TSTP Solution File: GRP509-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP509-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 11:19:24 EDT 2022
% Result : Unsatisfiable 0.75s 1.03s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP509-1 : TPTP v8.1.0. Released v2.6.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 08:08:28 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.75/1.03 ============================== Prover9 ===============================
% 0.75/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.03 Process 3978 was started by sandbox on n018.cluster.edu,
% 0.75/1.03 Tue Jun 14 08:08:29 2022
% 0.75/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_3631_n018.cluster.edu".
% 0.75/1.03 ============================== end of head ===========================
% 0.75/1.03
% 0.75/1.03 ============================== INPUT =================================
% 0.75/1.03
% 0.75/1.03 % Reading from file /tmp/Prover9_3631_n018.cluster.edu
% 0.75/1.03
% 0.75/1.03 set(prolog_style_variables).
% 0.75/1.03 set(auto2).
% 0.75/1.03 % set(auto2) -> set(auto).
% 0.75/1.03 % set(auto) -> set(auto_inference).
% 0.75/1.03 % set(auto) -> set(auto_setup).
% 0.75/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.03 % set(auto) -> set(auto_limits).
% 0.75/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.03 % set(auto) -> set(auto_denials).
% 0.75/1.03 % set(auto) -> set(auto_process).
% 0.75/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.03 % set(auto2) -> assign(stats, some).
% 0.75/1.03 % set(auto2) -> clear(echo_input).
% 0.75/1.03 % set(auto2) -> set(quiet).
% 0.75/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.03 % set(auto2) -> clear(print_given).
% 0.75/1.03 assign(lrs_ticks,-1).
% 0.75/1.03 assign(sos_limit,10000).
% 0.75/1.03 assign(order,kbo).
% 0.75/1.03 set(lex_order_vars).
% 0.75/1.03 clear(print_given).
% 0.75/1.03
% 0.75/1.03 % formulas(sos). % not echoed (2 formulas)
% 0.75/1.03
% 0.75/1.03 ============================== end of input ==========================
% 0.75/1.03
% 0.75/1.03 % From the command line: assign(max_seconds, 300).
% 0.75/1.03
% 0.75/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.03
% 0.75/1.03 % Formulas that are not ordinary clauses:
% 0.75/1.03
% 0.75/1.03 ============================== end of process non-clausal formulas ===
% 0.75/1.03
% 0.75/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.75/1.03
% 0.75/1.03 ============================== PREDICATE ELIMINATION =================
% 0.75/1.03
% 0.75/1.03 ============================== end predicate elimination =============
% 0.75/1.03
% 0.75/1.03 Auto_denials:
% 0.75/1.03 % copying label prove_these_axioms_1 to answer in negative clause
% 0.75/1.03
% 0.75/1.03 Term ordering decisions:
% 0.75/1.03
% 0.75/1.03 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 0.75/1.03 Function symbol KB weights: a1=1. b1=1. multiply=1. inverse=0.
% 0.75/1.03
% 0.75/1.03 ============================== end of process initial clauses ========
% 0.75/1.03
% 0.75/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.75/1.03
% 0.75/1.03 ============================== end of clauses for search =============
% 0.75/1.03
% 0.75/1.03 ============================== SEARCH ================================
% 0.75/1.03
% 0.75/1.03 % Starting search at 0.01 seconds.
% 0.75/1.03
% 0.75/1.03 ============================== PROOF =================================
% 0.75/1.03 % SZS status Unsatisfiable
% 0.75/1.03 % SZS output start Refutation
% 0.75/1.03
% 0.75/1.03 % Proof 1 at 0.03 (+ 0.00) seconds: prove_these_axioms_1.
% 0.75/1.03 % Length of proof is 43.
% 0.75/1.03 % Level of proof is 18.
% 0.75/1.03 % Maximum clause weight is 23.000.
% 0.75/1.03 % Given clauses 22.
% 0.75/1.03
% 0.75/1.03 1 multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B # label(single_axiom) # label(axiom). [assumption].
% 0.75/1.03 2 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) # label(prove_these_axioms_1) # label(negated_conjecture) # answer(prove_these_axioms_1). [assumption].
% 0.75/1.03 3 multiply(inverse(b1),b1) != multiply(inverse(a1),a1) # answer(prove_these_axioms_1). [copy(2),flip(a)].
