TSTP Solution File: SYN551+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SYN551+2 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 : Thu Jul 21 11:21:01 EDT 2022
% Result : Theorem 154.82s 155.12s
% Output : Refutation 154.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN551+2 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 13:42:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 51.51/51.83 ============================== Prover9 ===============================
% 51.51/51.83 Prover9 (32) version 2009-11A, November 2009.
% 51.51/51.83 Process 4683 was started by sandbox on n023.cluster.edu,
% 51.51/51.83 Mon Jul 11 13:42:55 2022
% 51.51/51.83 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4333_n023.cluster.edu".
% 51.51/51.83 ============================== end of head ===========================
% 51.51/51.83
% 51.51/51.83 ============================== INPUT =================================
% 51.51/51.83
% 51.51/51.83 % Reading from file /tmp/Prover9_4333_n023.cluster.edu
% 51.51/51.83
% 51.51/51.83 set(prolog_style_variables).
% 51.51/51.83 set(auto2).
% 51.51/51.83 % set(auto2) -> set(auto).
% 51.51/51.83 % set(auto) -> set(auto_inference).
% 51.51/51.83 % set(auto) -> set(auto_setup).
% 51.51/51.83 % set(auto_setup) -> set(predicate_elim).
% 51.51/51.83 % set(auto_setup) -> assign(eq_defs, unfold).
% 51.51/51.83 % set(auto) -> set(auto_limits).
% 51.51/51.83 % set(auto_limits) -> assign(max_weight, "100.000").
% 51.51/51.83 % set(auto_limits) -> assign(sos_limit, 20000).
% 51.51/51.83 % set(auto) -> set(auto_denials).
% 51.51/51.83 % set(auto) -> set(auto_process).
% 51.51/51.83 % set(auto2) -> assign(new_constants, 1).
% 51.51/51.83 % set(auto2) -> assign(fold_denial_max, 3).
% 51.51/51.83 % set(auto2) -> assign(max_weight, "200.000").
% 51.51/51.83 % set(auto2) -> assign(max_hours, 1).
% 51.51/51.83 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 51.51/51.83 % set(auto2) -> assign(max_seconds, 0).
% 51.51/51.83 % set(auto2) -> assign(max_minutes, 5).
% 51.51/51.83 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 51.51/51.83 % set(auto2) -> set(sort_initial_sos).
% 51.51/51.83 % set(auto2) -> assign(sos_limit, -1).
% 51.51/51.83 % set(auto2) -> assign(lrs_ticks, 3000).
% 51.51/51.83 % set(auto2) -> assign(max_megs, 400).
% 51.51/51.83 % set(auto2) -> assign(stats, some).
% 51.51/51.83 % set(auto2) -> clear(echo_input).
% 51.51/51.83 % set(auto2) -> set(quiet).
% 51.51/51.83 % set(auto2) -> clear(print_initial_clauses).
% 51.51/51.83 % set(auto2) -> clear(print_given).
% 51.51/51.83 assign(lrs_ticks,-1).
% 51.51/51.83 assign(sos_limit,10000).
% 51.51/51.83 assign(order,kbo).
% 51.51/51.83 set(lex_order_vars).
% 51.51/51.83 clear(print_given).
% 51.51/51.83
% 51.51/51.83 % formulas(sos). % not echoed (1 formulas)
% 51.51/51.83
% 51.51/51.83 ============================== end of input ==========================
% 51.51/51.83
% 51.51/51.83 % From the command line: assign(max_seconds, 300).
% 51.51/51.83
% 51.51/51.83 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 51.51/51.83
% 51.51/51.83 % Formulas that are not ordinary clauses:
% 51.51/51.83 1 -((exists X all Y (Y = f(g(Y)) <-> X = Y)) <-> (exists X all Y (Y = g(f(Y)) <-> X = Y))) # label(prove_this_cute_thing) # label(negated_conjecture) # label(non_clause). [assumption].
