TSTP Solution File: GRP518-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP518-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.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 11:19:26 EDT 2022
% Result : Unsatisfiable 0.54s 0.86s
% Output : Refutation 0.54s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP518-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.32 % Computer : n032.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Tue Jun 14 12:44:28 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.54/0.86 ============================== Prover9 ===============================
% 0.54/0.86 Prover9 (32) version 2009-11A, November 2009.
% 0.54/0.86 Process 30117 was started by sandbox on n032.cluster.edu,
% 0.54/0.86 Tue Jun 14 12:44:28 2022
% 0.54/0.86 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29963_n032.cluster.edu".
% 0.54/0.86 ============================== end of head ===========================
% 0.54/0.86
% 0.54/0.86 ============================== INPUT =================================
% 0.54/0.86
% 0.54/0.86 % Reading from file /tmp/Prover9_29963_n032.cluster.edu
% 0.54/0.86
% 0.54/0.86 set(prolog_style_variables).
% 0.54/0.86 set(auto2).
% 0.54/0.86 % set(auto2) -> set(auto).
% 0.54/0.86 % set(auto) -> set(auto_inference).
% 0.54/0.86 % set(auto) -> set(auto_setup).
% 0.54/0.86 % set(auto_setup) -> set(predicate_elim).
% 0.54/0.86 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.54/0.86 % set(auto) -> set(auto_limits).
% 0.54/0.86 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.54/0.86 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.54/0.86 % set(auto) -> set(auto_denials).
% 0.54/0.86 % set(auto) -> set(auto_process).
% 0.54/0.86 % set(auto2) -> assign(new_constants, 1).
% 0.54/0.86 % set(auto2) -> assign(fold_denial_max, 3).
% 0.54/0.86 % set(auto2) -> assign(max_weight, "200.000").
% 0.54/0.86 % set(auto2) -> assign(max_hours, 1).
% 0.54/0.86 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.54/0.86 % set(auto2) -> assign(max_seconds, 0).
% 0.54/0.86 % set(auto2) -> assign(max_minutes, 5).
% 0.54/0.86 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.54/0.86 % set(auto2) -> set(sort_initial_sos).
% 0.54/0.86 % set(auto2) -> assign(sos_limit, -1).
% 0.54/0.86 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.54/0.86 % set(auto2) -> assign(max_megs, 400).
% 0.54/0.86 % set(auto2) -> assign(stats, some).
% 0.54/0.86 % set(auto2) -> clear(echo_input).
% 0.54/0.86 % set(auto2) -> set(quiet).
% 0.54/0.86 % set(auto2) -> clear(print_initial_clauses).
% 0.54/0.86 % set(auto2) -> clear(print_given).
% 0.54/0.86 assign(lrs_ticks,-1).
% 0.54/0.86 assign(sos_limit,10000).
% 0.54/0.86 assign(order,kbo).
% 0.54/0.86 set(lex_order_vars).
% 0.54/0.86 clear(print_given).
% 0.54/0.86
% 0.54/0.86 % formulas(sos). % not echoed (2 formulas)
% 0.54/0.86
% 0.54/0.86 ============================== end of input ==========================
% 0.54/0.86
% 0.54/0.86 % From the command line: assign(max_seconds, 300).
% 0.54/0.86
% 0.54/0.86 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.54/0.86
% 0.54/0.86 % Formulas that are not ordinary clauses:
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% 0.54/0.86 ============================== end of process non-clausal formulas ===
% 0.54/0.86
% 0.54/0.86 ============================== PROCESS INITIAL CLAUSES ===============
% 0.54/0.86
% 0.54/0.86 ============================== PREDICATE ELIMINATION =================
% 0.54/0.86
% 0.54/0.86 ============================== end predicate elimination =============
% 0.54/0.86
% 0.54/0.86 Auto_denials:
% 0.54/0.86 % copying label prove_these_axioms_2 to answer in negative clause
% 0.54/0.86
% 0.54/0.86 Term ordering decisions:
% 0.54/0.86
% 0.54/0.86 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 0.54/0.86 Function symbol KB weights: a2=1. b2=1. multiply=1. inverse=0.
% 0.54/0.86
% 0.54/0.86 ============================== end of process initial clauses ========
% 0.54/0.86
% 0.54/0.86 ============================== CLAUSES FOR SEARCH ====================
% 0.54/0.86
% 0.54/0.86 ============================== end of clauses for search =============
% 0.54/0.86
% 0.54/0.86 ============================== SEARCH ================================
% 0.54/0.86
% 0.54/0.86 % Starting search at 0.01 seconds.
