TSTP Solution File: GRP579-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP579-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 11:19:42 EDT 2022
% Result : Unsatisfiable 0.71s 1.12s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP579-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 11:45:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.71/1.12 ============================== Prover9 ===============================
% 0.71/1.12 Prover9 (32) version 2009-11A, November 2009.
% 0.71/1.12 Process 16525 was started by sandbox on n017.cluster.edu,
% 0.71/1.12 Tue Jun 14 11:45:24 2022
% 0.71/1.12 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_16372_n017.cluster.edu".
% 0.71/1.12 ============================== end of head ===========================
% 0.71/1.12
% 0.71/1.12 ============================== INPUT =================================
% 0.71/1.12
% 0.71/1.12 % Reading from file /tmp/Prover9_16372_n017.cluster.edu
% 0.71/1.12
% 0.71/1.12 set(prolog_style_variables).
% 0.71/1.12 set(auto2).
% 0.71/1.12 % set(auto2) -> set(auto).
% 0.71/1.12 % set(auto) -> set(auto_inference).
% 0.71/1.12 % set(auto) -> set(auto_setup).
% 0.71/1.12 % set(auto_setup) -> set(predicate_elim).
% 0.71/1.12 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.71/1.12 % set(auto) -> set(auto_limits).
% 0.71/1.12 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.71/1.12 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.71/1.12 % set(auto) -> set(auto_denials).
% 0.71/1.12 % set(auto) -> set(auto_process).
% 0.71/1.12 % set(auto2) -> assign(new_constants, 1).
% 0.71/1.12 % set(auto2) -> assign(fold_denial_max, 3).
% 0.71/1.12 % set(auto2) -> assign(max_weight, "200.000").
% 0.71/1.12 % set(auto2) -> assign(max_hours, 1).
% 0.71/1.12 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.71/1.12 % set(auto2) -> assign(max_seconds, 0).
% 0.71/1.12 % set(auto2) -> assign(max_minutes, 5).
% 0.71/1.12 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.71/1.12 % set(auto2) -> set(sort_initial_sos).
% 0.71/1.12 % set(auto2) -> assign(sos_limit, -1).
% 0.71/1.12 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.71/1.12 % set(auto2) -> assign(max_megs, 400).
% 0.71/1.12 % set(auto2) -> assign(stats, some).
% 0.71/1.12 % set(auto2) -> clear(echo_input).
% 0.71/1.12 % set(auto2) -> set(quiet).
% 0.71/1.12 % set(auto2) -> clear(print_initial_clauses).
% 0.71/1.12 % set(auto2) -> clear(print_given).
% 0.71/1.12 assign(lrs_ticks,-1).
% 0.71/1.12 assign(sos_limit,10000).
% 0.71/1.12 assign(order,kbo).
% 0.71/1.12 set(lex_order_vars).
% 0.71/1.12 clear(print_given).
% 0.71/1.12
% 0.71/1.12 % formulas(sos). % not echoed (5 formulas)
% 0.71/1.12
% 0.71/1.12 ============================== end of input ==========================
% 0.71/1.12
% 0.71/1.12 % From the command line: assign(max_seconds, 300).
% 0.71/1.12
% 0.71/1.12 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.71/1.12
% 0.71/1.12 % Formulas that are not ordinary clauses:
% 0.71/1.12
% 0.71/1.12 ============================== end of process non-clausal formulas ===
% 0.71/1.12
% 0.71/1.12 ============================== PROCESS INITIAL CLAUSES ===============
% 0.71/1.12
% 0.71/1.12 ============================== PREDICATE ELIMINATION =================
% 0.71/1.12
% 0.71/1.12 ============================== end predicate elimination =============
% 0.71/1.12
% 0.71/1.12 Auto_denials:
% 0.71/1.12 % copying label prove_these_axioms_3 to answer in negative clause
% 0.71/1.12
% 0.71/1.12 Term ordering decisions:
% 0.71/1.12
% 0.71/1.12 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.71/1.12 Function symbol KB weights: identity=1. a3=1. b3=1. c3=1. double_divide=1. multiply=1. inverse=0.