% 51.51/51.83
% 51.51/51.83 ============================== end of process non-clausal formulas ===
% 51.51/51.83
% 51.51/51.83 ============================== PROCESS INITIAL CLAUSES ===============
% 51.51/51.83
% 51.51/51.83 ============================== PREDICATE ELIMINATION =================
% 51.51/51.83
% 51.51/51.83 ============================== end predicate elimination =============
% 51.51/51.83
% 51.51/51.83 Auto_denials: (non-Horn, no changes).
% 51.51/51.83
% 51.51/51.83 Term ordering decisions:
% 51.51/51.83 Function symbol KB weights: c1=1. c2=1. f=1. g=1. f1=1. f2=1.
% 51.51/51.83
% 51.51/51.83 ============================== end of process initial clauses ========
% 51.51/51.83
% 51.51/51.83 ============================== CLAUSES FOR SEARCH ====================
% 51.51/51.83
% 51.51/51.83 ============================== end of clauses for search =============
% 51.51/51.83
% 51.51/51.83 ============================== SEARCH ================================
% 51.51/51.83
% 51.51/51.83 % Starting search at 0.01 seconds.
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=57.000, iters=3333
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=55.000, iters=3333
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=54.000, iters=3333
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=53.000, iters=3333
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=49.000, iters=3340
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=48.000, iters=3333
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=47.000, iters=3340
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=46.000, iters=3333
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=45.000, iters=3346
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=44.000, iters=3333
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=43.000, iters=3339
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=42.000, iters=3337
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=41.000, iters=3333
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=40.000, iters=3339
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=39.000, iters=3333
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=38.000, iters=3351
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=37.000, iters=3333
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=36.000, iters=3335
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=35.000, iters=3341
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=34.000, iters=3335
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=33.000, iters=3344
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=32.000, iters=3385
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=31.000, iters=3366
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=30.000, iters=3360
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=29.000, iters=3349
% 51.51/51.83
% 51.51/51.83 Low Water (keep): wt=28.000, iters=3336
% 154.82/155.12
% 154.82/155.12 Low Water (keep): wt=27.000, iters=3352
% 154.82/155.12
% 154.82/155.12 Low Water (keep): wt=26.000, iters=3336
% 154.82/155.12
% 154.82/155.12 Low Water (keep): wt=25.000, iters=3371
% 154.82/155.12
% 154.82/155.12 Low Water (displace): id=16518, wt=49.000
% 154.82/155.12
% 154.82/155.12 Low Water (displace): id=16084, wt=48.000
% 154.82/155.12
% 154.82/155.12 Low Water (displace): id=32180, wt=24.000
% 154.82/155.12
% 154.82/155.12 Low Water (keep): wt=24.000, iters=3346
% 154.82/155.12
% 154.82/155.12 Low Water (displace): id=35208, wt=19.000
% 154.82/155.12
% 154.82/155.12 Low Water (displace): id=35211, wt=18.000
% 154.82/155.12
% 154.82/155.12 Low Water (displace): id=35738, wt=17.000
% 154.82/155.12
% 154.82/155.12 ============================== PROOF =================================
% 154.82/155.12 % SZS status Theorem
% 154.82/155.12 % SZS output start Refutation
% 154.82/155.12
% 154.82/155.12 % Proof 1 at 148.10 (+ 6.00) seconds.
% 154.82/155.12 % Length of proof is 110.
% 154.82/155.12 % Level of proof is 68.
% 154.82/155.12 % Maximum clause weight is 39.000.
% 154.82/155.12 % Given clauses 4838.
% 154.82/155.12
% 154.82/155.12 1 -((exists X all Y (Y = f(g(Y)) <-> X = Y)) <-> (exists X all Y (Y = g(f(Y)) <-> X = Y))) # label(prove_this_cute_thing) # label(negated_conjecture) # label(non_clause). [assumption].
