TSTP Solution File: GRP576-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP576-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.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 11:19:41 EDT 2022
% Result : Unsatisfiable 0.83s 1.09s
% Output : Refutation 0.83s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP576-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 13:36:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.83/1.09 ============================== Prover9 ===============================
% 0.83/1.09 Prover9 (32) version 2009-11A, November 2009.
% 0.83/1.09 Process 28797 was started by sandbox on n015.cluster.edu,
% 0.83/1.09 Mon Jun 13 13:36:08 2022
% 0.83/1.09 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_28408_n015.cluster.edu".
% 0.83/1.09 ============================== end of head ===========================
% 0.83/1.09
% 0.83/1.09 ============================== INPUT =================================
% 0.83/1.09
% 0.83/1.09 % Reading from file /tmp/Prover9_28408_n015.cluster.edu
% 0.83/1.09
% 0.83/1.09 set(prolog_style_variables).
% 0.83/1.09 set(auto2).
% 0.83/1.09 % set(auto2) -> set(auto).
% 0.83/1.09 % set(auto) -> set(auto_inference).
% 0.83/1.09 % set(auto) -> set(auto_setup).
% 0.83/1.09 % set(auto_setup) -> set(predicate_elim).
% 0.83/1.09 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.83/1.09 % set(auto) -> set(auto_limits).
% 0.83/1.09 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.83/1.09 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.83/1.09 % set(auto) -> set(auto_denials).
% 0.83/1.09 % set(auto) -> set(auto_process).
% 0.83/1.09 % set(auto2) -> assign(new_constants, 1).
% 0.83/1.09 % set(auto2) -> assign(fold_denial_max, 3).
% 0.83/1.09 % set(auto2) -> assign(max_weight, "200.000").
% 0.83/1.09 % set(auto2) -> assign(max_hours, 1).
% 0.83/1.09 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.83/1.09 % set(auto2) -> assign(max_seconds, 0).
% 0.83/1.09 % set(auto2) -> assign(max_minutes, 5).
% 0.83/1.09 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.83/1.09 % set(auto2) -> set(sort_initial_sos).
% 0.83/1.09 % set(auto2) -> assign(sos_limit, -1).
% 0.83/1.09 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.83/1.09 % set(auto2) -> assign(max_megs, 400).
% 0.83/1.09 % set(auto2) -> assign(stats, some).
% 0.83/1.09 % set(auto2) -> clear(echo_input).
% 0.83/1.09 % set(auto2) -> set(quiet).
% 0.83/1.09 % set(auto2) -> clear(print_initial_clauses).
% 0.83/1.09 % set(auto2) -> clear(print_given).
% 0.83/1.09 assign(lrs_ticks,-1).
% 0.83/1.09 assign(sos_limit,10000).
% 0.83/1.09 assign(order,kbo).
% 0.83/1.09 set(lex_order_vars).
% 0.83/1.09 clear(print_given).
% 0.83/1.09
% 0.83/1.09 % formulas(sos). % not echoed (5 formulas)
% 0.83/1.09
% 0.83/1.09 ============================== end of input ==========================
% 0.83/1.09
% 0.83/1.09 % From the command line: assign(max_seconds, 300).
% 0.83/1.09
% 0.83/1.09 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.83/1.09
% 0.83/1.09 % Formulas that are not ordinary clauses:
% 0.83/1.09
% 0.83/1.09 ============================== end of process non-clausal formulas ===
% 0.83/1.09
% 0.83/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.83/1.09
% 0.83/1.09 ============================== PREDICATE ELIMINATION =================
% 0.83/1.09
% 0.83/1.09 ============================== end predicate elimination =============
% 0.83/1.09
% 0.83/1.09 Auto_denials:
% 0.83/1.09 % copying label prove_these_axioms_4 to answer in negative clause
% 0.83/1.09
% 0.83/1.09 Term ordering decisions:
% 0.83/1.09
% 0.83/1.09 % Assigning unary symbol inverse kb_weight 0 and highest precedence (7).
% 0.83/1.09 Function symbol KB weights: identity=1. a=1. b=1. double_divide=1. multiply=1. inverse=0.
% 0.83/1.09
% 0.83/1.09 ============================== end of process initial clauses ========
% 0.83/1.09
% 0.83/1.09 ============================== CLAUSES FOR SEARCH ====================
% 0.83/1.09
% 0.83/1.09 ============================== end of clauses for search =============
% 0.83/1.09
% 0.83/1.09 ============================== SEARCH ================================
% 0.83/1.09
% 0.83/1.09 % Starting search at 0.01 seconds.
