TSTP Solution File: GRP072-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP072-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.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 11:17:02 EDT 2022
% Result : Unsatisfiable 0.93s 1.20s
% Output : Refutation 0.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP072-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.08/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n016.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 12:39:59 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.93/1.20 ============================== Prover9 ===============================
% 0.93/1.20 Prover9 (32) version 2009-11A, November 2009.
% 0.93/1.20 Process 12521 was started by sandbox on n016.cluster.edu,
% 0.93/1.20 Mon Jun 13 12:40:00 2022
% 0.93/1.20 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_12368_n016.cluster.edu".
% 0.93/1.20 ============================== end of head ===========================
% 0.93/1.20
% 0.93/1.20 ============================== INPUT =================================
% 0.93/1.20
% 0.93/1.20 % Reading from file /tmp/Prover9_12368_n016.cluster.edu
% 0.93/1.20
% 0.93/1.20 set(prolog_style_variables).
% 0.93/1.20 set(auto2).
% 0.93/1.20 % set(auto2) -> set(auto).
% 0.93/1.20 % set(auto) -> set(auto_inference).
% 0.93/1.20 % set(auto) -> set(auto_setup).
% 0.93/1.20 % set(auto_setup) -> set(predicate_elim).
% 0.93/1.20 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.93/1.20 % set(auto) -> set(auto_limits).
% 0.93/1.20 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.93/1.20 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.93/1.20 % set(auto) -> set(auto_denials).
% 0.93/1.20 % set(auto) -> set(auto_process).
% 0.93/1.20 % set(auto2) -> assign(new_constants, 1).
% 0.93/1.20 % set(auto2) -> assign(fold_denial_max, 3).
% 0.93/1.20 % set(auto2) -> assign(max_weight, "200.000").
% 0.93/1.20 % set(auto2) -> assign(max_hours, 1).
% 0.93/1.20 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.93/1.20 % set(auto2) -> assign(max_seconds, 0).
% 0.93/1.20 % set(auto2) -> assign(max_minutes, 5).
% 0.93/1.20 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.93/1.20 % set(auto2) -> set(sort_initial_sos).
% 0.93/1.20 % set(auto2) -> assign(sos_limit, -1).
% 0.93/1.20 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.93/1.20 % set(auto2) -> assign(max_megs, 400).
% 0.93/1.20 % set(auto2) -> assign(stats, some).
% 0.93/1.20 % set(auto2) -> clear(echo_input).
% 0.93/1.20 % set(auto2) -> set(quiet).
% 0.93/1.20 % set(auto2) -> clear(print_initial_clauses).
% 0.93/1.20 % set(auto2) -> clear(print_given).
% 0.93/1.20 assign(lrs_ticks,-1).
% 0.93/1.20 assign(sos_limit,10000).
% 0.93/1.20 assign(order,kbo).
% 0.93/1.20 set(lex_order_vars).
% 0.93/1.20 clear(print_given).
% 0.93/1.20
% 0.93/1.20 % formulas(sos). % not echoed (3 formulas)
% 0.93/1.20
% 0.93/1.20 ============================== end of input ==========================
% 0.93/1.20
% 0.93/1.20 % From the command line: assign(max_seconds, 300).
% 0.93/1.20
% 0.93/1.20 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.93/1.20
% 0.93/1.20 % Formulas that are not ordinary clauses:
% 0.93/1.20
% 0.93/1.20 ============================== end of process non-clausal formulas ===
% 0.93/1.20
% 0.93/1.20 ============================== PROCESS INITIAL CLAUSES ===============
% 0.93/1.20
% 0.93/1.20 ============================== PREDICATE ELIMINATION =================
% 0.93/1.20
% 0.93/1.20 ============================== end predicate elimination =============
% 0.93/1.20
% 0.93/1.20 Auto_denials:
% 0.93/1.20 % copying label prove_these_axioms to answer in negative clause
% 0.93/1.20
% 0.93/1.20 Term ordering decisions:
% 0.93/1.20
% 0.93/1.20 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 0.93/1.20 Function symbol KB weights: a1=1. a2=1. a3=1. b1=1. b2=1. b3=1. c3=1. divide=1. multiply=1. inverse=0.