% 154.82/155.12 2 f(g(f1(A))) = f1(A) | f1(A) = A | g(f(f2(B))) = f2(B) | f2(B) = B # label(prove_this_cute_thing) # label(negated_conjecture). [clausify(1)].
% 154.82/155.12 3 f(g(f1(A))) != f1(A) | f1(A) != A | g(f(f2(B))) != f2(B) | f2(B) != B # label(prove_this_cute_thing) # label(negated_conjecture). [clausify(1)].
% 154.82/155.12 4 f(g(A)) != A | A = c1 | g(f(B)) != B | B = c2 # label(prove_this_cute_thing) # label(negated_conjecture). [clausify(1)].
% 154.82/155.12 5 f(g(A)) != A | c1 = A | g(f(B)) != B | c2 = B. [copy(4),flip(b),flip(d)].
% 154.82/155.12 8 f(g(A)) = A | A != c1 | g(f(B)) != B | B = c2 # label(prove_this_cute_thing) # label(negated_conjecture). [clausify(1)].
% 154.82/155.12 9 f(g(A)) = A | c1 != A | g(f(B)) != B | c2 = B. [copy(8),flip(b),flip(d)].
% 154.82/155.12 10 f(g(A)) = A | A != c1 | g(f(B)) = B | B != c2 # label(prove_this_cute_thing) # label(negated_conjecture). [clausify(1)].
% 154.82/155.12 11 f(g(A)) = A | c1 != A | g(f(B)) = B | c2 != B. [copy(10),flip(b),flip(d)].
% 154.82/155.12 12 f(g(f1(A))) = f1(A) | f1(A) = A | g(f(f2(B))) != f2(B) | f2(B) != B # label(prove_this_cute_thing) # label(negated_conjecture). [clausify(1)].
% 154.82/155.12 13 f(g(f1(A))) != f1(A) | f1(A) != A | g(f(f2(B))) = f2(B) | f2(B) = B # label(prove_this_cute_thing) # label(negated_conjecture). [clausify(1)].
% 154.82/155.12 14 f1(A) = c1 | g(f(B)) != B | c2 = B | f1(A) = A | g(f(f2(C))) = f2(C) | f2(C) = C. [resolve(5,a,2,a),flip(a)].
% 154.82/155.12 15 f(g(A)) != A | c1 = A | f2(B) = c2 | f(g(f1(C))) = f1(C) | f1(C) = C | f2(B) = B. [resolve(5,c,2,c),flip(c)].
% 154.82/155.12 18 f1(c1) = c1 | g(f(A)) != A | c2 = A | g(f(f2(B))) = f2(B) | f2(B) = B. [factor(14,a,d)].
% 154.82/155.12 26 f(g(c1)) = c1 | g(f(A)) != A | c2 = A. [xx_res(9,b)].
% 154.82/155.12 32 f(g(c1)) = c1 | g(f(A)) = A | c2 != A. [xx_res(11,b)].
% 154.82/155.12 34 f1(A) = A | g(f(f2(B))) = f2(B) | f2(B) = B | f1(C) = c1 | g(f1(A)) = c2 | f1(C) = C | g(f(f2(D))) = f2(D) | f2(D) = D. [para(2(a,1),14(b,1,1)),flip(f),xx(e)].
% 154.82/155.12 37 f1(A) = A | g(f(f2(B))) = f2(B) | f2(B) = B | f1(C) = c1 | g(f1(A)) = c2 | f1(C) = C. [factor(34,b,g),merge(g)].
% 154.82/155.12 45 f(g(c1)) = c1 | f2(A) = c2 | f(g(f1(B))) = f1(B) | f1(B) = B | f2(A) = A. [resolve(26,b,2,c),flip(b)].
% 154.82/155.12 48 f(g(c1)) = c1 | g(f(c2)) = c2. [xx_res(32,c)].
% 154.82/155.12 49 f(g(c1)) = c1 | g(f(g(f(c2)))) = g(f(c2)). [resolve(48,b,32,c(flip)),merge(b)].
