TSTP Solution File: GRP483-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP483-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 11:19:17 EDT 2022
% Result : Unsatisfiable 0.72s 1.01s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP483-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 10:57:56 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.72/1.01 ============================== Prover9 ===============================
% 0.72/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.72/1.01 Process 5838 was started by sandbox2 on n029.cluster.edu,
% 0.72/1.01 Tue Jun 14 10:57:56 2022
% 0.72/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_5473_n029.cluster.edu".
% 0.72/1.01 ============================== end of head ===========================
% 0.72/1.01
% 0.72/1.01 ============================== INPUT =================================
% 0.72/1.01
% 0.72/1.01 % Reading from file /tmp/Prover9_5473_n029.cluster.edu
% 0.72/1.01
% 0.72/1.01 set(prolog_style_variables).
% 0.72/1.01 set(auto2).
% 0.72/1.01 % set(auto2) -> set(auto).
% 0.72/1.01 % set(auto) -> set(auto_inference).
% 0.72/1.01 % set(auto) -> set(auto_setup).
% 0.72/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.72/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/1.01 % set(auto) -> set(auto_limits).
% 0.72/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/1.01 % set(auto) -> set(auto_denials).
% 0.72/1.01 % set(auto) -> set(auto_process).
% 0.72/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.72/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.72/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.72/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.72/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.72/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.72/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.72/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.72/1.01 % set(auto2) -> assign(stats, some).
% 0.72/1.01 % set(auto2) -> clear(echo_input).
% 0.72/1.01 % set(auto2) -> set(quiet).
% 0.72/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.72/1.01 % set(auto2) -> clear(print_given).
% 0.72/1.01 assign(lrs_ticks,-1).
% 0.72/1.01 assign(sos_limit,10000).
% 0.72/1.01 assign(order,kbo).
% 0.72/1.01 set(lex_order_vars).
% 0.72/1.01 clear(print_given).
% 0.72/1.01
% 0.72/1.01 % formulas(sos). % not echoed (5 formulas)
% 0.72/1.01
% 0.72/1.01 ============================== end of input ==========================
% 0.72/1.01
% 0.72/1.01 % From the command line: assign(max_seconds, 300).
% 0.72/1.01
% 0.72/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/1.01
% 0.72/1.01 % Formulas that are not ordinary clauses:
% 0.72/1.01
% 0.72/1.01 ============================== end of process non-clausal formulas ===
% 0.72/1.01
% 0.72/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.72/1.01
% 0.72/1.01 ============================== PREDICATE ELIMINATION =================
% 0.72/1.01
% 0.72/1.01 ============================== end predicate elimination =============
% 0.72/1.01
% 0.72/1.01 Auto_denials:
% 0.72/1.01 % copying label prove_these_axioms_3 to answer in negative clause
% 0.72/1.01
% 0.72/1.01 Term ordering decisions:
% 0.72/1.01
% 0.72/1.01 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.72/1.01 Function symbol KB weights: identity=1. a3=1. b3=1. c3=1. double_divide=1. multiply=1. inverse=0.
% 0.72/1.01
% 0.72/1.01 ============================== end of process initial clauses ========
% 0.72/1.01
% 0.72/1.01 ============================== CLAUSES FOR SEARCH ====================
% 0.72/1.01
% 0.72/1.01 ============================== end of clauses for search =============
% 0.72/1.01
% 0.72/1.01 ============================== SEARCH ================================
% 0.72/1.01
% 0.72/1.01 % Starting search at 0.01 seconds.
% 0.72/1.01
% 0.72/1.01 ============================== PROOF =================================
% 0.72/1.01 % SZS status Unsatisfiable
% 0.72/1.01 % SZS output start Refutation
% 0.72/1.01
% 0.72/1.01 % Proof 1 at 0.04 (+ 0.00) seconds: prove_these_axioms_3.
% 0.72/1.01 % Length of proof is 51.
% 0.72/1.01 % Level of proof is 19.
% 0.72/1.01 % Maximum clause weight is 27.000.
% 0.72/1.01 % Given clauses 40.
% 0.72/1.01
% 0.72/1.01 1 inverse(A) = double_divide(A,identity) # label(inverse) # label(axiom). [assumption].
% 0.72/1.01 2 identity = double_divide(A,inverse(A)) # label(identity) # label(axiom). [assumption].
% 0.72/1.01 3 double_divide(A,double_divide(A,identity)) = identity. [copy(2),rewrite([1(2)]),flip(a)].
% 0.72/1.01 4 multiply(A,B) = double_divide(double_divide(B,A),identity) # label(multiply) # label(axiom). [assumption].
% 0.72/1.01 5 double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) = C # label(single_axiom) # label(axiom). [assumption].
