TSTP Solution File: GRP070-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP070-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 0.68s 0.99s
% Output : Refutation 0.68s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP070-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n010.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
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 19:32:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.68/0.99 ============================== Prover9 ===============================
% 0.68/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.68/0.99 Process 28612 was started by sandbox2 on n010.cluster.edu,
% 0.68/0.99 Mon Jun 13 19:32:40 2022
% 0.68/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_28328_n010.cluster.edu".
% 0.68/0.99 ============================== end of head ===========================
% 0.68/0.99
% 0.68/0.99 ============================== INPUT =================================
% 0.68/0.99
% 0.68/0.99 % Reading from file /tmp/Prover9_28328_n010.cluster.edu
% 0.68/0.99
% 0.68/0.99 set(prolog_style_variables).
% 0.68/0.99 set(auto2).
% 0.68/0.99 % set(auto2) -> set(auto).
% 0.68/0.99 % set(auto) -> set(auto_inference).
% 0.68/0.99 % set(auto) -> set(auto_setup).
% 0.68/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.68/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.68/0.99 % set(auto) -> set(auto_limits).
% 0.68/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.68/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.68/0.99 % set(auto) -> set(auto_denials).
% 0.68/0.99 % set(auto) -> set(auto_process).
% 0.68/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.68/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.68/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.68/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.68/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.68/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.68/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.68/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.68/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.68/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.68/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.68/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.68/0.99 % set(auto2) -> assign(stats, some).
% 0.68/0.99 % set(auto2) -> clear(echo_input).
% 0.68/0.99 % set(auto2) -> set(quiet).
% 0.68/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.68/0.99 % set(auto2) -> clear(print_given).
% 0.68/0.99 assign(lrs_ticks,-1).
% 0.68/0.99 assign(sos_limit,10000).
% 0.68/0.99 assign(order,kbo).
% 0.68/0.99 set(lex_order_vars).
% 0.68/0.99 clear(print_given).
% 0.68/0.99
% 0.68/0.99 % formulas(sos). % not echoed (3 formulas)
% 0.68/0.99
% 0.68/0.99 ============================== end of input ==========================
% 0.68/0.99
% 0.68/0.99 % From the command line: assign(max_seconds, 300).
% 0.68/0.99
% 0.68/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.68/0.99
% 0.68/0.99 % Formulas that are not ordinary clauses:
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% 0.68/0.99 ============================== end of process non-clausal formulas ===
% 0.68/0.99
% 0.68/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.68/0.99
% 0.68/0.99 ============================== PREDICATE ELIMINATION =================
% 0.68/0.99
% 0.68/0.99 ============================== end predicate elimination =============
% 0.68/0.99
% 0.68/0.99 Auto_denials:
% 0.68/0.99 % copying label prove_these_axioms to answer in negative clause
% 0.68/0.99
% 0.68/0.99 Term ordering decisions:
% 0.68/0.99
% 0.68/0.99 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 0.68/0.99 Function symbol KB weights: a1=1. a2=1. a3=1. b1=1. b2=1. b3=1. c3=1. divide=1. multiply=1. inverse=0.
% 0.68/0.99
% 0.68/0.99 ============================== end of process initial clauses ========
% 0.68/0.99
% 0.68/0.99 ============================== CLAUSES FOR SEARCH ====================
% 0.68/0.99
% 0.68/0.99 ============================== end of clauses for search =============
% 0.68/0.99
% 0.68/0.99 ============================== SEARCH ================================
% 0.68/0.99
% 0.68/0.99 % Starting search at 0.01 seconds.
% 0.68/0.99
% 0.68/0.99 ============================== PROOF =================================
% 0.68/0.99 % SZS status Unsatisfiable
% 0.68/0.99 % SZS output start Refutation
% 0.68/0.99
% 0.68/0.99 % Proof 1 at 0.03 (+ 0.00) seconds: prove_these_axioms.
% 0.68/0.99 % Length of proof is 38.
% 0.68/0.99 % Level of proof is 16.