% 154.82/155.12 50 f(g(f1(A))) = f1(A) | f1(A) = A | f2(B) = B | f(f2(B)) = c1 | f2(C) = c2 | f(g(f1(D))) = f1(D) | f1(D) = D | f2(C) = C. [para(2(c,1),15(a,1,1)),flip(e),xx(d)].
% 154.82/155.12 51 f(g(f1(A))) = f1(A) | f1(A) = A | f2(B) = B | f(f2(B)) = c1 | f2(C) = c2 | f2(C) = C. [factor(50,a,f),merge(f)].
% 154.82/155.12 58 f(g(c1)) = c1 | g(f(g(f(c2)))) = c2. [para(48(b,1),49(b,2)),merge(b)].
% 154.82/155.12 680 f1(A) = A | g(f(f2(B))) = f2(B) | f2(B) = B | f1(C) = c1 | f1(C) = C | f1(A) = f(c2) | g(f(f2(D))) = f2(D) | f2(D) = D. [para(37(e,1),2(a,1,1)),flip(f),merge(g)].
% 154.82/155.12 724 f1(A) = A | g(f(f2(B))) = f2(B) | f2(B) = B | f1(C) = c1 | f1(C) = C | f1(A) = f(c2). [factor(680,b,g),merge(g)].
% 154.82/155.12 762 f1(f(c2)) = f(c2) | g(f(f2(A))) = f2(A) | f2(A) = A | f1(f(c2)) = c1. [factor(724,e,f),merge(e)].
% 154.82/155.12 971 f(g(c1)) = c1 | f2(A) = c2 | f1(B) = B | f2(A) = A | g(f1(B)) = c2. [para(45(c,1),26(b,1,1)),flip(g),xx(f),merge(e)].
% 154.82/155.12 1073 f(g(f1(A))) = f1(A) | f1(A) = A | f2(B) = B | f2(C) = c2 | f2(C) = C | f(g(f1(D))) = f1(D) | f1(D) = D | f2(B) = g(c1). [para(51(d,1),2(c,1,1)),flip(h),merge(i)].
% 154.82/155.12 1120 f(g(f1(A))) = f1(A) | f1(A) = A | f2(B) = B | f2(C) = c2 | f2(C) = C | f2(B) = g(c1). [factor(1073,a,f),merge(f)].
% 154.82/155.12 1199 f(g(f1(A))) = f1(A) | f1(A) = A | f2(g(c1)) = g(c1) | f2(g(c1)) = c2. [factor(1120,e,f),merge(e)].
% 154.82/155.12 3494 f1(f(c2)) = f(c2) | f2(A) = A | f1(f(c2)) = c1 | f(g(B)) != B | c1 = B | f2(A) = c2. [resolve(762,b,5,c),flip(f)].
% 154.82/155.12 4413 f(g(c1)) = c1 | f2(A) = c2 | f1(B) = B | f2(A) = A | f2(C) = c2 | f1(B) = f(c2) | f2(C) = C. [para(971(e,1),45(c,1,1)),flip(g),merge(e),merge(h)].
% 154.82/155.12 4444 f(g(c1)) = c1 | f2(A) = c2 | f1(B) = B | f2(A) = A | f1(B) = f(c2). [factor(4413,b,e),merge(f)].
% 154.82/155.12 4460 f(g(c1)) = c1 | f2(A) = c2 | f1(f(c2)) = f(c2) | f2(A) = A. [factor(4444,c,e)].
% 154.82/155.12 6829 f(g(c1)) = c1 | f2(A) = c2 | f1(B) = B | f2(A) = A | f2(C) = c2 | f1(B) = f(g(f(c2))) | f2(C) = C. [para(4444(e,1),45(c,1,1,1)),flip(g),merge(e),merge(h)].
% 154.82/155.12 6863 f(g(c1)) = c1 | f2(A) = c2 | f1(B) = B | f2(A) = A | f1(B) = f(g(f(c2))). [factor(6829,b,e),merge(f)].
