TSTP Solution File: GRP553-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP553-1 : 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 11:19:35 EDT 2022
% Result : Unsatisfiable 0.75s 1.00s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP553-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 23:06:43 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.75/1.00 ============================== Prover9 ===============================
% 0.75/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.00 Process 12796 was started by sandbox on n018.cluster.edu,
% 0.75/1.00 Mon Jun 13 23:06:43 2022
% 0.75/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_12642_n018.cluster.edu".
% 0.75/1.00 ============================== end of head ===========================
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% 0.75/1.00 ============================== INPUT =================================
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% 0.75/1.00 % Reading from file /tmp/Prover9_12642_n018.cluster.edu
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% 0.75/1.00 set(prolog_style_variables).
% 0.75/1.00 set(auto2).
% 0.75/1.00 % set(auto2) -> set(auto).
% 0.75/1.00 % set(auto) -> set(auto_inference).
% 0.75/1.00 % set(auto) -> set(auto_setup).
% 0.75/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.00 % set(auto) -> set(auto_limits).
% 0.75/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.00 % set(auto) -> set(auto_denials).
% 0.75/1.00 % set(auto) -> set(auto_process).
% 0.75/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.00 % set(auto2) -> assign(stats, some).
% 0.75/1.00 % set(auto2) -> clear(echo_input).
% 0.75/1.00 % set(auto2) -> set(quiet).
% 0.75/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.00 % set(auto2) -> clear(print_given).
% 0.75/1.00 assign(lrs_ticks,-1).
% 0.75/1.00 assign(sos_limit,10000).
% 0.75/1.00 assign(order,kbo).
% 0.75/1.00 set(lex_order_vars).
% 0.75/1.00 clear(print_given).
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% 0.75/1.00 % formulas(sos). % not echoed (3 formulas)
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% 0.75/1.00 ============================== end of input ==========================
% 0.75/1.00
% 0.75/1.00 % From the command line: assign(max_seconds, 300).
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% 0.75/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
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% 0.75/1.00 % Formulas that are not ordinary clauses:
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% 0.75/1.00 ============================== end of process non-clausal formulas ===
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% 0.75/1.00 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.75/1.00 ============================== PREDICATE ELIMINATION =================
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% 0.75/1.00 ============================== end predicate elimination =============
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% 0.75/1.00 Auto_denials:
% 0.75/1.00 % copying label prove_these_axioms_1 to answer in negative clause
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% 0.75/1.00 Term ordering decisions:
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% 0.75/1.00 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.75/1.00 Function symbol KB weights: a1=1. b1=1. divide=1. multiply=1. inverse=0.
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% 0.75/1.00 ============================== end of process initial clauses ========
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% 0.75/1.00 ============================== CLAUSES FOR SEARCH ====================
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% 0.75/1.00 ============================== end of clauses for search =============
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% 0.75/1.00 ============================== SEARCH ================================
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% 0.75/1.00 % Starting search at 0.01 seconds.
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% 0.75/1.00 ============================== PROOF =================================
% 0.75/1.00 % SZS status Unsatisfiable
% 0.75/1.00 % SZS output start Refutation
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% 0.75/1.00 % Proof 1 at 0.01 (+ 0.00) seconds: prove_these_axioms_1.
% 0.75/1.00 % Length of proof is 24.
% 0.75/1.00 % Level of proof is 11.
% 0.75/1.00 % Maximum clause weight is 27.000.
% 0.75/1.00 % Given clauses 15.
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% 0.75/1.00 1 multiply(A,B) = divide(A,inverse(B)) # label(multiply) # label(axiom). [assumption].
% 0.75/1.00 2 divide(divide(A,inverse(divide(B,divide(A,C)))),C) = B # label(single_axiom) # label(axiom). [assumption].
% 0.75/1.00 3 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) # label(prove_these_axioms_1) # label(negated_conjecture) # answer(prove_these_axioms_1). [assumption].
% 0.75/1.00 4 divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) # answer(prove_these_axioms_1). [copy(3),rewrite([1(4),1(9)]),flip(a)].
% 0.75/1.00 5 divide(divide(divide(A,inverse(divide(B,divide(A,C)))),inverse(divide(D,B))),C) = D. [para(2(a,1),2(a,1,1,2,1,2))].
% 0.75/1.00 10 divide(A,inverse(divide(B,A))) = B. [para(2(a,1),5(a,1,1))].
