TSTP Solution File: GRP025-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP025-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 : Sat Jul 16 11:16:46 EDT 2022
% Result : Unsatisfiable 30.95s 31.28s
% Output : Refutation 30.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP025-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n020.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 05:26:05 EDT 2022
% 0.12/0.34 % CPUTime :
% 30.95/31.28 ============================== Prover9 ===============================
% 30.95/31.28 Prover9 (32) version 2009-11A, November 2009.
% 30.95/31.28 Process 16150 was started by sandbox2 on n020.cluster.edu,
% 30.95/31.28 Mon Jun 13 05:26:06 2022
% 30.95/31.28 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_15996_n020.cluster.edu".
% 30.95/31.28 ============================== end of head ===========================
% 30.95/31.28
% 30.95/31.28 ============================== INPUT =================================
% 30.95/31.28
% 30.95/31.28 % Reading from file /tmp/Prover9_15996_n020.cluster.edu
% 30.95/31.28
% 30.95/31.28 set(prolog_style_variables).
% 30.95/31.28 set(auto2).
% 30.95/31.28 % set(auto2) -> set(auto).
% 30.95/31.28 % set(auto) -> set(auto_inference).
% 30.95/31.28 % set(auto) -> set(auto_setup).
% 30.95/31.28 % set(auto_setup) -> set(predicate_elim).
% 30.95/31.28 % set(auto_setup) -> assign(eq_defs, unfold).
% 30.95/31.28 % set(auto) -> set(auto_limits).
% 30.95/31.28 % set(auto_limits) -> assign(max_weight, "100.000").
% 30.95/31.28 % set(auto_limits) -> assign(sos_limit, 20000).
% 30.95/31.28 % set(auto) -> set(auto_denials).
% 30.95/31.28 % set(auto) -> set(auto_process).
% 30.95/31.28 % set(auto2) -> assign(new_constants, 1).
% 30.95/31.28 % set(auto2) -> assign(fold_denial_max, 3).
% 30.95/31.28 % set(auto2) -> assign(max_weight, "200.000").
% 30.95/31.28 % set(auto2) -> assign(max_hours, 1).
% 30.95/31.28 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 30.95/31.28 % set(auto2) -> assign(max_seconds, 0).
% 30.95/31.28 % set(auto2) -> assign(max_minutes, 5).
% 30.95/31.28 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 30.95/31.28 % set(auto2) -> set(sort_initial_sos).
% 30.95/31.28 % set(auto2) -> assign(sos_limit, -1).
% 30.95/31.28 % set(auto2) -> assign(lrs_ticks, 3000).
% 30.95/31.28 % set(auto2) -> assign(max_megs, 400).
% 30.95/31.28 % set(auto2) -> assign(stats, some).
% 30.95/31.28 % set(auto2) -> clear(echo_input).
% 30.95/31.28 % set(auto2) -> set(quiet).
% 30.95/31.28 % set(auto2) -> clear(print_initial_clauses).
% 30.95/31.28 % set(auto2) -> clear(print_given).
% 30.95/31.28 assign(lrs_ticks,-1).
% 30.95/31.28 assign(sos_limit,10000).
% 30.95/31.28 assign(order,kbo).
% 30.95/31.28 set(lex_order_vars).
% 30.95/31.28 clear(print_given).
% 30.95/31.28
% 30.95/31.28 % formulas(sos). % not echoed (32 formulas)
% 30.95/31.28
% 30.95/31.28 ============================== end of input ==========================
% 30.95/31.28
% 30.95/31.28 % From the command line: assign(max_seconds, 300).
% 30.95/31.28
% 30.95/31.28 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 30.95/31.28
% 30.95/31.28 % Formulas that are not ordinary clauses:
% 30.95/31.28
% 30.95/31.28 ============================== end of process non-clausal formulas ===
% 30.95/31.28
% 30.95/31.28 ============================== PROCESS INITIAL CLAUSES ===============
% 30.95/31.28
% 30.95/31.28 ============================== PREDICATE ELIMINATION =================
% 30.95/31.28
% 30.95/31.28 ============================== end predicate elimination =============
% 30.95/31.28
% 30.95/31.28 Auto_denials: (non-Horn, no changes).
