TSTP Solution File: SYN551+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SYN551+3 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 0.89s 1.18s
% Output : Refutation 0.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN551+3 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 12 07:39:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.89/1.18 ============================== Prover9 ===============================
% 0.89/1.18 Prover9 (32) version 2009-11A, November 2009.
% 0.89/1.18 Process 16626 was started by sandbox2 on n027.cluster.edu,
% 0.89/1.18 Tue Jul 12 07:39:35 2022
% 0.89/1.18 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_16470_n027.cluster.edu".
% 0.89/1.18 ============================== end of head ===========================
% 0.89/1.18
% 0.89/1.18 ============================== INPUT =================================
% 0.89/1.18
% 0.89/1.18 % Reading from file /tmp/Prover9_16470_n027.cluster.edu
% 0.89/1.18
% 0.89/1.18 set(prolog_style_variables).
% 0.89/1.18 set(auto2).
% 0.89/1.18 % set(auto2) -> set(auto).
% 0.89/1.18 % set(auto) -> set(auto_inference).
% 0.89/1.18 % set(auto) -> set(auto_setup).
% 0.89/1.18 % set(auto_setup) -> set(predicate_elim).
% 0.89/1.18 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.89/1.18 % set(auto) -> set(auto_limits).
% 0.89/1.18 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.89/1.18 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.89/1.18 % set(auto) -> set(auto_denials).
% 0.89/1.18 % set(auto) -> set(auto_process).
% 0.89/1.18 % set(auto2) -> assign(new_constants, 1).
% 0.89/1.18 % set(auto2) -> assign(fold_denial_max, 3).
% 0.89/1.18 % set(auto2) -> assign(max_weight, "200.000").
% 0.89/1.18 % set(auto2) -> assign(max_hours, 1).
% 0.89/1.18 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.89/1.18 % set(auto2) -> assign(max_seconds, 0).
% 0.89/1.18 % set(auto2) -> assign(max_minutes, 5).
% 0.89/1.18 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.89/1.18 % set(auto2) -> set(sort_initial_sos).
% 0.89/1.18 % set(auto2) -> assign(sos_limit, -1).
% 0.89/1.18 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.89/1.18 % set(auto2) -> assign(max_megs, 400).
% 0.89/1.18 % set(auto2) -> assign(stats, some).
% 0.89/1.18 % set(auto2) -> clear(echo_input).
% 0.89/1.18 % set(auto2) -> set(quiet).
% 0.89/1.18 % set(auto2) -> clear(print_initial_clauses).
% 0.89/1.18 % set(auto2) -> clear(print_given).
% 0.89/1.18 assign(lrs_ticks,-1).
% 0.89/1.18 assign(sos_limit,10000).
% 0.89/1.18 assign(order,kbo).
% 0.89/1.18 set(lex_order_vars).
% 0.89/1.18 clear(print_given).
% 0.89/1.18
% 0.89/1.18 % formulas(sos). % not echoed (1 formulas)
% 0.89/1.18
% 0.89/1.18 ============================== end of input ==========================
% 0.89/1.18
% 0.89/1.18 % From the command line: assign(max_seconds, 300).
% 0.89/1.18
% 0.89/1.18 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.89/1.18
% 0.89/1.18 % Formulas that are not ordinary clauses:
% 0.89/1.18 1 -((exists X (X = f(g(X)) & (all Y (Y = f(g(Y)) -> Y = X)))) <-> (exists X (X = g(f(X)) & (all Y (Y = g(f(Y)) -> Y = X))))) # label(prove_this_cute_thing) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.89/1.18
% 0.89/1.18 ============================== end of process non-clausal formulas ===
% 0.89/1.18
% 0.89/1.18 ============================== PROCESS INITIAL CLAUSES ===============
% 0.89/1.18
% 0.89/1.18 ============================== PREDICATE ELIMINATION =================
% 0.89/1.18
% 0.89/1.18 ============================== end predicate elimination =============
% 0.89/1.18
% 0.89/1.18 Auto_denials: (non-Horn, no changes).
% 0.89/1.18
% 0.89/1.18 Term ordering decisions:
% 0.89/1.18 Function symbol KB weights: c1=1. c2=1. f=1. g=1. f1=1. f2=1.
