TSTP Solution File: GRP584-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP584-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 11:19:43 EDT 2022
% Result : Unsatisfiable 0.45s 1.02s
% Output : Refutation 0.45s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP584-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 13 17:17:09 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.45/1.02 ============================== Prover9 ===============================
% 0.45/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.02 Process 17615 was started by sandbox on n025.cluster.edu,
% 0.45/1.02 Mon Jun 13 17:17:09 2022
% 0.45/1.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_17461_n025.cluster.edu".
% 0.45/1.02 ============================== end of head ===========================
% 0.45/1.02
% 0.45/1.02 ============================== INPUT =================================
% 0.45/1.02
% 0.45/1.02 % Reading from file /tmp/Prover9_17461_n025.cluster.edu
% 0.45/1.02
% 0.45/1.02 set(prolog_style_variables).
% 0.45/1.02 set(auto2).
% 0.45/1.02 % set(auto2) -> set(auto).
% 0.45/1.02 % set(auto) -> set(auto_inference).
% 0.45/1.02 % set(auto) -> set(auto_setup).
% 0.45/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.02 % set(auto) -> set(auto_limits).
% 0.45/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.02 % set(auto) -> set(auto_denials).
% 0.45/1.02 % set(auto) -> set(auto_process).
% 0.45/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.02 % set(auto2) -> assign(stats, some).
% 0.45/1.02 % set(auto2) -> clear(echo_input).
% 0.45/1.02 % set(auto2) -> set(quiet).
% 0.45/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.02 % set(auto2) -> clear(print_given).
% 0.45/1.02 assign(lrs_ticks,-1).
% 0.45/1.02 assign(sos_limit,10000).
% 0.45/1.02 assign(order,kbo).
% 0.45/1.02 set(lex_order_vars).
% 0.45/1.02 clear(print_given).
% 0.45/1.02
% 0.45/1.02 % formulas(sos). % not echoed (5 formulas)
% 0.45/1.02
% 0.45/1.02 ============================== end of input ==========================
% 0.45/1.02
% 0.45/1.02 % From the command line: assign(max_seconds, 300).
% 0.45/1.02
% 0.45/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.02
% 0.45/1.02 % Formulas that are not ordinary clauses:
% 0.45/1.02
% 0.45/1.02 ============================== end of process non-clausal formulas ===
% 0.45/1.02
% 0.45/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/1.02
% 0.45/1.02 ============================== PREDICATE ELIMINATION =================
% 0.45/1.02
% 0.45/1.02 ============================== end predicate elimination =============
% 0.45/1.02
% 0.45/1.02 Auto_denials:
% 0.45/1.02 % copying label prove_these_axioms_4 to answer in negative clause
% 0.45/1.02
% 0.45/1.02 Term ordering decisions:
% 0.45/1.02
% 0.45/1.02 % Assigning unary symbol inverse kb_weight 0 and highest precedence (7).
% 0.45/1.02 Function symbol KB weights: identity=1. a=1. b=1. double_divide=1. multiply=1. inverse=0.
% 0.45/1.02
% 0.45/1.02 ============================== end of process initial clauses ========
% 0.45/1.02
% 0.45/1.02 ============================== CLAUSES FOR SEARCH ====================
% 0.45/1.02
% 0.45/1.02 ============================== end of clauses for search =============
% 0.45/1.02
% 0.45/1.02 ============================== SEARCH ================================
% 0.45/1.02
% 0.45/1.02 % Starting search at 0.01 seconds.
% 0.45/1.02
% 0.45/1.02 ============================== PROOF =================================
% 0.45/1.02 % SZS status Unsatisfiable
% 0.45/1.02 % SZS output start Refutation
% 0.45/1.02
% 0.45/1.02 % Proof 1 at 0.03 (+ 0.00) seconds: prove_these_axioms_4.
% 0.45/1.02 % Length of proof is 41.
% 0.45/1.02 % Level of proof is 16.
% 0.45/1.02 % Maximum clause weight is 27.000.
% 0.45/1.02 % Given clauses 22.
% 0.45/1.02
% 0.45/1.02 1 inverse(A) = double_divide(A,identity) # label(inverse) # label(axiom). [assumption].