% 154.82/155.12 6879 f(g(c1)) = c1 | f2(A) = c2 | f1(f(g(f(c2)))) = f(g(f(c2))) | f2(A) = A. [factor(6863,c,e)].
% 154.82/155.12 21032 f1(f(c2)) = f(c2) | f2(A) = A | f1(f(c2)) = c1 | f1(B) = c1 | f2(A) = c2 | f1(B) = B | f2(g(c1)) = g(c1) | f2(g(c1)) = c2. [resolve(3494,d,1199,a),flip(d)].
% 154.82/155.12 21037 f1(f(c2)) = f(c2) | f2(A) = A | f1(f(c2)) = c1 | f2(A) = c2 | f2(g(c1)) = g(c1) | f2(g(c1)) = c2. [factor(21032,a,f),merge(d)].
% 154.82/155.12 21041 f1(f(c2)) = f(c2) | f2(g(c1)) = g(c1) | f1(f(c2)) = c1 | f2(g(c1)) = c2. [factor(21037,b,e),merge(e)].
% 154.82/155.12 23899 f(g(c1)) = c1 | f2(A) = c2 | f(g(f(c2))) = f1(f(c2)) | f2(A) = A. [para(48(b,1),6879(c,1,1,1)),flip(d),merge(b)].
% 154.82/155.12 23913 f(g(c1)) = c1 | f2(A) = c2 | f2(A) = A | g(f1(f(c2))) = c2. [para(23899(c,1),58(b,1,1)),merge(d)].
% 154.82/155.12 23960 f(g(c1)) = c1 | f2(A) = A | g(f1(f(c2))) = c2 | g(f(f2(A))) = f2(A). [resolve(23913,b,32,c(flip)),merge(d)].
% 154.82/155.12 24189 f(g(c1)) = c1 | f2(A) = A | g(f(f2(A))) = f2(A) | f1(f(c2)) != f(c2) | g(f(f2(B))) = f2(B) | f2(B) = B. [para(23960(c,1),13(a,1,1)),flip(d),merge(e)].
% 154.82/155.12 24204 f(g(c1)) = c1 | f2(A) = A | g(f(f2(A))) = f2(A) | f1(f(c2)) != f(c2). [factor(24189,b,f),merge(e)].
% 154.82/155.12 24477 f(g(c1)) = c1 | f2(A) = A | g(f(f2(A))) = f2(A) | f2(B) = c2 | f2(B) = B. [resolve(24204,d,4460,c),merge(d)].
% 154.82/155.12 24510 f(g(c1)) = c1 | f2(A) = A | g(f(f2(A))) = f2(A) | f2(A) = c2. [factor(24477,b,e)].
% 154.82/155.12 24518 f(g(c1)) = c1 | f2(A) = A | f2(A) = c2. [resolve(24510,c,26,b),flip(e),merge(d),merge(e)].
% 154.82/155.12 24524 f(g(c1)) = c1 | f2(A) = A | g(f(f2(A))) = f2(A). [resolve(24518,c,32,c(flip)),merge(c)].
% 154.82/155.12 24594 f(g(c1)) = c1 | f2(A) = A | f2(A) = g(f(c2)). [para(24518(c,1),24524(c,1,1,1)),flip(e),merge(c),merge(d)].
% 154.82/155.12 24596 f(g(c1)) = c1 | f2(g(f(c2))) = g(f(c2)). [factor(24594,b,c)].
% 154.82/155.12 24601 f(g(c1)) = c1 | g(f(c2)) = f2(c2). [para(48(b,1),24596(b,1,1)),flip(c),merge(b)].
% 154.82/155.12 24602 f(g(c1)) = c1 | f2(g(f(c2))) = c2. [para(48(b,1),24596(b,2)),merge(b)].