% 0.89/1.18
% 0.89/1.18 ============================== end of process initial clauses ========
% 0.89/1.18
% 0.89/1.18 ============================== CLAUSES FOR SEARCH ====================
% 0.89/1.18
% 0.89/1.18 ============================== end of clauses for search =============
% 0.89/1.18
% 0.89/1.18 ============================== SEARCH ================================
% 0.89/1.18
% 0.89/1.18 % Starting search at 0.01 seconds.
% 0.89/1.18
% 0.89/1.18 ============================== PROOF =================================
% 0.89/1.18 % SZS status Theorem
% 0.89/1.18 % SZS output start Refutation
% 0.89/1.18
% 0.89/1.18 % Proof 1 at 0.21 (+ 0.01) seconds.
% 0.89/1.18 % Length of proof is 139.
% 0.89/1.18 % Level of proof is 58.
% 0.89/1.18 % Maximum clause weight is 27.000.
% 0.89/1.18 % Given clauses 322.
% 0.89/1.18
% 0.89/1.18 1 -((exists X (X = f(g(X)) & (all Y (Y = f(g(Y)) -> Y = X)))) <-> (exists X (X = g(f(X)) & (all Y (Y = g(f(Y)) -> Y = X))))) # label(prove_this_cute_thing) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.89/1.18 2 f(g(c1)) = c1 | g(f(c2)) = c2 # label(prove_this_cute_thing) # label(negated_conjecture). [clausify(1)].
% 0.89/1.18 3 f(g(A)) != A | f1(A) != A | g(f(B)) != B | f2(B) != B # label(prove_this_cute_thing) # label(negated_conjecture). [clausify(1)].
% 0.89/1.18 4 f(g(c1)) = c1 | g(f(A)) != A | A = c2 # label(prove_this_cute_thing) # label(negated_conjecture). [clausify(1)].
% 0.89/1.18 5 f(g(c1)) = c1 | g(f(A)) != A | c2 = A. [copy(4),flip(c)].
% 0.89/1.18 6 f(g(A)) != A | A = c1 | g(f(c2)) = c2 # label(prove_this_cute_thing) # label(negated_conjecture). [clausify(1)].
% 0.89/1.18 7 f(g(A)) != A | c1 = A | g(f(c2)) = c2. [copy(6),flip(b)].
% 0.89/1.18 8 f(g(A)) != A | A = c1 | g(f(B)) != B | B = c2 # label(prove_this_cute_thing) # label(negated_conjecture). [clausify(1)].
% 0.89/1.18 9 f(g(A)) != A | c1 = A | g(f(B)) != B | c2 = B. [copy(8),flip(b),flip(d)].
% 0.89/1.18 10 f(g(A)) != A | f(g(f1(A))) = f1(A) | g(f(B)) != B | f2(B) != B # label(prove_this_cute_thing) # label(negated_conjecture). [clausify(1)].
% 0.89/1.18 11 f(g(A)) != A | f1(A) != A | g(f(B)) != B | g(f(f2(B))) = f2(B) # label(prove_this_cute_thing) # label(negated_conjecture). [clausify(1)].
% 0.89/1.18 12 f(g(A)) != A | f(g(f1(A))) = f1(A) | g(f(B)) != B | g(f(f2(B))) = f2(B) # label(prove_this_cute_thing) # label(negated_conjecture). [clausify(1)].
% 0.89/1.18 13 f(g(A)) != A | f1(A) != A | f2(c2) != c2 | f(g(c1)) = c1. [resolve(3,c,2,b)].
% 0.89/1.18 14 f(g(c1)) = c1 | f1(f(c2)) != f(c2) | g(f(A)) != A | f2(A) != A. [para(2(b,1),3(a,1,1)),xx(b)].
% 0.89/1.18 15 f(g(A)) != A | f(g(f1(A))) = f1(A) | f2(c2) != c2 | f(g(c1)) = c1. [resolve(10,c,2,b)].
% 0.89/1.18 17 f(g(A)) != A | f1(A) != A | g(f(f2(c2))) = f2(c2) | f(g(c1)) = c1. [resolve(11,c,2,b)].
% 0.89/1.18 19 f(g(A)) != A | f(g(f1(A))) = f1(A) | g(f(f2(c2))) = f2(c2) | f(g(c1)) = c1. [resolve(12,c,2,b)].
% 0.89/1.18 21 f(g(c1)) = c1 | f1(f(c2)) != f(c2) | f2(c2) != c2. [para(2(b,1),13(a,1,1)),xx(b),merge(d)].
