TSTP Solution File: GRP606-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP606-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 11:19:49 EDT 2022
% Result : Unsatisfiable 0.68s 0.96s
% Output : Refutation 0.68s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP606-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.31 % Computer : n019.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 600
% 0.10/0.31 % DateTime : Tue Jun 14 12:49:54 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.68/0.96 ============================== Prover9 ===============================
% 0.68/0.96 Prover9 (32) version 2009-11A, November 2009.
% 0.68/0.96 Process 32362 was started by sandbox2 on n019.cluster.edu,
% 0.68/0.96 Tue Jun 14 12:49:55 2022
% 0.68/0.96 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_32116_n019.cluster.edu".
% 0.68/0.96 ============================== end of head ===========================
% 0.68/0.96
% 0.68/0.96 ============================== INPUT =================================
% 0.68/0.96
% 0.68/0.96 % Reading from file /tmp/Prover9_32116_n019.cluster.edu
% 0.68/0.96
% 0.68/0.96 set(prolog_style_variables).
% 0.68/0.96 set(auto2).
% 0.68/0.96 % set(auto2) -> set(auto).
% 0.68/0.96 % set(auto) -> set(auto_inference).
% 0.68/0.96 % set(auto) -> set(auto_setup).
% 0.68/0.96 % set(auto_setup) -> set(predicate_elim).
% 0.68/0.96 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.68/0.96 % set(auto) -> set(auto_limits).
% 0.68/0.96 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.68/0.96 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.68/0.96 % set(auto) -> set(auto_denials).
% 0.68/0.96 % set(auto) -> set(auto_process).
% 0.68/0.96 % set(auto2) -> assign(new_constants, 1).
% 0.68/0.96 % set(auto2) -> assign(fold_denial_max, 3).
% 0.68/0.96 % set(auto2) -> assign(max_weight, "200.000").
% 0.68/0.96 % set(auto2) -> assign(max_hours, 1).
% 0.68/0.96 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.68/0.96 % set(auto2) -> assign(max_seconds, 0).
% 0.68/0.96 % set(auto2) -> assign(max_minutes, 5).
% 0.68/0.96 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.68/0.96 % set(auto2) -> set(sort_initial_sos).
% 0.68/0.96 % set(auto2) -> assign(sos_limit, -1).
% 0.68/0.96 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.68/0.96 % set(auto2) -> assign(max_megs, 400).
% 0.68/0.96 % set(auto2) -> assign(stats, some).
% 0.68/0.96 % set(auto2) -> clear(echo_input).
% 0.68/0.96 % set(auto2) -> set(quiet).
% 0.68/0.96 % set(auto2) -> clear(print_initial_clauses).
% 0.68/0.96 % set(auto2) -> clear(print_given).
% 0.68/0.96 assign(lrs_ticks,-1).
% 0.68/0.96 assign(sos_limit,10000).
% 0.68/0.96 assign(order,kbo).
% 0.68/0.96 set(lex_order_vars).
% 0.68/0.96 clear(print_given).
% 0.68/0.96
% 0.68/0.96 % formulas(sos). % not echoed (3 formulas)
% 0.68/0.96
% 0.68/0.96 ============================== end of input ==========================
% 0.68/0.96
% 0.68/0.96 % From the command line: assign(max_seconds, 300).
% 0.68/0.96
% 0.68/0.96 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.68/0.96
% 0.68/0.96 % Formulas that are not ordinary clauses:
% 0.68/0.96
% 0.68/0.96 ============================== end of process non-clausal formulas ===
% 0.68/0.96
% 0.68/0.96 ============================== PROCESS INITIAL CLAUSES ===============
% 0.68/0.96
% 0.68/0.96 ============================== PREDICATE ELIMINATION =================
% 0.68/0.96
% 0.68/0.96 ============================== end predicate elimination =============
% 0.68/0.96
% 0.68/0.96 Auto_denials:
% 0.68/0.96 % copying label prove_these_axioms_2 to answer in negative clause
% 0.68/0.96
% 0.68/0.96 Term ordering decisions:
% 0.68/0.96
% 0.68/0.96 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.68/0.96 Function symbol KB weights: a2=1. b2=1. double_divide=1. multiply=1. inverse=0.
