TSTP Solution File: LCL084-10 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL084-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 : 600s
% DateTime : Sun Jul 17 13:43:53 EDT 2022
% Result : Unsatisfiable 95.13s 95.46s
% Output : Refutation 95.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL084-10 : TPTP v8.1.0. Released v7.5.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.36 % Computer : n004.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jul 4 16:50:37 EDT 2022
% 0.15/0.36 % CPUTime :
% 93.24/93.55 ============================== Prover9 ===============================
% 93.24/93.55 Prover9 (32) version 2009-11A, November 2009.
% 93.24/93.55 Process 16277 was started by sandbox on n004.cluster.edu,
% 93.24/93.55 Mon Jul 4 16:50:38 2022
% 93.24/93.55 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_16124_n004.cluster.edu".
% 93.24/93.55 ============================== end of head ===========================
% 93.24/93.55
% 93.24/93.55 ============================== INPUT =================================
% 93.24/93.55
% 93.24/93.55 % Reading from file /tmp/Prover9_16124_n004.cluster.edu
% 93.24/93.55
% 93.24/93.55 set(prolog_style_variables).
% 93.24/93.55 set(auto2).
% 93.24/93.55 % set(auto2) -> set(auto).
% 93.24/93.55 % set(auto) -> set(auto_inference).
% 93.24/93.55 % set(auto) -> set(auto_setup).
% 93.24/93.55 % set(auto_setup) -> set(predicate_elim).
% 93.24/93.55 % set(auto_setup) -> assign(eq_defs, unfold).
% 93.24/93.55 % set(auto) -> set(auto_limits).
% 93.24/93.55 % set(auto_limits) -> assign(max_weight, "100.000").
% 93.24/93.55 % set(auto_limits) -> assign(sos_limit, 20000).
% 93.24/93.55 % set(auto) -> set(auto_denials).
% 93.24/93.55 % set(auto) -> set(auto_process).
% 93.24/93.55 % set(auto2) -> assign(new_constants, 1).
% 93.24/93.55 % set(auto2) -> assign(fold_denial_max, 3).
% 93.24/93.55 % set(auto2) -> assign(max_weight, "200.000").
% 93.24/93.55 % set(auto2) -> assign(max_hours, 1).
% 93.24/93.55 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 93.24/93.55 % set(auto2) -> assign(max_seconds, 0).
% 93.24/93.55 % set(auto2) -> assign(max_minutes, 5).
% 93.24/93.55 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 93.24/93.55 % set(auto2) -> set(sort_initial_sos).
% 93.24/93.55 % set(auto2) -> assign(sos_limit, -1).
% 93.24/93.55 % set(auto2) -> assign(lrs_ticks, 3000).
% 93.24/93.55 % set(auto2) -> assign(max_megs, 400).
% 93.24/93.55 % set(auto2) -> assign(stats, some).
% 93.24/93.55 % set(auto2) -> clear(echo_input).
% 93.24/93.55 % set(auto2) -> set(quiet).
% 93.24/93.55 % set(auto2) -> clear(print_initial_clauses).
% 93.24/93.55 % set(auto2) -> clear(print_given).
% 93.24/93.55 assign(lrs_ticks,-1).
% 93.24/93.55 assign(sos_limit,10000).
% 93.24/93.55 assign(order,kbo).
% 93.24/93.55 set(lex_order_vars).
% 93.24/93.55 clear(print_given).
% 93.24/93.55
% 93.24/93.55 % formulas(sos). % not echoed (5 formulas)
% 93.24/93.55
% 93.24/93.55 ============================== end of input ==========================
% 93.24/93.55
% 93.24/93.55 % From the command line: assign(max_seconds, 300).
% 93.24/93.55
% 93.24/93.55 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 93.24/93.55
% 93.24/93.55 % Formulas that are not ordinary clauses:
% 93.24/93.55
% 93.24/93.55 ============================== end of process non-clausal formulas ===
% 93.24/93.55
% 93.24/93.55 ============================== PROCESS INITIAL CLAUSES ===============
% 93.24/93.55
% 93.24/93.55 ============================== PREDICATE ELIMINATION =================
% 93.24/93.55
% 93.24/93.55 ============================== end predicate elimination =============
% 93.24/93.55
% 93.24/93.55 Auto_denials:
% 93.24/93.55 % copying label prove_ic_4 to answer in negative clause
% 93.24/93.55
% 93.24/93.55 Term ordering decisions:
% 93.24/93.55
% 93.24/93.55 % Assigning unary symbol is_a_theorem kb_weight 0 and highest precedence (8).
% 93.24/93.55 Function symbol KB weights: true=1. a=1. b=1. c=1. implies=1. ifeq=1. is_a_theorem=0.
