TSTP Solution File: GRP567-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP567-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 0.72s 1.04s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP567-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n010.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 17:11:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.72/1.04 ============================== Prover9 ===============================
% 0.72/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.72/1.04 Process 31183 was started by sandbox on n010.cluster.edu,
% 0.72/1.04 Mon Jun 13 17:11:25 2022
% 0.72/1.04 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30815_n010.cluster.edu".
% 0.72/1.04 ============================== end of head ===========================
% 0.72/1.04
% 0.72/1.04 ============================== INPUT =================================
% 0.72/1.04
% 0.72/1.04 % Reading from file /tmp/Prover9_30815_n010.cluster.edu
% 0.72/1.04
% 0.72/1.04 set(prolog_style_variables).
% 0.72/1.04 set(auto2).
% 0.72/1.04 % set(auto2) -> set(auto).
% 0.72/1.04 % set(auto) -> set(auto_inference).
% 0.72/1.04 % set(auto) -> set(auto_setup).
% 0.72/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.72/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/1.04 % set(auto) -> set(auto_limits).
% 0.72/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/1.04 % set(auto) -> set(auto_denials).
% 0.72/1.04 % set(auto) -> set(auto_process).
% 0.72/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.72/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.72/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.72/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.72/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.72/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.72/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.72/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.72/1.04 % set(auto2) -> assign(stats, some).
% 0.72/1.04 % set(auto2) -> clear(echo_input).
% 0.72/1.04 % set(auto2) -> set(quiet).
% 0.72/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.72/1.04 % set(auto2) -> clear(print_given).
% 0.72/1.04 assign(lrs_ticks,-1).
% 0.72/1.04 assign(sos_limit,10000).
% 0.72/1.04 assign(order,kbo).
% 0.72/1.04 set(lex_order_vars).
% 0.72/1.04 clear(print_given).
% 0.72/1.04
% 0.72/1.04 % formulas(sos). % not echoed (5 formulas)
% 0.72/1.04
% 0.72/1.04 ============================== end of input ==========================
% 0.72/1.04
% 0.72/1.04 % From the command line: assign(max_seconds, 300).
% 0.72/1.04
% 0.72/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/1.04
% 0.72/1.04 % Formulas that are not ordinary clauses:
% 0.72/1.04
% 0.72/1.04 ============================== end of process non-clausal formulas ===
% 0.72/1.04
% 0.72/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.72/1.04
% 0.72/1.04 ============================== PREDICATE ELIMINATION =================
% 0.72/1.04
% 0.72/1.04 ============================== end predicate elimination =============
% 0.72/1.04
% 0.72/1.04 Auto_denials:
% 0.72/1.04 % copying label prove_these_axioms_3 to answer in negative clause
% 0.72/1.04
% 0.72/1.04 Term ordering decisions:
% 0.72/1.04
% 0.72/1.04 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.72/1.04 Function symbol KB weights: identity=1. a3=1. b3=1. c3=1. double_divide=1. multiply=1. inverse=0.
% 0.72/1.04
% 0.72/1.04 ============================== end of process initial clauses ========
% 0.72/1.04
% 0.72/1.04 ============================== CLAUSES FOR SEARCH ====================
% 0.72/1.04
% 0.72/1.04 ============================== end of clauses for search =============
% 0.72/1.04
% 0.72/1.04 ============================== SEARCH ================================
% 0.72/1.04
% 0.72/1.04 % Starting search at 0.01 seconds.
% 0.72/1.04
% 0.72/1.04 ============================== PROOF =================================
% 0.72/1.04 % SZS status Unsatisfiable
% 0.72/1.04 % SZS output start Refutation
% 0.72/1.04
% 0.72/1.04 % Proof 1 at 0.07 (+ 0.00) seconds: prove_these_axioms_3.
% 0.72/1.04 % Length of proof is 63.
% 0.72/1.04 % Level of proof is 25.
% 0.72/1.04 % Maximum clause weight is 23.000.
% 0.72/1.04 % Given clauses 56.
% 0.72/1.04
% 0.72/1.04 1 inverse(A) = double_divide(A,identity) # label(inverse) # label(axiom). [assumption].
% 0.72/1.04 2 identity = double_divide(A,inverse(A)) # label(identity) # label(axiom). [assumption].
% 0.72/1.04 3 double_divide(A,double_divide(A,identity)) = identity. [copy(2),rewrite([1(2)]),flip(a)].
% 0.72/1.04 4 multiply(A,B) = double_divide(double_divide(B,A),identity) # label(multiply) # label(axiom). [assumption].
% 0.72/1.04 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].
% 0.72/1.04 6 multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # label(prove_these_axioms_3) # label(negated_conjecture) # answer(prove_these_axioms_3). [assumption].