% 0.54/0.86
% 0.54/0.86 ============================== PROOF =================================
% 0.54/0.86 % SZS status Unsatisfiable
% 0.54/0.86 % SZS output start Refutation
% 0.54/0.86
% 0.54/0.86 % Proof 1 at 0.02 (+ 0.00) seconds: prove_these_axioms_2.
% 0.54/0.86 % Length of proof is 17.
% 0.54/0.86 % Level of proof is 10.
% 0.54/0.86 % Maximum clause weight is 18.000.
% 0.54/0.86 % Given clauses 10.
% 0.54/0.86
% 0.54/0.86 1 multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) = C # label(single_axiom) # label(axiom). [assumption].
% 0.54/0.86 2 multiply(multiply(inverse(b2),b2),a2) != a2 # label(prove_these_axioms_2) # label(negated_conjecture) # answer(prove_these_axioms_2). [assumption].
% 0.54/0.86 3 multiply(A,multiply(multiply(inverse(B),C),multiply(multiply(inverse(multiply(A,D)),B),D))) = C. [para(1(a,1),1(a,1,2,1,1,1))].
% 0.54/0.86 4 multiply(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D),C) = multiply(A,multiply(D,B)). [para(1(a,1),1(a,1,2,1)),flip(a)].
% 0.54/0.86 8 multiply(multiply(inverse(A),B),A) = B. [para(1(a,1),3(a,1,2))].
% 0.54/0.86 12 multiply(multiply(inverse(multiply(inverse(A),B)),C),B) = multiply(C,A). [para(1(a,1),8(a,1,1)),flip(a)].
% 0.54/0.86 13 multiply(multiply(inverse(A),B),multiply(multiply(inverse(C),D),multiply(multiply(inverse(B),C),A))) = D. [para(8(a,1),3(a,1,2,2,1,1,1))].
% 0.54/0.86 14 multiply(multiply(inverse(A),B),multiply(A,C)) = multiply(B,C). [para(3(a,1),8(a,1,1)),rewrite([12(8)]),flip(a)].
% 0.54/0.86 16 multiply(A,multiply(B,C)) = multiply(B,multiply(A,C)). [back_rewrite(4),rewrite([12(6)])].
% 0.54/0.86 17 multiply(A,multiply(multiply(inverse(A),B),C)) = multiply(B,C). [back_rewrite(14),rewrite([16(4)])].
% 0.54/0.86 23 multiply(multiply(A,B),C) = multiply(B,multiply(A,C)). [para(1(a,1),17(a,1,2,1)),rewrite([12(7)]),flip(a)].
% 0.54/0.86 27 multiply(A,B) = multiply(B,A). [para(8(a,1),17(a,1,2))].
% 0.54/0.86 32 multiply(A,multiply(B,multiply(C,inverse(A)))) = multiply(B,C). [para(17(a,1),16(a,2)),rewrite([27(2),16(4),27(3),16(3)])].
% 0.54/0.86 39 multiply(A,multiply(B,inverse(A))) = B. [back_rewrite(13),rewrite([27(2),27(4),27(6),27(7),16(8),16(7),23(6),16(6),27(5),32(7),16(6),16(5),27(4),16(4),27(3),16(5),32(5)])].
% 0.54/0.86 43 multiply(a2,multiply(b2,inverse(b2))) != a2 # answer(prove_these_axioms_2). [back_rewrite(2),rewrite([27(4),27(6)])].
% 0.54/0.86 47 multiply(A,multiply(B,inverse(B))) = A. [para(39(a,1),16(a,1)),flip(a)].
% 0.54/0.86 48 $F # answer(prove_these_axioms_2). [resolve(47,a,43,a)].
% 0.54/0.86
% 0.54/0.86 % SZS output end Refutation
% 0.54/0.86 ============================== end of proof ==========================
% 0.54/0.86
% 0.54/0.86 ============================== STATISTICS ============================
% 0.54/0.86
% 0.54/0.86 Given=10. Generated=121. Kept=47. proofs=1.
% 0.54/0.86 Usable=5. Sos=13. Demods=14. Limbo=0, Disabled=30. Hints=0.
% 0.54/0.86 Megabytes=0.07.
% 0.54/0.86 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.54/0.86
% 0.54/0.86 ============================== end of statistics =====================
% 0.54/0.86
% 0.54/0.86 ============================== end of search =========================
% 0.54/0.86
% 0.54/0.86 THEOREM PROVED
% 0.54/0.86 % SZS status Unsatisfiable
% 0.54/0.86
% 0.54/0.86 Exiting with 1 proof.
% 0.54/0.86
% 0.54/0.86 Process 30117 exit (max_proofs) Tue Jun 14 12:44:28 2022
% 0.54/0.86 Prover9 interrupted
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