TSTP Solution File: GRP492-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP492-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 11:19:19 EDT 2022
% Result : Unsatisfiable 0.65s 0.99s
% Output : Refutation 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP492-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 04:33:07 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.65/0.99 ============================== Prover9 ===============================
% 0.65/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.65/0.99 Process 32367 was started by sandbox on n008.cluster.edu,
% 0.65/0.99 Tue Jun 14 04:33:08 2022
% 0.65/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_32214_n008.cluster.edu".
% 0.65/0.99 ============================== end of head ===========================
% 0.65/0.99
% 0.65/0.99 ============================== INPUT =================================
% 0.65/0.99
% 0.65/0.99 % Reading from file /tmp/Prover9_32214_n008.cluster.edu
% 0.65/0.99
% 0.65/0.99 set(prolog_style_variables).
% 0.65/0.99 set(auto2).
% 0.65/0.99 % set(auto2) -> set(auto).
% 0.65/0.99 % set(auto) -> set(auto_inference).
% 0.65/0.99 % set(auto) -> set(auto_setup).
% 0.65/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.65/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.65/0.99 % set(auto) -> set(auto_limits).
% 0.65/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.65/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.65/0.99 % set(auto) -> set(auto_denials).
% 0.65/0.99 % set(auto) -> set(auto_process).
% 0.65/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.65/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.65/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.65/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.65/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.65/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.65/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.65/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.65/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.65/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.65/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.65/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.65/0.99 % set(auto2) -> assign(stats, some).
% 0.65/0.99 % set(auto2) -> clear(echo_input).
% 0.65/0.99 % set(auto2) -> set(quiet).
% 0.65/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.65/0.99 % set(auto2) -> clear(print_given).
% 0.65/0.99 assign(lrs_ticks,-1).
% 0.65/0.99 assign(sos_limit,10000).
% 0.65/0.99 assign(order,kbo).
% 0.65/0.99 set(lex_order_vars).
% 0.65/0.99 clear(print_given).
% 0.65/0.99
% 0.65/0.99 % formulas(sos). % not echoed (5 formulas)
% 0.65/0.99
% 0.65/0.99 ============================== end of input ==========================
% 0.65/0.99
% 0.65/0.99 % From the command line: assign(max_seconds, 300).
% 0.65/0.99
% 0.65/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.65/0.99
% 0.65/0.99 % Formulas that are not ordinary clauses:
% 0.65/0.99
% 0.65/0.99 ============================== end of process non-clausal formulas ===
% 0.65/0.99
% 0.65/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.65/0.99
% 0.65/0.99 ============================== PREDICATE ELIMINATION =================
% 0.65/0.99
% 0.65/0.99 ============================== end predicate elimination =============
% 0.65/0.99
% 0.65/0.99 Auto_denials:
% 0.65/0.99 % copying label prove_these_axioms_3 to answer in negative clause
% 0.65/0.99
% 0.65/0.99 Term ordering decisions:
% 0.65/0.99
% 0.65/0.99 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.65/0.99 Function symbol KB weights: identity=1. a3=1. b3=1. c3=1. double_divide=1. multiply=1. inverse=0.
% 0.65/0.99
% 0.65/0.99 ============================== end of process initial clauses ========
% 0.65/0.99
% 0.65/0.99 ============================== CLAUSES FOR SEARCH ====================
% 0.65/0.99
% 0.65/0.99 ============================== end of clauses for search =============
% 0.65/0.99
% 0.65/0.99 ============================== SEARCH ================================
% 0.65/0.99
% 0.65/0.99 % Starting search at 0.01 seconds.
% 0.65/0.99
% 0.65/0.99 ============================== PROOF =================================
% 0.65/0.99 % SZS status Unsatisfiable
% 0.65/0.99 % SZS output start Refutation
% 0.65/0.99
% 0.65/0.99 % Proof 1 at 0.04 (+ 0.00) seconds: prove_these_axioms_3.
% 0.65/0.99 % Length of proof is 48.
% 0.65/0.99 % Level of proof is 17.
% 0.65/0.99 % Maximum clause weight is 33.000.
% 0.65/0.99 % Given clauses 35.
% 0.65/0.99
% 0.65/0.99 1 inverse(A) = double_divide(A,identity) # label(inverse) # label(axiom). [assumption].
% 0.65/0.99 2 identity = double_divide(A,inverse(A)) # label(identity) # label(axiom). [assumption].
% 0.65/0.99 3 double_divide(A,double_divide(A,identity)) = identity. [copy(2),rewrite([1(2)]),flip(a)].
% 0.65/0.99 4 multiply(A,B) = double_divide(double_divide(B,A),identity) # label(multiply) # label(axiom). [assumption].
