TSTP Solution File: GRP498-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP498-1 : TPTP v8.1.0. Released v2.6.0.
% 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 11:19:21 EDT 2022
% Result : Unsatisfiable 0.41s 0.99s
% Output : Refutation 0.41s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP498-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n016.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 15:28:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/0.99 ============================== Prover9 ===============================
% 0.41/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.41/0.99 Process 15424 was started by sandbox on n016.cluster.edu,
% 0.41/0.99 Mon Jun 13 15:28:30 2022
% 0.41/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15271_n016.cluster.edu".
% 0.41/0.99 ============================== end of head ===========================
% 0.41/0.99
% 0.41/0.99 ============================== INPUT =================================
% 0.41/0.99
% 0.41/0.99 % Reading from file /tmp/Prover9_15271_n016.cluster.edu
% 0.41/0.99
% 0.41/0.99 set(prolog_style_variables).
% 0.41/0.99 set(auto2).
% 0.41/0.99 % set(auto2) -> set(auto).
% 0.41/0.99 % set(auto) -> set(auto_inference).
% 0.41/0.99 % set(auto) -> set(auto_setup).
% 0.41/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.41/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/0.99 % set(auto) -> set(auto_limits).
% 0.41/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/0.99 % set(auto) -> set(auto_denials).
% 0.41/0.99 % set(auto) -> set(auto_process).
% 0.41/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.41/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.41/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.41/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.41/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.41/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.41/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.41/0.99 % set(auto2) -> assign(stats, some).
% 0.41/0.99 % set(auto2) -> clear(echo_input).
% 0.41/0.99 % set(auto2) -> set(quiet).
% 0.41/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.41/0.99 % set(auto2) -> clear(print_given).
% 0.41/0.99 assign(lrs_ticks,-1).
% 0.41/0.99 assign(sos_limit,10000).
% 0.41/0.99 assign(order,kbo).
% 0.41/0.99 set(lex_order_vars).
% 0.41/0.99 clear(print_given).
% 0.41/0.99
% 0.41/0.99 % formulas(sos). % not echoed (5 formulas)
% 0.41/0.99
% 0.41/0.99 ============================== end of input ==========================
% 0.41/0.99
% 0.41/0.99 % From the command line: assign(max_seconds, 300).
% 0.41/0.99
% 0.41/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/0.99
% 0.41/0.99 % Formulas that are not ordinary clauses:
% 0.41/0.99
% 0.41/0.99 ============================== end of process non-clausal formulas ===
% 0.41/0.99
% 0.41/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.41/0.99
% 0.41/0.99 ============================== PREDICATE ELIMINATION =================
% 0.41/0.99
% 0.41/0.99 ============================== end predicate elimination =============
% 0.41/0.99
% 0.41/0.99 Auto_denials:
% 0.41/0.99 % copying label prove_these_axioms_3 to answer in negative clause
% 0.41/0.99
% 0.41/0.99 Term ordering decisions:
% 0.41/0.99
% 0.41/0.99 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.41/0.99 Function symbol KB weights: identity=1. a3=1. b3=1. c3=1. double_divide=1. multiply=1. inverse=0.
% 0.41/0.99
% 0.41/0.99 ============================== end of process initial clauses ========
% 0.41/0.99
% 0.41/0.99 ============================== CLAUSES FOR SEARCH ====================
% 0.41/0.99
% 0.41/0.99 ============================== end of clauses for search =============
% 0.41/0.99
% 0.41/0.99 ============================== SEARCH ================================
% 0.41/0.99
% 0.41/0.99 % Starting search at 0.01 seconds.
% 0.41/0.99
% 0.41/0.99 ============================== PROOF =================================
% 0.41/0.99 % SZS status Unsatisfiable
% 0.41/0.99 % SZS output start Refutation
% 0.41/0.99
% 0.41/0.99 % Proof 1 at 0.04 (+ 0.00) seconds: prove_these_axioms_3.
% 0.41/0.99 % Length of proof is 46.
% 0.41/0.99 % Level of proof is 14.
% 0.41/0.99 % Maximum clause weight is 23.000.
% 0.41/0.99 % Given clauses 35.
% 0.41/0.99
% 0.41/0.99 1 inverse(A) = double_divide(A,identity) # label(inverse) # label(axiom). [assumption].
% 0.41/0.99 2 identity = double_divide(A,inverse(A)) # label(identity) # label(axiom). [assumption].
