TSTP Solution File: GRP486-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP486-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 11:19:18 EDT 2022
% Result : Unsatisfiable 0.46s 1.03s
% Output : Refutation 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP486-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n007.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 10:15:24 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.46/1.03 ============================== Prover9 ===============================
% 0.46/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.03 Process 24338 was started by sandbox on n007.cluster.edu,
% 0.46/1.03 Mon Jun 13 10:15:24 2022
% 0.46/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_24185_n007.cluster.edu".
% 0.46/1.03 ============================== end of head ===========================
% 0.46/1.03
% 0.46/1.03 ============================== INPUT =================================
% 0.46/1.03
% 0.46/1.03 % Reading from file /tmp/Prover9_24185_n007.cluster.edu
% 0.46/1.03
% 0.46/1.03 set(prolog_style_variables).
% 0.46/1.03 set(auto2).
% 0.46/1.03 % set(auto2) -> set(auto).
% 0.46/1.03 % set(auto) -> set(auto_inference).
% 0.46/1.03 % set(auto) -> set(auto_setup).
% 0.46/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.03 % set(auto) -> set(auto_limits).
% 0.46/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.03 % set(auto) -> set(auto_denials).
% 0.46/1.03 % set(auto) -> set(auto_process).
% 0.46/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.03 % set(auto2) -> assign(stats, some).
% 0.46/1.03 % set(auto2) -> clear(echo_input).
% 0.46/1.03 % set(auto2) -> set(quiet).
% 0.46/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.03 % set(auto2) -> clear(print_given).
% 0.46/1.03 assign(lrs_ticks,-1).
% 0.46/1.03 assign(sos_limit,10000).
% 0.46/1.03 assign(order,kbo).
% 0.46/1.03 set(lex_order_vars).
% 0.46/1.03 clear(print_given).
% 0.46/1.03
% 0.46/1.03 % formulas(sos). % not echoed (5 formulas)
% 0.46/1.03
% 0.46/1.03 ============================== end of input ==========================
% 0.46/1.03
% 0.46/1.03 % From the command line: assign(max_seconds, 300).
% 0.46/1.03
% 0.46/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.03
% 0.46/1.03 % Formulas that are not ordinary clauses:
% 0.46/1.03
% 0.46/1.03 ============================== end of process non-clausal formulas ===
% 0.46/1.03
% 0.46/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.46/1.03
% 0.46/1.03 ============================== PREDICATE ELIMINATION =================
% 0.46/1.03
% 0.46/1.03 ============================== end predicate elimination =============
% 0.46/1.03
% 0.46/1.03 Auto_denials:
% 0.46/1.03 % copying label prove_these_axioms_3 to answer in negative clause
% 0.46/1.03
% 0.46/1.03 Term ordering decisions:
% 0.46/1.03
% 0.46/1.03 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.46/1.03 Function symbol KB weights: identity=1. a3=1. b3=1. c3=1. double_divide=1. multiply=1. inverse=0.
% 0.46/1.03
% 0.46/1.03 ============================== end of process initial clauses ========
% 0.46/1.03
% 0.46/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.46/1.03
% 0.46/1.03 ============================== end of clauses for search =============
% 0.46/1.03
% 0.46/1.03 ============================== SEARCH ================================
% 0.46/1.03
% 0.46/1.03 % Starting search at 0.01 seconds.
% 0.46/1.03
% 0.46/1.03 ============================== PROOF =================================
% 0.46/1.03 % SZS status Unsatisfiable
% 0.46/1.03 % SZS output start Refutation
% 0.46/1.03
% 0.46/1.03 % Proof 1 at 0.02 (+ 0.00) seconds: prove_these_axioms_3.
% 0.46/1.03 % Length of proof is 51.
% 0.46/1.03 % Level of proof is 21.
% 0.46/1.03 % Maximum clause weight is 27.000.
% 0.46/1.03 % Given clauses 32.
% 0.46/1.03
% 0.46/1.03 1 inverse(A) = double_divide(A,identity) # label(inverse) # label(axiom). [assumption].
% 0.46/1.03 2 identity = double_divide(A,inverse(A)) # label(identity) # label(axiom). [assumption].
% 0.46/1.03 3 double_divide(A,double_divide(A,identity)) = identity. [copy(2),rewrite([1(2)]),flip(a)].
% 0.46/1.03 4 multiply(A,B) = double_divide(double_divide(B,A),identity) # label(multiply) # label(axiom). [assumption].
% 0.46/1.03 5 double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) = C # label(single_axiom) # label(axiom). [assumption].
% 0.46/1.03 6 multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # label(prove_these_axioms_3) # label(negated_conjecture) # answer(prove_these_axioms_3). [assumption].
% 0.46/1.03 7 double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) # answer(prove_these_axioms_3). [copy(6),rewrite([4(3),4(7),4(13),4(16)]),flip(a)].