% 0.89/1.18 22 f(g(c1)) = c1 | f(g(f1(f(c2)))) = f1(f(c2)) | f2(c2) != c2. [para(2(b,1),15(a,1,1)),xx(b),merge(d)].
% 0.89/1.18 23 f(g(c1)) = c1 | f1(f(c2)) != f(c2) | g(f(f2(c2))) = f2(c2). [para(2(b,1),17(a,1,1)),xx(b),merge(d)].
% 0.89/1.18 24 f(g(c1)) = c1 | f(g(f1(f(c2)))) = f1(f(c2)) | g(f(f2(c2))) = f2(c2). [para(2(b,1),19(a,1,1)),xx(b),merge(d)].
% 0.89/1.18 25 f(g(c1)) = c1 | g(f(f2(c2))) = f2(c2) | f(g(f1(f1(f(c2))))) = f1(f1(f(c2))). [resolve(24,b,19,a),merge(d),merge(e)].
% 0.89/1.18 27 f(g(c1)) = c1 | g(f(f2(c2))) = f2(c2) | g(f1(f(c2))) = c2. [para(24(b,1),5(b,1,1)),flip(e),xx(d),merge(c)].
% 0.89/1.18 28 f(g(c1)) = c1 | g(f(f2(c2))) = f2(c2) | f1(f(c2)) = f(c2). [para(27(c,1),24(b,1,1)),flip(d),merge(c),merge(e)].
% 0.89/1.18 35 f(g(c1)) = c1 | f1(f(c2)) = f(c2) | f2(c2) = c2. [resolve(28,b,5,b),flip(d),merge(c)].
% 0.89/1.18 43 f(g(c1)) = c1 | f2(c2) = c2 | g(f(f2(c2))) = f2(c2). [resolve(35,b,23,b),merge(c)].
% 0.89/1.18 46 f(g(c1)) = c1 | g(f(f2(c2))) = f2(c2) | f(g(f1(f1(f1(f(c2)))))) = f1(f1(f1(f(c2)))). [resolve(25,c,19,a),merge(d),merge(e)].
% 0.89/1.18 47 f(g(c1)) = c1 | g(f(f2(c2))) = f2(c2) | f1(f1(f1(f(c2)))) != f1(f1(f(c2))). [resolve(25,c,17,a),merge(d),merge(e)].
% 0.89/1.18 48 f(g(c1)) = c1 | g(f(f2(c2))) = f2(c2) | g(f1(f1(f(c2)))) = c2. [para(25(c,1),5(b,1,1)),flip(e),xx(d),merge(c)].
% 0.89/1.18 57 f(g(c1)) = c1 | f2(c2) = c2. [resolve(43,c,5,b),flip(d),merge(c),merge(d)].
% 0.89/1.18 58 f2(c2) = c2 | f(g(f1(c1))) = f1(c1) | g(f(A)) != A | g(f(f2(A))) = f2(A). [resolve(57,a,12,a)].
% 0.89/1.18 59 f2(c2) = c2 | f1(c1) != c1 | g(f(A)) != A | g(f(f2(A))) = f2(A). [resolve(57,a,11,a)].
% 0.89/1.18 60 f2(c2) = c2 | f(g(f1(c1))) = f1(c1) | g(f(A)) != A | f2(A) != A. [resolve(57,a,10,a)].
% 0.89/1.18 61 f2(c2) = c2 | f1(c1) != c1 | g(f(A)) != A | f2(A) != A. [resolve(57,a,3,a)].
% 0.89/1.18 63 f2(c2) = c2 | f(g(A)) != A | c1 = A | g(c1) = c2. [para(57(a,1),9(c,1,1)),flip(e),xx(d)].
% 0.89/1.18 66 f2(c2) = c2 | f(g(A)) != A | f(g(f1(A))) = f1(A) | g(f(f2(g(c1)))) = f2(g(c1)). [para(57(a,1),12(c,1,1)),xx(d)].
% 0.89/1.18 67 f2(c2) = c2 | f1(c1) != c1 | f2(g(c1)) != g(c1). [para(57(a,1),61(c,1,1)),xx(d),merge(b)].
% 0.89/1.18 68 f(g(c1)) = c1 | g(f(f2(c2))) = f2(c2) | f1(f1(f(c2))) = f(c2). [para(48(c,1),25(c,1,1)),flip(e),merge(c),merge(d)].