% 30.95/31.28
% 30.95/31.28 Term ordering decisions:
% 30.95/31.28 Function symbol KB weights: g1=1. a=1. b=1. c=1. d=1. g2=1. d1=1. d2=1. d3=1. inverse=1. identity_for=1. an_isomorphism=1. multiply=1.
% 30.95/31.28
% 30.95/31.28 ============================== end of process initial clauses ========
% 30.95/31.28
% 30.95/31.28 ============================== CLAUSES FOR SEARCH ====================
% 30.95/31.28
% 30.95/31.28 ============================== end of clauses for search =============
% 30.95/31.28
% 30.95/31.28 ============================== SEARCH ================================
% 30.95/31.28
% 30.95/31.28 % Starting search at 0.01 seconds.
% 30.95/31.28
% 30.95/31.28 Low Water (keep): wt=28.000, iters=3767
% 30.95/31.28
% 30.95/31.28 Low Water (keep): wt=21.000, iters=3362
% 30.95/31.28
% 30.95/31.28 Low Water (keep): wt=20.000, iters=3451
% 30.95/31.28
% 30.95/31.28 Low Water (keep): wt=18.000, iters=3405
% 30.95/31.28
% 30.95/31.28 Low Water (keep): wt=16.000, iters=3336
% 30.95/31.28
% 30.95/31.28 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 161 (0.00 of 0.35 sec).
% 30.95/31.28
% 30.95/31.28 Low Water (keep): wt=15.000, iters=3339
% 30.95/31.28
% 30.95/31.28 Low Water (keep): wt=14.000, iters=3361
% 30.95/31.28
% 30.95/31.28 Low Water (keep): wt=13.000, iters=3336
% 30.95/31.28
% 30.95/31.28 ============================== PROOF =================================
% 30.95/31.28 % SZS status Unsatisfiable
% 30.95/31.28 % SZS output start Refutation
% 30.95/31.28
% 30.95/31.28 % Proof 1 at 29.69 (+ 0.60) seconds.
% 30.95/31.28 % Length of proof is 134.
% 30.95/31.28 % Level of proof is 15.
% 30.95/31.28 % Maximum clause weight is 24.000.
% 30.95/31.28 % Given clauses 10062.
% 30.95/31.28
% 30.95/31.28 1 group_member(a,g1) # label(a_member_of_group1) # label(hypothesis). [assumption].
% 30.95/31.28 2 group_member(b,g1) # label(b_member_of_group1) # label(hypothesis). [assumption].
% 30.95/31.28 5 group_member(d1,g1) # label(d1_member_of_group1) # label(hypothesis). [assumption].
% 30.95/31.28 6 group_member(d2,g1) # label(d2_member_of_group1) # label(hypothesis). [assumption].
% 30.95/31.28 7 group_member(d3,g1) # label(d3_member_of_group1) # label(hypothesis). [assumption].
% 30.95/31.28 9 an_isomorphism(a) = c # label(a_maps_to_c) # label(hypothesis). [assumption].
% 30.95/31.28 10 an_isomorphism(b) = d # label(b_maps_to_d) # label(hypothesis). [assumption].
% 30.95/31.28 11 product(g1,a,a,a) # label(a_times_a_is_a) # label(hypothesis). [assumption].
% 30.95/31.28 12 product(g1,a,b,b) # label(a_times_b_is_b) # label(hypothesis). [assumption].
% 30.95/31.28 14 product(g1,b,b,a) # label(b_times_b_is_a) # label(hypothesis). [assumption].
% 30.95/31.28 16 product(g2,c,d,d) # label(c_times_d_is_d) # label(hypothesis). [assumption].
% 30.95/31.28 18 product(g2,d,d,c) # label(d_times_d_is_c) # label(hypothesis). [assumption].
% 30.95/31.28 19 product(g1,d1,d2,d3) # label(d1_times_d2_is_d3) # label(hypothesis). [assumption].