% 0.72/1.04 7 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) # answer(prove_these_axioms_3). [copy(6),rewrite([4(3),4(7),4(13),4(16)]),flip(a)].
% 0.72/1.04 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))].
% 0.72/1.04 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)])].
% 0.72/1.04 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))].
% 0.72/1.04 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))].
% 0.72/1.04 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))].
% 0.72/1.04 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))].
% 0.72/1.04 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)])].
% 0.72/1.04 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))].
% 0.72/1.04 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)].
% 0.72/1.04 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)].
% 0.72/1.04 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))].
% 0.72/1.04 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)].
% 0.72/1.04 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)].
% 0.72/1.04 24 double_divide(identity,identity) = identity. [para(22(a,1),3(a,1))].
% 0.72/1.04 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)].
% 0.72/1.04 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)].
% 0.72/1.04 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)])].
% 0.72/1.04 32 double_divide(identity,double_divide(A,identity)) = A. [back_rewrite(10),rewrite([24(3),24(9),28(8)])].
% 0.72/1.04 33 double_divide(identity,A) = double_divide(A,identity). [back_rewrite(21),rewrite([26(5),32(5)])].
% 0.72/1.04 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)])].
% 0.72/1.04 36 double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,double_divide(A,identity))))) = B. [back_rewrite(28),rewrite([33(5,R),33(8,R),32(12)])].
% 0.72/1.04 37 double_divide(A,double_divide(double_divide(B,identity),A)) = double_divide(B,identity). [back_rewrite(18),rewrite([32(6)])].
% 0.72/1.04 39 double_divide(double_divide(A,identity),double_divide(identity,double_divide(B,A))) = double_divide(B,identity). [back_rewrite(22),rewrite([33(5,R)])].
% 0.72/1.04 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)])].
% 0.72/1.04 41 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)))) # answer(prove_these_axioms_3). [back_rewrite(7),rewrite([33(5,R),33(9,R),33(15,R),33(18,R)])].
% 0.72/1.04 42 multiply(A,B) = double_divide(identity,double_divide(B,A)). [back_rewrite(4),rewrite([33(4,R)])].
% 0.72/1.04 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)])].
% 0.72/1.04 47 double_divide(double_divide(A,B),A) = B. [para(44(a,1),44(a,1,2))].
% 0.72/1.04 49 double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(double_divide(A,identity),B). [para(47(a,1),36(a,1,2,2,2)),rewrite([33(3)])].
% 0.72/1.04 52 double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(identity,double_divide(A,B)). [para(39(a,1),47(a,1,1))].
% 0.72/1.04 57 double_divide(double_divide(A,double_divide(B,C)),double_divide(C,identity)) = double_divide(double_divide(A,identity),B). [para(40(a,1),47(a,1,1)),flip(a)].
% 0.72/1.04 59 double_divide(identity,double_divide(double_divide(A,B),C)) = double_divide(A,double_divide(C,double_divide(B,identity))). [para(47(a,1),40(a,1,2,1)),rewrite([33(8,R)]),flip(a)].
% 0.72/1.04 61 double_divide(A,double_divide(A,B)) = B. [para(47(a,1),40(a,1,2)),rewrite([33(6,R),44(6)])].
% 0.72/1.04 65 double_divide(double_divide(A,identity),B) = double_divide(B,double_divide(A,identity)). [para(40(a,1),39(a,1,2)),rewrite([33(4,R),44(4),33(5),33(8,R),49(8)]),flip(a)].
% 0.72/1.04 69 double_divide(double_divide(A,double_divide(B,C)),double_divide(C,double_divide(A,identity))) = double_divide(B,identity). [para(40(a,1),40(a,1,2,1)),rewrite([33(8,R),44(8),65(5)])].
% 0.72/1.04 72 double_divide(double_divide(A,identity),double_divide(B,double_divide(C,A))) = double_divide(C,double_divide(B,identity)). [back_rewrite(57),rewrite([65(5,R),65(8)])].
% 0.72/1.04 74 double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(B,double_divide(A,identity)). [back_rewrite(49),rewrite([65(8)])].
% 0.72/1.04 77 double_divide(A,B) = double_divide(B,A). [para(44(a,1),61(a,1,2))].
% 0.72/1.04 78 double_divide(double_divide(A,identity),double_divide(B,double_divide(A,C))) = double_divide(C,double_divide(B,identity)). [back_rewrite(72),rewrite([77(3)])].
% 0.72/1.04 80 double_divide(identity,double_divide(A,double_divide(B,C))) = double_divide(B,double_divide(A,double_divide(C,identity))). [back_rewrite(59),rewrite([77(3)])].