% 0.89/1.18 75 f2(c2) = c2 | f1(c1) != c1 | g(f(f2(g(c1)))) = f2(g(c1)). [para(57(a,1),59(c,1,1)),xx(d),merge(b)].
% 0.89/1.18 76 f2(c2) = c2 | f(g(f1(c1))) = f1(c1) | f2(g(c1)) != g(c1). [para(57(a,1),60(c,1,1)),xx(d),merge(b)].
% 0.89/1.18 106 f(g(c1)) = c1 | g(f(f2(c2))) = f2(c2) | f1(f1(f1(f(c2)))) != f(c2). [para(68(c,1),47(c,2)),merge(c),merge(d)].
% 0.89/1.18 113 f2(c2) = c2 | f(g(f1(c1))) = f1(c1) | g(f(f2(g(c1)))) = f2(g(c1)). [para(57(a,1),58(c,1,1)),xx(d),merge(b)].
% 0.89/1.18 118 f2(c2) = c2 | f(g(f1(c1))) = f1(c1) | g(f(f2(f2(g(c1))))) = f2(f2(g(c1))). [resolve(113,c,58,c),merge(c),merge(d)].
% 0.89/1.18 120 f2(c2) = c2 | f(g(f1(c1))) = f1(c1) | f(f2(g(c1))) = c1 | g(f(c2)) = c2. [para(113(c,1),7(a,1,1)),flip(d),xx(c)].
% 0.89/1.18 122 f2(c2) = c2 | f(g(f1(c1))) = f1(c1) | f(f2(g(c1))) = c1 | g(c1) = c2. [para(113(c,1),63(b,1,1)),flip(e),xx(d),merge(c)].
% 0.89/1.18 123 f2(c2) = c2 | f(g(f1(c1))) = f1(c1) | g(c1) = c2 | f2(g(c1)) = g(c1). [para(122(c,1),113(c,1,1)),flip(f),merge(d),merge(e)].
% 0.89/1.18 125 f2(c2) = c2 | g(c1) = c2 | f2(g(c1)) = g(c1) | f1(c1) = c1. [resolve(123,b,63,b),flip(e),merge(d),merge(f)].
% 0.89/1.18 136 f2(c2) = c2 | g(c1) = c2 | f1(c1) = c1 | f(g(f1(c1))) = f1(c1). [resolve(125,c,76,c),merge(d)].
% 0.89/1.18 141 f2(c2) = c2 | g(c1) = c2 | f1(c1) = c1. [resolve(136,d,63,b),flip(e),merge(d),merge(e),merge(f)].
% 0.89/1.18 142 g(c1) = c2 | f1(c1) = c1 | f(g(c1)) = c1 | f(g(f1(f(c2)))) = f1(f(c2)). [resolve(141,a,22,c)].
% 0.89/1.18 154 f2(c2) = c2 | f(g(f1(c1))) = f1(c1) | f2(f2(f2(g(c1)))) != f2(f2(g(c1))). [resolve(118,c,60,c),merge(c),merge(d)].
% 0.89/1.18 156 f2(c2) = c2 | f(g(f1(c1))) = f1(c1) | g(f(f2(f2(f2(g(c1)))))) = f2(f2(f2(g(c1)))). [resolve(118,c,58,c),merge(c),merge(d)].
% 0.89/1.18 161 f2(c2) = c2 | f(g(f1(c1))) = f1(c1) | g(f(c2)) = c2 | f2(g(c1)) = g(c1). [para(120(c,1),113(c,1,1)),flip(f),merge(d),merge(e)].
% 0.89/1.18 173 g(c1) = c2 | f1(c1) = c1 | f(g(c1)) = c1 | g(f1(f(c2))) = c2. [para(142(d,1),5(b,1,1)),flip(f),xx(e),merge(d)].
% 0.89/1.18 181 g(c1) = c2 | f1(c1) = c1 | f(g(c1)) = c1 | f1(f(c2)) = f(c2). [para(173(d,1),142(d,1,1)),flip(g),merge(d),merge(e),merge(f)].
% 0.89/1.18 183 g(c1) = c2 | f1(c1) = c1 | f(g(c1)) = c1 | f2(c2) != c2. [resolve(181,d,21,b),merge(d)].
