TSTP Solution File: NUN062+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUN062+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 : Mon Jul 18 16:37:06 EDT 2022
% Result : Theorem 0.82s 1.09s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN062+2 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n028.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 : Thu Jun 2 02:48:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.73/0.99 ============================== Prover9 ===============================
% 0.73/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.73/0.99 Process 8160 was started by sandbox on n028.cluster.edu,
% 0.73/0.99 Thu Jun 2 02:48:53 2022
% 0.73/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_8007_n028.cluster.edu".
% 0.73/0.99 ============================== end of head ===========================
% 0.73/0.99
% 0.73/0.99 ============================== INPUT =================================
% 0.73/0.99
% 0.73/0.99 % Reading from file /tmp/Prover9_8007_n028.cluster.edu
% 0.73/0.99
% 0.73/0.99 set(prolog_style_variables).
% 0.73/0.99 set(auto2).
% 0.73/0.99 % set(auto2) -> set(auto).
% 0.73/0.99 % set(auto) -> set(auto_inference).
% 0.73/0.99 % set(auto) -> set(auto_setup).
% 0.73/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.73/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/0.99 % set(auto) -> set(auto_limits).
% 0.73/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/0.99 % set(auto) -> set(auto_denials).
% 0.73/0.99 % set(auto) -> set(auto_process).
% 0.73/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.73/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.73/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.73/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.73/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.73/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.73/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.73/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.73/0.99 % set(auto2) -> assign(stats, some).
% 0.73/0.99 % set(auto2) -> clear(echo_input).
% 0.73/0.99 % set(auto2) -> set(quiet).
% 0.73/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.73/0.99 % set(auto2) -> clear(print_given).
% 0.73/0.99 assign(lrs_ticks,-1).
% 0.73/0.99 assign(sos_limit,10000).
% 0.73/0.99 assign(order,kbo).
% 0.73/0.99 set(lex_order_vars).
% 0.73/0.99 clear(print_given).
% 0.73/0.99
% 0.73/0.99 % formulas(sos). % not echoed (12 formulas)
% 0.73/0.99
% 0.73/0.99 ============================== end of input ==========================
% 0.73/0.99
% 0.73/0.99 % From the command line: assign(max_seconds, 300).
% 0.73/0.99
% 0.73/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/0.99
% 0.73/0.99 % Formulas that are not ordinary clauses:
% 0.73/0.99 1 (exists Y24 all X19 (-r1(X19) & X19 != Y24 | r1(X19) & X19 = Y24)) # label(axiom_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 2 (all X11 exists Y21 all X12 (-r2(X11,X12) & X12 != Y21 | r2(X11,X12) & X12 = Y21)) # label(axiom_2) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 3 (all X13 all X14 exists Y22 all X15 (-r3(X13,X14,X15) & X15 != Y22 | r3(X13,X14,X15) & X15 = Y22)) # label(axiom_3) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 4 (all X16 all X17 exists Y23 all X18 (-r4(X16,X17,X18) & X18 != Y23 | r4(X16,X17,X18) & X18 = Y23)) # label(axiom_4) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 5 (all X1 all X8 exists Y4 ((exists Y5 ((exists Y15 (r2(X8,Y15) & r3(X1,Y15,Y5))) & Y5 = Y4)) & (exists Y7 (r2(Y7,Y4) & r3(X1,X8,Y7))))) # label(axiom_1a) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 6 (all X2 all X9 exists Y2 ((exists Y3 ((exists Y14 (r2(X9,Y14) & r4(X2,Y14,Y3))) & Y3 = Y2)) & (exists Y6 (r3(Y6,X2,Y2) & r4(X2,X9,Y6))))) # label(axiom_2a) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 7 (all X3 all X10 ((all Y12 ((all Y13 (-r2(X3,Y13) | Y13 != Y12)) | -r2(X10,Y12))) | X3 = X10)) # label(axiom_3a) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 8 (all X4 exists Y9 ((exists Y16 (r1(Y16) & r3(X4,Y16,Y9))) & Y9 = X4)) # label(axiom_4a) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 9 (all X5 exists Y8 ((exists Y17 (r1(Y17) & r4(X5,Y17,Y8))) & (exists Y18 (r1(Y18) & Y8 = Y18)))) # label(axiom_5a) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 10 (all X6 ((exists Y19 (r1(Y19) & X6 = Y19)) | (exists Y1 exists Y11 (r2(Y1,Y11) & X6 = Y11)))) # label(axiom_6a) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 11 (all X7 all Y10 ((all Y20 (-r1(Y20) | Y20 != Y10)) | -r2(X7,Y10))) # label(axiom_7a) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 12 -(all X1 exists Y2 exists Y1 ((all Y4 (-r1(Y4) | Y1 != Y4)) & (exists Y3 (r3(X1,Y1,Y3) & Y3 = Y2)))) # label(infiniteNumbers) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.82/1.09
% 0.82/1.09 ============================== end of process non-clausal formulas ===
% 0.82/1.09
% 0.82/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.09
% 0.82/1.09 ============================== PREDICATE ELIMINATION =================
% 0.82/1.09 13 -r1(A) | A != B | -r2(C,B) # label(axiom_7a) # label(axiom). [clausify(11)].