% 93.24/93.55
% 93.24/93.55 ============================== end of process initial clauses ========
% 93.24/93.55
% 93.24/93.55 ============================== CLAUSES FOR SEARCH ====================
% 93.24/93.55
% 93.24/93.55 ============================== end of clauses for search =============
% 93.24/93.55
% 93.24/93.55 ============================== SEARCH ================================
% 93.24/93.55
% 93.24/93.55 % Starting search at 0.01 seconds.
% 93.24/93.55
% 93.24/93.55 Low Water (keep): wt=36.000, iters=3359
% 93.24/93.55
% 93.24/93.55 Low Water (keep): wt=34.000, iters=3347
% 93.24/93.55
% 93.24/93.55 Low Water (keep): wt=32.000, iters=3333
% 93.24/93.55
% 93.24/93.55 Low Water (keep): wt=30.000, iters=3334
% 93.24/93.55
% 93.24/93.55 Low Water (keep): wt=29.000, iters=3342
% 93.24/93.55
% 93.24/93.55 Low Water (keep): wt=28.000, iters=3338
% 93.24/93.55
% 93.24/93.55 Low Water (displace): id=4950, wt=42.000
% 93.24/93.55
% 93.24/93.55 Low Water (displace): id=3762, wt=40.000
% 93.24/93.55
% 93.24/93.55 Low Water (displace): id=6388, wt=38.000
% 93.24/93.55
% 93.24/93.55 Low Water (displace): id=4948, wt=37.000
% 93.24/93.55
% 93.24/93.55 Low Water (displace): id=6602, wt=36.000
% 93.24/93.55
% 93.24/93.55 Low Water (displace): id=3568, wt=35.000
% 93.24/93.55
% 93.24/93.55 Low Water (displace): id=6683, wt=34.000
% 93.24/93.55
% 93.24/93.55 Low Water (displace): id=13122, wt=26.000
% 93.24/93.55
% 93.24/93.55 Low Water (displace): id=13123, wt=24.000
% 93.24/93.55
% 93.24/93.55 Low Water (keep): wt=27.000, iters=3658
% 93.24/93.55
% 93.24/93.55 Low Water (keep): wt=26.000, iters=3351
% 93.24/93.55
% 93.24/93.55 Low Water (displace): id=15442, wt=23.000
% 93.24/93.55
% 93.24/93.55 Low Water (displace): id=15465, wt=22.000
% 93.24/93.55
% 93.24/93.55 Low Water (displace): id=15531, wt=21.000
% 93.24/93.55
% 93.24/93.55 Low Water (displace): id=15542, wt=20.000
% 93.24/93.55
% 93.24/93.55 Low Water (keep): wt=25.000, iters=3345
% 93.24/93.55
% 93.24/93.55 Low Water (keep): wt=24.000, iters=3333
% 93.24/93.55
% 93.24/93.55 Low Water (keep): wt=23.000, iters=3333
% 93.24/93.55
% 93.24/93.55 Low Water (displace): id=27822, wt=19.000
% 93.24/93.55
% 93.24/93.55 Low Water (displace): id=27835, wt=18.000
% 95.13/95.46
% 95.13/95.46 Low Water (displace): id=28202, wt=16.000
% 95.13/95.46
% 95.13/95.46 Low Water (keep): wt=22.000, iters=3336
% 95.13/95.46
% 95.13/95.46 ============================== PROOF =================================
% 95.13/95.46 % SZS status Unsatisfiable
% 95.13/95.46 % SZS output start Refutation
% 95.13/95.46
% 95.13/95.46 % Proof 1 at 87.46 (+ 6.96) seconds: prove_ic_4.
% 95.13/95.46 % Length of proof is 124.
% 95.13/95.46 % Level of proof is 47.
% 95.13/95.46 % Maximum clause weight is 28.000.
% 95.13/95.46 % Given clauses 5490.
% 95.13/95.46
% 95.13/95.46 1 is_a_theorem(implies(A,A)) = true # label(ic_1) # label(axiom). [assumption].
% 95.13/95.46 2 ifeq(A,A,B,C) = B # label(ifeq_axiom) # label(axiom). [assumption].
% 95.13/95.46 3 ifeq(is_a_theorem(implies(A,B)),true,ifeq(is_a_theorem(A),true,is_a_theorem(B),true),true) = true # label(condensed_detachment) # label(axiom). [assumption].
% 95.13/95.46 4 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(C,A),implies(D,A)))) = true # label(ic_JLukasiewicz) # label(axiom). [assumption].
% 95.13/95.46 5 is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c)))) != true # label(prove_ic_4) # label(negated_conjecture) # answer(prove_ic_4). [assumption].