% 154.82/155.12 24625 f(g(c1)) = c1 | g(f(f2(c2))) = c2. [para(24601(b,1),58(b,1,1,1)),merge(b)].
% 154.82/155.12 24656 f(g(c1)) = c1 | f2(f2(c2)) = g(f(c2)). [para(24601(b,1),24596(b,1,1)),merge(b)].
% 154.82/155.12 24667 f(g(c1)) = c1 | f2(f2(c2)) = c2. [para(24601(b,1),24602(b,1,1)),merge(b)].
% 154.82/155.12 24671 f(g(c1)) = c1 | g(f(f2(f2(c2)))) = f2(f2(c2)). [resolve(24667,b,32,c(flip)),merge(b)].
% 154.82/155.12 24680 f(g(c1)) = c1 | f(g(f1(A))) != f1(A) | f1(A) != A | f2(c2) != c2. [para(24625(b,1),3(c,1)),flip(d),merge(e)].
% 154.82/155.12 24707 f(g(c1)) = c1 | f2(f2(c2)) = f2(c2). [para(24601(b,1),24656(b,2)),merge(b)].
% 154.82/155.12 24751 f(g(c1)) = c1 | f(g(f1(A))) = f1(A) | f1(A) = A | f2(f2(c2)) != f2(c2). [resolve(24671,b,12,c)].
% 154.82/155.12 24864 f(g(c1)) = c1 | f2(A) = A | f2(c2) = f2(A). [para(24594(c,2),24601(b,1)),flip(d),merge(c)].
% 154.82/155.12 33837 f(g(c1)) = c1 | f(g(f1(A))) = f1(A) | f1(A) = A. [resolve(24751,d,24707,b),merge(d)].
% 154.82/155.12 33840 f(g(c1)) = c1 | f1(A) = A | g(f1(A)) = c2. [para(33837(b,1),26(b,1,1)),flip(e),xx(d),merge(c)].
% 154.82/155.12 33846 f(g(c1)) = c1 | f1(A) = A | f1(A) = f(c2). [para(33840(c,1),33837(b,1,1)),flip(d),merge(c),merge(e)].
% 154.82/155.12 33848 f(g(c1)) = c1 | f1(f(c2)) = f(c2). [factor(33846,b,c)].
% 154.82/155.12 34680 f(g(c1)) = c1 | f1(A) = A | f1(A) = f(g(f(c2))). [para(33846(c,1),33837(b,1,1,1)),flip(d),merge(c),merge(e)].
% 154.82/155.12 34693 f(g(c1)) = c1 | f1(f(g(f(c2)))) = f(g(f(c2))). [factor(34680,b,c)].
% 154.82/155.12 34942 f(g(c1)) = c1 | f(g(f(c2))) = f1(f(c2)). [para(48(b,1),34693(b,1,1,1)),flip(c),merge(b)].
% 154.82/155.12 34953 f(g(c1)) = c1 | g(f1(f(c2))) = c2. [para(34942(b,1),58(b,1,1)),merge(b)].
% 154.82/155.12 35351 f(g(c1)) = c1 | f1(f(c2)) != f(c2) | f2(c2) != c2. [para(34953(b,1),24680(b,1,1)),flip(c),merge(b),merge(d)].
% 154.82/155.12 35813 f(g(c1)) = c1 | f2(c2) != c2. [resolve(35351,b,33848,b),merge(c)].
% 154.82/155.12 35929 f(g(c1)) = c1 | f2(A) = A | f2(A) != c2. [para(24864(c,1),35813(b,1)),merge(c)].
% 154.82/155.12 35933 f(g(c1)) = c1 | f2(A) = A. [resolve(35929,c,24518,c),merge(c),merge(d)].
% 154.82/155.12 35949 f(g(c1)) = c1. [resolve(35933,b,35813,b),merge(b)].
% 154.82/155.12 35954 f2(A) = A | f1(c1) = c1 | g(c1) = c2 | g(f(f2(B))) = f2(B) | f2(B) = B. [para(35933(a,1),18(b,1,1)),flip(d),xx(c)].