% 0.71/1.12
% 0.71/1.12 ============================== end of process initial clauses ========
% 0.71/1.12
% 0.71/1.12 ============================== CLAUSES FOR SEARCH ====================
% 0.71/1.12
% 0.71/1.12 ============================== end of clauses for search =============
% 0.71/1.12
% 0.71/1.12 ============================== SEARCH ================================
% 0.71/1.12
% 0.71/1.12 % Starting search at 0.01 seconds.
% 0.71/1.12
% 0.71/1.12 ============================== PROOF =================================
% 0.71/1.12 % SZS status Unsatisfiable
% 0.71/1.12 % SZS output start Refutation
% 0.71/1.12
% 0.71/1.12 % Proof 1 at 0.16 (+ 0.01) seconds: prove_these_axioms_3.
% 0.71/1.12 % Length of proof is 71.
% 0.71/1.12 % Level of proof is 26.
% 0.71/1.12 % Maximum clause weight is 23.000.
% 0.71/1.12 % Given clauses 69.
% 0.71/1.12
% 0.71/1.12 1 inverse(A) = double_divide(A,identity) # label(inverse) # label(axiom). [assumption].
% 0.71/1.12 2 identity = double_divide(A,inverse(A)) # label(identity) # label(axiom). [assumption].
% 0.71/1.12 3 double_divide(A,double_divide(A,identity)) = identity. [copy(2),rewrite([1(2)]),flip(a)].
% 0.71/1.12 4 multiply(A,B) = double_divide(double_divide(B,A),identity) # label(multiply) # label(axiom). [assumption].
% 0.71/1.12 5 double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) = C # label(single_axiom) # label(axiom). [assumption].
% 0.71/1.12 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].
% 0.71/1.12 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)].
% 0.71/1.12 8 double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,B),double_divide(A,identity))),double_divide(identity,identity)) = B. [para(3(a,1),5(a,1,1,2,1,1))].
% 0.71/1.12 9 double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(B,A),identity). [para(3(a,1),5(a,1,1,2,1))].
% 0.71/1.12 11 double_divide(double_divide(double_divide(double_divide(double_divide(A,B),C),double_divide(A,identity)),double_divide(C,double_divide(B,identity))),double_divide(identity,identity)) = double_divide(identity,identity). [para(5(a,1),5(a,1,1,2,1))].
% 0.71/1.12 13 double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),double_divide(identity,identity)) = A. [para(3(a,1),8(a,1,1,2))].
% 0.71/1.12 17 double_divide(double_divide(double_divide(identity,identity),identity),double_divide(identity,identity)) = double_divide(identity,identity). [para(3(a,1),13(a,1,1,1,1))].
% 0.71/1.12 18 double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(A,B),double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),identity))),double_divide(identity,identity)) = B. [para(13(a,1),5(a,1,1,2,1,1))].
% 0.71/1.12 21 double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(identity,identity). [para(17(a,1),5(a,1,1,2,1)),rewrite([3(10)])].
% 0.71/1.12 23 double_divide(identity,identity) = identity. [para(21(a,1),5(a,1,1,2,1)),rewrite([21(8),3(5),3(5)]),flip(a)].
% 0.71/1.12 26 double_divide(double_divide(identity,double_divide(double_divide(A,B),double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),identity))),identity) = B. [back_rewrite(18),rewrite([23(3),23(15)])].
% 0.71/1.12 30 double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),identity) = A. [back_rewrite(13),rewrite([23(9)])].
% 0.71/1.12 32 double_divide(double_divide(double_divide(double_divide(double_divide(A,B),C),double_divide(A,identity)),double_divide(C,double_divide(B,identity))),identity) = identity. [back_rewrite(11),rewrite([23(12),23(14)])].
% 0.71/1.12 34 double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),identity) = double_divide(double_divide(B,A),identity). [back_rewrite(9),rewrite([23(8)])].