% 0.72/1.01 6 double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,identity),double_divide(A,identity))),B) = C. [copy(5),rewrite([3(6)])].
% 0.72/1.01 7 multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # label(prove_these_axioms_3) # label(negated_conjecture) # answer(prove_these_axioms_3). [assumption].
% 0.72/1.01 8 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(7),rewrite([4(3),4(7),4(13),4(16)]),flip(a)].
% 0.72/1.01 9 double_divide(double_divide(double_divide(A,double_divide(identity,identity)),double_divide(double_divide(B,identity),double_divide(A,identity))),B) = identity. [para(6(a,1),3(a,1,2))].
% 0.72/1.01 10 double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,identity))),B) = A. [para(3(a,1),6(a,1,1,1))].
% 0.72/1.01 14 double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(C,double_divide(A,identity))),B) = double_divide(double_divide(D,double_divide(identity,identity)),double_divide(double_divide(C,identity),double_divide(D,identity))). [para(6(a,1),6(a,1,1,2,1))].
% 0.72/1.01 16 double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(identity,identity))),A) = identity. [para(3(a,1),9(a,1,1,1))].
% 0.72/1.01 21 double_divide(double_divide(identity,identity),double_divide(A,identity)) = A. [para(3(a,1),10(a,1,1,2))].
% 0.72/1.01 24 double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(C,double_divide(A,identity))),B) = double_divide(identity,double_divide(double_divide(C,identity),double_divide(identity,identity))). [para(10(a,1),6(a,1,1,2,1))].
% 0.72/1.01 28 double_divide(double_divide(A,double_divide(double_divide(B,identity),double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(double_divide(identity,identity),identity))),identity))),B) = identity. [para(10(a,1),9(a,1,1,1))].
% 0.72/1.01 31 double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),A) = double_divide(double_divide(B,double_divide(identity,identity)),B). [para(9(a,1),10(a,1,1,2,1)),rewrite([21(17)])].
% 0.72/1.01 32 double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),double_divide(double_divide(B,double_divide(identity,identity)),B)) = A. [para(9(a,1),10(a,1,1,2,2)),rewrite([21(16)])].
% 0.72/1.01 33 double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),B) = double_divide(identity,double_divide(double_divide(A,identity),double_divide(identity,identity))). [para(10(a,1),10(a,1,1,2,1))].
% 0.72/1.01 34 double_divide(double_divide(identity,double_divide(double_divide(A,identity),B)),double_divide(identity,double_divide(double_divide(B,identity),double_divide(identity,identity)))) = A. [para(10(a,1),10(a,1,1,2,2))].
% 0.72/1.01 35 double_divide(double_divide(A,double_divide(identity,identity)),double_divide(double_divide(B,identity),double_divide(A,identity))) = double_divide(identity,double_divide(double_divide(B,identity),double_divide(identity,identity))). [back_rewrite(14),rewrite([24(8)]),flip(a)].
% 0.72/1.01 36 double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),double_divide(identity,identity))) = A. [back_rewrite(6),rewrite([24(10)])].
% 0.72/1.01 37 double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),A) = c_0. [new_symbol(31)].
% 0.72/1.01 38 double_divide(double_divide(A,double_divide(identity,identity)),A) = c_0. [back_rewrite(31),rewrite([37(7)]),flip(a)].
% 0.72/1.01 39 double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),c_0) = A. [back_rewrite(32),rewrite([38(11)])].
% 0.72/1.01 40 double_divide(identity,identity) = identity. [para(21(a,1),3(a,1))].
% 0.72/1.01 43 double_divide(identity,double_divide(double_divide(A,identity),identity)) = double_divide(identity,A). [para(10(a,1),21(a,1,2)),rewrite([40(3),40(8)]),flip(a)].
% 0.72/1.01 44 double_divide(double_divide(A,identity),A) = c_0. [back_rewrite(38),rewrite([40(3)])].
% 0.72/1.01 45 double_divide(identity,double_divide(A,identity)) = A. [back_rewrite(36),rewrite([40(8),43(8)])].
% 0.72/1.01 46 double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(A,identity))) = double_divide(B,identity). [back_rewrite(35),rewrite([40(3),40(14),45(14)])].
% 0.72/1.01 47 double_divide(double_divide(identity,double_divide(double_divide(A,identity),B)),double_divide(B,identity)) = A. [back_rewrite(34),rewrite([40(11),45(11)])].
% 0.72/1.01 48 double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),B) = double_divide(A,identity). [back_rewrite(33),rewrite([40(12),45(12)])].
% 0.72/1.01 51 double_divide(double_divide(A,double_divide(double_divide(B,identity),double_divide(double_divide(A,identity),identity))),B) = identity. [back_rewrite(28),rewrite([40(8),40(8),45(8)])].
