TSTP Solution File: GRP489-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP489-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 0.71s 1.00s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP489-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n029.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 10:39:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.71/1.00 ============================== Prover9 ===============================
% 0.71/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.71/1.00 Process 7918 was started by sandbox2 on n029.cluster.edu,
% 0.71/1.00 Tue Jun 14 10:39:26 2022
% 0.71/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7747_n029.cluster.edu".
% 0.71/1.00 ============================== end of head ===========================
% 0.71/1.00
% 0.71/1.00 ============================== INPUT =================================
% 0.71/1.00
% 0.71/1.00 % Reading from file /tmp/Prover9_7747_n029.cluster.edu
% 0.71/1.00
% 0.71/1.00 set(prolog_style_variables).
% 0.71/1.00 set(auto2).
% 0.71/1.00 % set(auto2) -> set(auto).
% 0.71/1.00 % set(auto) -> set(auto_inference).
% 0.71/1.00 % set(auto) -> set(auto_setup).
% 0.71/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.71/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.71/1.00 % set(auto) -> set(auto_limits).
% 0.71/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.71/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.71/1.00 % set(auto) -> set(auto_denials).
% 0.71/1.00 % set(auto) -> set(auto_process).
% 0.71/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.71/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.71/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.71/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.71/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.71/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.71/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.71/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.71/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.71/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.71/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.71/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.71/1.00 % set(auto2) -> assign(stats, some).
% 0.71/1.00 % set(auto2) -> clear(echo_input).
% 0.71/1.00 % set(auto2) -> set(quiet).
% 0.71/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.71/1.00 % set(auto2) -> clear(print_given).
% 0.71/1.00 assign(lrs_ticks,-1).
% 0.71/1.00 assign(sos_limit,10000).
% 0.71/1.00 assign(order,kbo).
% 0.71/1.00 set(lex_order_vars).
% 0.71/1.00 clear(print_given).
% 0.71/1.00
% 0.71/1.00 % formulas(sos). % not echoed (5 formulas)
% 0.71/1.00
% 0.71/1.00 ============================== end of input ==========================
% 0.71/1.00
% 0.71/1.00 % From the command line: assign(max_seconds, 300).
% 0.71/1.00
% 0.71/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.71/1.00
% 0.71/1.00 % Formulas that are not ordinary clauses:
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% 0.71/1.00 ============================== end of process non-clausal formulas ===
% 0.71/1.00
% 0.71/1.00 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.71/1.00 ============================== PREDICATE ELIMINATION =================
% 0.71/1.00
% 0.71/1.00 ============================== end predicate elimination =============
% 0.71/1.00
% 0.71/1.00 Auto_denials:
% 0.71/1.00 % copying label prove_these_axioms_3 to answer in negative clause
% 0.71/1.00
% 0.71/1.00 Term ordering decisions:
% 0.71/1.00
% 0.71/1.00 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.71/1.00 Function symbol KB weights: identity=1. a3=1. b3=1. c3=1. double_divide=1. multiply=1. inverse=0.
% 0.71/1.00
% 0.71/1.00 ============================== end of process initial clauses ========
% 0.71/1.00
% 0.71/1.00 ============================== CLAUSES FOR SEARCH ====================
% 0.71/1.00
% 0.71/1.00 ============================== end of clauses for search =============
% 0.71/1.00
% 0.71/1.00 ============================== SEARCH ================================
% 0.71/1.00
% 0.71/1.00 % Starting search at 0.01 seconds.
% 0.71/1.00
% 0.71/1.00 ============================== PROOF =================================
% 0.71/1.00 % SZS status Unsatisfiable
% 0.71/1.00 % SZS output start Refutation
% 0.71/1.00
% 0.71/1.00 % Proof 1 at 0.03 (+ 0.00) seconds: prove_these_axioms_3.
% 0.71/1.00 % Length of proof is 44.
% 0.71/1.00 % Level of proof is 15.
% 0.71/1.00 % Maximum clause weight is 33.000.
% 0.71/1.00 % Given clauses 14.
