TSTP Solution File: GRP575-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP575-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 0.73s 1.03s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP575-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 14 05:07:44 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.73/1.03 ============================== Prover9 ===============================
% 0.73/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.73/1.03 Process 10419 was started by sandbox2 on n013.cluster.edu,
% 0.73/1.03 Tue Jun 14 05:07:44 2022
% 0.73/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_10142_n013.cluster.edu".
% 0.73/1.03 ============================== end of head ===========================
% 0.73/1.03
% 0.73/1.03 ============================== INPUT =================================
% 0.73/1.03
% 0.73/1.03 % Reading from file /tmp/Prover9_10142_n013.cluster.edu
% 0.73/1.03
% 0.73/1.03 set(prolog_style_variables).
% 0.73/1.03 set(auto2).
% 0.73/1.03 % set(auto2) -> set(auto).
% 0.73/1.03 % set(auto) -> set(auto_inference).
% 0.73/1.03 % set(auto) -> set(auto_setup).
% 0.73/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.73/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/1.03 % set(auto) -> set(auto_limits).
% 0.73/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/1.03 % set(auto) -> set(auto_denials).
% 0.73/1.03 % set(auto) -> set(auto_process).
% 0.73/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.73/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.73/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.73/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.73/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.73/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.73/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.73/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.73/1.03 % set(auto2) -> assign(stats, some).
% 0.73/1.03 % set(auto2) -> clear(echo_input).
% 0.73/1.03 % set(auto2) -> set(quiet).
% 0.73/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.73/1.03 % set(auto2) -> clear(print_given).
% 0.73/1.03 assign(lrs_ticks,-1).
% 0.73/1.03 assign(sos_limit,10000).
% 0.73/1.03 assign(order,kbo).
% 0.73/1.03 set(lex_order_vars).
% 0.73/1.03 clear(print_given).
% 0.73/1.03
% 0.73/1.03 % formulas(sos). % not echoed (5 formulas)
% 0.73/1.03
% 0.73/1.03 ============================== end of input ==========================
% 0.73/1.03
% 0.73/1.03 % From the command line: assign(max_seconds, 300).
% 0.73/1.03
% 0.73/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/1.03
% 0.73/1.03 % Formulas that are not ordinary clauses:
% 0.73/1.03
% 0.73/1.03 ============================== end of process non-clausal formulas ===
% 0.73/1.03
% 0.73/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.03
% 0.73/1.03 ============================== PREDICATE ELIMINATION =================
% 0.73/1.03
% 0.73/1.03 ============================== end predicate elimination =============
% 0.73/1.03
% 0.73/1.03 Auto_denials:
% 0.73/1.03 % copying label prove_these_axioms_3 to answer in negative clause
% 0.73/1.03
% 0.73/1.03 Term ordering decisions:
% 0.73/1.03
% 0.73/1.03 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.73/1.03 Function symbol KB weights: identity=1. a3=1. b3=1. c3=1. double_divide=1. multiply=1. inverse=0.
% 0.73/1.03
% 0.73/1.03 ============================== end of process initial clauses ========
% 0.73/1.03
% 0.73/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.03
% 0.73/1.03 ============================== end of clauses for search =============
% 0.73/1.03
% 0.73/1.03 ============================== SEARCH ================================
% 0.73/1.03
% 0.73/1.03 % Starting search at 0.01 seconds.
% 0.73/1.03
% 0.73/1.03 ============================== PROOF =================================
% 0.73/1.03 % SZS status Unsatisfiable
% 0.73/1.03 % SZS output start Refutation
% 0.73/1.03
% 0.73/1.03 % Proof 1 at 0.03 (+ 0.00) seconds: prove_these_axioms_3.
% 0.73/1.03 % Length of proof is 52.
% 0.73/1.03 % Level of proof is 20.
% 0.73/1.03 % Maximum clause weight is 29.000.
% 0.73/1.03 % Given clauses 42.
% 0.73/1.03
% 0.73/1.03 1 inverse(A) = double_divide(A,identity) # label(inverse) # label(axiom). [assumption].
% 0.73/1.03 2 identity = double_divide(A,inverse(A)) # label(identity) # label(axiom). [assumption].
% 0.73/1.03 3 double_divide(A,double_divide(A,identity)) = identity. [copy(2),rewrite([1(2)]),flip(a)].
% 0.73/1.03 4 multiply(A,B) = double_divide(double_divide(B,A),identity) # label(multiply) # label(axiom). [assumption].
% 0.73/1.03 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].
% 0.73/1.03 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].
% 0.73/1.03 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)].
% 0.73/1.03 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))].
% 0.73/1.03 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))].
% 0.73/1.03 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(C,B)),double_divide(C,identity))). [para(5(a,1),5(a,1,1,2,1))].
% 0.73/1.03 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))].
% 0.73/1.03 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))].
% 0.73/1.03 15 double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity. [para(3(a,1),9(a,1,1,2))].
% 0.73/1.03 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))].
% 0.73/1.03 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))].
% 0.73/1.03 18 double_divide(double_divide(double_divide(A,identity),A),double_divide(identity,identity)) = identity. [para(9(a,1),5(a,1,1,2))].
% 0.73/1.03 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)].