% 95.13/95.46 7 ifeq(is_a_theorem(implies(implies(A,A),B)),true,is_a_theorem(B),true) = true. [para(1(a,1),3(a,1,3,1)),rewrite([2(9)])].
% 95.13/95.46 9 ifeq(is_a_theorem(implies(implies(A,B),C)),true,is_a_theorem(implies(implies(C,A),implies(D,A))),true) = true. [para(4(a,1),3(a,1,1)),rewrite([2(14)])].
% 95.13/95.46 10 ifeq(is_a_theorem(implies(implies(implies(implies(A,B),C),implies(implies(C,A),implies(D,A))),E)),true,is_a_theorem(E),true) = true. [para(4(a,1),3(a,1,3,1)),rewrite([2(14)])].
% 95.13/95.46 14 is_a_theorem(implies(implies(implies(A,B),A),implies(C,A))) = true. [para(4(a,1),7(a,1,1)),rewrite([2(9)])].
% 95.13/95.46 17 ifeq(is_a_theorem(implies(implies(implies(implies(A,B),A),implies(C,A)),D)),true,is_a_theorem(D),true) = true. [para(14(a,1),3(a,1,3,1)),rewrite([2(12)])].
% 95.13/95.46 24 is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),implies(B,D)),implies(E,implies(B,D)))) = true. [para(4(a,1),9(a,1,1)),rewrite([2(13)])].
% 95.13/95.46 25 is_a_theorem(implies(implies(implies(A,B),implies(B,C)),implies(D,implies(B,C)))) = true. [para(14(a,1),9(a,1,1)),rewrite([2(11)])].
% 95.13/95.46 46 ifeq(is_a_theorem(implies(implies(implies(implies(A,B),implies(B,C)),implies(D,implies(B,C))),E)),true,is_a_theorem(E),true) = true. [para(25(a,1),3(a,1,3,1)),rewrite([2(14)])].
% 95.13/95.46 47 is_a_theorem(implies(implies(implies(A,implies(B,C)),implies(D,B)),implies(E,implies(D,B)))) = true. [para(25(a,1),9(a,1,1)),rewrite([2(12)])].
% 95.13/95.46 60 is_a_theorem(implies(A,implies(B,implies(C,B)))) = true. [para(24(a,1),17(a,1,1)),rewrite([2(8)])].
% 95.13/95.46 63 is_a_theorem(implies(A,implies(B,A))) = true. [para(60(a,1),7(a,1,1)),rewrite([2(7)])].
% 95.13/95.46 67 is_a_theorem(implies(implies(implies(A,implies(B,C)),B),implies(D,B))) = true. [para(63(a,1),9(a,1,1)),rewrite([2(10)])].
% 95.13/95.46 85 ifeq(is_a_theorem(implies(implies(implies(implies(A,implies(B,C)),B),implies(D,B)),E)),true,is_a_theorem(E),true) = true. [para(67(a,1),3(a,1,3,1)),rewrite([2(13)])].
% 95.13/95.46 153 is_a_theorem(implies(implies(implies(A,implies(B,C)),implies(D,implies(C,E))),implies(F,implies(D,implies(C,E))))) = true. [para(47(a,1),9(a,1,1)),rewrite([2(14)])].
% 95.13/95.46 154 is_a_theorem(implies(A,implies(implies(implies(implies(B,C),D),C),implies(B,C)))) = true. [para(47(a,1),10(a,1,1)),rewrite([2(11)])].
% 95.13/95.46 159 is_a_theorem(implies(implies(implies(implies(A,B),C),B),implies(A,B))) = true. [para(154(a,1),7(a,1,1)),rewrite([2(10)])].
% 95.13/95.46 163 ifeq(is_a_theorem(implies(implies(implies(A,B),C),B)),true,is_a_theorem(implies(A,B)),true) = true. [para(159(a,1),3(a,1,1)),rewrite([2(13)])].
% 95.13/95.46 165 is_a_theorem(implies(implies(implies(A,B),implies(implies(A,B),C)),implies(D,implies(implies(A,B),C)))) = true. [para(159(a,1),9(a,1,1)),rewrite([2(13)])].
% 95.13/95.46 291 is_a_theorem(implies(A,implies(implies(implies(B,C),B),B))) = true. [para(165(a,1),17(a,1,1)),rewrite([2(9)])].
% 95.13/95.46 295 is_a_theorem(implies(A,implies(implies(implies(B,C),implies(C,D)),implies(C,D)))) = true. [para(165(a,1),46(a,1,1)),rewrite([2(11)])].
% 95.13/95.46 300 is_a_theorem(implies(implies(implies(A,B),A),A)) = true. [para(291(a,1),7(a,1,1)),rewrite([2(8)])].