% 0.71/1.12 36 double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),identity) = C. [back_rewrite(5),rewrite([23(9)])].
% 0.71/1.12 37 double_divide(double_divide(identity,double_divide(double_divide(A,B),A)),identity) = B. [back_rewrite(26),rewrite([30(10)])].
% 0.71/1.12 41 double_divide(double_divide(identity,double_divide(double_divide(A,B),A)),B) = identity. [para(37(a,1),3(a,1,2))].
% 0.71/1.12 42 double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(A,identity). [para(3(a,1),37(a,1,1,2,1))].
% 0.71/1.12 43 double_divide(double_divide(A,identity),identity) = double_divide(double_divide(B,A),B). [para(37(a,1),30(a,1,1,1))].
% 0.71/1.12 50 double_divide(double_divide(A,identity),A) = identity. [para(41(a,1),37(a,1,1,2)),rewrite([23(3),23(3)]),flip(a)].
% 0.71/1.12 53 double_divide(double_divide(A,identity),identity) = A. [para(50(a,1),37(a,1,1,2,1)),rewrite([34(8)])].
% 0.71/1.12 56 double_divide(double_divide(A,B),A) = B. [back_rewrite(43),rewrite([53(4)]),flip(a)].
% 0.71/1.12 61 double_divide(identity,A) = double_divide(A,identity). [back_rewrite(42),rewrite([56(6)])].
% 0.71/1.12 62 double_divide(identity,double_divide(A,identity)) = A. [back_rewrite(37),rewrite([56(3),61(2),61(4,R)])].
% 0.71/1.12 64 double_divide(identity,double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)))) = C. [back_rewrite(36),rewrite([61(8,R)])].
% 0.71/1.12 66 double_divide(identity,double_divide(A,B)) = double_divide(identity,double_divide(B,A)). [back_rewrite(34),rewrite([62(4),61(3,R),61(6,R)])].
% 0.71/1.12 67 double_divide(identity,double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(double_divide(C,B),A),double_divide(C,identity)))) = identity. [back_rewrite(32),rewrite([61(11,R),66(11)])].
% 0.71/1.12 69 double_divide(identity,double_divide(c3,double_divide(identity,double_divide(a3,b3)))) != double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))) # answer(prove_these_axioms_3). [back_rewrite(7),rewrite([61(5,R),66(5),61(9,R),66(9),61(15,R),66(15),61(18,R)]),flip(a)].
% 0.71/1.12 70 multiply(A,B) = double_divide(identity,double_divide(A,B)). [back_rewrite(4),rewrite([61(4,R),66(4)])].
% 0.71/1.12 72 double_divide(A,double_divide(B,A)) = B. [para(56(a,1),56(a,1,1))].
% 0.71/1.12 73 double_divide(identity,double_divide(identity,double_divide(A,B))) = double_divide(B,A). [para(66(a,1),56(a,1,1)),rewrite([61(5,R)])].
% 0.71/1.12 75 double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,double_divide(A,identity))))) = B. [para(23(a,1),64(a,1,2,2,2)),rewrite([61(3),61(6,R),66(6)])].
% 0.71/1.12 76 double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))) = double_divide(C,identity). [para(64(a,1),56(a,1,1)),flip(a)].
% 0.71/1.12 77 double_divide(identity,double_divide(A,double_divide(double_divide(B,C),double_divide(identity,double_divide(A,B))))) = C. [para(56(a,1),64(a,1,2,2,1,1)),rewrite([61(5,R)])].
% 0.71/1.12 81 double_divide(identity,double_divide(A,double_divide(B,double_divide(C,identity)))) = double_divide(B,double_divide(C,A)). [para(72(a,1),64(a,1,2,2,1))].
% 0.71/1.12 82 double_divide(identity,double_divide(double_divide(A,B),double_divide(identity,double_divide(C,double_divide(identity,double_divide(A,B)))))) = C. [para(66(a,1),64(a,1,2,2,1,1)),rewrite([66(5),23(9),61(8,R),66(8)])].