% 0.68/0.99 % Maximum clause weight is 36.000.
% 0.68/0.99 % Given clauses 33.
% 0.68/0.99
% 0.68/0.99 1 multiply(A,B) = divide(A,inverse(B)) # label(multiply) # label(axiom). [assumption].
% 0.68/0.99 2 divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))) = C # label(single_axiom) # label(axiom). [assumption].
% 0.68/0.99 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)) # label(prove_these_axioms) # label(negated_conjecture) # answer(prove_these_axioms). [assumption].
% 0.68/0.99 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)))) # 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)].
% 0.68/0.99 6 divide(divide(A,A),divide(divide(divide(B,divide(C,D)),inverse(C)),divide(B,inverse(D)))) = divide(E,E). [para(2(a,1),2(a,1,2,2,1))].
% 0.68/0.99 14 divide(inverse(A),inverse(A)) = divide(divide(B,B),divide(divide(divide(C,divide(D,E)),inverse(D)),divide(C,inverse(E)))). [para(6(a,2),1(a,2)),rewrite([1(2)])].
% 0.68/0.99 15 divide(divide(A,A),divide(divide(B,inverse(C)),divide(divide(D,D),inverse(divide(divide(B,divide(E,C)),inverse(E)))))) = divide(F,F). [para(6(a,1),2(a,1,2,2,1))].
% 0.68/0.99 17 divide(divide(A,A),divide(B,divide(divide(C,divide(divide(D,D),divide(divide(divide(E,divide(F,V6)),inverse(F)),divide(E,inverse(V6))))),inverse(B)))) = C. [para(6(a,2),2(a,1,2,2,1,2))].
% 0.68/0.99 18 divide(divide(A,A),divide(B,divide(divide(divide(C,C),divide(divide(divide(D,divide(E,F)),inverse(E)),divide(D,inverse(F)))),inverse(V6)))) = divide(V6,B). [para(6(a,2),2(a,1,2,2,1))].
% 0.68/0.99 31 divide(A,A) = divide(B,B). [para(6(a,1),6(a,1))].
% 0.68/0.99 37 divide(A,A) = c_0. [new_symbol(31)].
% 0.68/0.99 39 divide(c_0,inverse(a2)) != a2 | divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) # answer(prove_these_axioms). [back_unit_del(4),rewrite([37(5),37(6),37(8)]),xx(a)].
% 0.68/0.99 56 divide(c_0,divide(A,divide(divide(c_0,divide(divide(divide(B,divide(C,D)),inverse(C)),divide(B,inverse(D)))),inverse(E)))) = divide(E,A). [back_rewrite(18),rewrite([37(1),37(2)])].
% 0.68/0.99 57 divide(c_0,divide(A,divide(divide(B,divide(c_0,divide(divide(divide(C,divide(D,E)),inverse(D)),divide(C,inverse(E))))),inverse(A)))) = B. [back_rewrite(17),rewrite([37(1),37(2)])].
% 0.68/0.99 59 divide(c_0,divide(divide(A,inverse(B)),divide(c_0,inverse(divide(divide(A,divide(C,B)),inverse(C)))))) = c_0. [back_rewrite(15),rewrite([37(1),37(4),37(13)])].
% 0.68/0.99 60 divide(c_0,divide(divide(divide(A,divide(B,C)),inverse(B)),divide(A,inverse(C)))) = c_0. [back_rewrite(14),rewrite([37(3),37(2)]),flip(a)].
% 0.68/0.99 69 divide(c_0,divide(A,divide(divide(B,divide(C,A)),inverse(C)))) = B. [back_rewrite(2),rewrite([37(1)])].
% 0.68/0.99 70 divide(c_0,divide(A,divide(divide(B,c_0),inverse(A)))) = B. [back_rewrite(57),rewrite([60(10)])].
% 0.68/0.99 71 divide(c_0,divide(A,divide(c_0,inverse(B)))) = divide(B,A). [back_rewrite(56),rewrite([60(10)])].