% 95.13/95.46 306 is_a_theorem(implies(implies(A,implies(A,B)),implies(C,implies(A,B)))) = true. [para(300(a,1),9(a,1,1)),rewrite([2(10)])].
% 95.13/95.46 334 ifeq(is_a_theorem(implies(A,implies(A,B))),true,is_a_theorem(implies(C,implies(A,B))),true) = true. [para(306(a,1),3(a,1,1)),rewrite([2(13)])].
% 95.13/95.46 335 ifeq(is_a_theorem(implies(implies(implies(A,implies(A,B)),implies(C,implies(A,B))),D)),true,is_a_theorem(D),true) = true. [para(306(a,1),3(a,1,3,1)),rewrite([2(13)])].
% 95.13/95.46 352 is_a_theorem(implies(implies(implies(A,B),implies(B,C)),implies(B,C))) = true. [para(295(a,1),7(a,1,1)),rewrite([2(10)])].
% 95.13/95.46 358 is_a_theorem(implies(implies(implies(A,B),implies(C,A)),implies(D,implies(C,A)))) = true. [para(352(a,1),9(a,1,1)),rewrite([2(11)])].
% 95.13/95.46 359 is_a_theorem(implies(A,implies(implies(implies(B,implies(C,D)),C),C))) = true. [para(306(a,1),85(a,1,1)),rewrite([2(10)])].
% 95.13/95.46 362 is_a_theorem(implies(implies(implies(A,implies(B,C)),B),B)) = true. [para(359(a,1),7(a,1,1)),rewrite([2(9)])].
% 95.13/95.46 368 is_a_theorem(implies(implies(A,implies(B,implies(A,C))),implies(D,implies(B,implies(A,C))))) = true. [para(362(a,1),9(a,1,1)),rewrite([2(12)])].
% 95.13/95.46 409 is_a_theorem(implies(A,implies(B,implies(C,A)))) = true. [para(358(a,1),163(a,1,1)),rewrite([2(8)])].
% 95.13/95.46 411 ifeq(is_a_theorem(implies(implies(A,implies(B,implies(C,A))),D)),true,is_a_theorem(D),true) = true. [para(409(a,1),3(a,1,3,1)),rewrite([2(11)])].
% 95.13/95.46 412 is_a_theorem(implies(implies(implies(A,implies(B,implies(C,D))),C),implies(E,C))) = true. [para(409(a,1),9(a,1,1)),rewrite([2(11)])].
% 95.13/95.46 513 is_a_theorem(implies(A,implies(implies(B,implies(B,C)),implies(B,C)))) = true. [para(306(a,1),334(a,1,1)),rewrite([2(10)])].
% 95.13/95.46 521 is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))) = true. [para(513(a,1),7(a,1,1)),rewrite([2(9)])].
% 95.13/95.46 525 ifeq(is_a_theorem(implies(A,implies(A,B))),true,is_a_theorem(implies(A,B)),true) = true. [para(521(a,1),3(a,1,1)),rewrite([2(12)])].
% 95.13/95.46 546 is_a_theorem(implies(implies(implies(A,implies(B,implies(C,D))),C),C)) = true. [para(412(a,1),525(a,1,1)),rewrite([2(10)])].
% 95.13/95.46 557 is_a_theorem(implies(implies(A,implies(B,implies(C,implies(A,D)))),implies(E,implies(B,implies(C,implies(A,D)))))) = true. [para(546(a,1),9(a,1,1)),rewrite([2(14)])].
% 95.13/95.46 709 is_a_theorem(implies(A,implies(implies(implies(B,C),D),implies(C,D)))) = true. [para(153(a,1),10(a,1,1)),rewrite([2(10)])].
% 95.13/95.46 717 is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))) = true. [para(709(a,1),7(a,1,1)),rewrite([2(9)])].
% 95.13/95.46 722 ifeq(is_a_theorem(implies(implies(A,B),C)),true,is_a_theorem(implies(B,C)),true) = true. [para(717(a,1),3(a,1,1)),rewrite([2(12)])].
% 95.13/95.46 724 is_a_theorem(implies(A,implies(implies(A,B),implies(C,B)))) = true. [para(717(a,1),10(a,1,1)),rewrite([2(9)])].
% 95.13/95.46 727 ifeq(is_a_theorem(implies(implies(A,implies(implies(A,B),implies(C,B))),D)),true,is_a_theorem(D),true) = true. [para(724(a,1),3(a,1,3,1)),rewrite([2(12)])].
% 95.13/95.46 728 is_a_theorem(implies(implies(implies(implies(implies(A,B),C),implies(D,C)),A),implies(E,A))) = true. [para(724(a,1),9(a,1,1)),rewrite([2(12)])].