% 0.72/1.01 53 double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(C,double_divide(A,identity))),B) = double_divide(C,identity). [back_rewrite(24),rewrite([40(14),45(14)])].
% 0.72/1.01 56 c_0 = identity. [back_rewrite(16),rewrite([40(6),45(6),44(3)])].
% 0.72/1.01 57 double_divide(double_divide(A,identity),identity) = A. [back_rewrite(39),rewrite([45(6),56(3)])].
% 0.72/1.01 59 double_divide(double_divide(A,double_divide(double_divide(B,identity),A)),B) = identity. [back_rewrite(51),rewrite([57(6)])].
% 0.72/1.01 64 double_divide(identity,A) = double_divide(A,identity). [para(57(a,1),45(a,1,2))].
% 0.72/1.01 67 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(8),rewrite([64(5,R),64(9,R),64(15,R),64(18,R)])].
% 0.72/1.01 70 double_divide(A,double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,identity)))) = B. [para(46(a,1),47(a,1,1,2)),rewrite([45(4),64(7,R)])].
% 0.72/1.01 71 double_divide(identity,double_divide(A,double_divide(B,A))) = double_divide(B,identity). [para(59(a,1),48(a,1,1,2)),rewrite([40(3),64(2),64(6,R),45(6),64(6,R)]),flip(a)].
% 0.72/1.01 73 double_divide(identity,double_divide(identity,double_divide(A,B))) = double_divide(A,B). [para(48(a,1),48(a,1,1,2)),rewrite([45(4),64(6,R),45(6),64(6,R)]),flip(a)].
% 0.72/1.01 77 double_divide(identity,double_divide(double_divide(A,identity),B)) = double_divide(double_divide(B,identity),A). [para(47(a,1),71(a,1,2,2)),rewrite([64(12,R),73(12)])].
% 0.72/1.01 78 double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(B,double_divide(A,identity)). [para(48(a,1),71(a,1,2,2)),rewrite([64(12,R),73(12)])].
% 0.72/1.01 79 double_divide(A,double_divide(B,A)) = B. [back_rewrite(70),rewrite([78(7),64(4,R),45(4)])].
% 0.72/1.01 82 double_divide(double_divide(A,B),A) = B. [para(79(a,1),79(a,1,2))].
% 0.72/1.01 89 double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(identity,double_divide(B,A)). [para(82(a,1),77(a,1,2,1)),rewrite([64(7)]),flip(a)].
% 0.72/1.01 98 double_divide(double_divide(double_divide(A,double_divide(B,identity)),C),B) = double_divide(double_divide(C,identity),A). [para(82(a,1),53(a,1,1,2)),rewrite([64(10,R),77(10)])].
% 0.72/1.01 99 double_divide(double_divide(identity,double_divide(A,B)),double_divide(B,identity)) = double_divide(A,identity). [para(77(a,1),53(a,1,1,1)),rewrite([40(3),64(2),40(5),89(5)])].
% 0.72/1.01 102 double_divide(identity,double_divide(double_divide(A,B),double_divide(C,double_divide(A,identity)))) = double_divide(C,B). [para(53(a,1),53(a,1,1,2)),rewrite([98(7),64(4,R),79(4),64(5,R),79(5),64(8,R)]),flip(a)].
% 0.72/1.01 160 double_divide(double_divide(identity,double_divide(A,B)),C) = double_divide(A,double_divide(identity,double_divide(B,C))). [para(99(a,1),102(a,1,2,2)),rewrite([78(6),64(3,R)]),flip(a)].
% 0.72/1.01 162 $F # answer(prove_these_axioms_3). [back_rewrite(67),rewrite([160(8)]),xx(a)].
% 0.72/1.01
% 0.72/1.01 % SZS output end Refutation
% 0.72/1.01 ============================== end of proof ==========================
% 0.72/1.01
% 0.72/1.01 ============================== STATISTICS ============================
% 0.72/1.01
% 0.72/1.01 Given=40. Generated=1112. Kept=158. proofs=1.
% 0.72/1.01 Usable=12. Sos=17. Demods=30. Limbo=2, Disabled=132. Hints=0.
% 0.72/1.01 Megabytes=0.15.
% 0.72/1.01 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.72/1.01
% 0.72/1.01 ============================== end of statistics =====================
% 0.72/1.01
% 0.72/1.01 ============================== end of search =========================
% 0.72/1.01
% 0.72/1.01 THEOREM PROVED
% 0.72/1.01 % SZS status Unsatisfiable
% 0.72/1.01
% 0.72/1.01 Exiting with 1 proof.
% 0.72/1.01
% 0.72/1.01 Process 5838 exit (max_proofs) Tue Jun 14 10:57:56 2022
% 0.72/1.01 Prover9 interrupted
%------------------------------------------------------------------------------