% 0.83/1.09
% 0.83/1.09 ============================== PROOF =================================
% 0.83/1.09 % SZS status Unsatisfiable
% 0.83/1.09 % SZS output start Refutation
% 0.83/1.09
% 0.83/1.09 % Proof 1 at 0.02 (+ 0.00) seconds: prove_these_axioms_4.
% 0.83/1.09 % Length of proof is 43.
% 0.83/1.09 % Level of proof is 17.
% 0.83/1.09 % Maximum clause weight is 29.000.
% 0.83/1.09 % Given clauses 29.
% 0.83/1.09
% 0.83/1.09 1 inverse(A) = double_divide(A,identity) # label(inverse) # label(axiom). [assumption].
% 0.83/1.09 2 identity = double_divide(A,inverse(A)) # label(identity) # label(axiom). [assumption].
% 0.83/1.09 3 double_divide(A,double_divide(A,identity)) = identity. [copy(2),rewrite([1(2)]),flip(a)].
% 0.83/1.09 4 multiply(A,B) = double_divide(double_divide(B,A),identity) # label(multiply) # label(axiom). [assumption].
% 0.83/1.09 5 double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B # label(single_axiom) # label(axiom). [assumption].
% 0.83/1.09 6 multiply(a,b) != multiply(b,a) # label(prove_these_axioms_4) # label(negated_conjecture) # answer(prove_these_axioms_4). [assumption].
% 0.83/1.09 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)])].
% 0.83/1.09 8 double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(A,identity))),double_divide(identity,identity)) = B. [para(3(a,1),5(a,1,1,2,1,2))].
% 0.83/1.09 9 double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),double_divide(identity,identity)) = A. [para(3(a,1),5(a,1,1,2,1))].
% 0.83/1.09 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(C,B)),double_divide(C,identity))). [para(5(a,1),5(a,1,1,2,1))].
% 0.83/1.09 12 double_divide(double_divide(double_divide(double_divide(A,identity),identity),identity),double_divide(identity,identity)) = A. [para(3(a,1),8(a,1,1,2))].
% 0.83/1.09 14 double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(double_divide(B,identity),double_divide(double_divide(A,identity),double_divide(B,identity))). [para(8(a,1),5(a,1,1,2,1))].
% 0.83/1.09 15 double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity. [para(3(a,1),9(a,1,1,2))].
% 0.83/1.09 16 double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(A,B),double_divide(double_divide(identity,double_divide(identity,double_divide(B,identity))),identity))),double_divide(identity,identity)) = A. [para(9(a,1),5(a,1,1,2,1,2))].
% 0.83/1.09 17 double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,double_divide(A,identity))). [para(9(a,1),5(a,1,1,2,1))].
% 0.83/1.09 18 double_divide(double_divide(double_divide(A,identity),A),double_divide(identity,identity)) = identity. [para(9(a,1),5(a,1,1,2))].
% 0.83/1.09 19 double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(A,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))). [back_rewrite(14),rewrite([17(10)]),flip(a)].
% 0.83/1.09 20 double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))). [back_rewrite(11),rewrite([17(10)]),flip(a)].
% 0.83/1.09 23 double_divide(double_divide(double_divide(identity,identity),double_divide(A,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,identity),identity))),identity))),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,double_divide(A,identity))). [para(9(a,1),16(a,1,1,2,1))].
% 0.83/1.09 24 double_divide(double_divide(A,identity),A) = double_divide(identity,identity). [para(18(a,1),16(a,1,1,2,1)),rewrite([23(21),3(6)]),flip(a)].
% 0.83/1.09 25 double_divide(double_divide(double_divide(identity,identity),double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(A,identity),identity),identity). [para(12(a,1),16(a,1,1,2,1)),rewrite([24(10),3(9),24(8)])].
% 0.83/1.09 26 double_divide(double_divide(identity,identity),double_divide(double_divide(A,B),double_divide(double_divide(identity,double_divide(identity,double_divide(B,identity))),identity))) = double_divide(double_divide(double_divide(A,identity),identity),identity). [para(16(a,1),16(a,1,1,2,1)),rewrite([24(10),3(9),24(8),25(12)]),flip(a)].
% 0.83/1.09 27 double_divide(double_divide(double_divide(A,identity),identity),identity) = double_divide(identity,double_divide(identity,double_divide(A,identity))). [back_rewrite(23),rewrite([24(10),3(9),24(8),25(12)])].