% 0.73/1.03 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)].
% 0.73/1.03 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))].
% 0.73/1.03 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)].
% 0.73/1.03 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)])].
% 0.73/1.03 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)].
% 0.73/1.03 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)])].
% 0.73/1.03 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)])].
% 0.73/1.03 30 double_divide(identity,identity) = identity. [para(24(a,1),9(a,1,1,2,2)),rewrite([3(6),15(7)]),flip(a)].
% 0.73/1.03 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)])].
% 0.73/1.03 33 double_divide(double_divide(A,identity),A) = identity. [back_rewrite(24),rewrite([30(6)])].
% 0.73/1.03 35 double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity) = A. [back_rewrite(9),rewrite([30(9)])].
% 0.73/1.03 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)])].
% 0.73/1.03 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))].
% 0.73/1.03 40 double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = A. [back_rewrite(35),rewrite([39(8)])].
% 0.73/1.03 42 double_divide(double_divide(A,identity),identity) = A. [para(33(a,1),19(a,1,2)),rewrite([40(12)])].
% 0.73/1.03 43 double_divide(identity,double_divide(identity,A)) = A. [back_rewrite(40),rewrite([42(6)])].
% 0.73/1.03 44 double_divide(identity,double_divide(double_divide(A,B),B)) = double_divide(A,identity). [back_rewrite(36),rewrite([43(10)])].
% 0.73/1.03 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)])].
% 0.73/1.03 50 double_divide(identity,double_divide(A,identity)) = A. [para(42(a,1),44(a,1,2,1)),rewrite([42(8)])].
% 0.73/1.03 51 double_divide(identity,A) = double_divide(A,identity). [para(42(a,1),44(a,1,2))].
% 0.73/1.03 52 double_divide(double_divide(A,B),B) = A. [para(44(a,1),43(a,1,2)),rewrite([50(4)]),flip(a)].
% 0.73/1.03 53 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([51(5,R),51(9,R),51(15,R),51(18,R)])].
% 0.73/1.03 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)])].
% 0.73/1.03 58 double_divide(double_divide(A,identity),double_divide(identity,double_divide(B,A))) = double_divide(B,identity). [para(50(a,1),46(a,1,2,1,2)),rewrite([30(6),51(5,R)])].
% 0.73/1.03 61 double_divide(identity,double_divide(A,double_divide(B,C))) = double_divide(C,double_divide(A,double_divide(B,identity))). [para(52(a,1),46(a,1,2,1)),rewrite([51(8,R)]),flip(a)].
% 0.73/1.03 66 double_divide(A,double_divide(B,A)) = B. [para(52(a,1),56(a,1,2,1)),rewrite([51(6,R),50(6)])].
% 0.73/1.03 70 double_divide(A,double_divide(A,B)) = B. [para(66(a,1),52(a,1,1))].
% 0.73/1.03 71 double_divide(A,B) = double_divide(B,A). [para(52(a,1),66(a,1,2))].
% 0.73/1.03 78 double_divide(double_divide(A,identity),double_divide(identity,double_divide(A,B))) = double_divide(B,identity). [back_rewrite(58),rewrite([71(4)])].
% 0.73/1.03 80 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(53),rewrite([71(5),71(8),71(15)]),flip(a)].
% 0.73/1.03 81 double_divide(A,double_divide(B,A)) = B. [back_rewrite(52),rewrite([71(2)])].
% 0.73/1.03 84 double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(identity,double_divide(A,B)). [para(78(a,1),70(a,1,2))].
% 0.73/1.03 91 double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))) != double_divide(double_divide(identity,c3),double_divide(a3,b3)) # answer(prove_these_axioms_3). [para(61(a,1),80(a,1)),rewrite([30(7),71(6),71(7)]),flip(a)].
% 0.73/1.03 104 double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(double_divide(C,identity),double_divide(A,B)). [para(84(a,1),61(a,1,2,2)),rewrite([71(12),81(12)])].
% 0.73/1.03 109 $F # answer(prove_these_axioms_3). [back_rewrite(91),rewrite([104(9),71(3)]),xx(a)].
% 0.73/1.03
% 0.73/1.03 % SZS output end Refutation
% 0.73/1.03 ============================== end of proof ==========================
% 0.73/1.03
% 0.73/1.03 ============================== STATISTICS ============================
% 0.73/1.03
% 0.73/1.03 Given=42. Generated=535. Kept=106. proofs=1.
% 0.73/1.03 Usable=11. Sos=16. Demods=27. Limbo=5, Disabled=79. Hints=0.
% 0.73/1.03 Megabytes=0.10.
% 0.73/1.03 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.73/1.03
% 0.73/1.03 ============================== end of statistics =====================
% 0.73/1.03
% 0.73/1.03 ============================== end of search =========================
% 0.73/1.03
% 0.73/1.03 THEOREM PROVED
% 0.73/1.03 % SZS status Unsatisfiable
% 0.73/1.03
% 0.73/1.03 Exiting with 1 proof.
% 0.73/1.03
% 0.73/1.03 Process 10419 exit (max_proofs) Tue Jun 14 05:07:44 2022
% 0.73/1.03 Prover9 interrupted
%------------------------------------------------------------------------------