% 95.13/95.46 746 is_a_theorem(implies(A,implies(implies(implies(B,A),C),implies(D,C)))) = true. [para(724(a,1),722(a,1,1)),rewrite([2(10)])].
% 95.13/95.46 749 ifeq(is_a_theorem(implies(implies(A,implies(implies(implies(B,A),C),implies(D,C))),E)),true,is_a_theorem(E),true) = true. [para(746(a,1),3(a,1,3,1)),rewrite([2(13)])].
% 95.13/95.46 1096 is_a_theorem(implies(A,implies(implies(B,C),implies(implies(implies(C,D),B),C)))) = true. [para(368(a,1),10(a,1,1)),rewrite([2(11)])].
% 95.13/95.46 1099 is_a_theorem(implies(implies(A,implies(B,implies(A,C))),implies(B,implies(A,C)))) = true. [para(368(a,1),525(a,1,1)),rewrite([2(11)])].
% 95.13/95.46 1106 is_a_theorem(implies(implies(A,B),implies(implies(implies(B,C),A),B))) = true. [para(1096(a,1),7(a,1,1)),rewrite([2(10)])].
% 95.13/95.46 1114 ifeq(is_a_theorem(implies(A,B)),true,is_a_theorem(implies(implies(implies(B,C),A),B)),true) = true. [para(1106(a,1),3(a,1,1)),rewrite([2(13)])].
% 95.13/95.46 1118 is_a_theorem(implies(implies(implies(implies(A,B),C),implies(implies(B,D),B)),implies(A,B))) = true. [para(1106(a,1),17(a,1,1)),rewrite([2(12)])].
% 95.13/95.46 1132 is_a_theorem(implies(implies(implies(implies(A,implies(B,C)),D),C),implies(A,implies(B,C)))) = true. [para(1106(a,1),411(a,1,1)),rewrite([2(12)])].
% 95.13/95.46 1155 ifeq(is_a_theorem(implies(A,implies(B,implies(A,C)))),true,is_a_theorem(implies(B,implies(A,C))),true) = true. [para(1099(a,1),3(a,1,1)),rewrite([2(14)])].
% 95.13/95.46 1246 is_a_theorem(implies(implies(implies(implies(A,B),C),implies(implies(D,A),B)),implies(A,B))) = true. [para(717(a,1),1114(a,1,1)),rewrite([2(12)])].
% 95.13/95.46 1247 is_a_theorem(implies(implies(implies(implies(implies(A,B),implies(C,B)),D),A),implies(implies(A,B),implies(C,B)))) = true. [para(724(a,1),1114(a,1,1)),rewrite([2(14)])].
% 95.13/95.46 1571 is_a_theorem(implies(implies(implies(A,B),implies(implies(implies(B,C),D),implies(E,D))),implies(F,implies(implies(implies(B,C),D),implies(E,D))))) = true. [para(728(a,1),9(a,1,1)),rewrite([2(17)])].
% 95.13/95.46 1575 is_a_theorem(implies(implies(implies(implies(implies(A,B),C),implies(D,C)),A),A)) = true. [para(728(a,1),525(a,1,1)),rewrite([2(11)])].
% 95.13/95.46 1593 is_a_theorem(implies(implies(A,implies(implies(implies(A,B),C),implies(D,C))),implies(E,implies(implies(implies(A,B),C),implies(D,C))))) = true. [para(1575(a,1),9(a,1,1)),rewrite([2(16)])].
% 95.13/95.46 1768 ifeq(is_a_theorem(implies(implies(implies(A,B),C),implies(implies(B,D),B))),true,is_a_theorem(implies(A,B)),true) = true. [para(1118(a,1),3(a,1,1)),rewrite([2(15)])].
% 95.13/95.46 1786 ifeq(is_a_theorem(implies(implies(implies(A,implies(B,C)),D),C)),true,is_a_theorem(implies(A,implies(B,C))),true) = true. [para(1132(a,1),3(a,1,1)),rewrite([2(15)])].
% 95.13/95.46 1883 ifeq(is_a_theorem(implies(implies(implies(A,B),C),implies(implies(D,A),B))),true,is_a_theorem(implies(A,B)),true) = true. [para(1246(a,1),3(a,1,1)),rewrite([2(15)])].
% 95.13/95.46 4555 is_a_theorem(implies(implies(implies(implies(implies(implies(A,B),C),implies(A,B)),D),B),implies(A,B))) = true. [para(1575(a,1),1768(a,1,1)),rewrite([2(13)])].
% 95.13/95.46 4571 is_a_theorem(implies(implies(implies(implies(implies(A,B),A),C),implies(implies(A,B),A)),A)) = true. [para(4555(a,1),1768(a,1,1)),rewrite([2(12)])].