% 30.95/31.28 20 product(A,identity_for(A),B,B) # label(left_identity) # label(axiom). [assumption].
% 30.95/31.28 21 product(A,B,identity_for(A),B) # label(right_identity) # label(axiom). [assumption].
% 30.95/31.28 22 product(A,inverse(A,B),B,identity_for(A)) # label(left_inverse) # label(axiom). [assumption].
% 30.95/31.28 23 product(A,B,inverse(A,B),identity_for(A)) # label(right_inverse) # label(axiom). [assumption].
% 30.95/31.28 24 -product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)) # label(prove_product_holds_in_group2) # label(negated_conjecture). [assumption].
% 30.95/31.28 25 -group_member(A,B) | group_member(inverse(B,A),B) # label(inverse_in_group) # label(axiom). [assumption].
% 30.95/31.28 26 -group_member(A,g1) | A = a | A = b # label(a_and_b_only_members_of_group1) # label(hypothesis). [assumption].
% 30.95/31.28 27 -group_member(A,g1) | a = A | b = A. [copy(26),flip(b),flip(c)].
% 30.95/31.28 30 -group_member(A,B) | -group_member(C,B) | group_member(multiply(B,A,C),B) # label(total_function1_2) # label(axiom). [assumption].
% 30.95/31.28 31 -product(A,B,C,D) | -product(A,B,C,E) | E = D # label(total_function2) # label(axiom). [assumption].
% 30.95/31.28 32 -group_member(A,B) | -group_member(C,B) | product(B,A,C,multiply(B,A,C)) # label(total_function1_1) # label(axiom). [assumption].
% 30.95/31.28 33 -product(A,B,C,D) | -product(A,C,E,F) | -product(A,D,E,V6) | product(A,B,F,V6) # label(associativity1) # label(axiom). [assumption].
% 30.95/31.28 34 -product(A,B,C,D) | -product(A,C,E,F) | -product(A,B,F,V6) | product(A,D,E,V6) # label(associativity2) # label(axiom). [assumption].
% 30.95/31.28 35 -group_member(A,B) | group_member(multiply(B,A,A),B). [factor(30,a,b)].
% 30.95/31.28 36 -group_member(A,B) | product(B,A,A,multiply(B,A,A)). [factor(32,a,b)].
% 30.95/31.28 44 group_member(inverse(g1,d3),g1). [resolve(25,a,7,a)].
% 30.95/31.28 52 d3 = a | d3 = b. [resolve(27,a,7,a),flip(a),flip(b)].
% 30.95/31.28 53 d2 = a | d2 = b. [resolve(27,a,6,a),flip(a),flip(b)].
% 30.95/31.28 54 d1 = a | d1 = b. [resolve(27,a,5,a),flip(a),flip(b)].
% 30.95/31.28 72 -product(A,B,inverse(A,B),C) | identity_for(A) = C. [resolve(31,a,23,a),flip(b)].
% 30.95/31.28 74 -product(A,B,identity_for(A),C) | C = B. [resolve(31,a,21,a)].
% 30.95/31.28 75 -product(A,identity_for(A),B,C) | C = B. [resolve(31,a,20,a)].
% 30.95/31.28 76 -product(g1,d1,d2,A) | d3 = A. [resolve(31,a,19,a),flip(b)].
% 30.95/31.28 81 -product(g1,b,b,A) | a = A. [resolve(31,a,14,a),flip(b)].
% 30.95/31.28 84 -product(g1,a,a,A) | a = A. [resolve(31,a,11,a),flip(b)].
% 30.95/31.28 85 -product(A,B,identity_for(A),C) | B = C. [resolve(31,b,21,a)].
% 30.95/31.28 86 -product(A,identity_for(A),B,C) | B = C. [resolve(31,b,20,a)].
% 30.95/31.28 88 -group_member(A,g1) | product(g1,d3,A,multiply(g1,d3,A)). [resolve(32,a,7,a)].
% 30.95/31.28 90 -group_member(A,g1) | product(g1,d1,A,multiply(g1,d1,A)). [resolve(32,a,5,a)].