% 0.89/1.18 188 g(c1) = c2 | f1(c1) = c1 | f(g(c1)) = c1. [resolve(183,d,141,a),merge(d),merge(e)].
% 0.89/1.18 189 g(c1) = c2 | f1(c1) = c1 | f(g(f1(c1))) = f1(c1) | g(f(A)) != A | g(f(f2(A))) = f2(A). [resolve(188,c,12,a)].
% 0.89/1.18 190 g(c1) = c2 | f1(c1) = c1 | f(g(f1(c1))) = f1(c1) | g(f(A)) != A | f2(A) != A. [resolve(188,c,10,a)].
% 0.89/1.18 192 g(c1) = c2 | f1(c1) = c1 | f(g(A)) != A | c1 = A. [para(188(c,1),9(c,1,1)),flip(f),xx(e),merge(e)].
% 0.89/1.18 202 f2(c2) = c2 | g(f(c2)) = c2 | f2(g(c1)) = g(c1) | f1(c1) = c1. [resolve(161,b,7,a),flip(d),merge(e)].
% 0.89/1.18 210 f2(c2) = c2 | g(f(c2)) = c2 | f1(c1) = c1 | f(g(f1(c1))) = f1(c1). [resolve(202,c,76,c),merge(d)].
% 0.89/1.18 220 f2(c2) = c2 | g(f(c2)) = c2 | f1(c1) = c1. [resolve(210,d,7,a),flip(d),merge(d),merge(e)].
% 0.89/1.18 221 f2(c2) = c2 | f1(c1) = c1 | f(g(f1(c1))) = f1(c1) | g(f(f2(c2))) = f2(c2). [resolve(220,b,58,c),merge(c)].
% 0.89/1.18 223 f2(c2) = c2 | f1(c1) = c1 | f(g(A)) != A | f1(A) != A | g(f(f2(c2))) = f2(c2). [resolve(220,b,11,c)].
% 0.89/1.18 239 f(g(c1)) = c1 | g(f(f2(c2))) = f2(c2) | g(f1(f1(f1(f(c2))))) = c2. [para(46(c,1),5(b,1,1)),flip(e),xx(d),merge(c)].
% 0.89/1.18 245 f(g(c1)) = c1 | g(f(f2(c2))) = f2(c2) | f1(f1(f1(f(c2)))) = f(c2). [para(239(c,1),46(c,1,1)),flip(e),merge(c),merge(d)].
% 0.89/1.18 246 f(g(c1)) = c1 | g(f(f2(c2))) = f2(c2). [resolve(245,c,106,c),merge(c),merge(d)].
% 0.89/1.18 250 f(g(c1)) = c1 | f1(f(c2)) != f(c2) | f2(f2(c2)) != f2(c2). [resolve(246,b,14,c),merge(b)].
% 0.89/1.18 263 f2(c2) = c2 | f1(c1) = c1 | f(g(f1(f(c2)))) = f1(f(c2)) | g(f(f2(g(c1)))) = f2(g(c1)). [para(220(b,1),66(b,1,1)),xx(d),merge(c)].
% 0.89/1.18 272 f2(c2) = c2 | f1(c1) = c1 | f(g(f1(c1))) = f1(c1) | f(g(A)) != A | c1 = A. [resolve(221,d,9,c),flip(f),merge(f)].
% 0.89/1.18 466 f2(c2) = c2 | f(g(f1(c1))) = f1(c1) | f1(c1) = c1 | f(f2(f2(g(c1)))) = c1. [para(118(c,1),272(d,1,1)),flip(g),xx(f),merge(c),merge(e)].
% 0.89/1.18 483 f2(c2) = c2 | f(g(f1(c1))) = f1(c1) | f1(c1) = c1 | f2(f2(g(c1))) = g(c1). [para(466(d,1),118(c,1,1)),flip(f),merge(d),merge(e)].
% 0.89/1.18 486 f2(c2) = c2 | f(g(f1(c1))) = f1(c1) | f1(c1) = c1 | f2(f2(f2(g(c1)))) != g(c1). [para(483(d,1),154(c,2)),merge(d),merge(e)].
% 0.89/1.18 531 f2(c2) = c2 | f(g(f1(c1))) = f1(c1) | f1(c1) = c1 | f(f2(f2(f2(g(c1))))) = c1. [para(156(c,1),272(d,1,1)),flip(g),xx(f),merge(c),merge(e)].