% 0.41/0.99 3 double_divide(A,double_divide(A,identity)) = identity. [copy(2),rewrite([1(2)]),flip(a)].
% 0.41/0.99 4 multiply(A,B) = double_divide(double_divide(B,A),identity) # label(multiply) # label(axiom). [assumption].
% 0.41/0.99 5 double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C # label(single_axiom) # label(axiom). [assumption].
% 0.41/0.99 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].
% 0.41/0.99 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)].
% 0.41/0.99 8 double_divide(identity,identity) = identity. [para(5(a,1),3(a,1))].
% 0.41/0.99 9 double_divide(identity,double_divide(double_divide(A,double_divide(B,A)),identity)) = B. [para(3(a,1),5(a,1,1,2)),rewrite([8(3)])].
% 0.41/0.99 11 double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity) = A. [para(3(a,1),5(a,1,2,1)),rewrite([8(9)])].
% 0.41/0.99 12 double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,double_divide(A,C)),double_divide(D,double_divide(identity,double_divide(C,double_divide(B,identity))))),identity)) = D. [para(5(a,1),5(a,1,1,2))].
% 0.41/0.99 14 double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),identity))),double_divide(C,identity)) = double_divide(B,double_divide(C,A)). [para(5(a,1),5(a,1,2,1))].
% 0.41/0.99 17 double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),identity)) = A. [para(3(a,1),9(a,1,2,1,2))].
% 0.41/0.99 18 double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,double_divide(A,B)),double_divide(C,identity)),identity)) = C. [para(9(a,1),5(a,1,1,2))].
% 0.41/0.99 19 double_divide(identity,double_divide(A,identity)) = double_divide(B,double_divide(A,B)). [para(9(a,1),5(a,1,2,1)),rewrite([8(5),8(4),8(3)])].
% 0.41/0.99 23 double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),double_divide(double_divide(A,B),identity)) = double_divide(identity,double_divide(identity,double_divide(B,identity))). [para(11(a,1),5(a,1,2,1,2))].
% 0.41/0.99 25 double_divide(identity,double_divide(double_divide(identity,A),identity)) = double_divide(identity,double_divide(identity,double_divide(A,identity))). [para(11(a,1),9(a,1,2,1,2))].
% 0.41/0.99 27 double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(identity,double_divide(identity,double_divide(A,identity))). [para(11(a,1),11(a,1,1,2,2))].
% 0.41/0.99 28 double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(A,double_divide(B,identity)),identity)))),double_divide(C,identity)) = double_divide(B,double_divide(C,A)). [back_rewrite(14),rewrite([25(10)])].
% 0.41/0.99 29 double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = A. [back_rewrite(11),rewrite([27(8)])].
% 0.41/0.99 32 double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(A,identity)). [para(17(a,1),5(a,1,2,1)),rewrite([8(5),8(4),8(3)]),flip(a)].
% 0.41/0.99 33 double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A. [back_rewrite(29),rewrite([32(6)])].
% 0.41/0.99 35 double_divide(double_divide(A,double_divide(B,identity)),double_divide(C,identity)) = double_divide(B,double_divide(C,A)). [back_rewrite(28),rewrite([33(11)])].
% 0.41/0.99 39 double_divide(double_divide(identity,double_divide(A,double_divide(B,A))),double_divide(double_divide(B,double_divide(C,identity)),identity)) = C. [para(19(a,1),5(a,1,1,2))].
% 0.41/0.99 42 double_divide(double_divide(double_divide(A,double_divide(B,C)),identity),B) = double_divide(identity,double_divide(identity,double_divide(double_divide(C,double_divide(A,identity)),identity))). [para(5(a,1),19(a,2,2)),rewrite([25(9)]),flip(a)].
% 0.41/0.99 44 double_divide(A,double_divide(double_divide(B,double_divide(C,B)),A)) = C. [para(19(a,1),9(a,1))].
% 0.41/0.99 49 double_divide(double_divide(A,B),double_divide(identity,double_divide(A,identity))) = double_divide(identity,double_divide(B,identity)). [para(19(a,2),19(a,2,2)),flip(a)].
% 0.41/0.99 58 double_divide(identity,double_divide(double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,double_divide(identity,double_divide(A,identity))))),identity)) = B. [para(8(a,1),12(a,1,2,1,1,2)),rewrite([8(3)])].
% 0.41/0.99 77 double_divide(identity,A) = double_divide(A,identity). [para(32(a,1),5(a,1,2,1,2)),rewrite([23(14),44(9)])].