% 30.95/31.28 94 -group_member(A,g1) | product(g1,a,A,multiply(g1,a,A)). [resolve(32,a,1,a)].
% 30.95/31.28 97 -group_member(A,g1) | product(g1,A,d2,multiply(g1,A,d2)). [resolve(32,b,6,a)].
% 30.95/31.28 110 -product(g2,d,A,B) | -product(g2,d,A,C) | product(g2,c,B,C). [resolve(33,a,16,a)].
% 30.95/31.28 114 -product(g1,b,A,B) | -product(g1,b,A,C) | product(g1,a,B,C). [resolve(33,a,12,a)].
% 30.95/31.28 120 -product(g1,A,d1,B) | -product(g1,B,d2,C) | product(g1,A,d3,C). [resolve(33,b,19,a)].
% 30.95/31.28 121 -product(g2,A,d,B) | -product(g2,B,d,C) | product(g2,A,c,C). [resolve(33,b,18,a)].
% 30.95/31.28 132 -product(A,B,C,identity_for(A)) | -product(A,C,D,E) | product(A,B,E,D). [resolve(33,c,20,a)].
% 30.95/31.28 142 -product(g2,inverse(g2,an_isomorphism(d1)),an_isomorphism(d3),an_isomorphism(d2)). [ur(33,a,23,a,c,20,a,d,24,a)].
% 30.95/31.28 144 -product(g2,d,A,B) | product(g2,c,B,B). [factor(110,a,b)].
% 30.95/31.28 146 -product(g1,b,A,B) | product(g1,a,B,B). [factor(114,a,b)].
% 30.95/31.28 155 -product(g1,d2,A,B) | -product(g1,d1,B,C) | product(g1,d3,A,C). [resolve(34,a,19,a)].
% 30.95/31.28 160 -product(g1,b,A,B) | -product(g1,b,B,C) | product(g1,a,A,C). [resolve(34,a,14,a)].
% 30.95/31.28 190 -product(g2,an_isomorphism(d3),inverse(g2,an_isomorphism(d2)),an_isomorphism(d1)). [ur(34,b,22,a,c,21,a,d,24,a)].
% 30.95/31.28 200 group_member(multiply(g1,d1,d1),g1). [resolve(35,a,5,a)].
% 30.95/31.28 207 product(g1,d2,d2,multiply(g1,d2,d2)). [resolve(36,a,6,a)].
% 30.95/31.28 208 product(g1,d1,d1,multiply(g1,d1,d1)). [resolve(36,a,5,a)].
% 30.95/31.28 211 product(g1,b,b,multiply(g1,b,b)). [resolve(36,a,2,a)].
% 30.95/31.28 212 product(g1,a,a,multiply(g1,a,a)). [resolve(36,a,1,a)].
% 30.95/31.28 254 -product(g2,an_isomorphism(d2),inverse(g2,an_isomorphism(d3)),inverse(g2,an_isomorphism(d1))). [ur(34,b,22,a,c,21,a,d,142,a)].
% 30.95/31.28 256 -product(g2,an_isomorphism(d1),inverse(g2,inverse(g2,an_isomorphism(d2))),an_isomorphism(d3)). [ur(34,b,22,a,c,21,a,d,190,a)].
% 30.95/31.28 259 -product(g2,inverse(g2,an_isomorphism(d2)),inverse(g2,an_isomorphism(d1)),inverse(g2,an_isomorphism(d3))). [ur(33,a,23,a,c,20,a,d,254,a)].
% 30.95/31.28 268 inverse(g1,d3) = a | inverse(g1,d3) = b. [resolve(44,a,27,a),flip(a),flip(b)].
% 30.95/31.28 302 -product(g2,an_isomorphism(d3),inverse(g2,inverse(g2,inverse(g2,an_isomorphism(d2)))),an_isomorphism(d1)). [ur(34,b,22,a,c,21,a,d,256,a)].