% 0.89/1.18 547 f2(c2) = c2 | f(g(f1(c1))) = f1(c1) | f1(c1) = c1 | f2(f2(f2(g(c1)))) = g(c1). [para(531(d,1),156(c,1,1)),flip(f),merge(d),merge(e)].
% 0.89/1.18 565 f2(c2) = c2 | f(g(f1(c1))) = f1(c1) | f1(c1) = c1. [resolve(547,d,486,d),merge(d),merge(e),merge(f)].
% 0.89/1.18 573 f2(c2) = c2 | f1(c1) = c1 | g(f(A)) != A | c2 = A. [resolve(565,b,9,a),flip(c),merge(c)].
% 0.89/1.18 583 g(c1) = c2 | f1(c1) = c1 | f(g(f1(c1))) = f1(c1) | g(f(f2(g(c1)))) = f2(g(c1)). [para(188(c,1),189(d,1,1)),xx(f),merge(c),merge(d)].
% 0.89/1.18 585 g(c1) = c2 | f1(c1) = c1 | f(g(f1(c1))) = f1(c1) | f2(g(c1)) != g(c1). [para(188(c,1),190(d,1,1)),xx(f),merge(c),merge(d)].
% 0.89/1.18 591 f2(c2) = c2 | f1(c1) = c1 | f1(f(c2)) != f(c2) | g(f(f2(c2))) = f2(c2). [para(220(b,1),223(c,1,1)),xx(e),merge(c),merge(d)].
% 0.89/1.18 618 g(c1) = c2 | f1(c1) = c1 | f(g(f1(c1))) = f1(c1) | f(f2(g(c1))) = c1. [para(583(d,1),192(c,1,1)),flip(g),xx(f),merge(d),merge(e)].
% 0.89/1.18 619 g(c1) = c2 | f1(c1) = c1 | f(g(f1(c1))) = f1(c1) | f2(g(c1)) = g(c1). [para(618(d,1),583(d,1,1)),flip(g),merge(d),merge(e),merge(f)].
% 0.89/1.18 622 g(c1) = c2 | f1(c1) = c1 | f2(g(c1)) = g(c1). [resolve(619,c,192,c),flip(f),merge(d),merge(e),merge(f)].
% 0.89/1.18 623 g(c1) = c2 | f1(c1) = c1 | f(g(f1(c1))) = f1(c1). [resolve(622,c,585,d),merge(c),merge(d)].
% 0.89/1.18 629 g(c1) = c2 | f1(c1) = c1. [resolve(623,c,192,c),flip(e),merge(c),merge(d),merge(e)].
% 0.89/1.18 631 g(c1) = c2 | f2(c2) = c2 | g(f(f2(g(c1)))) = f2(g(c1)). [resolve(629,b,75,b)].
% 0.89/1.18 650 g(c1) = c2 | f2(c2) = c2 | f(f2(g(c1))) = c1. [para(631(c,1),63(b,1,1)),flip(e),xx(d),merge(c),merge(e)].
% 0.89/1.18 653 g(c1) = c2 | f2(c2) = c2 | f2(g(c1)) = g(c1). [para(650(c,1),631(c,1,1)),flip(e),merge(c),merge(d)].
% 0.89/1.18 656 g(c1) = c2 | f2(c2) = c2 | f1(c1) != c1. [resolve(653,c,67,c),merge(c)].
% 0.89/1.18 661 g(c1) = c2 | f2(c2) = c2. [resolve(656,c,629,b),merge(c)].
% 0.89/1.18 666 g(c1) = c2 | f(g(c1)) = c1 | f(g(f1(f(c2)))) = f1(f(c2)). [resolve(661,b,22,c)].
% 0.89/1.18 669 g(c1) = c2 | f(g(c1)) = c1 | f1(f(c2)) != f(c2). [para(661(b,1),250(c,1,1)),xx(d)].
% 0.89/1.18 691 g(c1) = c2 | f(g(c1)) = c1 | g(f1(f(c2))) = c2. [para(666(c,1),5(b,1,1)),flip(e),xx(d),merge(c)].
% 0.89/1.18 693 g(c1) = c2 | f(g(c1)) = c1 | f1(f(c2)) = f(c2). [para(691(c,1),666(c,1,1)),flip(e),merge(c),merge(d)].
% 0.89/1.18 694 g(c1) = c2 | f(g(c1)) = c1. [resolve(693,c,669,c),merge(c),merge(d)].
