TSTP Solution File: GRP100-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP100-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 0.65s 1.03s
% Output : Refutation 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : GRP100-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.31 % Computer : n024.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 11:37:18 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.65/1.03 ============================== Prover9 ===============================
% 0.65/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.65/1.03 Process 27463 was started by sandbox on n024.cluster.edu,
% 0.65/1.03 Tue Jun 14 11:37:19 2022
% 0.65/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_27308_n024.cluster.edu".
% 0.65/1.03 ============================== end of head ===========================
% 0.65/1.03
% 0.65/1.03 ============================== INPUT =================================
% 0.65/1.03
% 0.65/1.03 % Reading from file /tmp/Prover9_27308_n024.cluster.edu
% 0.65/1.03
% 0.65/1.03 set(prolog_style_variables).
% 0.65/1.03 set(auto2).
% 0.65/1.03 % set(auto2) -> set(auto).
% 0.65/1.03 % set(auto) -> set(auto_inference).
% 0.65/1.03 % set(auto) -> set(auto_setup).
% 0.65/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.65/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.65/1.03 % set(auto) -> set(auto_limits).
% 0.65/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.65/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.65/1.03 % set(auto) -> set(auto_denials).
% 0.65/1.03 % set(auto) -> set(auto_process).
% 0.65/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.65/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.65/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.65/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.65/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.65/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.65/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.65/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.65/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.65/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.65/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.65/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.65/1.03 % set(auto2) -> assign(stats, some).
% 0.65/1.03 % set(auto2) -> clear(echo_input).
% 0.65/1.03 % set(auto2) -> set(quiet).
% 0.65/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.65/1.03 % set(auto2) -> clear(print_given).
% 0.65/1.03 assign(lrs_ticks,-1).
% 0.65/1.03 assign(sos_limit,10000).
% 0.65/1.03 assign(order,kbo).
% 0.65/1.03 set(lex_order_vars).
% 0.65/1.03 clear(print_given).
% 0.65/1.03
% 0.65/1.03 % formulas(sos). % not echoed (5 formulas)
% 0.65/1.03
% 0.65/1.03 ============================== end of input ==========================
% 0.65/1.03
% 0.65/1.03 % From the command line: assign(max_seconds, 300).
% 0.65/1.03
% 0.65/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.65/1.03
% 0.65/1.03 % Formulas that are not ordinary clauses:
% 0.65/1.03
% 0.65/1.03 ============================== end of process non-clausal formulas ===
% 0.65/1.03
% 0.65/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.65/1.03
% 0.65/1.03 ============================== PREDICATE ELIMINATION =================
% 0.65/1.03
% 0.65/1.03 ============================== end predicate elimination =============
% 0.65/1.03
% 0.65/1.03 Auto_denials:
% 0.65/1.03 % copying label prove_these_axioms to answer in negative clause
% 0.65/1.03
% 0.65/1.03 Term ordering decisions:
% 0.65/1.03
% 0.65/1.03 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 0.65/1.03 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.
% 0.65/1.03
% 0.65/1.03 ============================== end of process initial clauses ========
% 0.65/1.03
% 0.65/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.65/1.03
% 0.65/1.03 ============================== end of clauses for search =============
% 0.65/1.03
% 0.65/1.03 ============================== SEARCH ================================
% 0.65/1.03
% 0.65/1.03 % Starting search at 0.01 seconds.
% 0.65/1.03
% 0.65/1.03 ============================== PROOF =================================
% 0.65/1.03 % SZS status Unsatisfiable
% 0.65/1.03 % SZS output start Refutation
% 0.65/1.03
% 0.65/1.03 % Proof 1 at 0.12 (+ 0.01) seconds: prove_these_axioms.
% 0.65/1.03 % Length of proof is 48.
% 0.65/1.03 % Level of proof is 16.
% 0.65/1.03 % Maximum clause weight is 42.000.
% 0.65/1.03 % Given clauses 58.
% 0.65/1.03
% 0.65/1.03 1 inverse(A) = double_divide(A,identity) # label(inverse) # label(axiom). [assumption].
% 0.65/1.03 2 identity = double_divide(A,inverse(A)) # label(identity) # label(axiom). [assumption].
% 0.65/1.03 3 double_divide(A,double_divide(A,identity)) = identity. [copy(2),rewrite([1(2)]),flip(a)].
