TSTP Solution File: GRP403-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP403-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 11:18:57 EDT 2022
% Result : Unsatisfiable 2.12s 2.38s
% Output : Refutation 2.12s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP403-1 : TPTP v8.1.0. Released v2.6.0.
% 0.14/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jun 14 11:02:14 EDT 2022
% 0.22/0.36 % CPUTime :
% 2.12/2.38 ============================== Prover9 ===============================
% 2.12/2.38 Prover9 (32) version 2009-11A, November 2009.
% 2.12/2.38 Process 21971 was started by sandbox2 on n013.cluster.edu,
% 2.12/2.38 Tue Jun 14 11:02:14 2022
% 2.12/2.38 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_21817_n013.cluster.edu".
% 2.12/2.38 ============================== end of head ===========================
% 2.12/2.38
% 2.12/2.38 ============================== INPUT =================================
% 2.12/2.38
% 2.12/2.38 % Reading from file /tmp/Prover9_21817_n013.cluster.edu
% 2.12/2.38
% 2.12/2.38 set(prolog_style_variables).
% 2.12/2.38 set(auto2).
% 2.12/2.38 % set(auto2) -> set(auto).
% 2.12/2.38 % set(auto) -> set(auto_inference).
% 2.12/2.38 % set(auto) -> set(auto_setup).
% 2.12/2.38 % set(auto_setup) -> set(predicate_elim).
% 2.12/2.38 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.12/2.38 % set(auto) -> set(auto_limits).
% 2.12/2.38 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.12/2.38 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.12/2.38 % set(auto) -> set(auto_denials).
% 2.12/2.38 % set(auto) -> set(auto_process).
% 2.12/2.38 % set(auto2) -> assign(new_constants, 1).
% 2.12/2.38 % set(auto2) -> assign(fold_denial_max, 3).
% 2.12/2.38 % set(auto2) -> assign(max_weight, "200.000").
% 2.12/2.38 % set(auto2) -> assign(max_hours, 1).
% 2.12/2.38 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.12/2.38 % set(auto2) -> assign(max_seconds, 0).
% 2.12/2.38 % set(auto2) -> assign(max_minutes, 5).
% 2.12/2.38 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.12/2.38 % set(auto2) -> set(sort_initial_sos).
% 2.12/2.38 % set(auto2) -> assign(sos_limit, -1).
% 2.12/2.38 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.12/2.38 % set(auto2) -> assign(max_megs, 400).
% 2.12/2.38 % set(auto2) -> assign(stats, some).
% 2.12/2.38 % set(auto2) -> clear(echo_input).
% 2.12/2.38 % set(auto2) -> set(quiet).
% 2.12/2.38 % set(auto2) -> clear(print_initial_clauses).
% 2.12/2.38 % set(auto2) -> clear(print_given).
% 2.12/2.38 assign(lrs_ticks,-1).
% 2.12/2.38 assign(sos_limit,10000).
% 2.12/2.38 assign(order,kbo).
% 2.12/2.38 set(lex_order_vars).
% 2.12/2.38 clear(print_given).
% 2.12/2.38
% 2.12/2.38 % formulas(sos). % not echoed (2 formulas)
% 2.12/2.38
% 2.12/2.38 ============================== end of input ==========================
% 2.12/2.38
% 2.12/2.38 % From the command line: assign(max_seconds, 300).
% 2.12/2.38
% 2.12/2.38 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.12/2.38
% 2.12/2.38 % Formulas that are not ordinary clauses:
% 2.12/2.38
% 2.12/2.38 ============================== end of process non-clausal formulas ===
% 2.12/2.38
% 2.12/2.38 ============================== PROCESS INITIAL CLAUSES ===============
% 2.12/2.38
% 2.12/2.38 ============================== PREDICATE ELIMINATION =================
% 2.12/2.38
% 2.12/2.38 ============================== end predicate elimination =============
% 2.12/2.38
% 2.12/2.38 Auto_denials:
% 2.12/2.38 % copying label prove_these_axioms_1 to answer in negative clause
% 2.12/2.38
% 2.12/2.38 Term ordering decisions:
% 2.12/2.38
% 2.12/2.38 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 2.12/2.38 Function symbol KB weights: a1=1. b1=1. multiply=1. inverse=0.
% 2.12/2.38
% 2.12/2.38 ============================== end of process initial clauses ========
% 2.12/2.38
% 2.12/2.38 ============================== CLAUSES FOR SEARCH ====================
% 2.12/2.38
% 2.12/2.38 ============================== end of clauses for search =============
% 2.12/2.38
% 2.12/2.38 ============================== SEARCH ================================
% 2.12/2.38
% 2.12/2.38 % Starting search at 0.01 seconds.
% 2.12/2.38
% 2.12/2.38 ============================== PROOF =================================
% 2.12/2.38 % SZS status Unsatisfiable
% 2.12/2.38 % SZS output start Refutation
% 2.12/2.38
% 2.12/2.38 % Proof 1 at 1.34 (+ 0.01) seconds: prove_these_axioms_1.
% 2.12/2.38 % Length of proof is 18.
% 2.12/2.38 % Level of proof is 10.
% 2.12/2.38 % Maximum clause weight is 63.000.