% 0.89/1.18 696 g(c1) = c2 | f1(c1) != c1 | g(f(A)) != A | g(f(f2(A))) = f2(A). [resolve(694,b,11,a)].
% 0.89/1.18 698 g(c1) = c2 | f1(c1) != c1 | g(f(A)) != A | f2(A) != A. [resolve(694,b,3,a)].
% 0.89/1.18 700 g(c1) = c2 | f(g(A)) != A | c1 = A. [para(694(b,1),9(c,1,1)),flip(e),xx(d),merge(d)].
% 0.89/1.18 705 g(c1) = c2 | f1(c1) != c1 | f2(g(c1)) != g(c1). [para(694(b,1),698(c,1,1)),xx(d),merge(b)].
% 0.89/1.18 707 g(c1) = c2 | f1(c1) != c1 | g(f(f2(g(c1)))) = f2(g(c1)). [para(694(b,1),696(c,1,1)),xx(d),merge(b)].
% 0.89/1.18 708 g(c1) = c2 | g(f(f2(g(c1)))) = f2(g(c1)). [resolve(707,b,629,b),merge(c)].
% 0.89/1.18 721 g(c1) = c2 | f(f2(g(c1))) = c1. [para(708(b,1),700(b,1,1)),flip(d),xx(c),merge(b)].
% 0.89/1.18 723 g(c1) = c2 | f2(g(c1)) = g(c1). [para(721(b,1),708(b,1,1)),flip(c),merge(b)].
% 0.89/1.18 725 f2(c2) = c2 | f1(c1) = c1 | f(g(f1(f(c2)))) = f1(f(c2)) | f2(g(c1)) = c2. [resolve(263,d,573,c),flip(f),merge(d),merge(e)].
% 0.89/1.18 728 g(c1) = c2 | f1(c1) != c1. [resolve(723,b,705,c),merge(b)].
% 0.89/1.18 732 g(c1) = c2. [resolve(728,b,629,b),merge(b)].
% 0.89/1.18 735 f2(c2) = c2 | f1(c1) = c1 | f(g(f1(f(c2)))) = f1(f(c2)). [back_rewrite(725),rewrite([732(19)]),merge(d)].
% 0.89/1.18 807 f(c2) = c1 | f1(f(c2)) != f(c2) | f2(f2(c2)) != f2(c2). [back_rewrite(250),rewrite([732(2)])].
% 0.89/1.18 815 f(c2) = c1 | f2(c2) = c2. [back_rewrite(57),rewrite([732(2)])].
% 0.89/1.18 816 f(c2) = c1 | f(g(f1(f(c2)))) = f1(f(c2)) | f2(c2) != c2. [back_rewrite(22),rewrite([732(2)])].
% 0.89/1.18 824 f(c2) = c1 | g(f(A)) != A | c2 = A. [back_rewrite(5),rewrite([732(2)])].
% 0.89/1.18 826 f(c2) != c1 | f1(c1) != c1 | g(f(A)) != A | f2(A) != A. [para(732(a,1),3(a,1,1))].
% 0.89/1.18 827 f(c2) != c1 | f(g(f1(c1))) = f1(c1) | g(f(A)) != A | f2(A) != A. [para(732(a,1),10(a,1,1))].
% 0.89/1.18 828 f(c2) != c1 | f1(c1) != c1 | g(f(A)) != A | g(f(f2(A))) = f2(A). [para(732(a,1),11(a,1,1))].
% 0.89/1.18 842 f2(c2) = c2 | f1(c1) = c1 | g(f1(f(c2))) = c2. [para(735(c,1),573(c,1,1)),flip(f),xx(e),merge(c),merge(d)].
% 0.89/1.18 844 f2(c2) = c2 | f1(c1) = c1 | f1(f(c2)) = f(c2). [para(842(c,1),735(c,1,1)),flip(e),merge(c),merge(d)].
% 0.89/1.18 846 f2(c2) = c2 | f1(c1) = c1 | g(f(f2(c2))) = f2(c2). [resolve(844,c,591,c),merge(c),merge(d)].
% 0.89/1.18 852 f2(c2) = c2 | f1(c1) = c1. [resolve(846,c,573,c),flip(e),merge(c),merge(d),merge(e)].
% 0.89/1.18 866 f(c2) = c1 | f1(f(c2)) != f(c2). [para(815(b,1),807(c,1,1)),xx(d),merge(b)].