% 0.41/0.99 87 double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,double_divide(identity,double_divide(A,identity))))))) = B. [back_rewrite(58),rewrite([77(13,R)])].
% 0.41/0.99 94 double_divide(double_divide(identity,double_divide(A,double_divide(B,C))),B) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(C,double_divide(A,identity))))). [back_rewrite(42),rewrite([77(4,R),77(12,R)])].
% 0.41/0.99 96 double_divide(double_divide(identity,double_divide(A,double_divide(B,A))),double_divide(identity,double_divide(B,double_divide(C,identity)))) = C. [back_rewrite(39),rewrite([77(9,R)])].
% 0.41/0.99 101 double_divide(double_divide(A,identity),double_divide(identity,double_divide(double_divide(B,double_divide(A,B)),double_divide(C,identity)))) = C. [back_rewrite(18),rewrite([77(2),77(9,R)])].
% 0.41/0.99 103 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([77(5,R),77(9,R),77(15,R),77(18,R)])].
% 0.41/0.99 107 double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(identity,double_divide(B,A)). [para(8(a,1),35(a,1,1,2))].
% 0.41/0.99 108 double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(B,double_divide(A,identity)). [para(8(a,1),35(a,1,2)),rewrite([77(5,R),77(7)])].
% 0.41/0.99 109 double_divide(double_divide(A,double_divide(B,C)),double_divide(D,identity)) = double_divide(B,double_divide(D,double_divide(C,double_divide(A,identity)))). [para(35(a,1),35(a,1,1))].
% 0.41/0.99 110 double_divide(double_divide(identity,double_divide(A,B)),double_divide(C,double_divide(D,identity))) = double_divide(A,double_divide(C,double_divide(B,D))). [para(35(a,1),35(a,2,2)),rewrite([107(5),77(8,R),108(8)])].
% 0.41/0.99 116 double_divide(double_divide(A,identity),double_divide(B,double_divide(A,identity))) = B. [back_rewrite(101),rewrite([109(8),3(6),108(7)])].
% 0.41/0.99 120 double_divide(A,double_divide(B,double_divide(double_divide(C,A),C))) = B. [back_rewrite(96),rewrite([108(9),110(8)])].
% 0.41/0.99 121 double_divide(double_divide(identity,double_divide(A,double_divide(B,C))),B) = double_divide(A,double_divide(C,identity)). [back_rewrite(94),rewrite([108(12),108(11),108(10)])].
% 0.41/0.99 123 double_divide(identity,double_divide(A,identity)) = A. [back_rewrite(87),rewrite([108(10),8(7),116(8),77(3)])].
% 0.41/0.99 133 double_divide(double_divide(A,B),A) = B. [back_rewrite(49),rewrite([123(5),123(6)])].
% 0.41/0.99 134 double_divide(A,double_divide(B,A)) = B. [back_rewrite(120),rewrite([133(2)])].
% 0.41/0.99 187 double_divide(double_divide(identity,double_divide(A,B)),C) = double_divide(A,double_divide(identity,double_divide(B,C))). [para(134(a,1),121(a,1,1,2,2)),rewrite([77(7,R)])].
% 0.41/0.99 198 $F # answer(prove_these_axioms_3). [back_rewrite(103),rewrite([187(8)]),xx(a)].
% 0.41/0.99
% 0.41/0.99 % SZS output end Refutation
% 0.41/0.99 ============================== end of proof ==========================
% 0.41/0.99
% 0.41/0.99 ============================== STATISTICS ============================
% 0.41/0.99
% 0.41/0.99 Given=35. Generated=951. Kept=195. proofs=1.
% 0.41/0.99 Usable=14. Sos=30. Demods=54. Limbo=11, Disabled=145. Hints=0.
% 0.41/0.99 Megabytes=0.18.
% 0.41/0.99 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.41/0.99
% 0.41/0.99 ============================== end of statistics =====================
% 0.41/0.99
% 0.41/0.99 ============================== end of search =========================
% 0.41/0.99
% 0.41/0.99 THEOREM PROVED
% 0.41/0.99 % SZS status Unsatisfiable
% 0.41/0.99
% 0.41/0.99 Exiting with 1 proof.
% 0.41/0.99
% 0.41/0.99 Process 15424 exit (max_proofs) Mon Jun 13 15:28:30 2022
% 0.41/0.99 Prover9 interrupted
%------------------------------------------------------------------------------