TSTP Solution File: GRP101-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP101-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 11:17:09 EDT 2022
% Result : Unsatisfiable 0.74s 1.02s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : GRP101-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.05/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n021.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 23:37:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.74/1.02 ============================== Prover9 ===============================
% 0.74/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.74/1.02 Process 14326 was started by sandbox2 on n021.cluster.edu,
% 0.74/1.02 Mon Jun 13 23:37:28 2022
% 0.74/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_14173_n021.cluster.edu".
% 0.74/1.02 ============================== end of head ===========================
% 0.74/1.02
% 0.74/1.02 ============================== INPUT =================================
% 0.74/1.02
% 0.74/1.02 % Reading from file /tmp/Prover9_14173_n021.cluster.edu
% 0.74/1.02
% 0.74/1.02 set(prolog_style_variables).
% 0.74/1.02 set(auto2).
% 0.74/1.02 % set(auto2) -> set(auto).
% 0.74/1.02 % set(auto) -> set(auto_inference).
% 0.74/1.02 % set(auto) -> set(auto_setup).
% 0.74/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.74/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.74/1.02 % set(auto) -> set(auto_limits).
% 0.74/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.74/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.74/1.02 % set(auto) -> set(auto_denials).
% 0.74/1.02 % set(auto) -> set(auto_process).
% 0.74/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.74/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.74/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.74/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.74/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.74/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.74/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.74/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.74/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.74/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.74/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.74/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.74/1.02 % set(auto2) -> assign(stats, some).
% 0.74/1.02 % set(auto2) -> clear(echo_input).
% 0.74/1.02 % set(auto2) -> set(quiet).
% 0.74/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.74/1.02 % set(auto2) -> clear(print_given).
% 0.74/1.02 assign(lrs_ticks,-1).
% 0.74/1.02 assign(sos_limit,10000).
% 0.74/1.02 assign(order,kbo).
% 0.74/1.02 set(lex_order_vars).
% 0.74/1.02 clear(print_given).
% 0.74/1.02
% 0.74/1.02 % formulas(sos). % not echoed (5 formulas)
% 0.74/1.02
% 0.74/1.02 ============================== end of input ==========================
% 0.74/1.02
% 0.74/1.02 % From the command line: assign(max_seconds, 300).
% 0.74/1.02
% 0.74/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.74/1.02
% 0.74/1.02 % Formulas that are not ordinary clauses:
% 0.74/1.02
% 0.74/1.02 ============================== end of process non-clausal formulas ===
% 0.74/1.02
% 0.74/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.74/1.02
% 0.74/1.02 ============================== PREDICATE ELIMINATION =================
% 0.74/1.02
% 0.74/1.02 ============================== end predicate elimination =============
% 0.74/1.02
% 0.74/1.02 Auto_denials:
% 0.74/1.02 % copying label prove_these_axioms to answer in negative clause
% 0.74/1.02
% 0.74/1.02 Term ordering decisions:
% 0.74/1.02
% 0.74/1.02 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 0.74/1.02 Function symbol KB weights: identity=1. a1=1. a2=1. a3=1. a4=1. b3=1. b4=1. c3=1. double_divide=1. multiply=1. inverse=0.
% 0.74/1.02
% 0.74/1.02 ============================== end of process initial clauses ========
% 0.74/1.02
% 0.74/1.02 ============================== CLAUSES FOR SEARCH ====================
% 0.74/1.02
% 0.74/1.02 ============================== end of clauses for search =============
% 0.74/1.02
% 0.74/1.02 ============================== SEARCH ================================
% 0.74/1.02
% 0.74/1.02 % Starting search at 0.01 seconds.
% 0.74/1.02
% 0.74/1.02 ============================== PROOF =================================
% 0.74/1.02 % SZS status Unsatisfiable
% 0.74/1.02 % SZS output start Refutation
% 0.74/1.02
% 0.74/1.02 % Proof 1 at 0.03 (+ 0.00) seconds: prove_these_axioms.
% 0.74/1.02 % Length of proof is 54.
% 0.74/1.02 % Level of proof is 20.
% 0.74/1.02 % Maximum clause weight is 42.000.
% 0.74/1.02 % Given clauses 43.
% 0.74/1.02
% 0.74/1.02 1 inverse(A) = double_divide(A,identity) # label(inverse) # label(axiom). [assumption].
% 0.74/1.02 2 identity = double_divide(A,inverse(A)) # label(identity) # label(axiom). [assumption].
% 0.74/1.02 3 double_divide(A,double_divide(A,identity)) = identity. [copy(2),rewrite([1(2)]),flip(a)].
% 0.74/1.02 4 multiply(A,B) = double_divide(double_divide(B,A),identity) # label(multiply) # label(axiom). [assumption].
% 0.74/1.02 5 double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B # label(single_axiom) # label(axiom). [assumption].
% 0.74/1.02 6 multiply(inverse(a1),a1) != identity | multiply(identity,a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) | multiply(a4,b4) != multiply(b4,a4) # label(prove_these_axioms) # label(negated_conjecture) # answer(prove_these_axioms). [assumption].
