TSTP Solution File: GRP568-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP568-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 11:19:39 EDT 2022
% Result : Unsatisfiable 0.68s 0.95s
% Output : Refutation 0.68s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP568-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n012.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 21:09:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.68/0.95 ============================== Prover9 ===============================
% 0.68/0.95 Prover9 (32) version 2009-11A, November 2009.
% 0.68/0.95 Process 13329 was started by sandbox on n012.cluster.edu,
% 0.68/0.95 Mon Jun 13 21:09:11 2022
% 0.68/0.95 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13176_n012.cluster.edu".
% 0.68/0.95 ============================== end of head ===========================
% 0.68/0.95
% 0.68/0.95 ============================== INPUT =================================
% 0.68/0.95
% 0.68/0.95 % Reading from file /tmp/Prover9_13176_n012.cluster.edu
% 0.68/0.95
% 0.68/0.95 set(prolog_style_variables).
% 0.68/0.95 set(auto2).
% 0.68/0.95 % set(auto2) -> set(auto).
% 0.68/0.95 % set(auto) -> set(auto_inference).
% 0.68/0.95 % set(auto) -> set(auto_setup).
% 0.68/0.95 % set(auto_setup) -> set(predicate_elim).
% 0.68/0.95 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.68/0.95 % set(auto) -> set(auto_limits).
% 0.68/0.95 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.68/0.95 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.68/0.95 % set(auto) -> set(auto_denials).
% 0.68/0.95 % set(auto) -> set(auto_process).
% 0.68/0.95 % set(auto2) -> assign(new_constants, 1).
% 0.68/0.95 % set(auto2) -> assign(fold_denial_max, 3).
% 0.68/0.95 % set(auto2) -> assign(max_weight, "200.000").
% 0.68/0.95 % set(auto2) -> assign(max_hours, 1).
% 0.68/0.95 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.68/0.95 % set(auto2) -> assign(max_seconds, 0).
% 0.68/0.95 % set(auto2) -> assign(max_minutes, 5).
% 0.68/0.95 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.68/0.95 % set(auto2) -> set(sort_initial_sos).
% 0.68/0.95 % set(auto2) -> assign(sos_limit, -1).
% 0.68/0.95 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.68/0.95 % set(auto2) -> assign(max_megs, 400).
% 0.68/0.95 % set(auto2) -> assign(stats, some).
% 0.68/0.95 % set(auto2) -> clear(echo_input).
% 0.68/0.95 % set(auto2) -> set(quiet).
% 0.68/0.95 % set(auto2) -> clear(print_initial_clauses).
% 0.68/0.95 % set(auto2) -> clear(print_given).
% 0.68/0.95 assign(lrs_ticks,-1).
% 0.68/0.95 assign(sos_limit,10000).
% 0.68/0.95 assign(order,kbo).
% 0.68/0.95 set(lex_order_vars).
% 0.68/0.95 clear(print_given).
% 0.68/0.95
% 0.68/0.95 % formulas(sos). % not echoed (5 formulas)
% 0.68/0.95
% 0.68/0.95 ============================== end of input ==========================
% 0.68/0.95
% 0.68/0.95 % From the command line: assign(max_seconds, 300).
% 0.68/0.95
% 0.68/0.95 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.68/0.95
% 0.68/0.95 % Formulas that are not ordinary clauses:
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% 0.68/0.95 ============================== end of process non-clausal formulas ===
% 0.68/0.95
% 0.68/0.95 ============================== PROCESS INITIAL CLAUSES ===============
% 0.68/0.95
% 0.68/0.95 ============================== PREDICATE ELIMINATION =================
% 0.68/0.95
% 0.68/0.95 ============================== end predicate elimination =============
% 0.68/0.95
% 0.68/0.95 Auto_denials:
% 0.68/0.95 % copying label prove_these_axioms_4 to answer in negative clause
% 0.68/0.95
% 0.68/0.95 Term ordering decisions:
% 0.68/0.95
% 0.68/0.95 % Assigning unary symbol inverse kb_weight 0 and highest precedence (7).