% 0.93/1.20
% 0.93/1.20 ============================== end of process initial clauses ========
% 0.93/1.20
% 0.93/1.20 ============================== CLAUSES FOR SEARCH ====================
% 0.93/1.20
% 0.93/1.20 ============================== end of clauses for search =============
% 0.93/1.20
% 0.93/1.20 ============================== SEARCH ================================
% 0.93/1.20
% 0.93/1.20 % Starting search at 0.01 seconds.
% 0.93/1.20
% 0.93/1.20 ============================== PROOF =================================
% 0.93/1.20 % SZS status Unsatisfiable
% 0.93/1.20 % SZS output start Refutation
% 0.93/1.20
% 0.93/1.20 % Proof 1 at 0.21 (+ 0.01) seconds: prove_these_axioms.
% 0.93/1.20 % Length of proof is 63.
% 0.93/1.20 % Level of proof is 17.
% 0.93/1.20 % Maximum clause weight is 43.000.
% 0.93/1.20 % Given clauses 34.
% 0.93/1.20
% 0.93/1.20 1 multiply(A,B) = divide(A,inverse(B)) # label(multiply) # label(axiom). [assumption].
% 0.93/1.20 2 divide(divide(inverse(divide(A,B)),divide(divide(C,D),A)),divide(D,C)) = B # label(single_axiom) # label(axiom). [assumption].
% 0.93/1.20 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)) # label(prove_these_axioms) # label(negated_conjecture) # answer(prove_these_axioms). [assumption].
% 0.93/1.20 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)))) # answer(prove_these_axioms). [copy(3),rewrite([1(4),1(9),1(15),1(18),1(24),1(27),1(32),1(34)]),flip(a)].
% 0.93/1.20 5 divide(divide(inverse(A),divide(divide(B,C),divide(inverse(divide(D,A)),divide(divide(E,F),D)))),divide(C,B)) = divide(F,E). [para(2(a,1),2(a,1,1,1,1))].
% 0.93/1.20 6 divide(divide(inverse(divide(A,B)),divide(C,A)),divide(divide(D,E),divide(inverse(divide(F,C)),divide(divide(E,D),F)))) = B. [para(2(a,1),2(a,1,1,2,1))].
% 0.93/1.20 7 divide(divide(inverse(divide(divide(A,B),C)),D),divide(divide(divide(B,A),E),inverse(divide(E,D)))) = C. [para(2(a,1),2(a,1,1,2))].
% 0.93/1.20 9 divide(divide(inverse(divide(A,B)),divide(divide(C,D),divide(inverse(E),divide(divide(F,V6),divide(inverse(divide(V7,E)),divide(divide(B,A),V7)))))),divide(D,C)) = divide(V6,F). [para(5(a,1),2(a,1,1,1,1))].
% 0.93/1.20 14 divide(divide(inverse(A),divide(divide(B,C),divide(inverse(divide(D,A)),divide(E,D)))),divide(C,B)) = divide(divide(F,V6),divide(inverse(divide(V7,E)),divide(divide(V6,F),V7))). [para(2(a,1),5(a,1,1,2,2,2,1))].
% 0.93/1.20 20 divide(divide(A,B),divide(inverse(C),divide(divide(B,A),divide(inverse(divide(D,C)),divide(divide(E,F),D))))) = divide(E,F). [para(5(a,1),5(a,1,1,2,2,2,1)),rewrite([5(11)]),flip(a)].
% 0.93/1.20 47 divide(divide(inverse(A),divide(divide(B,C),divide(inverse(divide(D,A)),divide(E,D)))),divide(C,B)) = divide(divide(divide(F,V6),divide(inverse(divide(V7,V8)),divide(divide(V6,F),V7))),divide(inverse(divide(V9,E)),divide(V8,V9))). [para(6(a,1),5(a,1,1,2,2,2,1))].