% 0.74/1.02 7 double_divide(identity,identity) != identity | double_divide(double_divide(a2,identity),identity) != a2 | 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) | double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity) # answer(prove_these_axioms). [copy(6),rewrite([1(2),4(5),3(5),4(8),4(15),4(19),4(25),4(28),4(34),4(39)]),flip(c)].
% 0.74/1.02 8 double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(A,identity))),double_divide(identity,identity)) = B. [para(3(a,1),5(a,1,1,2,1,2))].
% 0.74/1.02 9 double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),double_divide(identity,identity)) = A. [para(3(a,1),5(a,1,1,2,1))].
% 0.74/1.02 11 double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(A,double_divide(C,B)),double_divide(C,identity))). [para(5(a,1),5(a,1,1,2,1))].
% 0.74/1.02 12 double_divide(double_divide(double_divide(double_divide(A,identity),identity),identity),double_divide(identity,identity)) = A. [para(3(a,1),8(a,1,1,2))].
% 0.74/1.02 14 double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(double_divide(B,identity),double_divide(double_divide(A,identity),double_divide(B,identity))). [para(8(a,1),5(a,1,1,2,1))].
% 0.74/1.02 15 double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity. [para(3(a,1),9(a,1,1,2))].
% 0.74/1.02 16 double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(A,B),double_divide(double_divide(identity,double_divide(identity,double_divide(B,identity))),identity))),double_divide(identity,identity)) = A. [para(9(a,1),5(a,1,1,2,1,2))].
% 0.74/1.02 17 double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,double_divide(A,identity))). [para(9(a,1),5(a,1,1,2,1))].
% 0.74/1.02 18 double_divide(double_divide(double_divide(A,identity),A),double_divide(identity,identity)) = identity. [para(9(a,1),5(a,1,1,2))].
% 0.74/1.02 19 double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(A,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))). [back_rewrite(14),rewrite([17(10)]),flip(a)].
% 0.74/1.02 20 double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))). [back_rewrite(11),rewrite([17(10)]),flip(a)].
% 0.74/1.02 23 double_divide(double_divide(double_divide(identity,identity),double_divide(A,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,identity),identity))),identity))),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,double_divide(A,identity))). [para(9(a,1),16(a,1,1,2,1))].
% 0.74/1.02 24 double_divide(double_divide(A,identity),A) = double_divide(identity,identity). [para(18(a,1),16(a,1,1,2,1)),rewrite([23(21),3(6)]),flip(a)].
% 0.74/1.02 25 double_divide(double_divide(double_divide(identity,identity),double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(A,identity),identity),identity). [para(12(a,1),16(a,1,1,2,1)),rewrite([24(10),3(9),24(8)])].
% 0.74/1.02 26 double_divide(double_divide(identity,identity),double_divide(double_divide(A,B),double_divide(double_divide(identity,double_divide(identity,double_divide(B,identity))),identity))) = double_divide(double_divide(double_divide(A,identity),identity),identity). [para(16(a,1),16(a,1,1,2,1)),rewrite([24(10),3(9),24(8),25(12)]),flip(a)].
% 0.74/1.02 27 double_divide(double_divide(double_divide(A,identity),identity),identity) = double_divide(identity,double_divide(identity,double_divide(A,identity))). [back_rewrite(23),rewrite([24(10),3(9),24(8),25(12)])].
% 0.74/1.02 28 double_divide(double_divide(identity,identity),double_divide(double_divide(A,B),double_divide(double_divide(identity,double_divide(identity,double_divide(B,identity))),identity))) = double_divide(identity,double_divide(identity,double_divide(A,identity))). [back_rewrite(26),rewrite([27(20)])].
% 0.74/1.02 30 double_divide(identity,identity) = identity. [para(24(a,1),9(a,1,1,2,2)),rewrite([3(6),15(7)]),flip(a)].
% 0.74/1.02 32 double_divide(identity,double_divide(double_divide(A,B),double_divide(double_divide(identity,double_divide(identity,double_divide(B,identity))),identity))) = double_divide(identity,double_divide(identity,double_divide(A,identity))). [back_rewrite(28),rewrite([30(3)])].
% 0.74/1.02 33 double_divide(double_divide(A,identity),A) = identity. [back_rewrite(24),rewrite([30(6)])].
% 0.74/1.02 35 double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity) = A. [back_rewrite(9),rewrite([30(9)])].
% 0.74/1.02 36 double_divide(double_divide(a2,identity),identity) != a2 | 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) | double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity) # answer(prove_these_axioms). [back_rewrite(7),rewrite([30(3)]),xx(a)].
% 0.74/1.02 37 double_divide(identity,double_divide(double_divide(A,B),B)) = double_divide(identity,double_divide(identity,double_divide(A,identity))). [back_rewrite(32),rewrite([35(10)])].
% 0.74/1.02 40 double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(identity,double_divide(identity,double_divide(A,identity))). [para(35(a,1),35(a,1,1,2,2))].