% 0.75/1.03 4 multiply(multiply(A,B),inverse(multiply(multiply(multiply(C,A),D),B))) = inverse(multiply(C,D)). [para(1(a,1),1(a,1,1,1))].
% 0.75/1.03 5 multiply(A,inverse(multiply(multiply(B,A),inverse(multiply(B,C))))) = C. [para(1(a,1),1(a,1,1))].
% 0.75/1.03 6 multiply(multiply(multiply(multiply(multiply(A,B),C),D),inverse(multiply(A,C))),inverse(B)) = D. [para(1(a,1),1(a,1,2,1))].
% 0.75/1.03 11 inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(multiply(C,D),inverse(multiply(B,D))). [para(1(a,1),4(a,1,2,1,1)),flip(a)].
% 0.75/1.03 12 multiply(multiply(A,inverse(multiply(B,C))),inverse(A)) = inverse(multiply(B,C)). [para(1(a,1),4(a,1,2,1))].
% 0.75/1.03 20 inverse(multiply(A,inverse(multiply(multiply(B,multiply(A,C)),inverse(multiply(B,D)))))) = multiply(multiply(C,E),inverse(multiply(D,E))). [para(5(a,1),4(a,1,2,1,1)),flip(a)].
% 0.75/1.03 22 inverse(multiply(A,multiply(B,inverse(multiply(multiply(A,B),C))))) = C. [para(5(a,1),4(a,1)),flip(a)].
% 0.75/1.03 25 multiply(inverse(multiply(multiply(A,B),inverse(multiply(A,C)))),inverse(multiply(C,inverse(multiply(B,D))))) = D. [para(5(a,1),5(a,1,2,1,1))].
% 0.75/1.03 26 inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(D,inverse(multiply(multiply(B,D),inverse(C)))). [para(5(a,1),5(a,1,2,1,2,1)),flip(a)].
% 0.75/1.03 27 multiply(multiply(multiply(A,B),multiply(C,inverse(multiply(multiply(A,C),D)))),D) = B. [para(22(a,1),1(a,1,2))].
% 0.75/1.03 28 inverse(multiply(multiply(multiply(A,B),C),multiply(inverse(multiply(A,C)),inverse(multiply(B,D))))) = D. [para(1(a,1),22(a,1,1,2,2,1,1))].
% 0.75/1.03 29 inverse(multiply(multiply(A,B),multiply(C,inverse(B)))) = inverse(multiply(A,C)). [para(1(a,1),22(a,1,1,2,2,1))].
% 0.75/1.03 32 inverse(multiply(multiply(multiply(A,B),C),D)) = inverse(multiply(B,multiply(D,inverse(inverse(multiply(A,C)))))). [para(4(a,1),22(a,1,1,2,2,1)),flip(a)].
% 0.75/1.03 36 inverse(multiply(multiply(A,multiply(B,C)),inverse(multiply(A,D)))) = inverse(multiply(B,multiply(C,inverse(D)))). [para(5(a,1),22(a,1,1,2,2,1)),flip(a)].
% 0.75/1.03 40 inverse(multiply(A,inverse(multiply(A,B)))) = B. [back_rewrite(28),rewrite([32(9),12(9)])].
% 0.75/1.03 50 multiply(multiply(A,B),inverse(multiply(C,B))) = multiply(A,inverse(C)). [back_rewrite(20),rewrite([36(6),40(6)]),flip(a)].
% 0.75/1.03 53 inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(C,inverse(B)). [back_rewrite(11),rewrite([50(9)])].
% 0.75/1.03 54 multiply(multiply(A,B),inverse(A)) = B. [back_rewrite(1),rewrite([50(5)])].
% 0.75/1.03 61 inverse(multiply(A,multiply(B,inverse(C)))) = multiply(C,inverse(multiply(A,B))). [back_rewrite(36),rewrite([53(6)]),flip(a)].
% 0.75/1.03 62 multiply(A,inverse(multiply(multiply(B,A),inverse(C)))) = multiply(C,inverse(B)). [back_rewrite(26),rewrite([53(5)]),flip(a)].
% 0.75/1.03 63 multiply(multiply(A,inverse(B)),inverse(multiply(A,inverse(multiply(B,C))))) = C. [back_rewrite(25),rewrite([53(5)])].