% 2.12/2.38 % Given clauses 39.
% 2.12/2.38
% 2.12/2.38 1 multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(B,multiply(inverse(B),B)))))) = C # label(single_axiom) # label(axiom). [assumption].
% 2.12/2.38 2 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) # label(prove_these_axioms_1) # label(negated_conjecture) # answer(prove_these_axioms_1). [assumption].
% 2.12/2.38 3 multiply(inverse(b1),b1) != multiply(inverse(a1),a1) # answer(prove_these_axioms_1). [copy(2),flip(a)].
% 2.12/2.38 4 multiply(A,inverse(multiply(inverse(multiply(inverse(B),C)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),inverse(multiply(D,multiply(inverse(D),D))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),inverse(multiply(D,multiply(inverse(D),D)))))),inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),inverse(multiply(D,multiply(inverse(D),D))))))))))) = C. [para(1(a,1),1(a,1,2,1,1,1,1,1))].
% 2.12/2.38 5 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D)),inverse(multiply(C,multiply(inverse(C),C))))) = multiply(A,inverse(multiply(inverse(D),inverse(multiply(B,multiply(inverse(B),B)))))). [para(1(a,1),1(a,1,2,1,1,1)),flip(a)].
% 2.12/2.38 17 multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(C),inverse(multiply(B,multiply(inverse(B),B))))))) = C. [para(5(a,1),1(a,1,2))].
% 2.12/2.38 43 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(A),C))),inverse(multiply(B,multiply(inverse(B),B))))) = C. [para(5(a,2),4(a,1)),rewrite([1(11)])].
% 2.12/2.38 95 multiply(inverse(multiply(inverse(A),B)),multiply(inverse(A),C)) = multiply(inverse(multiply(D,B)),multiply(D,C)). [para(43(a,1),17(a,1,2,2)),flip(a)].
% 2.12/2.38 96 inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(B,multiply(inverse(B),B))))) = C. [para(43(a,1),43(a,1,1,1,1,1,1,1)),rewrite([43(15)])].
% 2.12/2.38 145 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)). [para(95(a,1),95(a,1))].
% 2.12/2.38 172 multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),D)),inverse(multiply(multiply(B,C),multiply(inverse(multiply(E,C)),multiply(E,C))))))) = D. [para(145(a,1),1(a,1,2,1,2,1,2))].
% 2.12/2.38 226 multiply(inverse(multiply(A,inverse(multiply(B,multiply(inverse(B),B))))),multiply(A,C)) = multiply(D,multiply(inverse(multiply(inverse(multiply(E,B)),multiply(E,D))),C)). [para(96(a,1),145(a,1,1)),flip(a)].
% 2.12/2.38 939 inverse(multiply(A,multiply(inverse(A),A))) = multiply(inverse(multiply(B,A)),inverse(multiply(C,inverse(multiply(multiply(B,C),multiply(inverse(multiply(D,C)),multiply(D,C))))))). [para(96(a,1),172(a,1,2,1,1)),flip(a)].
% 2.12/2.38 1137 multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),D)) = multiply(E,multiply(inverse(multiply(inverse(multiply(F,C)),multiply(F,E))),D)). [para(96(a,1),226(a,1,1))].
% 2.12/2.38 3326 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),inverse(multiply(B,multiply(inverse(B),B)))) = C. [para(939(a,2),17(a,1,2))].
% 2.12/2.38 3716 multiply(inverse(A),A) = multiply(B,multiply(inverse(multiply(inverse(multiply(C,D)),multiply(C,B))),inverse(multiply(D,multiply(inverse(D),D))))). [para(3326(a,1),1137(a,1,2))].
% 2.12/2.38 4162 multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),inverse(multiply(C,multiply(inverse(C),C))))) != multiply(inverse(a1),a1) # answer(prove_these_axioms_1). [para(3716(a,1),3(a,1))].
% 2.12/2.38 4163 $F # answer(prove_these_axioms_1). [resolve(4162,a,3716,a(flip))].
% 2.12/2.38
% 2.12/2.38 % SZS output end Refutation
% 2.12/2.38 ============================== end of proof ==========================
% 2.12/2.38
% 2.12/2.38 ============================== STATISTICS ============================
% 2.12/2.38
% 2.12/2.38 Given=39. Generated=11076. Kept=4161. proofs=1.
% 2.12/2.38 Usable=35. Sos=3481. Demods=1288. Limbo=6, Disabled=640. Hints=0.
% 2.12/2.38 Megabytes=16.51.
% 2.12/2.38 User_CPU=1.34, System_CPU=0.01, Wall_clock=2.
% 2.12/2.38
% 2.12/2.38 ============================== end of statistics =====================
% 2.12/2.38
% 2.12/2.38 ============================== end of search =========================
% 2.12/2.38
% 2.12/2.38 THEOREM PROVED
% 2.12/2.38 % SZS status Unsatisfiable
% 2.12/2.38
% 2.12/2.38 Exiting with 1 proof.
% 2.12/2.38
% 2.12/2.38 Process 21971 exit (max_proofs) Tue Jun 14 11:02:16 2022
% 2.12/2.38 Prover9 interrupted
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