% 0.72/1.04 83 multiply(A,B) = double_divide(identity,double_divide(A,B)). [back_rewrite(42),rewrite([77(3)])].
% 0.72/1.04 84 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_3). [back_rewrite(41),rewrite([77(5),77(8),77(15)]),flip(a)].
% 0.72/1.04 85 double_divide(identity,double_divide(A,identity)) = A. [para(61(a,1),83(a,2)),rewrite([83(2),77(3)])].
% 0.72/1.04 91 double_divide(double_divide(A,B),double_divide(identity,double_divide(A,B))) = identity. [para(85(a,1),69(a,1,1,2)),rewrite([52(6),77(3),24(8)])].
% 0.72/1.04 93 double_divide(double_divide(identity,double_divide(A,B)),double_divide(A,double_divide(identity,double_divide(C,B)))) = C. [para(52(a,1),69(a,1,1,2)),rewrite([52(9),77(6),77(8),77(12),85(12)])].
% 0.72/1.04 97 double_divide(A,double_divide(identity,double_divide(B,double_divide(A,B)))) = identity. [para(61(a,1),91(a,1,1)),rewrite([77(2)])].
% 0.72/1.04 98 double_divide(identity,double_divide(A,double_divide(B,A))) = double_divide(B,identity). [para(97(a,1),61(a,1,2)),flip(a)].
% 0.72/1.04 103 double_divide(A,double_divide(B,A)) = B. [para(98(a,1),61(a,1,2)),rewrite([85(4)]),flip(a)].
% 0.72/1.04 105 double_divide(double_divide(A,double_divide(B,identity)),double_divide(C,identity)) = double_divide(B,double_divide(A,C)). [para(69(a,1),103(a,1,2)),rewrite([77(7)])].
% 0.72/1.04 112 double_divide(identity,double_divide(A,double_divide(B,double_divide(C,identity)))) = double_divide(B,double_divide(A,C)). [para(74(a,1),78(a,1,2,2)),rewrite([24(3),105(12),77(7)])].
% 0.72/1.04 116 double_divide(double_divide(A,double_divide(B,C)),double_divide(D,identity)) = double_divide(B,double_divide(D,double_divide(C,double_divide(A,identity)))). [para(78(a,1),78(a,1,2,2)),rewrite([77(4),103(4)]),flip(a)].
% 0.72/1.04 122 double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(double_divide(B,identity),double_divide(A,C)). [para(52(a,1),80(a,1,2,2)),rewrite([77(12),103(12)])].
% 0.72/1.04 124 double_divide(double_divide(identity,b3),double_divide(a3,c3)) != double_divide(double_divide(identity,a3),double_divide(b3,c3)) # answer(prove_these_axioms_3). [para(80(a,1),84(a,1)),rewrite([77(7),122(9),77(3),77(6),122(16),77(10)]),flip(a)].
% 0.72/1.04 158 double_divide(double_divide(A,B),double_divide(C,D)) = double_divide(double_divide(C,A),double_divide(D,B)). [para(93(a,1),78(a,1,2,2)),rewrite([77(5),61(5),77(5),116(10),112(10),77(5)]),flip(a)].
% 0.72/1.04 255 double_divide(double_divide(A,B),double_divide(C,D)) = double_divide(double_divide(A,C),double_divide(B,D)). [para(158(a,1),77(a,1))].
% 0.72/1.04 256 $F # answer(prove_these_axioms_3). [resolve(255,a,124,a)].
% 0.72/1.04
% 0.72/1.04 % SZS output end Refutation
% 0.72/1.04 ============================== end of proof ==========================
% 0.72/1.04
% 0.72/1.04 ============================== STATISTICS ============================
% 0.72/1.04
% 0.72/1.04 Given=56. Generated=1549. Kept=253. proofs=1.
% 0.72/1.04 Usable=13. Sos=58. Demods=31. Limbo=0, Disabled=186. Hints=0.
% 0.72/1.04 Megabytes=0.21.
% 0.72/1.04 User_CPU=0.07, System_CPU=0.00, Wall_clock=0.
% 0.72/1.04
% 0.72/1.04 ============================== end of statistics =====================
% 0.72/1.04
% 0.72/1.04 ============================== end of search =========================
% 0.72/1.04
% 0.72/1.04 THEOREM PROVED
% 0.72/1.04 % SZS status Unsatisfiable
% 0.72/1.04
% 0.72/1.04 Exiting with 1 proof.
% 0.72/1.04
% 0.72/1.04 Process 31183 exit (max_proofs) Mon Jun 13 17:11:25 2022
% 0.72/1.04 Prover9 interrupted
%------------------------------------------------------------------------------