% 0.65/0.99 5 double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C # label(single_axiom) # label(axiom). [assumption].
% 0.65/0.99 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].
% 0.65/0.99 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)].
% 0.65/0.99 8 double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),A),identity),double_divide(B,A)))) = B. [para(3(a,1),5(a,1,1))].
% 0.65/0.99 10 double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(B,identity)),identity),identity))) = B. [para(3(a,1),5(a,1,2,2,2))].
% 0.65/0.99 11 double_divide(double_divide(identity,A),double_divide(identity,identity)) = double_divide(double_divide(A,identity),identity). [para(3(a,1),5(a,1,2,2))].
% 0.65/0.99 13 double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(identity,double_divide(double_divide(double_divide(B,C),identity),double_divide(D,C)))),identity),D))) = double_divide(identity,B). [para(5(a,1),5(a,1,2,2,2))].
% 0.65/0.99 15 double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(A,identity)),identity),identity))) = A. [para(3(a,1),8(a,1,2,2,2))].
% 0.65/0.99 16 double_divide(double_divide(double_divide(identity,identity),identity),identity) = identity. [para(3(a,1),8(a,1,2,2)),rewrite([3(5)]),flip(a)].
% 0.65/0.99 22 double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A. [para(16(a,1),5(a,1,2,2,1)),rewrite([3(5)])].
% 0.65/0.99 24 double_divide(double_divide(identity,identity),identity) = double_divide(identity,identity). [para(16(a,1),8(a,1,2,2,2)),rewrite([16(9),3(6)]),flip(a)].
% 0.65/0.99 27 double_divide(identity,identity) = identity. [back_rewrite(16),rewrite([24(5),24(5)])].
% 0.65/0.99 31 double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(A,identity)),identity),identity))) = A. [back_rewrite(15),rewrite([27(5)])].
% 0.65/0.99 32 double_divide(double_divide(identity,A),identity) = double_divide(double_divide(A,identity),identity). [back_rewrite(11),rewrite([27(5)])].
% 0.65/0.99 34 double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),double_divide(B,A)))) = B. [back_rewrite(8),rewrite([27(5),32(6)])].
% 0.65/0.99 35 double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity))) = A. [back_rewrite(31),rewrite([32(10,R)])].
% 0.65/0.99 39 double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),identity))) = B. [back_rewrite(10),rewrite([32(10,R)])].
% 0.65/0.99 45 double_divide(identity,A) = double_divide(A,identity). [para(32(a,1),5(a,1,2,2,2)),rewrite([5(14)]),flip(a)].
% 0.65/0.99 46 double_divide(double_divide(identity,double_divide(A,identity)),double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),double_divide(B,identity)))) = B. [para(32(a,2),5(a,1,2,2,1,1)),rewrite([45(7),45(9,R),45(11,R)])].
% 0.65/0.99 48 double_divide(double_divide(A,identity),double_divide(identity,double_divide(double_divide(identity,double_divide(A,identity)),double_divide(identity,double_divide(B,identity))))) = double_divide(B,identity). [para(32(a,2),5(a,1,2,2,2)),rewrite([45(2),45(7,R),45(9),45(11,R)])].
% 0.65/0.99 52 double_divide(double_divide(A,identity),double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,double_divide(B,identity)))))) = B. [back_rewrite(39),rewrite([45(2),45(10,R)])].
% 0.65/0.99 56 double_divide(identity,double_divide(A,identity)) = A. [back_rewrite(35),rewrite([45(10,R),22(10),45(3)])].
% 0.65/0.99 57 double_divide(identity,double_divide(identity,double_divide(A,double_divide(B,A)))) = B. [back_rewrite(34),rewrite([45(6,R),56(6)])].
% 0.65/0.99 60 double_divide(double_divide(A,identity),double_divide(identity,double_divide(double_divide(identity,double_divide(A,double_divide(identity,double_divide(double_divide(identity,double_divide(B,C)),double_divide(D,C))))),D))) = double_divide(B,identity). [back_rewrite(13),rewrite([45(2),45(7,R),45(13,R),45(18)])].
% 0.65/0.99 62 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([45(5,R),45(9,R),45(15,R),45(18,R)])].
% 0.65/0.99 63 double_divide(double_divide(A,identity),double_divide(identity,double_divide(double_divide(identity,double_divide(A,B)),double_divide(C,B)))) = C. [back_rewrite(5),rewrite([45(2),45(6,R)])].
% 0.65/0.99 69 double_divide(double_divide(A,identity),double_divide(identity,double_divide(A,B))) = double_divide(B,identity). [back_rewrite(48),rewrite([56(7),56(7)])].
% 0.65/0.99 70 double_divide(A,double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,identity)))) = B. [back_rewrite(46),rewrite([56(4),56(6),45(3)])].