% 0.45/1.02 2 identity = double_divide(A,inverse(A)) # label(identity) # label(axiom). [assumption].
% 0.45/1.02 3 double_divide(A,double_divide(A,identity)) = identity. [copy(2),rewrite([1(2)]),flip(a)].
% 0.45/1.02 4 multiply(A,B) = double_divide(double_divide(B,A),identity) # label(multiply) # label(axiom). [assumption].
% 0.45/1.02 5 double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C # label(single_axiom) # label(axiom). [assumption].
% 0.45/1.02 6 multiply(a,b) != multiply(b,a) # label(prove_these_axioms_4) # label(negated_conjecture) # answer(prove_these_axioms_4). [assumption].
% 0.45/1.02 7 double_divide(double_divide(b,a),identity) != double_divide(double_divide(a,b),identity) # answer(prove_these_axioms_4). [copy(6),rewrite([4(3),4(8)])].
% 0.45/1.02 8 double_divide(double_divide(A,double_divide(identity,double_divide(B,double_divide(double_divide(identity,identity),A)))),double_divide(identity,identity)) = B. [para(3(a,1),5(a,1,1,2,1))].
% 0.45/1.02 9 double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),double_divide(B,identity))),double_divide(identity,identity)) = B. [para(3(a,1),5(a,1,1,2,2,2))].
% 0.45/1.02 11 double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A))))),double_divide(D,C))),double_divide(identity,identity)) = D. [para(5(a,1),5(a,1,1,2,2,2))].
% 0.45/1.02 12 double_divide(double_divide(identity,double_divide(double_divide(identity,identity),A)),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(identity,C),double_divide(A,double_divide(C,B)))). [para(5(a,1),5(a,1,1,2,2))].
% 0.45/1.02 13 double_divide(double_divide(double_divide(double_divide(identity,identity),identity),double_divide(identity,double_divide(A,identity))),double_divide(identity,identity)) = A. [para(3(a,1),8(a,1,1,2,2,2))].
% 0.45/1.02 14 double_divide(identity,identity) = identity. [para(3(a,1),8(a,1,1,2,2)),rewrite([3(5),3(5)]),flip(a)].
% 0.45/1.02 17 double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))) = double_divide(double_divide(identity,double_divide(identity,B)),identity). [para(8(a,1),5(a,1,1,2,2)),rewrite([14(4),14(7),14(10)]),flip(a)].
% 0.45/1.02 18 double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity) = A. [back_rewrite(13),rewrite([14(3),14(3),14(9)])].
% 0.45/1.02 19 double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))) = double_divide(double_divide(identity,double_divide(identity,C)),identity). [back_rewrite(12),rewrite([14(4),14(7)]),flip(a)].
% 0.45/1.02 20 double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,A)),identity)),double_divide(B,A))),identity) = B. [back_rewrite(11),rewrite([14(3),19(8),14(15)])].
% 0.45/1.02 22 double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),double_divide(B,identity))),identity) = B. [back_rewrite(9),rewrite([14(11)])].
% 0.45/1.02 23 double_divide(double_divide(double_divide(identity,double_divide(identity,A)),identity),identity) = A. [back_rewrite(8),rewrite([14(4),17(6),14(9)])].
% 0.45/1.02 24 double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),A) = identity. [para(18(a,1),3(a,1,2))].
% 0.45/1.02 25 double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(identity,double_divide(identity,double_divide(A,identity))). [para(18(a,1),18(a,1,1,2,2))].
% 0.45/1.02 26 double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = A. [back_rewrite(23),rewrite([25(6),25(8)])].
% 0.45/1.02 27 double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),double_divide(B,A))),identity) = B. [back_rewrite(20),rewrite([25(8)])].
% 0.45/1.02 28 double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))) = double_divide(identity,double_divide(identity,double_divide(C,identity))). [back_rewrite(19),rewrite([25(12)])].
% 0.45/1.02 29 double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))) = double_divide(identity,double_divide(identity,double_divide(B,identity))). [back_rewrite(17),rewrite([25(12)])].
% 0.45/1.02 33 double_divide(double_divide(double_divide(A,identity),identity),identity) = double_divide(identity,A). [para(3(a,1),22(a,1,1,2))].