% 0.68/0.96
% 0.68/0.96 ============================== end of process initial clauses ========
% 0.68/0.96
% 0.68/0.96 ============================== CLAUSES FOR SEARCH ====================
% 0.68/0.96
% 0.68/0.96 ============================== end of clauses for search =============
% 0.68/0.96
% 0.68/0.96 ============================== SEARCH ================================
% 0.68/0.96
% 0.68/0.96 % Starting search at 0.01 seconds.
% 0.68/0.96
% 0.68/0.96 ============================== PROOF =================================
% 0.68/0.96 % SZS status Unsatisfiable
% 0.68/0.96 % SZS output start Refutation
% 0.68/0.96
% 0.68/0.96 % Proof 1 at 0.03 (+ 0.00) seconds: prove_these_axioms_2.
% 0.68/0.96 % Length of proof is 36.
% 0.68/0.96 % Level of proof is 19.
% 0.68/0.96 % Maximum clause weight is 35.000.
% 0.68/0.96 % Given clauses 20.
% 0.68/0.96
% 0.68/0.96 1 multiply(A,B) = inverse(double_divide(B,A)) # label(multiply) # label(axiom). [assumption].
% 0.68/0.96 2 double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C) = B # label(single_axiom) # label(axiom). [assumption].
% 0.68/0.96 3 multiply(multiply(inverse(b2),b2),a2) != a2 # label(prove_these_axioms_2) # label(negated_conjecture) # answer(prove_these_axioms_2). [assumption].
% 0.68/0.96 4 inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 # answer(prove_these_axioms_2). [copy(3),rewrite([1(4),1(7)])].
% 0.68/0.96 5 double_divide(inverse(double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),inverse(double_divide(inverse(D),B)))),C) = D. [para(2(a,1),2(a,1,1,1,2,1,2))].
% 0.68/0.96 6 double_divide(A,inverse(double_divide(inverse(B),double_divide(A,double_divide(C,D))))) = double_divide(inverse(double_divide(C,inverse(B))),D). [para(2(a,1),2(a,1,1,1,2,1)),flip(a)].
% 0.68/0.96 10 double_divide(inverse(A),inverse(double_divide(inverse(B),A))) = B. [para(2(a,1),5(a,1,1,1))].
% 0.68/0.96 11 double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),inverse(double_divide(inverse(D),B)))),inverse(double_divide(inverse(E),D)))),inverse(double_divide(inverse(F),E)))),C) = F. [para(5(a,1),5(a,1,1,1,1,1,2,1,2))].
% 0.68/0.96 14 double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C)))) = double_divide(inverse(C),inverse(B)). [para(2(a,1),10(a,1,2,1)),flip(a)].
% 0.68/0.96 17 double_divide(inverse(double_divide(inverse(A),inverse(B))),inverse(double_divide(inverse(C),B))) = double_divide(inverse(A),inverse(C)). [para(5(a,1),10(a,1,2,1)),rewrite([14(8)]),flip(a)].
% 0.68/0.96 18 double_divide(inverse(inverse(double_divide(inverse(A),B))),inverse(A)) = B. [para(10(a,1),10(a,1,2,1))].
% 0.68/0.96 20 double_divide(inverse(double_divide(inverse(A),inverse(B))),A) = B. [back_rewrite(11),rewrite([14(5),17(8),17(8),17(8)])].
% 0.68/0.96 21 double_divide(inverse(double_divide(A,inverse(B))),C) = double_divide(inverse(double_divide(A,C)),inverse(B)). [back_rewrite(6),rewrite([14(6)]),flip(a)].
% 0.68/0.96 22 double_divide(inverse(A),double_divide(inverse(inverse(B)),inverse(A))) = B. [para(20(a,1),20(a,1,1,1))].
% 0.68/0.96 23 inverse(double_divide(inverse(A),B)) = double_divide(inverse(inverse(A)),inverse(B)). [para(18(a,1),10(a,1,2,1)),flip(a)].
% 0.68/0.96 24 double_divide(double_divide(inverse(inverse(A)),inverse(inverse(B))),A) = B. [back_rewrite(20),rewrite([23(4)])].
% 0.68/0.96 28 double_divide(A,double_divide(inverse(inverse(B)),inverse(double_divide(A,C)))) = double_divide(inverse(C),inverse(B)). [back_rewrite(14),rewrite([23(4)])].
% 0.68/0.96 41 double_divide(double_divide(double_divide(inverse(inverse(inverse(A))),inverse(inverse(B))),inverse(inverse(C))),double_divide(inverse(A),B)) = C. [para(23(a,1),24(a,1,1,1,1)),rewrite([23(5)])].
