TSTP Solution File: GRP096-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP096-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 11:17:08 EDT 2022
% Result : Unsatisfiable 0.71s 0.99s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP096-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n025.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
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 22:26:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.71/0.99 ============================== Prover9 ===============================
% 0.71/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.71/0.99 Process 2100 was started by sandbox on n025.cluster.edu,
% 0.71/0.99 Mon Jun 13 22:26:10 2022
% 0.71/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_1941_n025.cluster.edu".
% 0.71/0.99 ============================== end of head ===========================
% 0.71/0.99
% 0.71/0.99 ============================== INPUT =================================
% 0.71/0.99
% 0.71/0.99 % Reading from file /tmp/Prover9_1941_n025.cluster.edu
% 0.71/0.99
% 0.71/0.99 set(prolog_style_variables).
% 0.71/0.99 set(auto2).
% 0.71/0.99 % set(auto2) -> set(auto).
% 0.71/0.99 % set(auto) -> set(auto_inference).
% 0.71/0.99 % set(auto) -> set(auto_setup).
% 0.71/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.71/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.71/0.99 % set(auto) -> set(auto_limits).
% 0.71/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.71/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.71/0.99 % set(auto) -> set(auto_denials).
% 0.71/0.99 % set(auto) -> set(auto_process).
% 0.71/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.71/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.71/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.71/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.71/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.71/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.71/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.71/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.71/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.71/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.71/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.71/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.71/0.99 % set(auto2) -> assign(stats, some).
% 0.71/0.99 % set(auto2) -> clear(echo_input).
% 0.71/0.99 % set(auto2) -> set(quiet).
% 0.71/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.71/0.99 % set(auto2) -> clear(print_given).
% 0.71/0.99 assign(lrs_ticks,-1).
% 0.71/0.99 assign(sos_limit,10000).
% 0.71/0.99 assign(order,kbo).
% 0.71/0.99 set(lex_order_vars).
% 0.71/0.99 clear(print_given).
% 0.71/0.99
% 0.71/0.99 % formulas(sos). % not echoed (3 formulas)
% 0.71/0.99
% 0.71/0.99 ============================== end of input ==========================
% 0.71/0.99
% 0.71/0.99 % From the command line: assign(max_seconds, 300).
% 0.71/0.99
% 0.71/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.71/0.99
% 0.71/0.99 % Formulas that are not ordinary clauses:
% 0.71/0.99
% 0.71/0.99 ============================== end of process non-clausal formulas ===
% 0.71/0.99
% 0.71/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.71/0.99
% 0.71/0.99 ============================== PREDICATE ELIMINATION =================
% 0.71/0.99
% 0.71/0.99 ============================== end predicate elimination =============
% 0.71/0.99
% 0.71/0.99 Auto_denials:
% 0.71/0.99 % copying label prove_these_axioms to answer in negative clause
% 0.71/0.99
% 0.71/0.99 Term ordering decisions:
% 0.71/0.99
% 0.71/0.99 % Assigning unary symbol inverse kb_weight 0 and highest precedence (13).
% 0.71/0.99 Function symbol KB weights: a1=1. a2=1. a3=1. a4=1. b1=1. b2=1. b3=1. b4=1. c3=1. divide=1. multiply=1. inverse=0.
% 0.71/0.99
% 0.71/0.99 ============================== end of process initial clauses ========
% 0.71/0.99
% 0.71/0.99 ============================== CLAUSES FOR SEARCH ====================
% 0.71/0.99
% 0.71/0.99 ============================== end of clauses for search =============
% 0.71/0.99
% 0.71/0.99 ============================== SEARCH ================================
% 0.71/0.99
% 0.71/0.99 % Starting search at 0.01 seconds.
% 0.71/0.99
% 0.71/0.99 ============================== PROOF =================================
% 0.71/0.99 % SZS status Unsatisfiable
% 0.71/0.99 % SZS output start Refutation
% 0.71/0.99
% 0.71/0.99 % Proof 1 at 0.02 (+ 0.00) seconds: prove_these_axioms.
% 0.71/0.99 % Length of proof is 48.
% 0.71/0.99 % Level of proof is 20.
% 0.71/0.99 % Maximum clause weight is 46.000.
% 0.71/0.99 % Given clauses 30.
% 0.71/0.99
% 0.71/0.99 1 multiply(A,B) = divide(A,inverse(B)) # label(multiply) # label(axiom). [assumption].
% 0.71/0.99 2 divide(divide(A,inverse(divide(B,divide(A,C)))),C) = B # label(single_axiom) # label(axiom). [assumption].
% 0.71/0.99 3 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].
% 0.71/0.99 4 divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) | divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2 | divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) | divide(b4,inverse(a4)) != divide(a4,inverse(b4)) # answer(prove_these_axioms). [copy(3),rewrite([1(4),1(9),1(15),1(18),1(24),1(27),1(32),1(34),1(39),1(43)]),flip(a),flip(d)].