% 0.71/1.12 83 double_divide(identity,double_divide(double_divide(A,identity),double_divide(identity,double_divide(A,B)))) = B. [para(64(a,1),64(a,1,2,2,1,1)),rewrite([76(7),23(7),61(6,R)])].
% 0.71/1.12 85 double_divide(double_divide(double_divide(A,B),C),double_divide(A,double_divide(C,double_divide(B,identity)))) = identity. [back_rewrite(67),rewrite([81(11)])].
% 0.71/1.12 86 double_divide(A,double_divide(A,B)) = B. [para(56(a,1),73(a,1,2,2)),rewrite([61(3),72(4)]),flip(a)].
% 0.71/1.12 87 double_divide(A,B) = double_divide(B,A). [para(61(a,1),73(a,1,2)),rewrite([61(4,R),86(5)])].
% 0.71/1.12 88 double_divide(double_divide(A,double_divide(B,C)),double_divide(B,double_divide(A,double_divide(C,identity)))) = identity. [back_rewrite(85),rewrite([87(2)])].
% 0.71/1.12 89 double_divide(identity,double_divide(A,double_divide(B,double_divide(C,identity)))) = double_divide(B,double_divide(A,C)). [back_rewrite(81),rewrite([87(7)])].
% 0.71/1.12 93 double_divide(identity,double_divide(A,identity)) = A. [para(86(a,1),70(a,2)),rewrite([70(2),87(3)])].
% 0.71/1.12 94 double_divide(A,double_divide(identity,double_divide(B,double_divide(A,identity)))) = double_divide(B,identity). [para(75(a,1),86(a,1,2)),rewrite([87(2)]),flip(a)].
% 0.71/1.12 95 double_divide(double_divide(A,identity),double_divide(identity,double_divide(B,A))) = double_divide(B,identity). [para(83(a,1),86(a,1,2)),rewrite([87(2),87(6)]),flip(a)].
% 0.71/1.12 97 double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(B,double_divide(A,identity)). [para(94(a,1),86(a,1,2)),flip(a)].
% 0.71/1.12 98 double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(identity,double_divide(A,B)). [para(95(a,1),86(a,1,2)),rewrite([87(7)])].
% 0.71/1.12 99 double_divide(double_divide(A,identity),double_divide(identity,double_divide(A,B))) = double_divide(B,identity). [para(87(a,1),95(a,1,1)),rewrite([87(2),87(4)])].
% 0.71/1.12 100 double_divide(A,double_divide(B,A)) = B. [para(83(a,1),95(a,1,2)),rewrite([87(5),86(5),87(2),87(6),93(6)])].
% 0.71/1.12 101 double_divide(A,double_divide(double_divide(B,C),double_divide(identity,double_divide(A,C)))) = double_divide(B,identity). [para(77(a,1),86(a,1,2)),rewrite([87(2),87(3)]),flip(a)].
% 0.71/1.12 112 double_divide(double_divide(A,B),double_divide(identity,double_divide(C,double_divide(identity,double_divide(A,B))))) = double_divide(C,identity). [para(82(a,1),86(a,1,2)),rewrite([87(2)]),flip(a)].
% 0.71/1.12 115 double_divide(identity,double_divide(A,double_divide(B,C))) = double_divide(B,double_divide(A,double_divide(C,identity))). [para(88(a,1),86(a,1,2)),rewrite([87(4)])].
% 0.71/1.12 119 double_divide(double_divide(A,double_divide(identity,double_divide(B,C))),double_divide(double_divide(B,identity),double_divide(A,C))) = identity. [para(98(a,1),88(a,1,1,2)),rewrite([87(10),100(10)])].
% 0.71/1.12 121 double_divide(double_divide(A,double_divide(B,identity)),double_divide(B,double_divide(A,C))) = double_divide(C,identity). [para(89(a,1),95(a,1,2)),rewrite([87(5),97(5),87(4)])].
% 0.71/1.12 124 double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(double_divide(B,identity),double_divide(A,C)). [para(98(a,1),89(a,1,2,2))].