% 0.68/0.96 46 double_divide(double_divide(inverse(inverse(inverse(A))),inverse(inverse(B))),inverse(C)) = double_divide(inverse(B),double_divide(inverse(inverse(C)),inverse(A))). [para(22(a,1),28(a,1,2,2,1)),rewrite([23(11)]),flip(a)].
% 0.68/0.96 58 double_divide(double_divide(inverse(A),double_divide(inverse(inverse(inverse(B))),inverse(C))),double_divide(inverse(C),A)) = B. [back_rewrite(41),rewrite([46(9)])].
% 0.68/0.96 63 double_divide(inverse(A),double_divide(inverse(B),B)) = A. [para(22(a,1),58(a,1,1))].
% 0.68/0.96 83 double_divide(A,double_divide(inverse(inverse(B)),A)) = B. [para(63(a,1),58(a,1,1))].
% 0.68/0.96 88 double_divide(double_divide(inverse(A),A),inverse(B)) = B. [para(63(a,1),83(a,1,2))].
% 0.68/0.96 90 double_divide(inverse(A),inverse(B)) = double_divide(inverse(B),inverse(A)). [para(88(a,1),21(a,2,1,1)),rewrite([88(4)])].
% 0.68/0.96 93 double_divide(double_divide(inverse(A),A),double_divide(inverse(B),inverse(inverse(C)))) = double_divide(inverse(C),B). [para(23(a,1),88(a,1,2)),rewrite([90(6)])].
% 0.68/0.96 94 double_divide(inverse(A),inverse(inverse(B))) = double_divide(inverse(A),B). [para(88(a,1),28(a,1,2,2,1)),rewrite([90(6),93(7),90(6)]),flip(a)].
% 0.68/0.96 135 inverse(double_divide(inverse(A),B)) = double_divide(inverse(B),A). [back_rewrite(23),rewrite([90(7),94(7)])].
% 0.68/0.96 141 double_divide(double_divide(inverse(inverse(A)),B),A) = B. [back_rewrite(24),rewrite([94(5)])].
% 0.68/0.96 154 double_divide(inverse(A),A) = double_divide(inverse(B),B). [para(63(a,1),141(a,1,1))].
% 0.68/0.96 156 inverse(inverse(A)) = A. [para(141(a,1),88(a,1))].
% 0.68/0.96 157 double_divide(inverse(A),A) = c_0. [new_symbol(154)].
% 0.68/0.96 183 double_divide(c_0,inverse(A)) = A. [back_rewrite(88),rewrite([157(2)])].
% 0.68/0.96 198 double_divide(inverse(A),B) = double_divide(B,inverse(A)). [para(156(a,1),90(a,1,1)),rewrite([156(5)]),flip(a)].
% 0.68/0.96 213 double_divide(A,inverse(A)) = c_0. [back_rewrite(157),rewrite([198(2)])].
% 0.68/0.96 215 inverse(double_divide(A,inverse(B))) = double_divide(B,inverse(A)). [back_rewrite(135),rewrite([198(2),198(5)])].
% 0.68/0.96 219 $F # answer(prove_these_axioms_2). [back_rewrite(4),rewrite([213(5),215(5),183(4)]),xx(a)].
% 0.68/0.96
% 0.68/0.96 % SZS output end Refutation
% 0.68/0.96 ============================== end of proof ==========================
% 0.68/0.97
% 0.68/0.97 ============================== STATISTICS ============================
% 0.68/0.97
% 0.68/0.97 Given=20. Generated=362. Kept=217. proofs=1.
% 0.68/0.97 Usable=2. Sos=25. Demods=24. Limbo=6, Disabled=187. Hints=0.
% 0.68/0.97 Megabytes=0.18.
% 0.68/0.97 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.68/0.97
% 0.68/0.97 ============================== end of statistics =====================
% 0.68/0.97
% 0.68/0.97 ============================== end of search =========================
% 0.68/0.97
% 0.68/0.97 THEOREM PROVED
% 0.68/0.97 % SZS status Unsatisfiable
% 0.68/0.97
% 0.68/0.97 Exiting with 1 proof.
% 0.68/0.97
% 0.68/0.97 Process 32362 exit (max_proofs) Tue Jun 14 12:49:55 2022
% 0.68/0.97 Prover9 interrupted
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