TSTP Solution File: GRP566-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP566-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 11:19:38 EDT 2022
% Result : Unsatisfiable 0.41s 1.06s
% Output : Refutation 0.41s
% 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 : GRP566-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n025.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 : Tue Jun 14 01:45:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/1.06 ============================== Prover9 ===============================
% 0.41/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.41/1.06 Process 25289 was started by sandbox2 on n025.cluster.edu,
% 0.41/1.06 Tue Jun 14 01:45:40 2022
% 0.41/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_25136_n025.cluster.edu".
% 0.41/1.06 ============================== end of head ===========================
% 0.41/1.06
% 0.41/1.06 ============================== INPUT =================================
% 0.41/1.06
% 0.41/1.06 % Reading from file /tmp/Prover9_25136_n025.cluster.edu
% 0.41/1.06
% 0.41/1.06 set(prolog_style_variables).
% 0.41/1.06 set(auto2).
% 0.41/1.06 % set(auto2) -> set(auto).
% 0.41/1.06 % set(auto) -> set(auto_inference).
% 0.41/1.06 % set(auto) -> set(auto_setup).
% 0.41/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.41/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/1.06 % set(auto) -> set(auto_limits).
% 0.41/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/1.06 % set(auto) -> set(auto_denials).
% 0.41/1.06 % set(auto) -> set(auto_process).
% 0.41/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.41/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.41/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.41/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.41/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.41/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.41/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.41/1.06 % set(auto2) -> assign(stats, some).
% 0.41/1.06 % set(auto2) -> clear(echo_input).
% 0.41/1.06 % set(auto2) -> set(quiet).
% 0.41/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.41/1.06 % set(auto2) -> clear(print_given).
% 0.41/1.06 assign(lrs_ticks,-1).
% 0.41/1.06 assign(sos_limit,10000).
% 0.41/1.06 assign(order,kbo).
% 0.41/1.06 set(lex_order_vars).
% 0.41/1.06 clear(print_given).
% 0.41/1.06
% 0.41/1.06 % formulas(sos). % not echoed (5 formulas)
% 0.41/1.06
% 0.41/1.06 ============================== end of input ==========================
% 0.41/1.06
% 0.41/1.06 % From the command line: assign(max_seconds, 300).
% 0.41/1.06
% 0.41/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/1.06
% 0.41/1.06 % Formulas that are not ordinary clauses:
% 0.41/1.06
% 0.41/1.06 ============================== end of process non-clausal formulas ===
% 0.41/1.06
% 0.41/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.41/1.06
% 0.41/1.06 ============================== PREDICATE ELIMINATION =================
% 0.41/1.06
% 0.41/1.06 ============================== end predicate elimination =============
% 0.41/1.06
% 0.41/1.06 Auto_denials:
% 0.41/1.06 % copying label prove_these_axioms_2 to answer in negative clause
% 0.41/1.06
% 0.41/1.06 Term ordering decisions:
% 0.41/1.06
% 0.41/1.06 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.41/1.06 Function symbol KB weights: identity=1. a2=1. double_divide=1. multiply=1. inverse=0.
% 0.41/1.06
% 0.41/1.06 ============================== end of process initial clauses ========
% 0.41/1.06
% 0.41/1.06 ============================== CLAUSES FOR SEARCH ====================
% 0.41/1.06
% 0.41/1.06 ============================== end of clauses for search =============
% 0.41/1.06
% 0.41/1.06 ============================== SEARCH ================================
% 0.41/1.06
% 0.41/1.06 % Starting search at 0.01 seconds.
% 0.41/1.06
% 0.41/1.06 ============================== PROOF =================================
% 0.41/1.06 % SZS status Unsatisfiable
% 0.41/1.06 % SZS output start Refutation
% 0.41/1.06
% 0.41/1.06 % Proof 1 at 0.02 (+ 0.00) seconds: prove_these_axioms_2.
% 0.41/1.06 % Length of proof is 34.
% 0.41/1.06 % Level of proof is 14.
% 0.41/1.06 % Maximum clause weight is 23.000.
% 0.41/1.06 % Given clauses 31.