% 95.13/95.46 4577 is_a_theorem(implies(implies(A,implies(implies(implies(A,B),A),C)),implies(D,implies(implies(implies(A,B),A),C)))) = true. [para(4571(a,1),9(a,1,1)),rewrite([2(14)])].
% 95.13/95.46 4827 is_a_theorem(implies(implies(A,implies(B,implies(C,implies(A,D)))),implies(B,implies(C,implies(A,D))))) = true. [para(557(a,1),525(a,1,1)),rewrite([2(13)])].
% 95.13/95.46 4837 ifeq(is_a_theorem(implies(A,implies(B,implies(C,implies(A,D))))),true,is_a_theorem(implies(B,implies(C,implies(A,D)))),true) = true. [para(4827(a,1),3(a,1,1)),rewrite([2(16)])].
% 95.13/95.46 7897 is_a_theorem(implies(implies(implies(A,implies(implies(implies(B,C),B),D)),B),implies(E,B))) = true. [para(4577(a,1),9(a,1,1)),rewrite([2(12)])].
% 95.13/95.46 7948 is_a_theorem(implies(implies(implies(A,implies(implies(implies(B,C),B),D)),B),B)) = true. [para(7897(a,1),525(a,1,1)),rewrite([2(11)])].
% 95.13/95.46 7960 ifeq(is_a_theorem(implies(implies(implies(implies(A,implies(implies(implies(B,C),B),D)),B),B),E)),true,is_a_theorem(E),true) = true. [para(7948(a,1),3(a,1,3,1)),rewrite([2(14)])].
% 95.13/95.46 11291 is_a_theorem(implies(implies(A,B),implies(implies(implies(A,C),A),B))) = true. [para(1247(a,1),7960(a,1,1)),rewrite([2(10)])].
% 95.13/95.46 11293 ifeq(is_a_theorem(implies(A,B)),true,is_a_theorem(implies(implies(implies(A,C),A),B)),true) = true. [para(11291(a,1),3(a,1,1)),rewrite([2(13)])].
% 95.13/95.46 11309 is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,C),implies(D,C)))) = true. [para(11291(a,1),727(a,1,1)),rewrite([2(11)])].
% 95.13/95.46 11339 is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),implies(A,D)),implies(E,implies(A,D)))) = true. [para(11309(a,1),9(a,1,1)),rewrite([2(13)])].
% 95.13/95.46 11348 is_a_theorem(implies(A,implies(B,implies(implies(A,C),implies(D,C))))) = true. [para(11309(a,1),1786(a,1,1)),rewrite([2(10)])].
% 95.13/95.46 11352 ifeq(is_a_theorem(implies(implies(A,implies(B,implies(implies(A,C),implies(D,C)))),E)),true,is_a_theorem(E),true) = true. [para(11348(a,1),3(a,1,3,1)),rewrite([2(13)])].
% 95.13/95.46 11948 is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),implies(A,D)),implies(A,D))) = true. [para(11339(a,1),525(a,1,1)),rewrite([2(12)])].
% 95.13/95.46 11955 is_a_theorem(implies(A,implies(B,implies(implies(B,C),C)))) = true. [para(11339(a,1),335(a,1,1)),rewrite([2(9)])].
% 95.13/95.46 11964 is_a_theorem(implies(A,implies(implies(A,B),B))) = true. [para(11955(a,1),7(a,1,1)),rewrite([2(8)])].
% 95.13/95.46 11975 is_a_theorem(implies(A,implies(implies(implies(B,A),C),C))) = true. [para(11955(a,1),1883(a,1,1)),rewrite([2(9)])].
% 95.13/95.46 11985 is_a_theorem(implies(implies(implies(implies(implies(A,B),B),C),A),implies(implies(A,B),B))) = true. [para(11964(a,1),1114(a,1,1)),rewrite([2(12)])].
% 95.13/95.46 11990 is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,C),C))) = true. [para(11964(a,1),11293(a,1,1)),rewrite([2(10)])].
% 95.13/95.46 11998 ifeq(is_a_theorem(implies(implies(A,implies(implies(implies(B,A),C),C)),D)),true,is_a_theorem(D),true) = true. [para(11975(a,1),3(a,1,3,1)),rewrite([2(12)])].
% 95.13/95.46 13449 is_a_theorem(implies(implies(implies(implies(A,B),B),implies(A,C)),implies(D,implies(A,C)))) = true. [para(11990(a,1),9(a,1,1)),rewrite([2(12)])].
% 95.13/95.46 13461 is_a_theorem(implies(A,implies(B,implies(implies(A,C),C)))) = true. [para(11990(a,1),1786(a,1,1)),rewrite([2(9)])].