% 0.65/0.99 72 double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,double_divide(B,identity))))),B))) = double_divide(A,identity). [para(52(a,1),57(a,1,2,2,2))].
% 0.65/0.99 74 double_divide(identity,double_divide(A,double_divide(B,A))) = double_divide(B,identity). [para(57(a,1),69(a,1,2)),rewrite([27(3),45(2),45(6,R)]),flip(a)].
% 0.65/0.99 76 double_divide(identity,double_divide(identity,double_divide(A,B))) = double_divide(A,B). [para(69(a,1),69(a,1,2,2)),rewrite([45(4,R),56(4),56(4),45(6,R)]),flip(a)].
% 0.65/0.99 78 double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),B) = double_divide(A,identity). [back_rewrite(72),rewrite([76(10),76(10)])].
% 0.65/0.99 81 double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(identity,double_divide(B,A)). [para(74(a,1),69(a,1,2)),rewrite([45(8,R)])].
% 0.65/0.99 83 double_divide(A,double_divide(B,A)) = B. [back_rewrite(70),rewrite([81(6),76(5)])].
% 0.65/0.99 84 double_divide(double_divide(A,B),A) = B. [para(83(a,1),83(a,1,2))].
% 0.65/0.99 90 double_divide(double_divide(A,identity),double_divide(identity,double_divide(double_divide(identity,double_divide(A,double_divide(identity,double_divide(double_divide(identity,double_divide(B,double_divide(identity,double_divide(C,D)))),double_divide(D,identity))))),double_divide(C,identity)))) = double_divide(B,identity). [para(69(a,1),60(a,1,2,2,1,2,2,2,2))].
% 0.65/0.99 97 double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(B,double_divide(A,identity)). [para(78(a,1),83(a,1,2)),flip(a)].
% 0.65/0.99 99 double_divide(double_divide(A,identity),double_divide(B,double_divide(A,double_divide(C,double_divide(D,double_divide(identity,double_divide(B,C))))))) = double_divide(D,identity). [back_rewrite(90),rewrite([97(15),45(12,R),76(12),97(15),45(12,R),76(12)])].
% 0.65/0.99 103 double_divide(double_divide(identity,double_divide(A,B)),double_divide(C,B)) = double_divide(A,double_divide(C,identity)). [para(63(a,1),69(a,1,2,2)),rewrite([45(4,R),83(4),45(2),45(12,R),76(12)]),flip(a)].
% 0.65/0.99 123 double_divide(double_divide(A,identity),double_divide(B,double_divide(A,double_divide(C,D)))) = double_divide(identity,double_divide(double_divide(identity,double_divide(B,C)),D)). [para(84(a,1),99(a,1,2,2,2,2)),rewrite([45(12,R)])].
% 0.65/0.99 134 double_divide(double_divide(A,identity),double_divide(B,double_divide(A,C))) = double_divide(C,double_divide(B,identity)). [para(83(a,1),103(a,1,1,2)),rewrite([45(2)])].
% 0.65/0.99 138 double_divide(double_divide(identity,double_divide(A,B)),C) = double_divide(A,double_divide(identity,double_divide(B,C))). [para(84(a,1),103(a,1,2)),rewrite([45(7,R)])].
% 0.65/0.99 143 double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(double_divide(B,C),double_divide(A,identity)). [back_rewrite(123),rewrite([134(6),138(9)]),flip(a)].
% 0.65/0.99 144 $F # answer(prove_these_axioms_3). [back_rewrite(62),rewrite([138(8),143(9),45(6,R),143(16),45(13,R)]),xx(a)].
% 0.65/0.99
% 0.65/0.99 % SZS output end Refutation
% 0.65/0.99 ============================== end of proof ==========================
% 0.65/0.99
% 0.65/0.99 ============================== STATISTICS ============================
% 0.65/0.99
% 0.65/0.99 Given=35. Generated=942. Kept=141. proofs=1.
% 0.65/0.99 Usable=11. Sos=9. Demods=24. Limbo=6, Disabled=120. Hints=0.
% 0.65/0.99 Megabytes=0.14.
% 0.65/0.99 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.65/0.99
% 0.65/0.99 ============================== end of statistics =====================
% 0.65/0.99
% 0.65/0.99 ============================== end of search =========================
% 0.65/0.99
% 0.65/0.99 THEOREM PROVED
% 0.65/0.99 % SZS status Unsatisfiable
% 0.65/0.99
% 0.65/0.99 Exiting with 1 proof.
% 0.65/0.99
% 0.65/0.99 Process 32367 exit (max_proofs) Tue Jun 14 04:33:08 2022
% 0.65/0.99 Prover9 interrupted
%------------------------------------------------------------------------------