% 0.71/1.00
% 0.71/1.00 1 inverse(A) = double_divide(A,identity) # label(inverse) # label(axiom). [assumption].
% 0.71/1.00 2 identity = double_divide(A,inverse(A)) # label(identity) # label(axiom). [assumption].
% 0.71/1.00 3 double_divide(A,double_divide(A,identity)) = identity. [copy(2),rewrite([1(2)]),flip(a)].
% 0.71/1.00 4 multiply(A,B) = double_divide(double_divide(B,A),identity) # label(multiply) # label(axiom). [assumption].
% 0.71/1.00 5 double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C # label(single_axiom) # label(axiom). [assumption].
% 0.71/1.00 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].
% 0.71/1.00 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)].
% 0.71/1.00 8 double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),B),identity)) = double_divide(B,identity). [para(3(a,1),5(a,1,2,1,1,2,2))].
% 0.71/1.00 9 double_divide(A,double_divide(double_divide(double_divide(identity,identity),double_divide(A,identity)),identity)) = identity. [para(3(a,1),5(a,1,2,1,1,2))].
% 0.71/1.00 10 double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity) = double_divide(D,double_divide(double_divide(double_divide(identity,double_divide(double_divide(D,identity),C)),A),identity)). [para(5(a,1),5(a,1,2,1,1,2,2)),flip(a)].
% 0.71/1.00 12 double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),identity),identity) = double_divide(A,double_divide(identity,identity)). [para(3(a,1),8(a,1,2,1)),flip(a)].
% 0.71/1.00 13 double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,identity))),C),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(C,identity),identity)),B),identity). [para(8(a,1),5(a,1,2,1,1,2,2))].
% 0.71/1.00 19 double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity. [para(3(a,1),9(a,1,2,1))].
% 0.71/1.00 20 double_divide(double_divide(double_divide(identity,identity),double_divide(A,identity)),identity) = double_divide(A,identity). [para(9(a,1),5(a,1,2,1,1,2,2)),rewrite([8(10)]),flip(a)].
% 0.71/1.00 24 double_divide(double_divide(identity,identity),identity) = double_divide(identity,identity). [para(19(a,1),5(a,1,2,1,1,2,2)),rewrite([8(13)])].
% 0.71/1.00 28 double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(A,B))),A),identity)) = B. [para(24(a,1),5(a,1,2,1,1,2,1))].
% 0.71/1.00 29 double_divide(identity,identity) = identity. [para(24(a,1),5(a,1,2,1,1,2,2)),rewrite([13(15),24(6),24(6),3(5),24(5)])].
% 0.71/1.00 30 double_divide(identity,double_divide(double_divide(identity,A),identity)) = double_divide(A,identity). [para(24(a,1),8(a,1,2,1,1,2,1)),rewrite([29(3),29(5),29(5),29(4)])].
% 0.71/1.00 31 double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(A,B))),A),identity)) = B. [back_rewrite(28),rewrite([29(3),29(5)])].
% 0.71/1.00 34 double_divide(double_divide(identity,double_divide(A,identity)),identity) = double_divide(A,identity). [back_rewrite(20),rewrite([29(3)])].
% 0.71/1.00 37 double_divide(double_divide(double_divide(A,identity),identity),identity) = double_divide(A,identity). [back_rewrite(12),rewrite([34(8),29(9)])].
% 0.71/1.00 61 double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,double_divide(double_divide(double_divide(identity,double_divide(C,identity)),D),identity)))),B),identity) = double_divide(C,double_divide(double_divide(double_divide(identity,double_divide(D,identity)),A),identity)). [para(8(a,1),10(a,2,2,1,1,2)),rewrite([37(10)])].
% 0.71/1.00 63 double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(A,B))),A),identity) = double_divide(C,double_divide(double_divide(double_divide(identity,double_divide(double_divide(C,identity),B)),identity),identity)). [para(29(a,1),10(a,1,1,1,2,1))].
% 0.71/1.00 64 double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,C)),A),identity)). [para(29(a,1),10(a,2,2,1,1,2,1))].