% 0.75/1.03 65 multiply(A,inverse(multiply(multiply(B,A),C))) = inverse(multiply(B,C)). [back_rewrite(29),rewrite([61(5)])].
% 0.75/1.03 66 inverse(multiply(A,inverse(B))) = multiply(B,inverse(A)). [back_rewrite(62),rewrite([65(5)])].
% 0.75/1.03 68 multiply(multiply(multiply(A,B),inverse(multiply(A,C))),C) = B. [back_rewrite(27),rewrite([65(5)])].
% 0.75/1.03 69 multiply(multiply(A,inverse(B)),multiply(multiply(B,C),inverse(A))) = C. [back_rewrite(63),rewrite([66(6)])].
% 0.75/1.03 70 multiply(multiply(A,B),inverse(multiply(A,C))) = multiply(B,inverse(C)). [back_rewrite(53),rewrite([66(5)])].
% 0.75/1.03 71 multiply(multiply(A,inverse(B)),B) = A. [back_rewrite(68),rewrite([70(4)])].
% 0.75/1.03 72 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(54(a,1),54(a,1,1))].
% 0.75/1.03 78 inverse(multiply(A,B)) = multiply(inverse(A),inverse(B)). [para(54(a,1),6(a,1,1,1)),rewrite([72(3)]),flip(a)].
% 0.75/1.03 100 inverse(inverse(A)) = A. [para(71(a,1),54(a,1)),flip(a)].
% 0.75/1.03 101 multiply(A,B) = multiply(B,A). [para(54(a,1),71(a,1,1))].
% 0.75/1.03 115 multiply(inverse(A),multiply(A,B)) = B. [back_rewrite(54),rewrite([101(3)])].
% 0.75/1.03 116 multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) # answer(prove_these_axioms_1). [back_rewrite(3),rewrite([101(4),101(8)])].
% 0.75/1.03 117 multiply(inverse(A),multiply(B,A)) = B. [para(115(a,1),101(a,1)),rewrite([101(1),101(3)]),flip(a)].
% 0.75/1.03 123 multiply(multiply(A,B),multiply(C,inverse(A))) = multiply(B,C). [para(115(a,1),69(a,1,2,1)),rewrite([100(2)])].
% 0.75/1.03 130 multiply(A,multiply(inverse(A),inverse(B))) = inverse(B). [para(117(a,1),117(a,1,2)),rewrite([78(2),101(4)])].
% 0.75/1.03 140 multiply(A,multiply(B,C)) = multiply(B,multiply(A,C)). [para(115(a,1),123(a,1,1)),rewrite([100(2),101(3),101(4)])].
% 0.75/1.03 141 multiply(A,multiply(B,multiply(C,inverse(A)))) = multiply(B,C). [para(123(a,1),117(a,1,2)),rewrite([78(3),100(3),101(2),101(3),140(4),101(3),140(3)])].
% 0.75/1.03 159 multiply(A,inverse(A)) = multiply(B,inverse(B)). [para(130(a,1),141(a,1,2))].
% 0.75/1.03 160 $F # answer(prove_these_axioms_1). [resolve(159,a,116,a)].
% 0.75/1.03
% 0.75/1.03 % SZS output end Refutation
% 0.75/1.03 ============================== end of proof ==========================
% 0.75/1.03
% 0.75/1.03 ============================== STATISTICS ============================
% 0.75/1.03
% 0.75/1.03 Given=22. Generated=394. Kept=158. proofs=1.
% 0.75/1.03 Usable=10. Sos=16. Demods=25. Limbo=0, Disabled=133. Hints=0.
% 0.75/1.03 Megabytes=0.15.
% 0.75/1.03 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.75/1.03
% 0.75/1.03 ============================== end of statistics =====================
% 0.75/1.03
% 0.75/1.03 ============================== end of search =========================
% 0.75/1.03
% 0.75/1.03 THEOREM PROVED
% 0.75/1.03 % SZS status Unsatisfiable
% 0.75/1.03
% 0.75/1.03 Exiting with 1 proof.
% 0.75/1.03
% 0.75/1.03 Process 3978 exit (max_proofs) Tue Jun 14 08:08:29 2022
% 0.75/1.03 Prover9 interrupted
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