% 30.95/31.28 325 d3 = a | -product(g2,an_isomorphism(d1),an_isomorphism(d2),d). [para(52(b,1),24(a,4,1)),rewrite([10(10)])].
% 30.95/31.28 335 d2 = a | -product(g2,an_isomorphism(d1),d,an_isomorphism(d3)). [para(53(b,1),24(a,3,1)),rewrite([10(8)])].
% 30.95/31.28 359 -product(g2,an_isomorphism(d1),inverse(g2,inverse(g2,inverse(g2,inverse(g2,an_isomorphism(d2))))),an_isomorphism(d3)). [ur(34,b,22,a,c,21,a,d,302,a)].
% 30.95/31.28 560 -product(g2,an_isomorphism(d3),inverse(g2,inverse(g2,inverse(g2,inverse(g2,inverse(g2,an_isomorphism(d2)))))),an_isomorphism(d1)). [ur(34,b,22,a,c,21,a,d,359,a)].
% 30.95/31.28 881 -product(g2,an_isomorphism(d1),inverse(g2,inverse(g2,inverse(g2,inverse(g2,inverse(g2,inverse(g2,an_isomorphism(d2))))))),an_isomorphism(d3)). [ur(34,b,22,a,c,21,a,d,560,a)].
% 30.95/31.28 1445 -product(g2,an_isomorphism(d3),inverse(g2,inverse(g2,inverse(g2,inverse(g2,inverse(g2,inverse(g2,inverse(g2,an_isomorphism(d2)))))))),an_isomorphism(d1)). [ur(34,b,22,a,c,21,a,d,881,a)].
% 30.95/31.28 1687 d2 = a | product(g1,d2,d2,multiply(g1,b,d2)). [para(53(b,1),207(a,4,2))].
% 30.95/31.28 1836 multiply(g1,b,b) = a. [resolve(211,a,81,a),flip(a)].
% 30.95/31.28 1837 multiply(g1,a,a) = a. [resolve(212,a,84,a),flip(a)].
% 30.95/31.28 1838 inverse(A,identity_for(A)) = identity_for(A). [resolve(72,a,20,a),flip(a)].
% 30.95/31.28 1891 d2 = a | -product(g2,an_isomorphism(d3),inverse(g2,inverse(g2,inverse(g2,inverse(g2,inverse(g2,inverse(g2,inverse(g2,d))))))),an_isomorphism(d1)). [para(53(b,1),1445(a,3,2,2,2,2,2,2,2,1)),rewrite([10(15)])].
% 30.95/31.28 2642 product(g1,d3,d2,multiply(g1,d3,d2)). [resolve(88,a,6,a)].
% 30.95/31.28 2998 product(g1,d1,d3,multiply(g1,d1,d3)). [resolve(90,a,7,a)].
% 30.95/31.28 2999 product(g1,d1,d2,multiply(g1,d1,d2)). [resolve(90,a,6,a)].
% 30.95/31.28 3001 product(g1,d1,a,multiply(g1,d1,a)). [resolve(90,a,1,a)].
% 30.95/31.28 3631 product(g1,a,d3,multiply(g1,a,d3)). [resolve(94,a,7,a)].
% 30.95/31.28 3632 product(g1,a,d2,multiply(g1,a,d2)). [resolve(94,a,6,a)].
% 30.95/31.28 4240 product(g1,multiply(g1,d1,d1),d2,multiply(g1,multiply(g1,d1,d1),d2)). [resolve(97,a,200,a)].
% 30.95/31.28 4802 -product(g1,d3,d2,A) | multiply(g1,d3,d2) = A. [resolve(2642,a,31,b)].
% 30.95/31.28 4881 -product(g1,d1,d3,A) | multiply(g1,d1,d3) = A. [resolve(2998,a,31,b)].
% 30.95/31.28 4919 multiply(g1,d1,d2) = d3. [resolve(2999,a,76,a),flip(a)].
% 30.95/31.28 4922 d2 = a | multiply(g1,d1,b) = d3. [para(53(b,1),4919(a,1,3))].