% 154.82/155.12 36120 f2(A) = A | f1(c1) = c1 | g(c1) = c2 | g(f(f2(A))) = f2(A). [factor(35954,a,e)].
% 154.82/155.12 37481 f(g(A)) != A | c1 = A | g(c1) = c2. [para(35949(a,1),5(c,1,1)),flip(d),xx(c)].
% 154.82/155.12 37764 f2(A) = A | f1(c1) = c1 | g(c1) = c2 | f(f2(A)) = c1. [para(36120(d,1),37481(a,1,1)),flip(e),xx(d),merge(e)].
% 154.82/155.12 37786 f2(A) = A | f1(c1) = c1 | g(c1) = c2 | f2(A) = g(c1). [para(37764(d,1),36120(d,1,1)),flip(g),merge(d),merge(e),merge(f)].
% 154.82/155.12 37806 f2(g(c1)) = g(c1) | f1(c1) = c1 | g(c1) = c2. [factor(37786,a,d)].
% 154.82/155.12 37808 f1(c1) = c1 | g(c1) = c2 | f(g(f1(A))) = f1(A) | f1(A) = A | f2(g(c1)) != g(c1). [para(37806(a,1),12(c,1,1,1)),rewrite([35949(18)]),flip(e),merge(f)].
% 154.82/155.12 37821 f1(c1) = c1 | g(c1) = c2 | f(g(f1(c1))) = f1(c1) | f2(g(c1)) != g(c1). [factor(37808,a,d)].
% 154.82/155.12 41799 f1(c1) = c1 | g(c1) = c2 | f(g(f1(c1))) = f1(c1). [resolve(37821,d,37806,a),merge(d),merge(e)].
% 154.82/155.12 41801 f1(c1) = c1 | g(c1) = c2. [resolve(41799,c,37481,a),flip(c),merge(c),merge(d)].
% 154.82/155.12 41804 g(c1) = c2 | f1(c1) != c1 | g(f(f2(A))) != f2(A) | f2(A) != A. [para(41801(a,1),3(a,1,1,1)),rewrite([35949(7)]),flip(b),merge(c)].
% 154.82/155.12 41805 g(c1) = c2 | f1(c1) != c1 | g(f(f2(A))) = f2(A) | f2(A) = A. [para(41801(a,1),13(a,1,1,1)),rewrite([35949(7)]),flip(b),merge(c)].
% 154.82/155.12 41847 g(c1) = c2 | g(f(f2(A))) = f2(A) | f2(A) = A. [resolve(41805,b,41801,a),merge(d)].
% 154.82/155.12 41864 g(c1) = c2 | f2(A) = A | f(f2(A)) = c1. [para(41847(b,1),37481(a,1,1)),flip(d),xx(c),merge(d)].
% 154.82/155.12 41901 g(c1) = c2 | f2(A) = A | f2(A) = g(c1). [para(41864(c,1),41847(b,1,1)),flip(d),merge(c),merge(e)].
% 154.82/155.12 41925 g(c1) = c2 | f2(g(c1)) = g(c1). [factor(41901,b,c)].
% 154.82/155.12 41934 g(c1) = c2 | f1(c1) != c1 | f2(g(c1)) != g(c1). [para(41925(b,1),41804(c,1,1,1)),rewrite([35949(15)]),flip(d),merge(b),merge(e)].
% 154.82/155.12 42103 g(c1) = c2 | f1(c1) != c1. [resolve(41934,c,41925,b),merge(c)].
% 154.82/155.12 42104 g(c1) = c2. [resolve(42103,b,41801,a),merge(b)].
% 154.82/155.12 42415 f(c2) = c1. [back_rewrite(35949),rewrite([42104(2)])].
% 154.82/155.12 42428 f1(c1) = c1 | f2(c2) = c2. [back_rewrite(21041),rewrite([42415(2),42415(4),42104(6),42104(8),42415(10),42104(14)]),merge(c),merge(d)].