% 0.65/1.03 4 multiply(A,B) = double_divide(double_divide(B,A),identity) # label(multiply) # label(axiom). [assumption].
% 0.65/1.03 5 double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(C,identity))),double_divide(identity,identity)) = B # label(single_axiom) # label(axiom). [assumption].
% 0.65/1.03 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].
% 0.65/1.03 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)].
% 0.65/1.03 8 double_divide(double_divide(A,double_divide(double_divide(B,identity),double_divide(double_divide(A,identity),identity))),double_divide(identity,identity)) = B. [para(3(a,1),5(a,1,1,2,1,2))].
% 0.65/1.03 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)])].
% 0.65/1.03 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(B,C)),double_divide(C,identity))). [para(5(a,1),5(a,1,1,2,1))].
% 0.65/1.03 13 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(double_divide(B,identity),identity))). [para(8(a,1),5(a,1,1,2,1))].
% 0.65/1.03 15 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))].
% 0.65/1.03 16 double_divide(A,double_divide(double_divide(B,identity),double_divide(double_divide(A,identity),identity))) = double_divide(B,identity). [back_rewrite(13),rewrite([15(10)]),flip(a)].
% 0.65/1.03 17 double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(C,identity))) = double_divide(B,identity). [back_rewrite(11),rewrite([15(10)]),flip(a)].
% 0.65/1.03 18 double_divide(identity,identity) = identity. [para(3(a,1),15(a,1,1,2)),rewrite([9(7)]),flip(a)].
% 0.65/1.03 20 double_divide(double_divide(identity,A),identity) = double_divide(double_divide(A,identity),identity). [para(9(a,1),15(a,1,1,2)),rewrite([18(5)])].
% 0.65/1.03 23 double_divide(double_divide(A,identity),identity) = A. [back_rewrite(9),rewrite([18(5)])].
% 0.65/1.03 24 double_divide(double_divide(identity,a2),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([18(3),20(8,R)]),xx(a)].
% 0.65/1.03 25 double_divide(double_divide(identity,A),identity) = A. [back_rewrite(20),rewrite([23(8)])].
% 0.65/1.03 26 double_divide(A,double_divide(double_divide(B,identity),A)) = double_divide(B,identity). [back_rewrite(16),rewrite([23(6)])].
% 0.65/1.03 27 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(24),rewrite([25(5)]),xx(a)].
% 0.65/1.03 28 double_divide(double_divide(A,identity),A) = identity. [para(23(a,1),3(a,1,2))].
% 0.65/1.03 29 double_divide(identity,A) = double_divide(A,identity). [para(18(a,1),17(a,1,2,1,2)),rewrite([18(6),23(5)])].
% 0.65/1.03 31 double_divide(double_divide(A,identity),double_divide(identity,double_divide(B,A))) = double_divide(B,identity). [para(23(a,1),17(a,1,2,1,2)),rewrite([18(6),29(5,R)])].
% 0.65/1.03 33 double_divide(identity,double_divide(A,identity)) = A. [para(23(a,1),17(a,2)),rewrite([17(8),29(4,R)])].
% 0.65/1.03 36 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(27),rewrite([29(5,R),29(9,R),29(15,R),29(18,R),29(24,R),29(29,R)])].
% 0.65/1.03 38 double_divide(identity,double_divide(identity,double_divide(A,B))) = double_divide(A,B). [para(28(a,1),17(a,1,2,1)),rewrite([33(4),29(4,R),29(6,R)]),flip(a)].
% 0.65/1.03 40 double_divide(identity,double_divide(double_divide(A,B),B)) = double_divide(A,identity). [para(33(a,1),17(a,1,2,1,2)),rewrite([29(6,R),33(6)])].
% 0.65/1.03 50 double_divide(double_divide(A,B),B) = A. [para(40(a,1),38(a,1,2)),rewrite([33(4)]),flip(a)].
% 0.65/1.03 51 double_divide(double_divide(A,B),double_divide(double_divide(C,A),double_divide(B,identity))) = double_divide(C,identity). [para(50(a,1),17(a,1,2,1,2))].
% 0.65/1.03 52 double_divide(identity,double_divide(A,double_divide(B,C))) = double_divide(B,double_divide(A,double_divide(C,identity))). [para(50(a,1),17(a,1,2,1)),rewrite([29(8,R)]),flip(a)].