% 95.13/95.46 13470 ifeq(is_a_theorem(implies(implies(A,implies(B,implies(implies(A,C),C))),D)),true,is_a_theorem(D),true) = true. [para(13461(a,1),3(a,1,3,1)),rewrite([2(12)])].
% 95.13/95.46 14208 ifeq(is_a_theorem(implies(implies(implies(implies(A,B),B),C),A)),true,is_a_theorem(implies(implies(A,B),B)),true) = true. [para(11985(a,1),3(a,1,1)),rewrite([2(15)])].
% 95.13/95.46 14337 is_a_theorem(implies(implies(implies(implies(A,B),B),implies(A,C)),implies(A,C))) = true. [para(13449(a,1),525(a,1,1)),rewrite([2(11)])].
% 95.13/95.46 14347 ifeq(is_a_theorem(implies(implies(implies(A,B),B),implies(A,C))),true,is_a_theorem(implies(A,C)),true) = true. [para(14337(a,1),3(a,1,1)),rewrite([2(14)])].
% 95.13/95.46 14349 is_a_theorem(implies(implies(implies(A,B),implies(implies(A,C),C)),implies(D,implies(implies(A,C),C)))) = true. [para(14337(a,1),9(a,1,1)),rewrite([2(13)])].
% 95.13/95.46 15059 is_a_theorem(implies(A,implies(implies(implies(implies(A,B),B),C),implies(D,C)))) = true. [para(11348(a,1),14347(a,1,1)),rewrite([2(11)])].
% 95.13/95.46 15123 is_a_theorem(implies(implies(implies(implies(A,B),B),C),implies(A,C))) = true. [para(15059(a,1),1155(a,1,1)),rewrite([2(10)])].
% 95.13/95.46 15145 ifeq(is_a_theorem(implies(implies(implies(A,B),B),C)),true,is_a_theorem(implies(A,C)),true) = true. [para(15123(a,1),3(a,1,1)),rewrite([2(13)])].
% 95.13/95.46 16619 is_a_theorem(implies(implies(implies(A,B),implies(implies(A,C),C)),implies(implies(A,C),C))) = true. [para(14349(a,1),525(a,1,1)),rewrite([2(12)])].
% 95.13/95.46 16623 ifeq(is_a_theorem(implies(implies(A,B),implies(implies(A,C),C))),true,is_a_theorem(implies(implies(A,C),C)),true) = true. [para(16619(a,1),3(a,1,1)),rewrite([2(15)])].
% 95.13/95.46 17859 is_a_theorem(implies(A,implies(implies(implies(implies(A,B),implies(C,B)),D),implies(E,D)))) = true. [para(11948(a,1),11352(a,1,1)),rewrite([2(12)])].
% 95.13/95.46 18335 is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(A,D))) = true. [para(17859(a,1),1155(a,1,1)),rewrite([2(11)])].
% 95.13/95.46 18368 is_a_theorem(implies(implies(A,B),implies(A,implies(C,B)))) = true. [para(18335(a,1),15145(a,1,1)),rewrite([2(9)])].
% 95.13/95.46 18374 ifeq(is_a_theorem(implies(implies(implies(A,B),implies(A,implies(C,B))),D)),true,is_a_theorem(D),true) = true. [para(18368(a,1),3(a,1,3,1)),rewrite([2(12)])].
% 95.13/95.46 19490 is_a_theorem(implies(A,implies(implies(implies(B,C),D),implies(implies(implies(E,B),D),D)))) = true. [para(1571(a,1),13470(a,1,1)),rewrite([2(12)])].
% 95.13/95.46 19623 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,A),C),C))) = true. [para(19490(a,1),7(a,1,1)),rewrite([2(11)])].
% 95.13/95.46 19630 ifeq(is_a_theorem(implies(implies(A,B),C)),true,is_a_theorem(implies(implies(implies(D,A),C),C)),true) = true. [para(19623(a,1),3(a,1,1)),rewrite([2(14)])].
% 95.13/95.46 19951 is_a_theorem(implies(A,implies(implies(implies(B,C),implies(D,E)),implies(implies(B,E),implies(D,E))))) = true. [para(1593(a,1),11352(a,1,1)),rewrite([2(13)])].
% 95.13/95.46 22505 is_a_theorem(implies(implies(implies(A,B),implies(C,D)),implies(implies(A,D),implies(C,D)))) = true. [para(19951(a,1),7(a,1,1)),rewrite([2(12)])].
% 95.13/95.46 22511 is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(implies(D,implies(A,E)),C),implies(B,C)))) = true. [para(22505(a,1),749(a,1,1)),rewrite([2(13)])].