% 0.82/1.09 14 r1(f13(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.82/1.09 15 r1(f15(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.82/1.09 16 r1(f16(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.82/1.09 17 r1(f17(A)) | f19(A) = A # label(axiom_6a) # label(axiom). [clausify(10)].
% 0.82/1.09 18 r1(f17(A)) | r2(f18(A),f19(A)) # label(axiom_6a) # label(axiom). [clausify(10)].
% 0.82/1.09 Derived: f13(A) != B | -r2(C,B). [resolve(13,a,14,a)].
% 0.82/1.09 Derived: f15(A) != B | -r2(C,B). [resolve(13,a,15,a)].
% 0.82/1.09 Derived: f16(A) != B | -r2(C,B). [resolve(13,a,16,a)].
% 0.82/1.09 Derived: f17(A) != B | -r2(C,B) | f19(A) = A. [resolve(13,a,17,a)].
% 0.82/1.09 Derived: f17(A) != B | -r2(C,B) | r2(f18(A),f19(A)). [resolve(13,a,18,a)].
% 0.82/1.09 19 -r1(A) | A = c1 # label(axiom_1) # label(axiom). [clausify(1)].
% 0.82/1.09 Derived: f13(A) = c1. [resolve(19,a,14,a)].
% 0.82/1.09 Derived: f15(A) = c1. [resolve(19,a,15,a)].
% 0.82/1.09 Derived: f16(A) = c1. [resolve(19,a,16,a)].
% 0.82/1.09 Derived: f17(A) = c1 | f19(A) = A. [resolve(19,a,17,a)].
% 0.82/1.09 Derived: f17(A) = c1 | r2(f18(A),f19(A)). [resolve(19,a,18,a)].
% 0.82/1.09 20 A != c1 | r1(A) # label(axiom_1) # label(axiom). [clausify(1)].
% 0.82/1.09 Derived: A != c1 | A != B | -r2(C,B). [resolve(20,b,13,a)].
% 0.82/1.09 21 r1(f20(A,B)) | -r3(c2,B,C) | C != A # label(infiniteNumbers) # label(negated_conjecture). [clausify(12)].
% 0.82/1.09 Derived: -r3(c2,A,B) | B != C | f20(C,A) != D | -r2(E,D). [resolve(21,a,13,a)].
% 0.82/1.09 Derived: -r3(c2,A,B) | B != C | f20(C,A) = c1. [resolve(21,a,19,a)].
% 0.82/1.09 22 -r4(A,B,C) | C = f3(A,B) # label(axiom_4) # label(axiom). [clausify(4)].
% 0.82/1.09 23 r4(A,B,f11(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.82/1.09 24 r4(A,f15(A),f14(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.82/1.09 25 r4(A,f10(A,B),f9(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.82/1.09 Derived: f11(A,B) = f3(A,B). [resolve(22,a,23,a)].
% 0.82/1.09 Derived: f14(A) = f3(A,f15(A)). [resolve(22,a,24,a)].
% 0.82/1.09 Derived: f9(A,B) = f3(A,f10(A,B)). [resolve(22,a,25,a)].
% 0.82/1.09 26 A != f3(B,C) | r4(B,C,A) # label(axiom_4) # label(axiom). [clausify(4)].
% 0.82/1.09
% 0.82/1.09 ============================== end predicate elimination =============
% 0.82/1.09
% 0.82/1.09 Auto_denials: (non-Horn, no changes).
% 0.82/1.09
% 0.82/1.09 Term ordering decisions:
% 0.82/1.09 Function symbol KB weights: c1=1. c2=1. f2=1. f3=1. f4=1. f5=1. f6=1. f7=1. f8=1. f9=1. f10=1. f11=1. f20=1. f1=1. f12=1. f13=1. f14=1. f15=1. f16=1. f17=1. f18=1. f19=1.