% 0.71/0.99 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))].
% 0.71/0.99 6 divide(A,inverse(divide(B,divide(A,divide(C,D))))) = divide(divide(C,inverse(B)),D). [para(2(a,1),2(a,1,1,2,1)),flip(a)].
% 0.71/0.99 10 divide(A,inverse(divide(B,A))) = B. [para(2(a,1),5(a,1,1))].
% 0.71/0.99 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))].
% 0.71/0.99 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))].
% 0.71/0.99 14 divide(A,inverse(divide(B,divide(A,C)))) = divide(C,inverse(B)). [para(2(a,1),10(a,1,2,1)),flip(a)].
% 0.71/0.99 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)].
% 0.71/0.99 18 divide(inverse(divide(A,B)),inverse(A)) = B. [para(10(a,1),10(a,1,2,1))].
% 0.71/0.99 19 divide(divide(divide(A,inverse(B)),inverse(C)),A) = divide(B,inverse(C)). [back_rewrite(12),rewrite([14(4),14(9),17(10)])].
% 0.71/0.99 20 divide(divide(A,inverse(B)),A) = B. [back_rewrite(11),rewrite([14(4),17(5),17(5),17(5)])].
% 0.71/0.99 21 divide(divide(A,inverse(B)),C) = divide(divide(A,C),inverse(B)). [back_rewrite(6),rewrite([14(5)]),flip(a)].
% 0.71/0.99 22 divide(A,divide(inverse(B),inverse(A))) = B. [para(20(a,1),20(a,1,1))].
% 0.71/0.99 23 inverse(divide(A,B)) = divide(inverse(A),inverse(B)). [para(18(a,1),10(a,1,2,1)),flip(a)].
% 0.71/0.99 29 divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) | divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2 | divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(b3),inverse(inverse(c3)))) | divide(b4,inverse(a4)) != divide(a4,inverse(b4)) # answer(prove_these_axioms). [back_rewrite(4),rewrite([23(34)])].
% 0.71/0.99 31 divide(divide(A,inverse(B)),divide(inverse(C),inverse(A))) = divide(C,inverse(B)). [para(20(a,1),19(a,1,1,1))].
% 0.71/0.99 34 divide(A,inverse(B)) = divide(B,inverse(A)). [para(19(a,1),19(a,1,1)),rewrite([31(6)])].
% 0.71/0.99 35 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([34(3),34(5),23(4),23(7),23(7),34(12),23(11),23(11),23(11)])].
% 0.71/0.99 40 divide(b1,inverse(inverse(b1))) != divide(a1,inverse(inverse(a1))) | divide(a2,divide(inverse(b2),inverse(inverse(inverse(b2))))) != a2 | divide(c3,divide(inverse(a3),inverse(inverse(b3)))) != divide(a3,divide(inverse(b3),inverse(inverse(c3)))) # answer(prove_these_axioms). [back_rewrite(29),rewrite([34(5),34(10),34(16),34(19),23(18),34(29),23(28),34(43)]),xx(d)].
% 0.71/0.99 46 inverse(divide(A,B)) = divide(B,inverse(inverse(A))). [back_rewrite(23),rewrite([34(5)])].
% 0.71/0.99 47 divide(A,divide(A,inverse(inverse(B)))) = B. [back_rewrite(22),rewrite([34(3)])].
% 0.71/0.99 48 divide(divide(A,inverse(B)),C) = divide(B,divide(C,inverse(inverse(A)))). [back_rewrite(21),rewrite([34(6),46(5)])].
% 0.71/0.99 49 divide(divide(A,divide(inverse(B),inverse(inverse(C)))),B) = divide(C,inverse(A)). [back_rewrite(19),rewrite([34(4),46(3),34(4)])].
% 0.71/0.99 52 divide(A,divide(B,inverse(inverse(B)))) = A. [back_rewrite(20),rewrite([48(3)])].
% 0.71/0.99 53 divide(b1,inverse(inverse(b1))) != divide(a1,inverse(inverse(a1))) | divide(c3,divide(inverse(a3),inverse(inverse(b3)))) != divide(a3,divide(inverse(b3),inverse(inverse(c3)))) # answer(prove_these_axioms). [back_rewrite(40),rewrite([52(20)]),xx(b)].
% 0.71/0.99 58 divide(A,inverse(inverse(A))) = divide(B,inverse(inverse(B))). [para(47(a,1),35(a,1,1,2,2)),rewrite([49(7),34(3)])].
% 0.71/0.99 59 divide(A,divide(inverse(inverse(B)),divide(divide(inverse(inverse(C)),divide(inverse(inverse(inverse(D))),inverse(inverse(inverse(inverse(inverse(A))))))),inverse(inverse(inverse(B)))))) = divide(D,inverse(C)). [para(35(a,1),52(a,1)),rewrite([46(6),34(7),48(20)]),flip(a)].