% 0.71/1.00 72 double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(A,identity)),B),identity))),C),identity)) = double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(B,identity)),C),identity)). [back_rewrite(61),rewrite([64(16)])].
% 0.71/1.00 80 double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),B)),C),identity)) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,B)),C),identity)). [back_rewrite(10),rewrite([64(9)]),flip(a)].
% 0.71/1.00 91 double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(A,B))),A),identity) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,B)),identity),identity)). [back_rewrite(63),rewrite([80(18)])].
% 0.71/1.00 94 double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),B),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(B,identity),identity)),A),identity). [back_rewrite(13),rewrite([80(11)])].
% 0.71/1.00 96 double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),double_divide(double_divide(identity,double_divide(B,identity)),C)),identity) = double_divide(B,double_divide(double_divide(double_divide(identity,double_divide(C,identity)),A),identity)). [back_rewrite(72),rewrite([94(16)])].
% 0.71/1.00 100 double_divide(double_divide(double_divide(identity,A),identity),identity) = double_divide(identity,double_divide(double_divide(A,identity),identity)). [para(30(a,1),30(a,1,2,1)),flip(a)].
% 0.71/1.00 101 double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(A,B))),A),identity) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(B,identity),identity)))). [back_rewrite(91),rewrite([100(17),100(16)])].
% 0.71/1.00 104 double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(A,identity)). [para(34(a,1),30(a,1,2)),flip(a)].
% 0.71/1.00 105 double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(A,identity)). [para(30(a,1),34(a,1,1)),rewrite([104(4)]),flip(a)].
% 0.71/1.00 106 double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity))))) = double_divide(A,identity). [para(34(a,1),34(a,2)),rewrite([105(7),104(6),105(10),105(9),105(8),104(7)])].
% 0.71/1.00 108 double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(A,B))),A),identity) = double_divide(B,identity). [back_rewrite(101),rewrite([104(15),106(18)])].
% 0.71/1.00 110 double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),double_divide(double_divide(identity,double_divide(B,identity)),C)),identity) = double_divide(B,double_divide(double_divide(double_divide(identity,double_divide(C,identity)),A),identity)). [back_rewrite(96),rewrite([104(5)])].
% 0.71/1.00 111 double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),B),identity)) = double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(B,identity))),A),identity). [back_rewrite(94),rewrite([104(16)])].
% 0.71/1.00 118 double_divide(identity,double_divide(identity,double_divide(A,identity))) = double_divide(A,identity). [back_rewrite(37),rewrite([104(4),105(6),104(5)])].
% 0.71/1.00 124 double_divide(identity,double_divide(A,identity)) = A. [back_rewrite(31),rewrite([108(9)])].
% 0.71/1.00 128 double_divide(double_divide(double_divide(identity,A),B),identity) = double_divide(double_divide(identity,B),A). [back_rewrite(111),rewrite([124(6),124(7),124(8)]),flip(a)].
% 0.71/1.00 129 double_divide(double_divide(identity,double_divide(A,B)),C) = double_divide(A,double_divide(double_divide(B,C),identity)). [back_rewrite(110),rewrite([124(5),124(6),128(6),124(8)])].
% 0.71/1.00 136 double_divide(identity,A) = double_divide(A,identity). [back_rewrite(118),rewrite([124(5)])].
% 0.71/1.00 160 double_divide(double_divide(identity,double_divide(A,B)),C) = double_divide(A,double_divide(identity,double_divide(B,C))). [back_rewrite(129),rewrite([136(7,R)])].
% 0.71/1.00 162 $F # answer(prove_these_axioms_3). [back_rewrite(7),rewrite([136(5,R),160(7),136(9,R),136(15,R),136(18,R)]),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=14. Generated=273. Kept=159. proofs=1.
% 0.71/1.00 Usable=4. Sos=2. Demods=31. Limbo=26, Disabled=132. Hints=0.
% 0.71/1.00 Megabytes=0.20.
% 0.71/1.00 User_CPU=0.03, 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 7918 exit (max_proofs) Tue Jun 14 10:39:26 2022
% 0.71/1.00 Prover9 interrupted
%------------------------------------------------------------------------------