% 0.68/0.99 77 divide(divide(divide(A,divide(B,C)),inverse(B)),divide(A,inverse(C))) = c_0. [back_rewrite(59),rewrite([71(12)])].
% 0.68/0.99 80 divide(A,divide(c_0,inverse(A))) = c_0. [para(37(a,1),71(a,1,2)),rewrite([37(3)]),flip(a)].
% 0.68/0.99 82 divide(c_0,inverse(A)) = A. [para(80(a,1),69(a,1,2,2,1)),rewrite([71(8)])].
% 0.68/0.99 86 divide(c_0,divide(A,B)) = divide(B,A). [back_rewrite(71),rewrite([82(4)])].
% 0.68/0.99 87 divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) # answer(prove_these_axioms). [back_rewrite(39),rewrite([82(4)]),xx(a)].
% 0.68/0.99 93 divide(divide(divide(A,c_0),inverse(B)),B) = A. [back_rewrite(70),rewrite([86(7)])].
% 0.68/0.99 101 divide(inverse(A),c_0) = divide(c_0,A). [para(82(a,1),86(a,1,2)),flip(a)].
% 0.68/0.99 110 divide(inverse(inverse(A)),c_0) = A. [para(101(a,2),1(a,2)),rewrite([1(2),82(3)]),flip(a)].
% 0.68/0.99 112 divide(A,c_0) = A. [para(101(a,1),86(a,1,2)),rewrite([86(4),82(5)])].
% 0.68/0.99 113 inverse(divide(A,B)) = divide(B,A). [para(101(a,2),86(a,1)),rewrite([112(4)])].
% 0.68/0.99 114 divide(c_0,A) = inverse(A). [para(101(a,2),86(a,2)),rewrite([112(3),112(5)])].
% 0.68/0.99 119 inverse(inverse(A)) = A. [back_rewrite(110),rewrite([112(4)])].
% 0.68/0.99 121 divide(divide(A,inverse(B)),B) = A. [back_rewrite(93),rewrite([112(2)])].
% 0.68/0.99 124 divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(c3),b3)) # answer(prove_these_axioms). [back_rewrite(87),rewrite([113(13)])].
% 0.68/0.99 142 divide(divide(A,B),inverse(B)) = A. [para(121(a,1),1(a,2)),rewrite([119(2),1(2)])].
% 0.68/0.99 148 divide(divide(divide(A,B),divide(C,B)),divide(A,C)) = c_0. [para(142(a,1),77(a,1,1,1,2)),rewrite([113(3),119(5)])].
% 0.68/0.99 169 divide(divide(A,B),divide(C,B)) = divide(A,C). [para(148(a,1),142(a,1,1)),rewrite([113(3),114(3),113(2)]),flip(a)].
% 0.68/0.99 176 divide(divide(A,inverse(B)),C) = divide(A,divide(C,B)). [para(121(a,1),169(a,1,1)),flip(a)].
% 0.68/0.99 177 $F # answer(prove_these_axioms). [resolve(176,a,124,a)].
% 0.68/0.99
% 0.68/0.99 % SZS output end Refutation
% 0.68/0.99 ============================== end of proof ==========================
% 0.68/0.99
% 0.68/0.99 ============================== STATISTICS ============================
% 0.68/0.99
% 0.68/0.99 Given=33. Generated=594. Kept=175. proofs=1.
% 0.68/0.99 Usable=15. Sos=16. Demods=30. Limbo=0, Disabled=146. Hints=0.
% 0.68/0.99 Megabytes=0.21.
% 0.68/0.99 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.68/0.99
% 0.68/0.99 ============================== end of statistics =====================
% 0.68/0.99
% 0.68/0.99 ============================== end of search =========================
% 0.68/0.99
% 0.68/0.99 THEOREM PROVED
% 0.68/0.99 % SZS status Unsatisfiable
% 0.68/0.99
% 0.68/0.99 Exiting with 1 proof.
% 0.68/0.99
% 0.68/0.99 Process 28612 exit (max_proofs) Mon Jun 13 19:32:40 2022
% 0.68/0.99 Prover9 interrupted
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