% 0.71/1.12 126 double_divide(double_divide(A,identity),double_divide(B,double_divide(A,C))) = double_divide(C,double_divide(B,identity)). [para(89(a,1),99(a,1,2)),rewrite([87(10),97(10)])].
% 0.71/1.12 127 double_divide(double_divide(A,B),double_divide(double_divide(A,identity),double_divide(B,C))) = double_divide(C,identity). [back_rewrite(112),rewrite([124(7),87(4)])].
% 0.71/1.12 128 double_divide(double_divide(identity,b3),double_divide(a3,c3)) != double_divide(double_divide(identity,a3),double_divide(b3,c3)) # answer(prove_these_axioms_3). [back_rewrite(69),rewrite([124(9),87(3),87(6),124(16),87(10)]),flip(a)].
% 0.71/1.12 141 double_divide(double_divide(A,B),double_divide(identity,double_divide(C,B))) = double_divide(C,double_divide(A,identity)). [para(101(a,1),86(a,1,2)),flip(a)].
% 0.71/1.12 165 double_divide(identity,double_divide(A,double_divide(B,double_divide(C,double_divide(D,identity))))) = double_divide(B,double_divide(identity,double_divide(D,double_divide(A,C)))). [para(115(a,2),89(a,2,2)),rewrite([87(6),97(6)])].
% 0.71/1.12 177 double_divide(double_divide(A,double_divide(B,identity)),double_divide(B,C)) = double_divide(identity,double_divide(A,C)). [para(86(a,1),121(a,1,2,2)),rewrite([87(8)])].
% 0.71/1.12 220 double_divide(double_divide(A,double_divide(B,C)),double_divide(D,identity)) = double_divide(B,double_divide(identity,double_divide(C,double_divide(D,A)))). [para(115(a,1),126(a,1,2,2)),rewrite([23(3),165(7)]),flip(a)].
% 0.71/1.12 296 double_divide(identity,double_divide(A,double_divide(double_divide(B,identity),double_divide(C,D)))) = double_divide(double_divide(B,D),double_divide(A,C)). [para(119(a,1),141(a,1,2,2)),rewrite([23(8),87(7),220(14),86(14)])].
% 0.71/1.12 331 double_divide(double_divide(A,B),double_divide(C,D)) = double_divide(double_divide(A,D),double_divide(C,B)). [para(127(a,1),177(a,1,2)),rewrite([87(3),220(7),87(4),86(7),296(10)])].
% 0.71/1.12 542 double_divide(double_divide(A,B),double_divide(C,D)) = double_divide(double_divide(A,C),double_divide(B,D)). [para(87(a,1),331(a,1,2)),rewrite([87(5)])].
% 0.71/1.12 543 $F # answer(prove_these_axioms_3). [resolve(542,a,128,a)].
% 0.71/1.12
% 0.71/1.12 % SZS output end Refutation
% 0.71/1.12 ============================== end of proof ==========================
% 0.71/1.12
% 0.71/1.12 ============================== STATISTICS ============================
% 0.71/1.12
% 0.71/1.12 Given=69. Generated=3567. Kept=540. proofs=1.
% 0.71/1.12 Usable=19. Sos=111. Demods=40. Limbo=3, Disabled=411. Hints=0.
% 0.71/1.12 Megabytes=0.42.
% 0.71/1.12 User_CPU=0.16, System_CPU=0.01, Wall_clock=0.
% 0.71/1.12
% 0.71/1.12 ============================== end of statistics =====================
% 0.71/1.12
% 0.71/1.12 ============================== end of search =========================
% 0.71/1.12
% 0.71/1.12 THEOREM PROVED
% 0.71/1.12 % SZS status Unsatisfiable
% 0.71/1.12
% 0.71/1.12 Exiting with 1 proof.
% 0.71/1.12
% 0.71/1.12 Process 16525 exit (max_proofs) Tue Jun 14 11:45:24 2022
% 0.71/1.12 Prover9 interrupted
%------------------------------------------------------------------------------