TSTP Solution File: GRP086-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP086-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 11:17:06 EDT 2022
% Result : Unsatisfiable 0.44s 1.02s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP086-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n006.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 : Tue Jun 14 06:22:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.44/1.02 ============================== Prover9 ===============================
% 0.44/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.02 Process 8580 was started by sandbox on n006.cluster.edu,
% 0.44/1.02 Tue Jun 14 06:22:57 2022
% 0.44/1.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_8427_n006.cluster.edu".
% 0.44/1.02 ============================== end of head ===========================
% 0.44/1.02
% 0.44/1.02 ============================== INPUT =================================
% 0.44/1.02
% 0.44/1.02 % Reading from file /tmp/Prover9_8427_n006.cluster.edu
% 0.44/1.02
% 0.44/1.02 set(prolog_style_variables).
% 0.44/1.02 set(auto2).
% 0.44/1.02 % set(auto2) -> set(auto).
% 0.44/1.02 % set(auto) -> set(auto_inference).
% 0.44/1.02 % set(auto) -> set(auto_setup).
% 0.44/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.02 % set(auto) -> set(auto_limits).
% 0.44/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.02 % set(auto) -> set(auto_denials).
% 0.44/1.02 % set(auto) -> set(auto_process).
% 0.44/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.02 % set(auto2) -> assign(stats, some).
% 0.44/1.02 % set(auto2) -> clear(echo_input).
% 0.44/1.02 % set(auto2) -> set(quiet).
% 0.44/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.02 % set(auto2) -> clear(print_given).
% 0.44/1.02 assign(lrs_ticks,-1).
% 0.44/1.02 assign(sos_limit,10000).
% 0.44/1.02 assign(order,kbo).
% 0.44/1.02 set(lex_order_vars).
% 0.44/1.02 clear(print_given).
% 0.44/1.02
% 0.44/1.02 % formulas(sos). % not echoed (2 formulas)
% 0.44/1.02
% 0.44/1.02 ============================== end of input ==========================
% 0.44/1.02
% 0.44/1.02 % From the command line: assign(max_seconds, 300).
% 0.44/1.02
% 0.44/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.02
% 0.44/1.02 % Formulas that are not ordinary clauses:
% 0.44/1.02
% 0.44/1.02 ============================== end of process non-clausal formulas ===
% 0.44/1.02
% 0.44/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.02
% 0.44/1.02 ============================== PREDICATE ELIMINATION =================
% 0.44/1.02
% 0.44/1.02 ============================== end predicate elimination =============
% 0.44/1.02
% 0.44/1.02 Auto_denials:
% 0.44/1.02 % copying label prove_these_axioms to answer in negative clause
% 0.44/1.02
% 0.44/1.02 Term ordering decisions:
% 0.44/1.02
% 0.44/1.02 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 0.44/1.02 Function symbol KB weights: a1=1. a2=1. a3=1. a4=1. b1=1. b2=1. b3=1. b4=1. c3=1. multiply=1. inverse=0.
% 0.44/1.02
% 0.44/1.02 ============================== end of process initial clauses ========
% 0.44/1.02
% 0.44/1.02 ============================== CLAUSES FOR SEARCH ====================
% 0.44/1.02
% 0.44/1.02 ============================== end of clauses for search =============
% 0.44/1.02
% 0.44/1.02 ============================== SEARCH ================================
% 0.44/1.02
% 0.44/1.02 % Starting search at 0.01 seconds.
% 0.44/1.02
% 0.44/1.02 ============================== PROOF =================================
% 0.44/1.02 % SZS status Unsatisfiable
% 0.44/1.02 % SZS output start Refutation
% 0.44/1.02
% 0.44/1.02 % Proof 1 at 0.02 (+ 0.00) seconds: prove_these_axioms.
% 0.44/1.02 % Length of proof is 25.
% 0.44/1.02 % Level of proof is 14.
% 0.44/1.02 % Maximum clause weight is 35.000.
% 0.44/1.02 % Given clauses 21.
% 0.44/1.02
% 0.44/1.02 1 multiply(A,multiply(multiply(B,C),inverse(multiply(A,C)))) = B # label(single_axiom) # label(axiom). [assumption].
% 0.44/1.02 2 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) | multiply(multiply(inverse(b2),b2),a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) | multiply(a4,b4) != multiply(b4,a4) # label(prove_these_axioms) # label(negated_conjecture) # answer(prove_these_axioms). [assumption].
% 0.44/1.02 3 multiply(inverse(b1),b1) != multiply(inverse(a1),a1) | multiply(multiply(inverse(b2),b2),a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) | multiply(b4,a4) != multiply(a4,b4) # answer(prove_these_axioms). [copy(2),flip(a),flip(d)].
% 0.44/1.02 4 multiply(A,multiply(B,inverse(multiply(A,multiply(multiply(B,C),inverse(multiply(D,C))))))) = D. [para(1(a,1),1(a,1,2,1))].