% 0.74/1.02 41 double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = A. [back_rewrite(35),rewrite([40(8)])].
% 0.74/1.02 43 double_divide(double_divide(A,identity),identity) = A. [para(33(a,1),19(a,1,2)),rewrite([41(12)])].
% 0.74/1.02 44 double_divide(identity,double_divide(identity,A)) = A. [back_rewrite(41),rewrite([43(6)])].
% 0.74/1.02 45 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) | double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity) # answer(prove_these_axioms). [back_rewrite(36),rewrite([43(5)]),xx(a)].
% 0.74/1.02 46 double_divide(identity,double_divide(double_divide(A,B),B)) = double_divide(A,identity). [back_rewrite(37),rewrite([44(10)])].
% 0.74/1.02 48 double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))) = double_divide(B,identity). [back_rewrite(20),rewrite([44(12)])].
% 0.74/1.02 52 double_divide(identity,double_divide(A,identity)) = A. [para(43(a,1),46(a,1,2,1)),rewrite([43(8)])].
% 0.74/1.02 53 double_divide(identity,A) = double_divide(A,identity). [para(43(a,1),46(a,1,2))].
% 0.74/1.02 54 double_divide(double_divide(A,B),B) = A. [para(46(a,1),44(a,1,2)),rewrite([52(4)]),flip(a)].
% 0.74/1.02 55 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)))) | double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(a4,b4)) # answer(prove_these_axioms). [back_rewrite(45),rewrite([53(5,R),53(9,R),53(15,R),53(18,R),53(24,R),53(29,R)])].
% 0.74/1.02 58 double_divide(A,double_divide(double_divide(B,identity),A)) = double_divide(B,identity). [para(33(a,1),48(a,1,2,1,2)),rewrite([53(6,R),52(6)])].
% 0.74/1.02 60 double_divide(double_divide(A,identity),double_divide(identity,double_divide(B,A))) = double_divide(B,identity). [para(52(a,1),48(a,1,2,1,2)),rewrite([30(6),53(5,R)])].
% 0.74/1.02 63 double_divide(identity,double_divide(A,double_divide(B,C))) = double_divide(C,double_divide(A,double_divide(B,identity))). [para(54(a,1),48(a,1,2,1)),rewrite([53(8,R)]),flip(a)].
% 0.74/1.02 68 double_divide(A,double_divide(B,A)) = B. [para(54(a,1),58(a,1,2,1)),rewrite([53(6,R),52(6)])].
% 0.74/1.02 72 double_divide(A,double_divide(A,B)) = B. [para(68(a,1),54(a,1,1))].
% 0.74/1.02 73 double_divide(A,B) = double_divide(B,A). [para(54(a,1),68(a,1,2))].
% 0.74/1.02 80 double_divide(double_divide(A,identity),double_divide(identity,double_divide(A,B))) = double_divide(B,identity). [back_rewrite(60),rewrite([73(4)])].
% 0.74/1.02 82 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). [back_rewrite(55),rewrite([73(5),73(8),73(15),73(23)]),flip(a),xx(b)].
% 0.74/1.02 83 double_divide(A,double_divide(B,A)) = B. [back_rewrite(54),rewrite([73(2)])].
% 0.74/1.02 86 double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(identity,double_divide(A,B)). [para(80(a,1),72(a,1,2))].
% 0.74/1.02 93 double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))) != double_divide(double_divide(identity,c3),double_divide(a3,b3)) # answer(prove_these_axioms). [para(63(a,1),82(a,1)),rewrite([30(7),73(6),73(7)]),flip(a)].
% 0.74/1.02 106 double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(double_divide(C,identity),double_divide(A,B)). [para(86(a,1),63(a,1,2,2)),rewrite([73(12),83(12)])].
% 0.74/1.02 111 $F # answer(prove_these_axioms). [back_rewrite(93),rewrite([106(9),73(3)]),xx(a)].
% 0.74/1.02
% 0.74/1.02 % SZS output end Refutation
% 0.74/1.02 ============================== end of proof ==========================
% 0.74/1.02
% 0.74/1.02 ============================== STATISTICS ============================
% 0.74/1.02
% 0.74/1.02 Given=43. Generated=537. Kept=108. proofs=1.
% 0.74/1.02 Usable=11. Sos=16. Demods=27. Limbo=5, Disabled=81. Hints=0.
% 0.74/1.02 Megabytes=0.12.
% 0.74/1.02 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.74/1.02
% 0.74/1.02 ============================== end of statistics =====================
% 0.74/1.02
% 0.74/1.02 ============================== end of search =========================
% 0.74/1.02
% 0.74/1.02 THEOREM PROVED
% 0.74/1.02 % SZS status Unsatisfiable
% 0.74/1.02
% 0.74/1.02 Exiting with 1 proof.
% 0.74/1.02
% 0.74/1.02 Process 14326 exit (max_proofs) Mon Jun 13 23:37:28 2022
% 0.74/1.02 Prover9 interrupted
%------------------------------------------------------------------------------