],[473, 472])).
% 0.48/0.68  tff(475,plain,
% 0.48/0.68      (![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))),
% 0.48/0.68      inference(modus_ponens,[status(thm)],[474, 470])).
% 0.48/0.68  tff(476,plain,(
% 0.48/0.68      ![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))),
% 0.48/0.68      inference(skolemize,[status(sab)],[475])).
% 0.48/0.68  tff(477,plain,
% 0.48/0.68      (![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))),
% 0.48/0.68      inference(modus_ponens,[status(thm)],[476, 469])).
% 0.48/0.68  tff(478,plain,
% 0.48/0.68      (((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | (s_e(Xd!0, Xc!1, Xa!3, Xb!2) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)))) <=> ((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | s_e(Xd!0, Xc!1, Xa!3, Xb!2) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)))),
% 0.48/0.68      inference(rewrite,[status(thm)],[])).
% 0.48/0.68  tff(479,plain,
% 0.48/0.68      ((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | (s_e(Xd!0, Xc!1, Xa!3, Xb!2) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)))),
% 0.48/0.68      inference(quant_inst,[status(thm)],[])).
% 0.48/0.68  tff(480,plain,
% 0.48/0.68      ((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | s_e(Xd!0, Xc!1, Xa!3, Xb!2) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1))),
% 0.48/0.68      inference(modus_ponens,[status(thm)],[479, 478])).
% 0.48/0.68  tff(481,plain,
% 0.48/0.68      (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)),
% 0.48/0.68      inference(unit_resolution,[status(thm)],[480, 477, 467, 298])).
% 0.48/0.68  tff(482,plain,
% 0.48/0.68      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | ((~s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0)) | s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | (~s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0)) | s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1))),
% 0.48/0.68      inference(rewrite,[status(thm)],[])).
% 0.48/0.68  tff(483,plain,
% 0.48/0.68      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | ((~s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0)) | s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1))),
% 0.48/0.68      inference(quant_inst,[status(thm)],[])).
% 0.48/0.68  tff(484,plain,
% 0.48/0.68      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | (~s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0)) | s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)),
% 0.48/0.68      inference(modus_ponens,[status(thm)],[483, 482])).
% 0.48/0.68  tff(485,plain,
% 0.48/0.68      (~s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0)),
% 0.48/0.68      inference(unit_resolution,[status(thm)],[484, 358, 481])).
% 0.48/0.68  tff(486,plain,
% 0.48/0.68      (s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0) <=> s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0)),
% 0.48/0.68      inference(monotonicity,[status(thm)],[349])).
% 0.48/0.68  tff(487,plain,
% 0.48/0.68      (s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0) <=> s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)),
% 0.48/0.68      inference(symmetry,[status(thm)],[486])).
% 0.48/0.68  tff(488,plain,
% 0.48/0.68      (s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)),
% 0.48/0.68      inference(modus_ponens,[status(thm)],[413, 487])).
% 0.48/0.68  tff(489,plain,
% 0.48/0.68      (((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | ((~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)) | s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)))) <=> ((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)) | s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)))),
% 0.48/0.68      inference(rewrite,[status(thm)],[])).
% 0.48/0.68  tff(490,plain,
% 0.48/0.68      ((s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1))) <=> ((~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)) | s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)))),
% 0.48/0.68      inference(rewrite,[status(thm)],[])).
% 0.48/0.68  tff(491,plain,
% 0.48/0.68      (((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | (s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)))) <=> ((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | ((~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)) | s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1))))),
% 0.48/0.68      inference(monotonicity,[status(thm)],[490])).
% 0.48/0.68  tff(492,plain,
% 0.48/0.68      (((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | (s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)))) <=> ((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)) | s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)))),
% 0.48/0.68      inference(transitivity,[status(thm)],[491, 489])).
% 0.48/0.68  tff(493,plain,
% 0.48/0.68      ((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | (s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)))),
% 0.48/0.68      inference(quant_inst,[status(thm)],[])).
% 0.48/0.68  tff(494,plain,
% 0.48/0.68      ((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)) | s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1))),
% 0.48/0.68      inference(modus_ponens,[status(thm)],[493, 492])).
