TSTP Solution File: GRP452-1 by Prover9---1109a
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- Process Solution
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% File : Prover9---1109a
% Problem : GRP452-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 11:19:09 EDT 2022
% Result : Unsatisfiable 0.44s 0.98s
% 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
% 0.04/0.13 % Problem : GRP452-1 : TPTP v8.1.0. Released v2.6.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 19:37:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/0.98 ============================== Prover9 ===============================
% 0.44/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.44/0.98 Process 2298 was started by sandbox2 on n012.cluster.edu,
% 0.44/0.98 Mon Jun 13 19:37:11 2022
% 0.44/0.98 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2141_n012.cluster.edu".
% 0.44/0.98 ============================== end of head ===========================
% 0.44/0.98
% 0.44/0.98 ============================== INPUT =================================
% 0.44/0.98
% 0.44/0.98 % Reading from file /tmp/Prover9_2141_n012.cluster.edu
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% 0.44/0.98 set(prolog_style_variables).
% 0.44/0.98 set(auto2).
% 0.44/0.98 % set(auto2) -> set(auto).
% 0.44/0.98 % set(auto) -> set(auto_inference).
% 0.44/0.98 % set(auto) -> set(auto_setup).
% 0.44/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.44/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/0.98 % set(auto) -> set(auto_limits).
% 0.44/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/0.98 % set(auto) -> set(auto_denials).
% 0.44/0.98 % set(auto) -> set(auto_process).
% 0.44/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.44/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.44/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.44/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.44/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.44/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.44/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.44/0.98 % set(auto2) -> assign(stats, some).
% 0.44/0.98 % set(auto2) -> clear(echo_input).
% 0.44/0.98 % set(auto2) -> set(quiet).
% 0.44/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.44/0.98 % set(auto2) -> clear(print_given).
% 0.44/0.98 assign(lrs_ticks,-1).
% 0.44/0.98 assign(sos_limit,10000).
% 0.44/0.98 assign(order,kbo).
% 0.44/0.98 set(lex_order_vars).
% 0.44/0.98 clear(print_given).
% 0.44/0.98
% 0.44/0.98 % formulas(sos). % not echoed (4 formulas)
% 0.44/0.98
% 0.44/0.98 ============================== end of input ==========================
% 0.44/0.98
% 0.44/0.98 % From the command line: assign(max_seconds, 300).
% 0.44/0.98
% 0.44/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/0.98
% 0.44/0.98 % Formulas that are not ordinary clauses:
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% 0.44/0.98 ============================== end of process non-clausal formulas ===
% 0.44/0.98
% 0.44/0.98 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.44/0.98 ============================== PREDICATE ELIMINATION =================
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% 0.44/0.98 ============================== end predicate elimination =============
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% 0.44/0.98 Auto_denials:
% 0.44/0.98 % copying label prove_these_axioms_2 to answer in negative clause
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% 0.44/0.98 Term ordering decisions:
% 0.44/0.98
% 0.44/0.98 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.44/0.98 Function symbol KB weights: a2=1. b2=1. divide=1. multiply=1. inverse=0.
% 0.44/0.98
% 0.44/0.98 ============================== end of process initial clauses ========
% 0.44/0.98
% 0.44/0.98 ============================== CLAUSES FOR SEARCH ====================
% 0.44/0.98
% 0.44/0.98 ============================== end of clauses for search =============
% 0.44/0.98
% 0.44/0.98 ============================== SEARCH ================================
% 0.44/0.98
% 0.44/0.98 % Starting search at 0.01 seconds.
% 0.44/0.98
% 0.44/0.98 ============================== PROOF =================================
% 0.44/0.98 % SZS status Unsatisfiable
% 0.44/0.98 % SZS output start Refutation
% 0.44/0.98
% 0.44/0.98 % Proof 1 at 0.02 (+ 0.00) seconds: prove_these_axioms_2.
% 0.44/0.98 % Length of proof is 25.
% 0.44/0.98 % Level of proof is 13.
% 0.44/0.98 % Maximum clause weight is 13.000.
% 0.44/0.98 % Given clauses 17.
% 0.44/0.98
% 0.44/0.98 1 inverse(A) = divide(divide(B,B),A) # label(inverse) # label(axiom). [assumption].
% 0.44/0.98 2 divide(divide(A,A),B) = inverse(B). [copy(1),flip(a)].
% 0.44/0.98 3 multiply(A,B) = divide(A,divide(divide(C,C),B)) # label(multiply) # label(axiom). [assumption].