% 0.93/1.20 107 divide(divide(A,B),divide(inverse(C),divide(divide(B,A),divide(inverse(divide(D,C)),divide(E,D))))) = E. [para(2(a,1),20(a,1,2,2,2,2,1)),rewrite([2(17)])].
% 0.93/1.20 184 divide(inverse(A),divide(divide(B,C),divide(inverse(divide(D,A)),divide(E,D)))) = divide(divide(inverse(E),divide(divide(F,V6),divide(C,B))),divide(V6,F)). [para(107(a,1),2(a,1,1,1,1)),flip(a)].
% 0.93/1.20 232 divide(divide(inverse(divide(A,B)),divide(B,A)),divide(C,D)) = divide(D,C). [para(107(a,1),9(a,1,1,2))].
% 0.93/1.20 241 divide(divide(inverse(divide(A,B)),divide(divide(C,D),divide(inverse(divide(E,F)),divide(F,E)))),divide(D,C)) = divide(B,A). [para(232(a,1),2(a,1,1,1,1))].
% 0.93/1.20 250 divide(divide(A,B),divide(inverse(divide(C,D)),divide(D,C))) = divide(A,B). [para(232(a,1),5(a,1,1,2,2,2,1)),rewrite([5(11)]),flip(a)].
% 0.93/1.20 277 divide(divide(inverse(divide(divide(A,B),inverse(divide(B,A)))),divide(divide(C,D),divide(inverse(E),divide(divide(F,V6),divide(inverse(divide(divide(V7,V8),E)),divide(V8,V7)))))),divide(D,C)) = divide(V6,F). [para(232(a,1),9(a,1,1,2,2,2,2,2))].
% 0.93/1.20 288 divide(divide(inverse(divide(A,B)),divide(C,D)),divide(D,C)) = divide(B,A). [back_rewrite(241),rewrite([250(8)])].
% 0.93/1.20 290 divide(A,divide(inverse(divide(B,C)),divide(C,B))) = A. [para(250(a,1),2(a,1,1,2)),rewrite([288(10)])].
% 0.93/1.20 318 divide(divide(A,B),divide(inverse(C),divide(B,A))) = C. [para(250(a,1),107(a,1,2,2))].
% 0.93/1.20 332 divide(divide(inverse(divide(A,B)),C),divide(divide(divide(divide(inverse(divide(D,E)),divide(E,D)),A),F),inverse(divide(F,C)))) = B. [para(290(a,1),7(a,1,1,1,1,1))].
% 0.93/1.20 333 divide(inverse(divide(divide(A,B),C)),divide(divide(divide(B,A),D),inverse(D))) = C. [para(290(a,1),7(a,1,1)),rewrite([290(10)])].
% 0.93/1.20 340 divide(divide(inverse(divide(A,B)),divide(divide(inverse(divide(C,D)),divide(D,C)),A)),divide(divide(E,F),divide(inverse(V6),divide(divide(F,E),V6)))) = B. [para(290(a,1),6(a,1,2,2,1,1))].
% 0.93/1.20 364 divide(inverse(divide(divide(A,B),inverse(divide(B,A)))),divide(C,D)) = divide(D,C). [para(290(a,1),232(a,1,1))].
% 0.93/1.20 367 divide(A,divide(inverse(divide(divide(inverse(divide(B,C)),divide(C,B)),D)),D)) = A. [para(290(a,1),290(a,1,2,2))].
% 0.93/1.20 369 divide(divide(divide(inverse(A),divide(divide(B,C),divide(inverse(divide(divide(D,E),A)),divide(E,D)))),divide(F,V6)),divide(V6,F)) = divide(C,B). [back_rewrite(277),rewrite([364(17)])].
% 0.93/1.20 458 divide(divide(inverse(A),divide(divide(B,C),divide(D,E))),divide(C,B)) = divide(inverse(A),divide(E,D)). [para(318(a,1),2(a,1,1,1,1))].