% 0.89/1.18 870 f(c2) = c1 | f(g(f1(f(c2)))) = f1(f(c2)). [resolve(816,c,815,b),merge(c)].
% 0.89/1.18 880 f(c2) = c1 | g(f1(f(c2))) = c2. [para(870(b,1),824(b,1,1)),flip(d),xx(c),merge(b)].
% 0.89/1.18 881 f(c2) = c1 | f1(f(c2)) = f(c2). [para(880(b,1),870(b,1,1)),flip(c),merge(b)].
% 0.89/1.18 882 f(c2) = c1. [resolve(881,b,866,b),merge(b)].
% 0.89/1.18 884 f1(c1) != c1 | g(f(A)) != A | g(f(f2(A))) = f2(A). [back_rewrite(828),rewrite([882(2)]),xx(a)].
% 0.89/1.18 885 f(g(f1(c1))) = f1(c1) | g(f(A)) != A | f2(A) != A. [back_rewrite(827),rewrite([882(2)]),xx(a)].
% 0.89/1.18 886 f1(c1) != c1 | g(f(A)) != A | f2(A) != A. [back_rewrite(826),rewrite([882(2)]),xx(a)].
% 0.89/1.18 895 f1(c1) != c1 | f2(c2) != c2. [para(882(a,1),886(b,1,1)),rewrite([732(6)]),xx(b)].
% 0.89/1.18 896 f1(c1) != c1 | g(f(f2(c2))) = f2(c2). [para(882(a,1),884(b,1,1)),rewrite([732(6)]),xx(b)].
% 0.89/1.18 897 f(g(f1(c1))) = f1(c1) | f2(c2) != c2. [para(882(a,1),885(b,1,1)),rewrite([732(9)]),xx(b)].
% 0.89/1.18 899 f(g(f1(c1))) = f1(c1) | f1(c1) = c1. [resolve(897,b,852,a)].
% 0.89/1.18 904 f1(c1) = c1 | g(f(A)) != A | c2 = A. [resolve(899,a,9,a),flip(b),merge(b)].
% 0.89/1.18 911 f1(c1) = c1 | g(f1(c1)) = c2. [para(899(a,1),904(b,1,1)),flip(d),xx(c),merge(b)].
% 0.89/1.18 912 f1(c1) = c1. [para(911(b,1),899(a,1,1)),rewrite([882(6)]),flip(b),merge(b),merge(c)].
% 0.89/1.18 913 g(f(f2(c2))) = f2(c2). [back_rewrite(896),rewrite([912(2)]),xx(a)].
% 0.89/1.18 914 f2(c2) != c2. [back_rewrite(895),rewrite([912(2)]),xx(a)].
% 0.89/1.18 918 f(g(A)) != A | c1 = A. [resolve(913,a,9,c),flip(c),unit_del(c,914)].
% 0.89/1.18 920 f(f2(c2)) = c1. [para(913(a,1),918(a,1,1)),flip(b),xx(a)].
% 0.89/1.18 921 $F. [back_rewrite(913),rewrite([920(3),732(2)]),flip(a),unit_del(a,914)].
% 0.89/1.18
% 0.89/1.18 % SZS output end Refutation
% 0.89/1.18 ============================== end of proof ==========================
% 0.89/1.18
% 0.89/1.18 ============================== STATISTICS ============================
% 0.89/1.18
% 0.89/1.18 Given=322. Generated=6580. Kept=916. proofs=1.
% 0.89/1.18 Usable=6. Sos=2. Demods=4. Limbo=1, Disabled=915. Hints=0.
% 0.89/1.18 Megabytes=0.83.
% 0.89/1.18 User_CPU=0.21, System_CPU=0.01, Wall_clock=0.
% 0.89/1.18
% 0.89/1.18 ============================== end of statistics =====================
% 0.89/1.18
% 0.89/1.18 ============================== end of search =========================
% 0.89/1.18
% 0.89/1.18 THEOREM PROVED
% 0.89/1.18 % SZS status Theorem
% 0.89/1.18
% 0.89/1.18 Exiting with 1 proof.
% 0.89/1.18
% 0.89/1.18 Process 16626 exit (max_proofs) Tue Jul 12 07:39:35 2022
% 0.89/1.18 Prover9 interrupted
%------------------------------------------------------------------------------