% 0.48/0.69  tff(495,plain,
% 0.48/0.69      (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)),
% 0.48/0.69      inference(unit_resolution,[status(thm)],[494, 477, 488, 485])).
% 0.48/0.69  tff(496,plain,
% 0.48/0.69      (s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1) <=> s_e(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1)),
% 0.48/0.69      inference(monotonicity,[status(thm)],[10])).
% 0.48/0.69  tff(497,plain,
% 0.48/0.69      (s_e(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1) <=> s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)),
% 0.48/0.69      inference(symmetry,[status(thm)],[496])).
% 0.48/0.69  tff(498,plain,
% 0.48/0.69      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | ((~s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))) | s_e(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | (~s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))) | s_e(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1))),
% 0.48/0.69      inference(rewrite,[status(thm)],[])).
% 0.48/0.69  tff(499,plain,
% 0.48/0.69      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | ((~s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))) | s_e(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1))),
% 0.48/0.69      inference(quant_inst,[status(thm)],[])).
% 0.48/0.69  tff(500,plain,
% 0.48/0.69      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | (~s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))) | s_e(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1)),
% 0.48/0.69      inference(modus_ponens,[status(thm)],[499, 498])).
% 0.48/0.69  tff(501,plain,
% 0.48/0.69      (s_e(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1)),
% 0.48/0.69      inference(unit_resolution,[status(thm)],[500, 452, 50])).
% 0.48/0.69  tff(502,plain,
% 0.48/0.69      (s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)),
% 0.48/0.69      inference(modus_ponens,[status(thm)],[501, 497])).
% 0.48/0.69  tff(503,plain,
% 0.48/0.69      (^[Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : refl(((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB))) <=> ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB))))),
% 0.48/0.69      inference(bind,[status(th)],[])).
% 0.48/0.69  tff(504,plain,
% 0.48/0.69      (![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB))) <=> ![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))),
% 0.48/0.69      inference(quant_intro,[status(thm)],[503])).
% 0.48/0.69  tff(505,plain,
% 0.48/0.69      (![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB))) <=> ![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))),
% 0.48/0.69      inference(rewrite,[status(thm)],[])).
% 0.48/0.69  tff(506,plain,
% 0.48/0.69      (^[Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~s_t(Xa, Xb, Xc)) | (~s_t(XA, XB, XC))) <=> ((~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)))), ((((~s_t(Xa, Xb, Xc)) | (~s_t(XA, XB, XC))) | (~s_e(Xa, Xb, XB, XC))) <=> (((~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc))) | (~s_e(Xa, Xb, XB, XC))))), rewrite((((~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc))) | (~s_e(Xa, Xb, XB, XC))) <=> ((~s_e(Xa, Xb, XB, XC)) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)))), ((((~s_t(Xa, Xb, Xc)) | (~s_t(XA, XB, XC))) | (~s_e(Xa, Xb, XB, XC))) <=> ((~s_e(Xa, Xb, XB, XC)) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc))))), (((((~s_t(Xa, Xb, Xc)) | (~s_t(XA, XB, XC))) | (~s_e(Xa, Xb, XB, XC))) | (~s_e(Xb, Xc, XA, XB))) <=> (((~s_e(Xa, Xb, XB, XC)) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc))) | (~s_e(Xb, Xc, XA, XB))))), rewrite((((~s_e(Xa, Xb, XB, XC)) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc))) | (~s_e(Xb, Xc, XA, XB))) <=> ((~s_e(Xa, Xb, XB, XC)) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))), (((((~s_t(Xa, Xb, Xc)) | (~s_t(XA, XB, XC))) | (~s_e(Xa, Xb, XB, XC))) | (~s_e(Xb, Xc, XA, XB))) <=> ((~s_e(Xa, Xb, XB, XC)) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB))))), ((((((~s_t(Xa, Xb, Xc)) | (~s_t(XA, XB, XC))) | (~s_e(Xa, Xb, XB, XC))) | (~s_e(Xb, Xc, XA, XB))) | s_e(Xa, Xc, XA, XC)) <=> (((~s_e(Xa, Xb, XB, XC)) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB))) | s_e(Xa, Xc, XA, XC)))), rewrite((((~s_e(Xa, Xb, XB, XC)) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB))) | s_e(Xa, Xc, XA, XC)) <=> ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))), ((((((~s_t(Xa, Xb, Xc)) | (~s_t(XA, XB, XC))) | (~s_e(Xa, Xb, XB, XC))) | (~s_e(Xb, Xc, XA, XB))) | s_e(Xa, Xc, XA, XC)) <=> ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))))),
% 0.48/0.69      inference(bind,[status(th)],[])).