% 0.65/1.03 54 double_divide(A,double_divide(B,A)) = B. [para(50(a,1),26(a,1,2,1)),rewrite([29(6,R),33(6)])].
% 0.65/1.03 59 double_divide(A,double_divide(A,B)) = B. [para(54(a,1),50(a,1,1))].
% 0.65/1.03 60 double_divide(A,B) = double_divide(B,A). [para(50(a,1),54(a,1,2))].
% 0.65/1.03 63 double_divide(double_divide(A,B),double_divide(double_divide(A,C),double_divide(B,identity))) = double_divide(C,identity). [back_rewrite(51),rewrite([60(2)])].
% 0.65/1.03 64 double_divide(A,double_divide(B,A)) = B. [back_rewrite(50),rewrite([60(2)])].
% 0.65/1.03 66 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(36),rewrite([60(5),60(8),60(15),60(23)]),flip(a),xx(b)].
% 0.65/1.03 70 double_divide(double_divide(A,identity),double_divide(identity,double_divide(A,B))) = double_divide(B,identity). [back_rewrite(31),rewrite([60(4)])].
% 0.65/1.03 73 double_divide(identity,double_divide(A,double_divide(B,double_divide(C,identity)))) = double_divide(B,double_divide(A,C)). [para(52(a,1),59(a,1,2))].
% 0.65/1.03 74 double_divide(A,double_divide(identity,double_divide(B,double_divide(A,C)))) = double_divide(B,double_divide(C,identity)). [para(52(a,2),59(a,1,2))].
% 0.65/1.03 82 double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(identity,double_divide(A,B)). [para(70(a,1),59(a,1,2))].
% 0.65/1.03 89 double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(double_divide(B,identity),double_divide(A,C)). [para(82(a,1),52(a,1,2,2)),rewrite([60(12),64(12)])].
% 0.65/1.03 94 double_divide(double_divide(identity,b3),double_divide(a3,c3)) != double_divide(double_divide(identity,a3),double_divide(b3,c3)) # answer(prove_these_axioms). [back_rewrite(66),rewrite([89(9),60(3),60(6),89(16),60(10)]),flip(a)].
% 0.65/1.03 107 double_divide(double_divide(A,B),double_divide(C,identity)) = double_divide(double_divide(A,C),double_divide(B,identity)). [para(63(a,1),59(a,1,2))].
% 0.65/1.03 132 double_divide(A,double_divide(B,double_divide(C,double_divide(D,A)))) = double_divide(C,double_divide(B,D)). [para(74(a,1),52(a,1,2,2)),rewrite([73(6),60(4),60(8),59(8)]),flip(a)].
% 0.65/1.03 195 double_divide(double_divide(A,B),double_divide(C,D)) = double_divide(double_divide(A,D),double_divide(C,B)). [para(107(a,1),52(a,1,2,2)),rewrite([132(7),60(8),64(8)])].
% 0.65/1.03 353 double_divide(double_divide(A,B),double_divide(C,D)) = double_divide(double_divide(A,C),double_divide(B,D)). [para(60(a,1),195(a,1,2)),rewrite([60(5)])].
% 0.65/1.03 354 $F # answer(prove_these_axioms). [resolve(353,a,94,a)].
% 0.65/1.03
% 0.65/1.03 % SZS output end Refutation
% 0.65/1.03 ============================== end of proof ==========================
% 0.65/1.03
% 0.65/1.03 ============================== STATISTICS ============================
% 0.65/1.03
% 0.65/1.03 Given=58. Generated=2731. Kept=351. proofs=1.
% 0.65/1.03 Usable=23. Sos=111. Demods=34. Limbo=1, Disabled=220. Hints=0.
% 0.65/1.03 Megabytes=0.31.
% 0.65/1.03 User_CPU=0.13, System_CPU=0.01, Wall_clock=0.
% 0.65/1.03
% 0.65/1.03 ============================== end of statistics =====================
% 0.65/1.03
% 0.65/1.03 ============================== end of search =========================
% 0.65/1.03
% 0.65/1.03 THEOREM PROVED
% 0.65/1.03 % SZS status Unsatisfiable
% 0.65/1.03
% 0.65/1.03 Exiting with 1 proof.
% 0.65/1.03
% 0.65/1.03 Process 27463 exit (max_proofs) Tue Jun 14 11:37:19 2022
% 0.65/1.03 Prover9 interrupted
%------------------------------------------------------------------------------