% 0.46/1.03 8 double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(double_divide(A,identity),identity))),double_divide(identity,identity)) = B. [para(3(a,1),5(a,1,1,2,1,1))].
% 0.46/1.03 12 double_divide(double_divide(double_divide(double_divide(A,identity),B),C),double_divide(B,identity)) = double_divide(double_divide(A,C),double_divide(identity,identity)). [para(5(a,1),5(a,1,1,2)),flip(a)].
% 0.46/1.03 13 double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity. [para(3(a,1),8(a,1,1,2))].
% 0.46/1.03 14 double_divide(double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(double_divide(A,identity),identity))),double_divide(double_divide(B,C),double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = C. [para(8(a,1),5(a,1,1,2,1,1))].
% 0.46/1.03 16 double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,identity),identity),identity)) = double_divide(double_divide(B,A),double_divide(identity,identity)). [para(8(a,1),5(a,1,1,2)),flip(a)].
% 0.46/1.03 17 double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,A),double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = A. [para(13(a,1),5(a,1,1,2,1,1))].
% 0.46/1.03 18 double_divide(identity,identity) = identity. [para(13(a,1),5(a,1,1,2,1)),rewrite([3(6),13(7)]),flip(a)].
% 0.46/1.03 19 double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),identity) = A. [back_rewrite(17),rewrite([18(3),18(6),18(6),18(9)])].
% 0.46/1.03 20 double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,identity),identity),identity)) = double_divide(double_divide(B,A),identity). [back_rewrite(16),rewrite([18(13)])].
% 0.46/1.03 22 double_divide(double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(double_divide(A,identity),identity))),double_divide(double_divide(B,C),identity)),identity) = C. [back_rewrite(14),rewrite([18(12),18(12),18(15)])].
% 0.46/1.03 23 double_divide(double_divide(double_divide(double_divide(A,identity),B),C),double_divide(B,identity)) = double_divide(double_divide(A,C),identity). [back_rewrite(12),rewrite([18(11)])].
% 0.46/1.03 27 double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(double_divide(A,identity),identity))),identity) = B. [back_rewrite(8),rewrite([18(11)])].
% 0.46/1.03 31 double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),B),identity) = double_divide(double_divide(identity,B),double_divide(double_divide(A,identity),identity)). [para(19(a,1),20(a,1,2,1,1)),flip(a)].
% 0.46/1.03 32 double_divide(identity,double_divide(double_divide(A,identity),identity)) = double_divide(A,identity). [para(19(a,1),20(a,2,1)),rewrite([18(3),19(9)])].
% 0.46/1.03 36 double_divide(identity,double_divide(A,identity)) = A. [para(19(a,1),32(a,1,2,1)),rewrite([19(12)])].
% 0.46/1.03 37 double_divide(double_divide(identity,A),identity) = A. [para(19(a,1),32(a,2)),rewrite([36(7),36(8)])].
% 0.46/1.03 38 double_divide(double_divide(A,identity),double_divide(double_divide(double_divide(B,identity),identity),identity)) = double_divide(double_divide(B,double_divide(double_divide(A,identity),identity)),identity). [para(32(a,1),20(a,1,1))].
% 0.46/1.03 39 double_divide(double_divide(identity,A),double_divide(double_divide(B,identity),identity)) = double_divide(double_divide(double_divide(identity,B),A),identity). [back_rewrite(31),rewrite([37(5)]),flip(a)].
% 0.46/1.03 42 double_divide(double_divide(A,double_divide(double_divide(double_divide(identity,A),B),identity)),identity) = B. [back_rewrite(27),rewrite([39(7)])].
% 0.46/1.03 43 double_divide(double_divide(double_divide(A,double_divide(double_divide(double_divide(identity,A),B),identity)),double_divide(double_divide(B,C),identity)),identity) = C. [back_rewrite(22),rewrite([39(7)])].
% 0.46/1.03 48 double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)) = double_divide(double_divide(double_divide(identity,A),C),identity). [para(37(a,1),23(a,1,1,1,1))].
% 0.46/1.03 50 double_divide(double_divide(double_divide(double_divide(A,identity),identity),B),double_divide(double_divide(C,identity),identity)) = double_divide(double_divide(double_divide(double_divide(A,identity),C),B),identity). [para(23(a,1),23(a,1,1,1))].
% 0.46/1.03 51 double_divide(double_divide(double_divide(A,identity),identity),identity) = double_divide(A,identity). [para(23(a,1),23(a,1,1)),rewrite([48(6),37(4),18(7)]),flip(a)].
% 0.46/1.03 52 double_divide(double_divide(A,double_divide(double_divide(B,identity),identity)),identity) = double_divide(double_divide(B,identity),double_divide(A,identity)). [back_rewrite(38),rewrite([51(8)]),flip(a)].
% 0.46/1.03 54 double_divide(double_divide(A,identity),identity) = A. [para(51(a,1),36(a,1,2)),rewrite([36(4)]),flip(a)].