% 30.95/31.28 5750 -product(g1,multiply(g1,d1,d1),d2,A) | product(g1,d1,d3,A). [resolve(120,a,208,a)].
% 30.95/31.28 5825 -product(g2,A,d,c) | product(g2,A,c,d). [resolve(121,b,16,a)].
% 30.95/31.28 6995 product(g2,c,identity_for(g2),identity_for(g2)). [resolve(144,a,23,a)].
% 30.95/31.28 7010 identity_for(g2) = c. [resolve(6995,a,85,a),flip(a)].
% 30.95/31.28 7034 product(g2,A,c,A). [para(7010(a,1),21(a,3))].
% 30.95/31.28 7035 product(g2,inverse(g2,A),A,c). [para(7010(a,1),22(a,4))].
% 30.95/31.28 7037 inverse(g2,c) = c. [para(7010(a,1),1838(a,1,2)),rewrite([7010(5)])].
% 30.95/31.28 7040 -product(g2,A,c,B) | A = B. [para(7010(a,1),85(a,3))].
% 30.95/31.28 7075 product(g1,a,identity_for(g1),identity_for(g1)). [resolve(146,a,23,a)].
% 30.95/31.28 7084 identity_for(g1) = a. [resolve(7075,a,85,a),flip(a)].
% 30.95/31.28 7119 product(g1,a,A,A). [para(7084(a,1),20(a,2))].
% 30.95/31.28 7120 product(g1,A,a,A). [para(7084(a,1),21(a,3))].
% 30.95/31.28 7124 -product(g1,A,a,B) | B = A. [para(7084(a,1),74(a,3))].
% 30.95/31.28 7125 -product(g1,a,A,B) | B = A. [para(7084(a,1),75(a,2))].
% 30.95/31.28 7127 -product(g1,a,A,B) | A = B. [para(7084(a,1),86(a,2))].
% 30.95/31.28 7128 -product(g1,A,a,a) | product(g1,A,B,B). [resolve(7119,a,132,b),rewrite([7084(4)])].
% 30.95/31.28 7181 multiply(g1,d1,a) = d1. [resolve(7124,a,3001,a)].
% 30.95/31.28 7237 multiply(g1,a,d2) = d2. [resolve(7125,a,3632,a)].
% 30.95/31.28 7238 multiply(g1,a,d3) = d3. [resolve(7125,a,3631,a)].
% 30.95/31.28 7466 -product(g1,d2,A,a) | product(g1,d3,A,d1). [resolve(155,b,7120,a)].
% 30.95/31.28 7706 -product(g1,b,A,a) | product(g1,a,A,b). [resolve(160,b,7120,a)].
% 30.95/31.28 8528 d1 = a | d2 = a | d3 = a. [para(54(b,1),4922(b,1,2)),rewrite([1836(10)]),flip(c)].
% 30.95/31.28 8577 inverse(g1,d3) = a | product(g1,b,d3,a). [para(268(b,1),22(a,2)),rewrite([7084(10)])].
% 30.95/31.28 8600 d1 = a | d3 = a | -product(g2,d,an_isomorphism(d2),d). [para(54(b,1),325(b,2,1)),rewrite([10(9)])].
% 30.95/31.28 8604 d1 = a | d2 = a | -product(g2,d,d,an_isomorphism(d3)). [para(54(b,1),335(b,2,1)),rewrite([10(9)])].
% 30.95/31.28 8964 product(g2,inverse(g2,d),c,d). [resolve(5825,a,7035,a)].
% 30.95/31.28 8965 inverse(g2,d) = d. [resolve(8964,a,7040,a)].
% 30.95/31.28 8970 d2 = a | -product(g2,an_isomorphism(d3),d,an_isomorphism(d1)). [back_rewrite(1891),rewrite([8965(15),8965(14),8965(13),8965(12),8965(11),8965(10),8965(9)])].
% 30.95/31.28 9159 inverse(g1,d3) = a | product(g1,a,d3,b). [resolve(8577,b,7706,a)].
% 30.95/31.28 9254 inverse(g1,d3) = a | d3 = b. [resolve(9159,b,7127,a)].