% 0.45/1.02 49 double_divide(identity,double_divide(identity,double_divide(identity,A))) = double_divide(A,identity). [para(33(a,1),26(a,1,2,2))].
% 0.45/1.02 51 double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(A,identity)). [para(33(a,1),33(a,1,1))].
% 0.45/1.02 53 double_divide(identity,double_divide(double_divide(double_divide(double_divide(A,identity),identity),double_divide(B,A)),identity)) = B. [back_rewrite(27),rewrite([49(9),51(10)])].
% 0.45/1.02 57 double_divide(identity,double_divide(identity,double_divide(A,B))) = double_divide(B,double_divide(identity,double_divide(A,identity))). [para(24(a,1),28(a,1,2,2)),rewrite([51(4),51(16),51(15),26(16)]),flip(a)].
% 0.45/1.02 80 double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),identity) = double_divide(identity,double_divide(identity,double_divide(double_divide(B,A),identity))). [para(57(a,1),4(a,2,1)),rewrite([4(5),51(7),51(6)]),flip(a)].
% 0.45/1.02 82 double_divide(A,double_divide(identity,A)) = identity. [para(24(a,1),57(a,1,2,2)),rewrite([14(4),14(3),80(10),26(10)]),flip(a)].
% 0.45/1.02 95 double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,A)),double_divide(identity,double_divide(identity,double_divide(A,B)))),identity)) = B. [para(57(a,2),53(a,1,2,1,2)),rewrite([51(7),51(9),33(8)])].
% 0.45/1.02 97 double_divide(double_divide(identity,double_divide(A,identity)),double_divide(identity,double_divide(B,identity))) = double_divide(identity,double_divide(double_divide(A,B),identity)). [para(57(a,2),57(a,1,2,2)),rewrite([49(8)]),flip(a)].
% 0.45/1.02 106 double_divide(identity,double_divide(identity,double_divide(A,identity))) = double_divide(A,identity). [para(82(a,1),28(a,1,2,2)),rewrite([14(3),14(3)]),flip(a)].
% 0.45/1.02 108 double_divide(identity,double_divide(A,identity)) = A. [para(82(a,1),53(a,1,2,1,2)),rewrite([51(5),51(7),51(9),33(8),51(7),51(6),106(7)])].
% 0.45/1.02 112 double_divide(identity,A) = double_divide(A,identity). [para(82(a,1),29(a,1,2,2)),rewrite([14(3),108(7)]),flip(a)].
% 0.45/1.02 140 double_divide(identity,double_divide(identity,double_divide(A,B))) = double_divide(A,B). [back_rewrite(97),rewrite([108(4),108(4),112(5,R)]),flip(a)].
% 0.45/1.02 141 double_divide(A,double_divide(A,B)) = B. [back_rewrite(95),rewrite([112(4),108(5),140(6),112(5,R),140(6)])].
% 0.45/1.02 143 double_divide(A,B) = double_divide(B,A). [back_rewrite(57),rewrite([141(5),108(5)])].
% 0.45/1.02 146 $F # answer(prove_these_axioms_4). [back_rewrite(7),rewrite([143(3),143(5),143(10)]),xx(a)].
% 0.45/1.02
% 0.45/1.02 % SZS output end Refutation
% 0.45/1.02 ============================== end of proof ==========================
% 0.45/1.02
% 0.45/1.02 ============================== STATISTICS ============================
% 0.45/1.02
% 0.45/1.02 Given=22. Generated=495. Kept=143. proofs=1.
% 0.45/1.02 Usable=4. Sos=2. Demods=40. Limbo=34, Disabled=108. Hints=0.
% 0.45/1.02 Megabytes=0.16.
% 0.45/1.02 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.45/1.02
% 0.45/1.02 ============================== end of statistics =====================
% 0.45/1.02
% 0.45/1.02 ============================== end of search =========================
% 0.45/1.02
% 0.45/1.02 THEOREM PROVED
% 0.45/1.02 % SZS status Unsatisfiable
% 0.45/1.02
% 0.45/1.02 Exiting with 1 proof.
% 0.45/1.02
% 0.45/1.02 Process 17615 exit (max_proofs) Mon Jun 13 17:17:09 2022
% 0.45/1.02 Prover9 interrupted
%------------------------------------------------------------------------------