% 95.13/95.46 22516 is_a_theorem(implies(implies(A,B),implies(implies(implies(C,implies(A,D)),B),B))) = true. [para(22505(a,1),11998(a,1,1)),rewrite([2(11)])].
% 95.13/95.46 22625 is_a_theorem(implies(A,implies(implies(implies(B,implies(implies(A,C),D)),C),C))) = true. [para(22516(a,1),15145(a,1,1)),rewrite([2(11)])].
% 95.13/95.46 22670 is_a_theorem(implies(implies(implies(A,B),A),implies(implies(implies(C,implies(implies(A,D),E)),D),D))) = true. [para(22625(a,1),11293(a,1,1)),rewrite([2(13)])].
% 95.13/95.46 23476 is_a_theorem(implies(implies(implies(A,implies(implies(B,C),D)),implies(E,C)),implies(B,implies(E,C)))) = true. [para(22511(a,1),18374(a,1,1)),rewrite([2(13)])].
% 95.13/95.46 23902 is_a_theorem(implies(implies(implies(A,implies(B,C)),implies(implies(A,C),D)),implies(implies(A,C),D))) = true. [para(23476(a,1),14208(a,1,1)),rewrite([2(13)])].
% 95.13/95.46 23908 is_a_theorem(implies(implies(A,B),implies(implies(implies(A,implies(C,B)),D),implies(E,D)))) = true. [para(23902(a,1),11352(a,1,1)),rewrite([2(12)])].
% 95.13/95.46 23962 is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(implies(A,C),D))) = true. [para(23908(a,1),1155(a,1,1)),rewrite([2(11)])].
% 95.13/95.46 23971 ifeq(is_a_theorem(implies(implies(A,implies(B,C)),D)),true,is_a_theorem(implies(implies(A,C),D)),true) = true. [para(23962(a,1),3(a,1,1)),rewrite([2(14)])].
% 95.13/95.46 25594 is_a_theorem(implies(implies(implies(A,implies(implies(A,B),C)),B),B)) = true. [para(22670(a,1),16623(a,1,1)),rewrite([2(10)])].
% 95.13/95.46 25625 is_a_theorem(implies(implies(implies(A,implies(B,implies(implies(B,C),D))),C),C)) = true. [para(25594(a,1),19630(a,1,1)),rewrite([2(11)])].
% 95.13/95.46 25676 is_a_theorem(implies(implies(A,implies(B,implies(implies(B,A),C))),implies(B,implies(implies(B,A),C)))) = true. [para(25625(a,1),14208(a,1,1)),rewrite([2(13)])].
% 95.13/95.46 27097 is_a_theorem(implies(implies(A,implies(implies(B,A),C)),implies(B,implies(implies(B,A),C)))) = true. [para(25676(a,1),23971(a,1,1)),rewrite([2(12)])].
% 95.13/95.46 28219 is_a_theorem(implies(implies(A,B),implies(C,implies(implies(C,A),B)))) = true. [para(27097(a,1),23971(a,1,1)),rewrite([2(10)])].
% 95.13/95.46 28430 is_a_theorem(implies(A,implies(implies(A,B),implies(implies(B,C),implies(D,C))))) = true. [para(28219(a,1),727(a,1,1)),rewrite([2(11)])].
% 95.13/95.46 29090 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) = true. [para(28430(a,1),4837(a,1,1)),rewrite([2(10)])].
% 95.13/95.46 29091 $F # answer(prove_ic_4). [resolve(29090,a,5,a)].
% 95.13/95.46
% 95.13/95.46 % SZS output end Refutation
% 95.13/95.46 ============================== end of proof ==========================
% 95.13/95.46
% 95.13/95.46 ============================== STATISTICS ============================
% 95.13/95.46
% 95.13/95.46 Given=5490. Generated=13718694. Kept=29090. proofs=1.
% 95.13/95.46 Usable=5433. Sos=9998. Demods=15448. Limbo=18, Disabled=13645. Hints=0.
% 95.13/95.46 Megabytes=26.02.
% 95.13/95.46 User_CPU=87.47, System_CPU=6.96, Wall_clock=95.
% 95.13/95.46
% 95.13/95.46 ============================== end of statistics =====================
% 95.13/95.46
% 95.13/95.46 ============================== end of search =========================
% 95.13/95.46
% 95.13/95.46 THEOREM PROVED
% 95.13/95.46 % SZS status Unsatisfiable
% 95.13/95.46
% 95.13/95.46 Exiting with 1 proof.
% 95.13/95.46
% 95.13/95.46 Process 16277 exit (max_proofs) Mon Jul 4 16:52:13 2022
% 95.13/95.47 Prover9 interrupted
%------------------------------------------------------------------------------