% 0.44/1.02 9 multiply(A,multiply(B,inverse(B))) = A. [para(1(a,1),4(a,1,2,2,1))].
% 0.44/1.02 12 multiply(A,multiply(B,inverse(A))) = B. [para(9(a,1),1(a,1,2,1)),rewrite([9(3)])].
% 0.44/1.02 17 multiply(multiply(A,B),multiply(C,inverse(multiply(C,B)))) = A. [para(12(a,1),4(a,1,2,2,1))].
% 0.44/1.02 19 multiply(multiply(A,B),multiply(multiply(C,multiply(D,inverse(multiply(D,B)))),inverse(A))) = C. [para(17(a,1),1(a,1,2,2,1))].
% 0.44/1.02 24 multiply(multiply(A,B),multiply(C,inverse(A))) = multiply(C,B). [para(17(a,1),4(a,1,2,2,1))].
% 0.44/1.02 31 multiply(multiply(A,multiply(B,inverse(multiply(B,C)))),C) = A. [back_rewrite(19),rewrite([24(8)])].
% 0.44/1.02 34 multiply(A,multiply(multiply(B,C),inverse(multiply(D,C)))) = multiply(B,multiply(A,inverse(D))). [para(1(a,1),24(a,1,1)),flip(a)].
% 0.44/1.02 38 multiply(A,multiply(B,inverse(multiply(B,multiply(C,inverse(D)))))) = multiply(D,multiply(A,inverse(C))). [para(4(a,1),24(a,1,1)),rewrite([34(8)]),flip(a)].
% 0.44/1.02 40 multiply(A,multiply(multiply(B,C),inverse(B))) = multiply(A,C). [para(24(a,1),17(a,1,1)),rewrite([38(7)])].
% 0.44/1.02 44 multiply(A,multiply(B,inverse(multiply(B,inverse(C))))) = multiply(C,A). [para(31(a,1),12(a,1,2)),flip(a)].
% 0.44/1.02 45 multiply(multiply(A,B),C) = multiply(multiply(A,C),B). [para(31(a,1),24(a,1,2)),rewrite([44(7)])].
% 0.44/1.02 48 multiply(inverse(b1),b1) != multiply(inverse(a1),a1) | multiply(multiply(inverse(b2),a2),b2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) | multiply(b4,a4) != multiply(a4,b4) # answer(prove_these_axioms). [back_rewrite(3),rewrite([45(15)])].
% 0.44/1.02 49 multiply(A,multiply(multiply(B,inverse(A)),C)) = multiply(B,C). [para(45(a,1),12(a,1,2))].
% 0.44/1.02 54 multiply(A,inverse(multiply(A,inverse(B)))) = B. [para(49(a,1),9(a,1))].
% 0.44/1.02 60 multiply(A,inverse(A)) = multiply(B,inverse(B)). [para(49(a,1),40(a,1))].
% 0.44/1.02 62 multiply(A,B) = multiply(B,A). [back_rewrite(44),rewrite([54(4)])].
% 0.44/1.02 64 multiply(A,inverse(A)) = c_0. [new_symbol(60)].
% 0.44/1.02 76 multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [back_rewrite(48),rewrite([62(4),64(4),62(5),64(5),62(7),62(9),12(9),62(11),62(20)]),xx(a),xx(b),xx(d)].
% 0.44/1.02 77 multiply(A,multiply(B,C)) = multiply(C,multiply(B,A)). [back_rewrite(45),rewrite([62(2),62(4)])].
% 0.44/1.02 85 multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [back_rewrite(76),rewrite([77(5)])].
% 0.44/1.02 98 $F # answer(prove_these_axioms). [para(77(a,1),85(a,2)),rewrite([62(9),77(10)]),xx(a)].
% 0.44/1.02
% 0.44/1.02 % SZS output end Refutation
% 0.44/1.02 ============================== end of proof ==========================
% 0.44/1.02
% 0.44/1.02 ============================== STATISTICS ============================
% 0.44/1.02
% 0.44/1.02 Given=21. Generated=302. Kept=96. proofs=1.
% 0.44/1.02 Usable=8. Sos=26. Demods=28. Limbo=0, Disabled=64. Hints=0.
% 0.44/1.02 Megabytes=0.11.
% 0.44/1.02 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.44/1.02
% 0.44/1.02 ============================== end of statistics =====================
% 0.44/1.02
% 0.44/1.02 ============================== end of search =========================
% 0.44/1.02
% 0.44/1.02 THEOREM PROVED
% 0.44/1.02 % SZS status Unsatisfiable
% 0.44/1.02
% 0.44/1.02 Exiting with 1 proof.
% 0.44/1.02
% 0.44/1.02 Process 8580 exit (max_proofs) Tue Jun 14 06:22:57 2022
% 0.44/1.02 Prover9 interrupted
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