% 0.68/0.95 Function symbol KB weights: identity=1. a=1. b=1. double_divide=1. multiply=1. inverse=0.
% 0.68/0.95
% 0.68/0.95 ============================== end of process initial clauses ========
% 0.68/0.95
% 0.68/0.95 ============================== CLAUSES FOR SEARCH ====================
% 0.68/0.95
% 0.68/0.95 ============================== end of clauses for search =============
% 0.68/0.95
% 0.68/0.95 ============================== SEARCH ================================
% 0.68/0.95
% 0.68/0.95 % Starting search at 0.01 seconds.
% 0.68/0.95
% 0.68/0.95 ============================== PROOF =================================
% 0.68/0.95 % SZS status Unsatisfiable
% 0.68/0.95 % SZS output start Refutation
% 0.68/0.95
% 0.68/0.95 % Proof 1 at 0.02 (+ 0.00) seconds: prove_these_axioms_4.
% 0.68/0.95 % Length of proof is 35.
% 0.68/0.95 % Level of proof is 15.
% 0.68/0.95 % Maximum clause weight is 23.000.
% 0.68/0.95 % Given clauses 28.
% 0.68/0.95
% 0.68/0.95 1 inverse(A) = double_divide(A,identity) # label(inverse) # label(axiom). [assumption].
% 0.68/0.95 2 identity = double_divide(A,inverse(A)) # label(identity) # label(axiom). [assumption].
% 0.68/0.95 3 double_divide(A,double_divide(A,identity)) = identity. [copy(2),rewrite([1(2)]),flip(a)].
% 0.68/0.95 4 multiply(A,B) = double_divide(double_divide(B,A),identity) # label(multiply) # label(axiom). [assumption].
% 0.68/0.95 5 double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B # label(single_axiom) # label(axiom). [assumption].
% 0.68/0.95 6 multiply(a,b) != multiply(b,a) # label(prove_these_axioms_4) # label(negated_conjecture) # answer(prove_these_axioms_4). [assumption].
% 0.68/0.95 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)])].
% 0.68/0.95 8 double_divide(double_divide(A,double_divide(double_divide(B,identity),double_divide(identity,double_divide(A,identity)))),double_divide(identity,identity)) = B. [para(3(a,1),5(a,1,1,2,1,2))].
% 0.68/0.95 9 double_divide(double_divide(A,identity),double_divide(identity,identity)) = A. [para(3(a,1),5(a,1,1,2,1)),rewrite([3(5)])].
% 0.68/0.95 10 double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,double_divide(identity,identity))),identity)),double_divide(identity,identity)) = B. [para(3(a,1),5(a,1,1,2,2))].
% 0.68/0.95 12 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(B,C)),double_divide(identity,C))). [para(5(a,1),5(a,1,1,2,1))].
% 0.68/0.95 13 double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),double_divide(identity,identity)) = A. [para(3(a,1),8(a,1,1,2,2))].
% 0.68/0.95 15 double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(A,identity),double_divide(identity,double_divide(B,identity)))). [para(8(a,1),5(a,1,1,2,1))].
% 0.68/0.95 16 double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(B,A),identity)),double_divide(identity,identity)) = B. [para(9(a,1),5(a,1,1,2,1,2)),rewrite([3(8)])].
% 0.68/0.95 17 double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(A,identity). [para(9(a,1),5(a,1,1,2,1))].
% 0.68/0.95 18 double_divide(A,double_divide(double_divide(B,identity),double_divide(identity,double_divide(A,identity)))) = double_divide(B,identity). [back_rewrite(15),rewrite([17(10)]),flip(a)].
% 0.68/0.95 19 double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))) = double_divide(B,identity). [back_rewrite(12),rewrite([17(10)]),flip(a)].
% 0.68/0.95 20 double_divide(double_divide(double_divide(double_divide(identity,identity),identity),double_divide(A,identity)),double_divide(identity,identity)) = double_divide(A,identity). [para(9(a,1),16(a,1,1,2,1))].
% 0.68/0.95 21 double_divide(identity,double_divide(double_divide(A,identity),identity)) = double_divide(A,identity). [para(13(a,1),16(a,1,1,2,1)),rewrite([20(12)]),flip(a)].