% 0.41/1.06
% 0.41/1.06 1 inverse(A) = double_divide(A,identity) # label(inverse) # label(axiom). [assumption].
% 0.41/1.06 2 identity = double_divide(A,inverse(A)) # label(identity) # label(axiom). [assumption].
% 0.41/1.06 3 double_divide(A,double_divide(A,identity)) = identity. [copy(2),rewrite([1(2)]),flip(a)].
% 0.41/1.06 4 multiply(A,B) = double_divide(double_divide(B,A),identity) # label(multiply) # label(axiom). [assumption].
% 0.41/1.06 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].
% 0.41/1.06 6 multiply(identity,a2) != a2 # label(prove_these_axioms_2) # label(negated_conjecture) # answer(prove_these_axioms_2). [assumption].
% 0.41/1.06 7 double_divide(double_divide(a2,identity),identity) != a2 # answer(prove_these_axioms_2). [copy(6),rewrite([4(3)])].
% 0.41/1.06 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))].
% 0.41/1.06 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)])].
% 0.41/1.06 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))].
% 0.41/1.06 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))].
% 0.41/1.06 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))].
% 0.41/1.06 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))].
% 0.41/1.06 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)])].
% 0.41/1.06 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))].
% 0.41/1.06 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)].
% 0.41/1.06 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)].
% 0.41/1.06 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))].
% 0.41/1.06 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)].
% 0.41/1.06 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)].
% 0.41/1.06 24 double_divide(identity,identity) = identity. [para(22(a,1),3(a,1))].
% 0.41/1.06 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)].
% 0.41/1.06 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)].
% 0.41/1.06 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)])].
% 0.41/1.06 32 double_divide(identity,double_divide(A,identity)) = A. [back_rewrite(10),rewrite([24(3),24(9),28(8)])].
% 0.41/1.06 33 double_divide(identity,A) = double_divide(A,identity). [back_rewrite(21),rewrite([26(5),32(5)])].
% 0.41/1.06 34 double_divide(identity,double_divide(identity,a2)) != a2 # answer(prove_these_axioms_2). [back_rewrite(7),rewrite([33(3,R),33(5,R)])].
% 0.41/1.06 36 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)])].
% 0.41/1.06 38 double_divide(A,double_divide(double_divide(B,identity),A)) = double_divide(B,identity). [back_rewrite(18),rewrite([32(6)])].
% 0.41/1.06 41 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)])].
% 0.41/1.06 44 double_divide(A,double_divide(B,A)) = B. [para(36(a,1),38(a,1,2,1)),rewrite([33(6),32(7),33(4),33(6,R),32(6)])].
% 0.41/1.06 50 double_divide(double_divide(A,B),A) = B. [para(44(a,1),44(a,1,2))].
% 0.41/1.06 65 double_divide(A,double_divide(A,B)) = B. [para(50(a,1),41(a,1,2)),rewrite([33(6,R),44(6)])].
% 0.41/1.06 66 $F # answer(prove_these_axioms_2). [resolve(65,a,34,a)].
% 0.41/1.06
% 0.41/1.06 % SZS output end Refutation
% 0.41/1.06 ============================== end of proof ==========================
% 0.41/1.06
% 0.41/1.06 ============================== STATISTICS ============================
% 0.41/1.06
% 0.41/1.06 Given=31. Generated=468. Kept=63. proofs=1.
% 0.41/1.06 Usable=16. Sos=2. Demods=24. Limbo=8, Disabled=41. Hints=0.
% 0.41/1.06 Megabytes=0.07.
% 0.41/1.06 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.41/1.06
% 0.41/1.06 ============================== end of statistics =====================
% 0.41/1.06
% 0.41/1.06 ============================== end of search =========================
% 0.41/1.06
% 0.41/1.06 THEOREM PROVED
% 0.41/1.06 % SZS status Unsatisfiable
% 0.41/1.06
% 0.41/1.06 Exiting with 1 proof.
% 0.41/1.06
% 0.41/1.06 Process 25289 exit (max_proofs) Tue Jun 14 01:45:40 2022
% 0.41/1.06 Prover9 interrupted
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