% 0.48/0.69  tff(507,plain,
% 0.48/0.69      (![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : (((((~s_t(Xa, Xb, Xc)) | (~s_t(XA, XB, XC))) | (~s_e(Xa, Xb, XB, XC))) | (~s_e(Xb, Xc, XA, XB))) | s_e(Xa, Xc, XA, XC)) <=> ![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))),
% 0.48/0.69      inference(quant_intro,[status(thm)],[506])).
% 0.48/0.69  tff(508,axiom,(![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : (((((~s_t(Xa, Xb, Xc)) | (~s_t(XA, XB, XC))) | (~s_e(Xa, Xb, XB, XC))) | (~s_e(Xb, Xc, XA, XB))) | s_e(Xa, Xc, XA, XC))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz2_15')).
% 0.48/0.69  tff(509,plain,
% 0.48/0.69      (![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))),
% 0.48/0.69      inference(modus_ponens,[status(thm)],[508, 507])).
% 0.48/0.69  tff(510,plain,
% 0.48/0.69      (![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))),
% 0.48/0.69      inference(modus_ponens,[status(thm)],[509, 505])).
% 0.48/0.69  tff(511,plain,(
% 0.48/0.69      ![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))),
% 0.48/0.69      inference(skolemize,[status(sab)],[510])).
% 0.48/0.69  tff(512,plain,
% 0.48/0.69      (![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))),
% 0.48/0.69      inference(modus_ponens,[status(thm)],[511, 504])).
% 0.48/0.69  tff(513,plain,
% 0.48/0.69      (((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | ((~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | (~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))),
% 0.48/0.69      inference(rewrite,[status(thm)],[])).
% 0.48/0.69  tff(514,plain,
% 0.48/0.69      (((~s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))) <=> ((~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))),
% 0.48/0.69      inference(rewrite,[status(thm)],[])).
% 0.48/0.69  tff(515,plain,
% 0.48/0.69      (((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | ((~s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | ((~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))))),
% 0.48/0.69      inference(monotonicity,[status(thm)],[514])).
% 0.48/0.69  tff(516,plain,
% 0.48/0.69      (((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | ((~s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | (~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))),
% 0.48/0.70      inference(transitivity,[status(thm)],[515, 513])).
% 0.48/0.70  tff(517,plain,
% 0.48/0.70      ((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | ((~s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))),
% 0.48/0.70      inference(quant_inst,[status(thm)],[])).
% 0.48/0.70  tff(518,plain,
% 0.48/0.70      ((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | (~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.48/0.70      inference(modus_ponens,[status(thm)],[517, 516])).
% 0.48/0.70  tff(519,plain,
% 0.48/0.70      (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.48/0.70      inference(unit_resolution,[status(thm)],[518, 512, 431, 502, 225, 495])).
% 0.48/0.70  tff(520,plain,
% 0.48/0.70      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | ((~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.48/0.70      inference(rewrite,[status(thm)],[])).
% 0.48/0.70  tff(521,plain,
% 0.48/0.70      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | ((~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.48/0.70      inference(quant_inst,[status(thm)],[])).
% 0.48/0.70  tff(522,plain,
% 0.48/0.70      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.48/0.70      inference(modus_ponens,[status(thm)],[521, 520])).
% 0.48/0.70  tff(523,plain,
% 0.48/0.70      (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.48/0.70      inference(unit_resolution,[status(thm)],[522, 452, 519])).
% 0.48/0.70  tff(524,plain,
% 0.48/0.70      (s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2) <=> s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.48/0.70      inference(monotonicity,[status(thm)],[379])).