% 0.71/0.99 62 divide(divide(A,divide(inverse(B),divide(inverse(inverse(C)),divide(inverse(inverse(inverse(inverse(A)))),divide(inverse(inverse(inverse(D))),inverse(inverse(inverse(inverse(inverse(E)))))))))),B) = divide(E,divide(D,inverse(inverse(C)))). [para(46(a,1),35(a,1,1,2,2,1,1)),rewrite([46(5),34(6),48(16),48(16),46(23)])].
% 0.71/1.00 66 divide(A,inverse(inverse(A))) = c_0. [new_symbol(58)].
% 0.71/1.00 67 divide(c3,divide(inverse(a3),inverse(inverse(b3)))) != divide(a3,divide(inverse(b3),inverse(inverse(c3)))) # answer(prove_these_axioms). [back_unit_del(53),rewrite([66(5),66(6)]),xx(a)].
% 0.71/1.00 68 divide(A,c_0) = A. [back_rewrite(52),rewrite([66(3)])].
% 0.71/1.00 71 inverse(c_0) = c_0. [para(66(a,1),46(a,1,1)),rewrite([34(7),66(7)])].
% 0.71/1.00 74 divide(A,A) = c_0. [para(71(a,1),47(a,1,2,2,1)),rewrite([71(2),68(2)])].
% 0.71/1.00 75 divide(divide(A,divide(inverse(B),divide(c_0,divide(inverse(inverse(inverse(C))),inverse(inverse(inverse(inverse(inverse(A))))))))),B) = C. [para(71(a,1),35(a,1,1,2,2,1,1)),rewrite([71(3),71(17),68(17)])].
% 0.71/1.00 77 inverse(inverse(A)) = A. [para(74(a,1),47(a,1,2)),rewrite([68(4)])].
% 0.71/1.00 78 divide(divide(A,divide(inverse(B),C)),B) = divide(A,inverse(C)). [para(74(a,1),35(a,1,1,2,2,2)),rewrite([77(3),68(3),77(6)])].
% 0.71/1.00 81 divide(A,divide(A,B)) = B. [back_rewrite(75),rewrite([77(4),77(5),77(5),34(5),77(4),78(7),46(4),71(3),71(3),68(3)])].
% 0.71/1.00 84 divide(c3,divide(inverse(a3),b3)) != divide(a3,divide(inverse(b3),c3)) # answer(prove_these_axioms). [back_rewrite(67),rewrite([77(6),77(12)])].
% 0.71/1.00 88 divide(A,divide(divide(A,divide(B,C)),D)) = divide(B,divide(C,D)). [back_rewrite(62),rewrite([77(3),77(3),77(3),77(3),77(4),77(4),34(4),77(3),78(7),46(4),77(4),77(6)])].
% 0.71/1.00 91 divide(A,divide(divide(A,B),C)) = divide(C,inverse(B)). [back_rewrite(59),rewrite([77(2),77(2),77(2),77(3),77(3),34(3),77(2),77(4),34(4),46(3),77(3),81(4),34(5)])].
% 0.71/1.00 97 inverse(divide(A,B)) = divide(B,A). [back_rewrite(46),rewrite([77(4)])].
% 0.71/1.00 100 divide(A,divide(B,C)) = divide(C,divide(B,A)). [back_rewrite(88),rewrite([91(4),97(2)])].
% 0.71/1.00 106 divide(b3,divide(inverse(a3),c3)) != divide(a3,divide(inverse(b3),c3)) # answer(prove_these_axioms). [back_rewrite(84),rewrite([100(6)])].
% 0.71/1.00 107 divide(inverse(A),B) = divide(inverse(B),A). [para(34(a,1),97(a,1,1)),rewrite([97(3)])].
% 0.71/1.00 118 $F # answer(prove_these_axioms). [para(100(a,1),106(a,2)),rewrite([107(11),100(12)]),xx(a)].
% 0.71/1.00
% 0.71/1.00 % SZS output end Refutation
% 0.71/1.00 ============================== end of proof ==========================
% 0.71/1.00
% 0.71/1.00 ============================== STATISTICS ============================
% 0.71/1.00
% 0.71/1.00 Given=30. Generated=380. Kept=116. proofs=1.
% 0.71/1.00 Usable=13. Sos=4. Demods=16. Limbo=0, Disabled=102. Hints=0.
% 0.71/1.00 Megabytes=0.15.
% 0.71/1.00 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.71/1.00
% 0.71/1.00 ============================== end of statistics =====================
% 0.71/1.00
% 0.71/1.00 ============================== end of search =========================
% 0.71/1.00
% 0.71/1.00 THEOREM PROVED
% 0.71/1.00 % SZS status Unsatisfiable
% 0.71/1.00
% 0.71/1.00 Exiting with 1 proof.
% 0.71/1.00
% 0.71/1.00 Process 2100 exit (max_proofs) Mon Jun 13 22:26:10 2022
% 0.71/1.00 Prover9 interrupted
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