% 0.46/1.03 55 double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(double_divide(B,A),identity). [back_rewrite(52),rewrite([54(4)]),flip(a)].
% 0.46/1.03 56 double_divide(double_divide(double_divide(double_divide(A,identity),B),C),identity) = double_divide(double_divide(A,C),B). [back_rewrite(50),rewrite([54(4),54(5)]),flip(a)].
% 0.46/1.03 58 double_divide(double_divide(double_divide(identity,A),B),identity) = double_divide(double_divide(identity,B),A). [back_rewrite(39),rewrite([54(6)]),flip(a)].
% 0.46/1.03 60 double_divide(double_divide(double_divide(A,double_divide(double_divide(identity,B),A)),double_divide(double_divide(B,C),identity)),identity) = C. [back_rewrite(43),rewrite([58(5)])].
% 0.46/1.03 61 double_divide(double_divide(A,double_divide(double_divide(identity,B),A)),identity) = B. [back_rewrite(42),rewrite([58(5)])].
% 0.46/1.03 63 double_divide(identity,A) = double_divide(A,identity). [para(54(a,1),36(a,1,2))].
% 0.46/1.03 64 double_divide(identity,double_divide(A,double_divide(double_divide(B,identity),A))) = B. [back_rewrite(61),rewrite([63(2),63(6,R)])].
% 0.46/1.03 65 double_divide(identity,double_divide(double_divide(A,double_divide(double_divide(B,identity),A)),double_divide(identity,double_divide(B,C)))) = C. [back_rewrite(60),rewrite([63(2),63(7,R),63(10,R)])].
% 0.46/1.03 67 double_divide(identity,double_divide(double_divide(A,identity),B)) = double_divide(double_divide(B,identity),A). [back_rewrite(58),rewrite([63(2),63(5,R),63(7)])].
% 0.46/1.03 69 double_divide(identity,double_divide(double_divide(double_divide(A,identity),B),C)) = double_divide(double_divide(A,C),B). [back_rewrite(56),rewrite([63(6,R)])].
% 0.46/1.03 70 double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(identity,double_divide(B,A)). [back_rewrite(55),rewrite([63(8,R)])].
% 0.46/1.03 72 double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))) # answer(prove_these_axioms_3). [back_rewrite(7),rewrite([63(5,R),63(9,R),63(15,R),63(18,R)])].
% 0.46/1.03 74 double_divide(double_divide(identity,double_divide(identity,double_divide(A,B))),A) = B. [para(67(a,1),64(a,1)),rewrite([70(5),63(5,R)])].
% 0.46/1.03 77 double_divide(identity,double_divide(identity,double_divide(A,B))) = double_divide(A,B). [para(74(a,1),67(a,2,1)),rewrite([63(7),36(8),63(5),70(6)])].
% 0.46/1.03 79 double_divide(A,double_divide(B,A)) = B. [para(74(a,1),74(a,1,1,2,2)),rewrite([63(3),36(4),77(5)])].
% 0.46/1.03 80 double_divide(double_divide(A,B),A) = B. [back_rewrite(65),rewrite([79(5),67(8),63(5,R),77(5)])].
% 0.46/1.03 93 double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(B,double_divide(A,identity)). [para(80(a,1),70(a,1,1)),rewrite([63(6)]),flip(a)].
% 0.46/1.03 99 double_divide(double_divide(identity,double_divide(A,B)),C) = double_divide(A,double_divide(identity,double_divide(B,C))). [para(70(a,1),69(a,2,1)),rewrite([63(5,R),79(5),93(6),63(3,R)]),flip(a)].
% 0.46/1.03 102 $F # answer(prove_these_axioms_3). [back_rewrite(72),rewrite([99(8)]),xx(a)].
% 0.46/1.03
% 0.46/1.03 % SZS output end Refutation
% 0.46/1.03 ============================== end of proof ==========================
% 0.46/1.03
% 0.46/1.03 ============================== STATISTICS ============================
% 0.46/1.03
% 0.46/1.03 Given=32. Generated=559. Kept=99. proofs=1.
% 0.46/1.03 Usable=12. Sos=12. Demods=26. Limbo=4, Disabled=76. Hints=0.
% 0.46/1.03 Megabytes=0.10.
% 0.46/1.03 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.46/1.03
% 0.46/1.03 ============================== end of statistics =====================
% 0.46/1.03
% 0.46/1.03 ============================== end of search =========================
% 0.46/1.03
% 0.46/1.03 THEOREM PROVED
% 0.46/1.03 % SZS status Unsatisfiable
% 0.46/1.03
% 0.46/1.03 Exiting with 1 proof.
% 0.46/1.03
% 0.46/1.03 Process 24338 exit (max_proofs) Mon Jun 13 10:15:24 2022
% 0.46/1.03 Prover9 interrupted
%------------------------------------------------------------------------------