% 30.95/31.28 9256 d3 = b | product(g1,d3,a,a). [para(9254(a,1),23(a,3)),rewrite([7084(8)])].
% 30.95/31.28 9266 d3 = b | product(g1,d3,A,A). [resolve(9256,b,7128,a)].
% 30.95/31.28 9721 d2 = a | product(g1,d2,d2,a). [para(53(b,1),1687(b,4,3)),rewrite([1836(13)]),merge(b)].
% 30.95/31.28 9731 d2 = a | product(g1,d3,d2,d1). [resolve(9721,b,7466,a)].
% 30.95/31.28 10491 multiply(g1,d3,d2) = d1 | d2 = a. [resolve(4802,a,9731,b)].
% 30.95/31.28 10494 multiply(g1,d3,d2) = d2 | d3 = b. [resolve(4802,a,9266,b)].
% 30.95/31.28 10516 d3 = b | d2 = d1 | d2 = a. [para(10494(a,1),10491(a,1))].
% 30.95/31.28 10552 d2 = d1 | d2 = a | -product(g2,d,d,an_isomorphism(d1)). [para(10516(a,1),8970(b,2,1)),rewrite([10(12)]),merge(c)].
% 30.95/31.28 22132 product(g1,d1,d3,multiply(g1,multiply(g1,d1,d1),d2)). [resolve(5750,a,4240,a)].
% 30.95/31.28 22143 multiply(g1,multiply(g1,d1,d1),d2) = multiply(g1,d1,d3). [resolve(22132,a,4881,a),flip(a)].
% 30.95/31.28 24012 d1 = a | d2 = a. [para(8528(c,1),8604(c,4,1)),rewrite([9(17)]),merge(c),merge(d),unit_del(c,18)].
% 30.95/31.28 24031 d1 = a | d3 = d1. [para(24012(b,1),4919(a,1,3)),rewrite([7181(7)]),flip(b)].
% 30.95/31.28 24141 d1 = a | d3 = a. [para(24012(b,1),8600(c,3,1)),rewrite([9(13)]),merge(b),unit_del(c,7034)].
% 30.95/31.28 24557 d1 = a. [para(24141(b,1),24031(b,1)),flip(c),merge(b),merge(c)].
% 30.95/31.28 25109 d3 = d2. [back_rewrite(22143),rewrite([24557(3),24557(4),1837(5),7237(4),24557(3),7238(5)]),flip(a)].
% 30.95/31.28 25380 d2 = a. [back_rewrite(10552),rewrite([24557(2),24557(10),9(11)]),merge(b),unit_del(b,18)].
% 30.95/31.28 25382 $F. [back_rewrite(259),rewrite([25380(3),9(4),7037(4),24557(4),9(5),7037(5),25109(5),25380(5),9(6),7037(6)]),unit_del(a,7034)].
% 30.95/31.28
% 30.95/31.28 % SZS output end Refutation
% 30.95/31.28 ============================== end of proof ==========================
% 30.95/31.28
% 30.95/31.28 ============================== STATISTICS ============================
% 30.95/31.28
% 30.95/31.28 Given=10062. Generated=1180542. Kept=25379. proofs=1.
% 30.95/31.28 Usable=2158. Sos=2293. Demods=56. Limbo=825, Disabled=20135. Hints=0.
% 30.95/31.28 Megabytes=21.55.
% 30.95/31.28 User_CPU=29.69, System_CPU=0.60, Wall_clock=30.
% 30.95/31.28
% 30.95/31.28 ============================== end of statistics =====================
% 30.95/31.28
% 30.95/31.28 ============================== end of search =========================
% 30.95/31.28
% 30.95/31.28 THEOREM PROVED
% 30.95/31.28 % SZS status Unsatisfiable
% 30.95/31.28
% 30.95/31.28 Exiting with 1 proof.
% 30.95/31.28
% 30.95/31.28 Process 16150 exit (max_proofs) Mon Jun 13 05:26:36 2022
% 30.95/31.28 Prover9 interrupted
%------------------------------------------------------------------------------