% 0.93/1.20 471 divide(divide(inverse(divide(A,B)),C),divide(divide(divide(divide(inverse(A),divide(D,E)),divide(E,D)),F),inverse(divide(F,C)))) = B. [para(318(a,1),7(a,1,1,1,1,1))].
% 0.93/1.20 472 divide(divide(inverse(A),B),divide(divide(divide(C,D),E),inverse(divide(E,B)))) = divide(inverse(A),divide(C,D)). [para(318(a,1),7(a,1,1,1,1))].
% 0.93/1.20 481 divide(divide(inverse(divide(A,B)),divide(C,A)),divide(divide(divide(inverse(D),divide(E,F)),divide(F,E)),divide(inverse(divide(V6,C)),divide(D,V6)))) = B. [para(318(a,1),6(a,1,2,2,2,1))].
% 0.93/1.20 499 divide(inverse(divide(A,B)),divide(divide(C,D),inverse(D))) = divide(divide(B,A),C). [para(318(a,1),9(a,1,1,2,2,2)),rewrite([458(10)])].
% 0.93/1.20 512 divide(divide(inverse(divide(A,B)),divide(B,A)),C) = divide(divide(inverse(C),divide(D,E)),divide(E,D)). [para(318(a,1),232(a,1,2))].
% 0.93/1.20 513 divide(divide(divide(A,B),inverse(divide(B,A))),inverse(C)) = C. [para(318(a,1),232(a,1)),flip(a)].
% 0.93/1.20 578 divide(inverse(A),divide(divide(B,C),divide(inverse(divide(D,A)),divide(E,D)))) = divide(inverse(E),divide(B,C)). [back_rewrite(184),rewrite([458(15)])].
% 0.93/1.20 607 divide(divide(inverse(A),divide(B,C)),divide(C,B)) = divide(divide(divide(D,E),divide(inverse(divide(F,V6)),divide(divide(E,D),F))),divide(inverse(divide(V7,A)),divide(V6,V7))). [back_rewrite(47),rewrite([578(8)])].
% 0.93/1.20 614 divide(divide(inverse(A),divide(B,C)),divide(C,B)) = divide(divide(D,E),divide(inverse(divide(F,A)),divide(divide(E,D),F))). [back_rewrite(14),rewrite([578(8)])].
% 0.93/1.20 615 divide(inverse(divide(A,B)),divide(divide(inverse(A),divide(C,D)),divide(D,C))) = B. [back_rewrite(471),rewrite([472(13)])].
% 0.93/1.20 617 divide(inverse(divide(A,B)),divide(divide(inverse(divide(C,D)),divide(D,C)),A)) = B. [back_rewrite(332),rewrite([472(13)])].
% 0.93/1.20 626 divide(inverse(divide(divide(A,B),C)),divide(B,A)) = C. [back_rewrite(7),rewrite([472(10)])].
% 0.93/1.20 629 divide(divide(A,divide(B,C)),divide(C,B)) = A. [back_rewrite(333),rewrite([499(8)])].
% 0.93/1.20 670 divide(A,divide(divide(B,C),divide(inverse(D),divide(divide(C,B),D)))) = A. [back_rewrite(340),rewrite([617(8)])].
% 0.93/1.20 674 divide(inverse(A),divide(divide(B,C),A)) = divide(C,B). [back_rewrite(369),rewrite([626(7),629(8)])].
% 0.93/1.20 678 divide(inverse(divide(A,B)),inverse(A)) = B. [back_rewrite(615),rewrite([629(7)])].
% 0.93/1.20 679 divide(divide(A,B),divide(inverse(divide(C,D)),divide(divide(B,A),C))) = inverse(D). [back_rewrite(614),rewrite([629(5)]),flip(a)].
% 0.93/1.20 681 divide(inverse(A),divide(inverse(divide(B,C)),divide(A,B))) = inverse(C). [back_rewrite(607),rewrite([629(5),679(8)]),flip(a)].