% 154.82/155.12 42494 f1(c1) = c1 | f(g(f1(A))) = f1(A) | f1(A) = A | f2(c2) != c2. [para(42428(b,1),12(c,1,1,1)),rewrite([42415(13),42104(13)]),flip(d),merge(e)].
% 154.82/155.12 42499 f1(c1) = c1 | f(g(f1(c1))) = f1(c1) | f2(c2) != c2. [factor(42494,a,c)].
% 154.82/155.12 42574 f1(c1) = c1 | f(g(f1(c1))) = f1(c1). [resolve(42499,c,42428,b),merge(c)].
% 154.82/155.12 42576 f1(c1) = c1 | g(f(A)) != A | c2 = A. [resolve(42574,b,5,a),flip(b),merge(b)].
% 154.82/155.12 42588 f1(c1) = c1 | g(f1(c1)) = c2. [para(42574(b,1),42576(b,1,1)),flip(d),xx(c),merge(b)].
% 154.82/155.12 42592 f1(c1) = c1. [para(42588(b,1),42574(b,1,1)),rewrite([42415(10)]),flip(c),merge(b),merge(c)].
% 154.82/155.12 42600 g(f(f2(A))) != f2(A) | f2(A) != A. [para(42592(a,1),3(a,1,1,1)),rewrite([42104(2),42415(2),42592(3),42592(5)]),xx(a),xx(b)].
% 154.82/155.12 42601 g(f(f2(A))) = f2(A) | f2(A) = A. [para(42592(a,1),13(a,1,1,1)),rewrite([42104(2),42415(2),42592(3),42592(5)]),xx(a),xx(b)].
% 154.82/155.12 42604 f2(A) = A | f(g(B)) != B | c1 = B | f2(A) = c2. [resolve(42601,a,5,c),flip(d)].
% 154.82/155.12 42608 f2(c2) = c2 | f(g(A)) != A | c1 = A. [factor(42604,a,d)].
% 154.82/155.12 42632 f2(A) = A | f2(c2) = c2 | f(f2(A)) = c1. [para(42601(a,1),42608(b,1,1)),flip(d),xx(c)].
% 154.82/155.12 42633 f2(c2) = c2 | f(f2(c2)) = c1. [factor(42632,a,b)].
% 154.82/155.12 42635 f2(c2) = c2. [para(42633(b,1),42601(a,1,1)),rewrite([42104(6)]),flip(b),merge(b),merge(c)].
% 154.82/155.12 42637 $F. [ur(42600,b,42635,a),rewrite([42635(2),42415(2),42104(2),42635(3)]),xx(a)].
% 154.82/155.12
% 154.82/155.12 % SZS output end Refutation
% 154.82/155.12 ============================== end of proof ==========================
% 154.82/155.12
% 154.82/155.12 ============================== STATISTICS ============================
% 154.82/155.12
% 154.82/155.12 Given=4838. Generated=12207883. Kept=42631. proofs=1.
% 154.82/155.12 Usable=11. Sos=46. Demods=4. Limbo=0, Disabled=42582. Hints=0.
% 154.82/155.12 Megabytes=40.18.
% 154.82/155.12 User_CPU=148.10, System_CPU=6.00, Wall_clock=154.
% 154.82/155.12
% 154.82/155.12 ============================== end of statistics =====================
% 154.82/155.12
% 154.82/155.12 ============================== end of search =========================
% 154.82/155.12
% 154.82/155.12 THEOREM PROVED
% 154.82/155.12 % SZS status Theorem
% 154.82/155.12
% 154.82/155.12 Exiting with 1 proof.
% 154.82/155.12
% 154.82/155.12 Process 4683 exit (max_proofs) Mon Jul 11 13:45:29 2022
% 154.82/155.12 Prover9 interrupted
%------------------------------------------------------------------------------