% 0.68/0.95 22 double_divide(double_divide(A,identity),double_divide(double_divide(B,A),identity)) = double_divide(B,identity). [para(16(a,1),16(a,1,1,2,1)),rewrite([20(12)]),flip(a)].
% 0.68/0.95 24 double_divide(identity,identity) = identity. [para(22(a,1),3(a,1))].
% 0.68/0.95 26 double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(A,identity)). [para(9(a,1),22(a,1,2,1)),rewrite([24(3),24(3)]),flip(a)].
% 0.68/0.95 28 double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,identity)),identity)),identity) = double_divide(identity,double_divide(B,identity)). [para(10(a,1),22(a,1,2,1)),rewrite([24(3),24(3),24(7)]),flip(a)].
% 0.68/0.95 29 double_divide(double_divide(identity,double_divide(double_divide(A,B),identity)),double_divide(identity,double_divide(A,identity))) = double_divide(identity,double_divide(B,identity)). [para(22(a,1),22(a,1,2,1)),rewrite([26(5),26(9),26(14)])].
% 0.68/0.95 32 double_divide(identity,double_divide(A,identity)) = A. [back_rewrite(10),rewrite([24(3),24(9),28(8)])].
% 0.68/0.95 33 double_divide(identity,A) = double_divide(A,identity). [back_rewrite(21),rewrite([26(5),32(5)])].
% 0.68/0.95 35 double_divide(double_divide(identity,double_divide(identity,double_divide(A,B))),A) = B. [back_rewrite(29),rewrite([33(4,R),32(9),32(10)])].
% 0.68/0.95 37 double_divide(A,double_divide(double_divide(B,identity),A)) = double_divide(B,identity). [back_rewrite(18),rewrite([32(6)])].
% 0.68/0.95 40 double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(C,identity))) = double_divide(B,identity). [back_rewrite(19),rewrite([33(4)])].
% 0.68/0.95 41 double_divide(identity,double_divide(b,a)) != double_divide(identity,double_divide(a,b)) # answer(prove_these_axioms_4). [back_rewrite(7),rewrite([33(5,R),33(10,R)])].
% 0.68/0.95 44 double_divide(A,double_divide(B,A)) = B. [para(35(a,1),37(a,1,2,1)),rewrite([33(6),32(7),33(4),33(6,R),32(6)])].
% 0.68/0.95 47 double_divide(double_divide(A,B),A) = B. [para(44(a,1),44(a,1,2))].
% 0.68/0.95 61 double_divide(A,double_divide(A,B)) = B. [para(47(a,1),40(a,1,2)),rewrite([33(6,R),44(6)])].
% 0.68/0.95 77 double_divide(A,B) = double_divide(B,A). [para(44(a,1),61(a,1,2))].
% 0.68/0.95 84 $F # answer(prove_these_axioms_4). [back_rewrite(41),rewrite([77(4)]),xx(a)].
% 0.68/0.95
% 0.68/0.95 % SZS output end Refutation
% 0.68/0.95 ============================== end of proof ==========================
% 0.68/0.95
% 0.68/0.95 ============================== STATISTICS ============================
% 0.68/0.95
% 0.68/0.95 Given=28. Generated=386. Kept=81. proofs=1.
% 0.68/0.95 Usable=3. Sos=5. Demods=14. Limbo=7, Disabled=71. Hints=0.
% 0.68/0.95 Megabytes=0.08.
% 0.68/0.95 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.68/0.95
% 0.68/0.95 ============================== end of statistics =====================
% 0.68/0.95
% 0.68/0.95 ============================== end of search =========================
% 0.68/0.95
% 0.68/0.95 THEOREM PROVED
% 0.68/0.95 % SZS status Unsatisfiable
% 0.68/0.95
% 0.68/0.95 Exiting with 1 proof.
% 0.68/0.95
% 0.68/0.95 Process 13329 exit (max_proofs) Mon Jun 13 21:09:11 2022
% 0.68/0.95 Prover9 interrupted
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