% 0.93/1.20 690 divide(divide(inverse(divide(A,B)),divide(B,A)),C) = inverse(C). [back_rewrite(512),rewrite([629(10)])].
% 0.93/1.20 698 divide(divide(inverse(divide(A,B)),divide(C,A)),inverse(C)) = B. [back_rewrite(481),rewrite([629(9),681(10)])].
% 0.93/1.20 702 inverse(divide(A,B)) = divide(B,A). [back_rewrite(288),rewrite([629(6)])].
% 0.93/1.20 708 divide(A,divide(divide(B,C),divide(B,C))) = A. [back_rewrite(670),rewrite([674(5)])].
% 0.93/1.20 849 divide(A,divide(B,B)) = A. [back_rewrite(367),rewrite([702(2),702(5),708(4)])].
% 0.93/1.20 897 divide(divide(divide(A,B),divide(C,B)),inverse(C)) = A. [back_rewrite(698),rewrite([702(2)])].
% 0.93/1.20 902 divide(divide(divide(A,B),divide(A,B)),C) = inverse(C). [back_rewrite(690),rewrite([702(2)])].
% 0.93/1.20 909 divide(divide(A,B),inverse(B)) = A. [back_rewrite(678),rewrite([702(2)])].
% 0.93/1.20 958 inverse(inverse(A)) = A. [back_rewrite(513),rewrite([702(3),902(5)])].
% 0.93/1.20 1020 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(c3),b3)) # answer(prove_these_axioms). [back_rewrite(4),rewrite([702(34)])].
% 0.93/1.20 1056 divide(divide(A,A),B) = inverse(B). [para(849(a,1),702(a,1,1)),flip(a)].
% 0.93/1.20 1057 divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) | divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(c3),b3)) # answer(prove_these_axioms). [back_rewrite(1020),rewrite([1056(19),958(14)]),xx(b)].
% 0.93/1.20 1100 divide(A,A) = divide(B,B). [para(1056(a,1),849(a,1)),rewrite([702(2)])].
% 0.93/1.20 1101 divide(A,A) = c_0. [new_symbol(1100)].
% 0.93/1.20 1102 divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(c3),b3)) # answer(prove_these_axioms). [back_unit_del(1057),rewrite([1101(5),1101(6)]),xx(a)].
% 0.93/1.20 1122 divide(divide(A,B),divide(C,B)) = divide(A,C). [para(897(a,1),909(a,1,1)),rewrite([958(2)]),flip(a)].
% 0.93/1.20 1143 divide(divide(A,B),C) = divide(A,divide(C,inverse(B))). [para(909(a,1),1122(a,1,1)),flip(a)].
% 0.93/1.20 1145 $F # answer(prove_these_axioms). [back_rewrite(1102),rewrite([1143(7),958(6)]),xx(a)].
% 0.93/1.20
% 0.93/1.20 % SZS output end Refutation
% 0.93/1.20 ============================== end of proof ==========================
% 0.93/1.20
% 0.93/1.20 ============================== STATISTICS ============================
% 0.93/1.20
% 0.93/1.20 Given=34. Generated=2237. Kept=1143. proofs=1.
% 0.93/1.20 Usable=11. Sos=5. Demods=18. Limbo=2, Disabled=1128. Hints=0.
% 0.93/1.20 Megabytes=1.48.
% 0.93/1.20 User_CPU=0.21, System_CPU=0.01, Wall_clock=0.
% 0.93/1.20
% 0.93/1.20 ============================== end of statistics =====================
% 0.93/1.20
% 0.93/1.20 ============================== end of search =========================
% 0.93/1.20
% 0.93/1.20 THEOREM PROVED
% 0.93/1.20 % SZS status Unsatisfiable
% 0.93/1.20
% 0.93/1.20 Exiting with 1 proof.
% 0.93/1.20
% 0.93/1.20 Process 12521 exit (max_proofs) Mon Jun 13 12:40:00 2022
% 0.93/1.20 Prover9 interrupted
%------------------------------------------------------------------------------