% 0.48/0.70  tff(525,plain,
% 0.48/0.70      (s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) <=> s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)),
% 0.48/0.70      inference(symmetry,[status(thm)],[524])).
% 0.48/0.70  tff(526,plain,
% 0.48/0.70      (((~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.48/0.70      inference(tautology,[status(thm)],[])).
% 0.48/0.70  tff(527,plain,
% 0.48/0.70      (s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.48/0.70      inference(unit_resolution,[status(thm)],[526, 108])).
% 0.48/0.70  tff(528,plain,
% 0.48/0.70      (s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)),
% 0.48/0.70      inference(modus_ponens,[status(thm)],[527, 525])).
% 0.48/0.70  tff(529,plain,
% 0.48/0.70      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | ((~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)) | s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | (~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)) | s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0)))),
% 0.48/0.70      inference(rewrite,[status(thm)],[])).
% 0.48/0.70  tff(530,plain,
% 0.48/0.70      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | ((~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)) | s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0)))),
% 0.48/0.70      inference(quant_inst,[status(thm)],[])).
% 0.48/0.70  tff(531,plain,
% 0.48/0.70      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | (~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)) | s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0))),
% 0.48/0.70      inference(modus_ponens,[status(thm)],[530, 529])).
% 0.48/0.70  tff(532,plain,
% 0.48/0.70      ((~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)) | s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0))),
% 0.48/0.70      inference(unit_resolution,[status(thm)],[531, 452])).
% 0.48/0.70  tff(533,plain,
% 0.48/0.70      (s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0))),
% 0.48/0.70      inference(unit_resolution,[status(thm)],[532, 528])).
% 0.48/0.70  tff(534,plain,
% 0.48/0.70      (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | ((~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0))) | s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | (~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0))) | s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.48/0.70      inference(rewrite,[status(thm)],[])).
% 0.48/0.70  tff(535,plain,
% 0.48/0.70      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | ((~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0))) | s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.48/0.70      inference(quant_inst,[status(thm)],[])).
% 0.48/0.70  tff(536,plain,
% 0.48/0.70      ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | (~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0))) | s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.48/0.70      inference(modus_ponens,[status(thm)],[535, 534])).
% 0.48/0.70  tff(537,plain,
% 0.48/0.70      (s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.48/0.70      inference(unit_resolution,[status(thm)],[536, 463, 533])).
% 0.48/0.70  tff(538,plain,
% 0.48/0.70      (((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | (s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | (~s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | (~s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))),
% 0.48/0.70      inference(rewrite,[status(thm)],[])).
% 0.48/0.70  tff(539,plain,
% 0.48/0.70      (((~s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0))) <=> (s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | (~s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))),
% 0.48/0.71      inference(rewrite,[status(thm)],[])).
% 0.48/0.71  tff(540,plain,
% 0.48/0.71      (((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | ((~s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | (s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | (~s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))))),
% 0.48/0.71      inference(monotonicity,[status(thm)],[539])).
% 0.48/0.71  tff(541,plain,
% 0.48/0.71      (((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | ((~s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | (~s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))),
% 0.55/0.72      inference(transitivity,[status(thm)],[540, 538])).
% 0.55/0.72  tff(542,plain,
% 0.55/0.72      ((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | ((~s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)))),
% 0.55/0.72      inference(quant_inst,[status(thm)],[])).
% 0.55/0.72  tff(543,plain,
% 0.55/0.72      ((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | (~s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.55/0.72      inference(modus_ponens,[status(thm)],[542, 541])).
% 0.55/0.72  tff(544,plain,
% 0.55/0.72      ((~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0))),
% 0.55/0.72      inference(unit_resolution,[status(thm)],[543, 512, 537, 523])).
% 0.55/0.72  tff(545,plain,
% 0.55/0.72      (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)),
% 0.55/0.72      inference(unit_resolution,[status(thm)],[544, 445, 417])).
% 0.55/0.72  tff(546,plain,
% 0.55/0.72      ($false),
% 0.55/0.72      inference(unit_resolution,[status(thm)],[545, 414])).
% 0.55/0.72  % SZS output end Proof
% 0.55/0.72  % E exiting
%------------------------------------------------------------------------------