% 0.83/1.09 28 double_divide(double_divide(identity,identity),double_divide(double_divide(A,B),double_divide(double_divide(identity,double_divide(identity,double_divide(B,identity))),identity))) = double_divide(identity,double_divide(identity,double_divide(A,identity))). [back_rewrite(26),rewrite([27(20)])].
% 0.83/1.09 30 double_divide(identity,identity) = identity. [para(24(a,1),9(a,1,1,2,2)),rewrite([3(6),15(7)]),flip(a)].
% 0.83/1.09 32 double_divide(identity,double_divide(double_divide(A,B),double_divide(double_divide(identity,double_divide(identity,double_divide(B,identity))),identity))) = double_divide(identity,double_divide(identity,double_divide(A,identity))). [back_rewrite(28),rewrite([30(3)])].
% 0.83/1.09 33 double_divide(double_divide(A,identity),A) = identity. [back_rewrite(24),rewrite([30(6)])].
% 0.83/1.09 35 double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity) = A. [back_rewrite(9),rewrite([30(9)])].
% 0.83/1.09 36 double_divide(identity,double_divide(double_divide(A,B),B)) = double_divide(identity,double_divide(identity,double_divide(A,identity))). [back_rewrite(32),rewrite([35(10)])].
% 0.83/1.09 39 double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(identity,double_divide(identity,double_divide(A,identity))). [para(35(a,1),35(a,1,1,2,2))].
% 0.83/1.09 40 double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = A. [back_rewrite(35),rewrite([39(8)])].
% 0.83/1.09 42 double_divide(double_divide(A,identity),identity) = A. [para(33(a,1),19(a,1,2)),rewrite([40(12)])].
% 0.83/1.09 43 double_divide(identity,double_divide(identity,A)) = A. [back_rewrite(40),rewrite([42(6)])].
% 0.83/1.09 44 double_divide(identity,double_divide(double_divide(A,B),B)) = double_divide(A,identity). [back_rewrite(36),rewrite([43(10)])].
% 0.83/1.09 46 double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))) = double_divide(B,identity). [back_rewrite(20),rewrite([43(12)])].
% 0.83/1.09 50 double_divide(identity,double_divide(A,identity)) = A. [para(42(a,1),44(a,1,2,1)),rewrite([42(8)])].
% 0.83/1.09 51 double_divide(identity,A) = double_divide(A,identity). [para(42(a,1),44(a,1,2))].
% 0.83/1.09 52 double_divide(double_divide(A,B),B) = A. [para(44(a,1),43(a,1,2)),rewrite([50(4)]),flip(a)].
% 0.83/1.09 53 double_divide(identity,double_divide(b,a)) != double_divide(identity,double_divide(a,b)) # answer(prove_these_axioms_4). [back_rewrite(7),rewrite([51(5,R),51(10,R)])].
% 0.83/1.09 56 double_divide(A,double_divide(double_divide(B,identity),A)) = double_divide(B,identity). [para(33(a,1),46(a,1,2,1,2)),rewrite([51(6,R),50(6)])].
% 0.83/1.09 66 double_divide(A,double_divide(B,A)) = B. [para(52(a,1),56(a,1,2,1)),rewrite([51(6,R),50(6)])].
% 0.83/1.09 71 double_divide(A,B) = double_divide(B,A). [para(52(a,1),66(a,1,2))].
% 0.83/1.09 80 $F # answer(prove_these_axioms_4). [back_rewrite(53),rewrite([71(4)]),xx(a)].
% 0.83/1.09
% 0.83/1.09 % SZS output end Refutation
% 0.83/1.09 ============================== end of proof ==========================
% 0.83/1.09
% 0.83/1.09 ============================== STATISTICS ============================
% 0.83/1.09
% 0.83/1.09 Given=29. Generated=321. Kept=77. proofs=1.
% 0.83/1.09 Usable=5. Sos=4. Demods=17. Limbo=9, Disabled=64. Hints=0.
% 0.83/1.09 Megabytes=0.08.
% 0.83/1.09 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.83/1.09
% 0.83/1.09 ============================== end of statistics =====================
% 0.83/1.09
% 0.83/1.09 ============================== end of search =========================
% 0.83/1.09
% 0.83/1.09 THEOREM PROVED
% 0.83/1.09 % SZS status Unsatisfiable
% 0.83/1.09
% 0.83/1.09 Exiting with 1 proof.
% 0.83/1.09
% 0.83/1.09 Process 28797 exit (max_proofs) Mon Jun 13 13:36:08 2022
% 0.83/1.09 Prover9 interrupted
%------------------------------------------------------------------------------