% 0.75/1.00 11 divide(divide(divide(divide(divide(A,inverse(divide(B,divide(A,C)))),inverse(divide(D,B))),inverse(divide(E,D))),inverse(divide(F,E))),C) = F. [para(5(a,1),5(a,1,1,1,2,1,2))].
% 0.75/1.00 12 divide(divide(divide(A,inverse(divide(B,divide(A,C)))),inverse(D)),C) = divide(divide(E,inverse(divide(F,divide(E,B)))),inverse(divide(D,F))). [para(5(a,1),5(a,1,1,2,1))].
% 0.75/1.00 14 divide(A,inverse(divide(B,divide(A,C)))) = divide(C,inverse(B)). [para(2(a,1),10(a,1,2,1)),flip(a)].
% 0.75/1.00 17 divide(divide(A,inverse(B)),inverse(divide(C,B))) = divide(A,inverse(C)). [para(5(a,1),10(a,1,2,1)),rewrite([14(6)]),flip(a)].
% 0.75/1.00 18 divide(inverse(divide(A,B)),inverse(A)) = B. [para(10(a,1),10(a,1,2,1))].
% 0.75/1.00 19 divide(divide(divide(A,inverse(B)),inverse(C)),A) = divide(B,inverse(C)). [back_rewrite(12),rewrite([14(4),14(9),17(10)])].
% 0.75/1.00 20 divide(divide(A,inverse(B)),A) = B. [back_rewrite(11),rewrite([14(4),17(5),17(5),17(5)])].
% 0.75/1.00 22 divide(A,divide(inverse(B),inverse(A))) = B. [para(20(a,1),20(a,1,1))].
% 0.75/1.00 23 inverse(divide(A,B)) = divide(inverse(A),inverse(B)). [para(18(a,1),10(a,1,2,1)),flip(a)].
% 0.75/1.00 30 divide(divide(A,inverse(B)),divide(inverse(C),inverse(A))) = divide(C,inverse(B)). [para(20(a,1),19(a,1,1,1))].
% 0.75/1.00 33 divide(A,inverse(B)) = divide(B,inverse(A)). [para(19(a,1),19(a,1,1)),rewrite([30(6)])].
% 0.75/1.00 34 divide(divide(A,divide(inverse(B),divide(inverse(inverse(C)),divide(inverse(inverse(inverse(D))),inverse(inverse(inverse(inverse(inverse(A))))))))),B) = divide(D,inverse(C)). [para(19(a,1),19(a,2)),rewrite([33(3),33(5),23(4),23(7),23(7),33(12),23(11),23(11),23(11)])].
% 0.75/1.00 44 inverse(divide(A,B)) = divide(B,inverse(inverse(A))). [back_rewrite(23),rewrite([33(5)])].
% 0.75/1.00 45 divide(A,divide(A,inverse(inverse(B)))) = B. [back_rewrite(22),rewrite([33(3)])].
% 0.75/1.00 47 divide(divide(A,divide(inverse(B),inverse(inverse(C)))),B) = divide(C,inverse(A)). [back_rewrite(19),rewrite([33(4),44(3),33(4)])].
% 0.75/1.00 48 divide(b1,inverse(inverse(b1))) != divide(a1,inverse(inverse(a1))) # answer(prove_these_axioms_1). [back_rewrite(4),rewrite([33(5),33(10)])].
% 0.75/1.00 56 divide(A,inverse(inverse(A))) = divide(B,inverse(inverse(B))). [para(45(a,1),34(a,1,1,2,2)),rewrite([47(7),33(3)])].
% 0.75/1.00 57 $F # answer(prove_these_axioms_1). [resolve(56,a,48,a)].
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% 0.75/1.00 % SZS output end Refutation
% 0.75/1.00 ============================== end of proof ==========================
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% 0.75/1.00 ============================== STATISTICS ============================
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% 0.75/1.00 Given=15. Generated=125. Kept=55. proofs=1.
% 0.75/1.00 Usable=7. Sos=10. Demods=18. Limbo=2, Disabled=38. Hints=0.
% 0.75/1.00 Megabytes=0.07.
% 0.75/1.00 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
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% 0.75/1.00 ============================== end of statistics =====================
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% 0.75/1.00 ============================== end of search =========================
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% 0.75/1.00 THEOREM PROVED
% 0.75/1.00 % SZS status Unsatisfiable
% 0.75/1.00
% 0.75/1.00 Exiting with 1 proof.
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% 0.75/1.00 Process 12796 exit (max_proofs) Mon Jun 13 23:06:43 2022
% 0.75/1.00 Prover9 interrupted
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