% 0.44/0.98 4 multiply(A,B) = divide(A,inverse(B)). [copy(3),rewrite([2(3)])].
% 0.44/0.98 5 divide(divide(divide(A,A),divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B # label(single_axiom) # label(axiom). [assumption].
% 0.44/0.98 6 divide(inverse(divide(A,divide(B,divide(inverse(A),C)))),C) = B. [copy(5),rewrite([2(3),2(6)])].
% 0.44/0.98 7 multiply(multiply(inverse(b2),b2),a2) != a2 # label(prove_these_axioms_2) # label(negated_conjecture) # answer(prove_these_axioms_2). [assumption].
% 0.44/0.98 8 inverse(inverse(a2)) != a2 # answer(prove_these_axioms_2). [copy(7),rewrite([4(4),4(7),2(8)])].
% 0.44/0.98 9 divide(inverse(divide(A,A)),B) = inverse(B). [para(2(a,1),2(a,1,1))].
% 0.44/0.98 11 divide(inverse(inverse(divide(A,inverse(B)))),B) = A. [para(2(a,1),6(a,1,1,1)),rewrite([9(3)])].
% 0.44/0.98 17 divide(inverse(inverse(inverse(inverse(A)))),A) = divide(B,B). [para(2(a,1),11(a,1,1,1,1))].
% 0.44/0.98 21 inverse(divide(A,A)) = divide(inverse(inverse(inverse(inverse(B)))),B). [para(9(a,1),11(a,1,1,1,1)),flip(a)].
% 0.44/0.98 23 divide(inverse(inverse(inverse(inverse(A)))),A) = c_0. [new_symbol(17)].
% 0.44/0.98 24 inverse(divide(A,A)) = c_0. [back_rewrite(21),rewrite([23(7)])].
% 0.44/0.98 25 divide(A,A) = c_0. [back_rewrite(17),rewrite([23(5)]),flip(a)].
% 0.44/0.98 30 inverse(c_0) = c_0. [back_rewrite(24),rewrite([25(1)])].
% 0.44/0.98 31 divide(c_0,A) = inverse(A). [back_rewrite(2),rewrite([25(1)])].
% 0.44/0.98 33 divide(inverse(inverse(divide(A,c_0))),c_0) = A. [para(30(a,1),11(a,1,1,1,1,2))].
% 0.44/0.98 34 divide(inverse(divide(A,divide(B,c_0))),inverse(A)) = B. [para(25(a,1),6(a,1,1,1,2,2))].
% 0.44/0.98 49 inverse(inverse(divide(A,c_0))) = divide(inverse(inverse(A)),c_0). [para(11(a,1),33(a,1,1,1,1)),rewrite([30(6)]),flip(a)].
% 0.44/0.98 61 divide(inverse(divide(A,B)),inverse(A)) = divide(inverse(inverse(B)),c_0). [para(11(a,1),34(a,1,1,1,2)),rewrite([30(6),49(8)])].
% 0.44/0.98 63 divide(inverse(inverse(A)),c_0) = A. [para(25(a,1),34(a,1,1,1)),rewrite([30(2),31(5),49(4)])].
% 0.44/0.98 64 divide(A,c_0) = A. [para(31(a,1),34(a,1,1,1)),rewrite([49(4),63(4),30(2)])].
% 0.44/0.98 67 inverse(inverse(A)) = A. [back_rewrite(34),rewrite([64(2),61(4),64(4)])].
% 0.44/0.98 68 $F # answer(prove_these_axioms_2). [resolve(67,a,8,a)].
% 0.44/0.98
% 0.44/0.98 % SZS output end Refutation
% 0.44/0.98 ============================== end of proof ==========================
% 0.44/0.98
% 0.44/0.98 ============================== STATISTICS ============================
% 0.44/0.98
% 0.44/0.98 Given=17. Generated=178. Kept=63. proofs=1.
% 0.44/0.98 Usable=7. Sos=18. Demods=31. Limbo=7, Disabled=34. Hints=0.
% 0.44/0.98 Megabytes=0.08.
% 0.44/0.98 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
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% 0.44/0.98 ============================== end of statistics =====================
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% 0.44/0.98 ============================== end of search =========================
% 0.44/0.98
% 0.44/0.98 THEOREM PROVED
% 0.44/0.98 % SZS status Unsatisfiable
% 0.44/0.98
% 0.44/0.98 Exiting with 1 proof.
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% 0.44/0.98 Process 2298 exit (max_proofs) Mon Jun 13 19:37:11 2022
% 0.44/0.98 Prover9 interrupted
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