% 0.82/1.09
% 0.82/1.09 ============================== end of process initial clauses ========
% 0.82/1.09
% 0.82/1.09 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.09
% 0.82/1.09 ============================== end of clauses for search =============
% 0.82/1.09
% 0.82/1.09 ============================== SEARCH ================================
% 0.82/1.09
% 0.82/1.09 % Starting search at 0.02 seconds.
% 0.82/1.09
% 0.82/1.09 ============================== PROOF =================================
% 0.82/1.09 % SZS status Theorem
% 0.82/1.09 % SZS output start Refutation
% 0.82/1.09
% 0.82/1.09 % Proof 1 at 0.11 (+ 0.00) seconds.
% 0.82/1.09 % Length of proof is 55.
% 0.82/1.09 % Level of proof is 8.
% 0.82/1.09 % Maximum clause weight is 15.000.
% 0.82/1.09 % Given clauses 186.
% 0.82/1.09
% 0.82/1.09 1 (exists Y24 all X19 (-r1(X19) & X19 != Y24 | r1(X19) & X19 = Y24)) # label(axiom_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 2 (all X11 exists Y21 all X12 (-r2(X11,X12) & X12 != Y21 | r2(X11,X12) & X12 = Y21)) # label(axiom_2) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 3 (all X13 all X14 exists Y22 all X15 (-r3(X13,X14,X15) & X15 != Y22 | r3(X13,X14,X15) & X15 = Y22)) # label(axiom_3) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 5 (all X1 all X8 exists Y4 ((exists Y5 ((exists Y15 (r2(X8,Y15) & r3(X1,Y15,Y5))) & Y5 = Y4)) & (exists Y7 (r2(Y7,Y4) & r3(X1,X8,Y7))))) # label(axiom_1a) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 8 (all X4 exists Y9 ((exists Y16 (r1(Y16) & r3(X4,Y16,Y9))) & Y9 = X4)) # label(axiom_4a) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 10 (all X6 ((exists Y19 (r1(Y19) & X6 = Y19)) | (exists Y1 exists Y11 (r2(Y1,Y11) & X6 = Y11)))) # label(axiom_6a) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 11 (all X7 all Y10 ((all Y20 (-r1(Y20) | Y20 != Y10)) | -r2(X7,Y10))) # label(axiom_7a) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 12 -(all X1 exists Y2 exists Y1 ((all Y4 (-r1(Y4) | Y1 != Y4)) & (exists Y3 (r3(X1,Y1,Y3) & Y3 = Y2)))) # label(infiniteNumbers) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.82/1.09 13 -r1(A) | A != B | -r2(C,B) # label(axiom_7a) # label(axiom). [clausify(11)].
% 0.82/1.09 14 r1(f13(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.82/1.09 17 r1(f17(A)) | f19(A) = A # label(axiom_6a) # label(axiom). [clausify(10)].
% 0.82/1.09 18 r1(f17(A)) | r2(f18(A),f19(A)) # label(axiom_6a) # label(axiom). [clausify(10)].
% 0.82/1.09 19 -r1(A) | A = c1 # label(axiom_1) # label(axiom). [clausify(1)].
% 0.82/1.09 20 A != c1 | r1(A) # label(axiom_1) # label(axiom). [clausify(1)].
% 0.82/1.09 21 r1(f20(A,B)) | -r3(c2,B,C) | C != A # label(infiniteNumbers) # label(negated_conjecture). [clausify(12)].
% 0.82/1.09 27 f12(A) = A # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.82/1.09 28 r2(A,f6(B,A)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.82/1.09 31 r3(A,B,f7(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.82/1.09 32 r3(A,f13(A),f12(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.82/1.09 33 r3(A,f13(A),A). [copy(32),rewrite([27(2)])].
% 0.82/1.09 34 f5(A,B) = f4(A,B) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.82/1.09 37 r3(A,f6(A,B),f5(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.82/1.09 38 r3(A,f6(A,B),f4(A,B)). [copy(37),rewrite([34(2)])].
% 0.82/1.09 40 f17(A) = A | f19(A) = A # label(axiom_6a) # label(axiom). [clausify(10)].
% 0.82/1.09 41 f17(A) = A | r2(f18(A),f19(A)) # label(axiom_6a) # label(axiom). [clausify(10)].
% 0.82/1.09 42 -r2(A,B) | B = f1(A) # label(axiom_2) # label(axiom). [clausify(2)].
% 0.82/1.09 43 -r2(A,B) | f1(A) = B. [copy(42),flip(b)].
% 0.82/1.09 44 A != f1(B) | r2(B,A) # label(axiom_2) # label(axiom). [clausify(2)].
% 0.82/1.09 45 f1(A) != B | r2(A,B). [copy(44),flip(a)].
% 0.82/1.09 46 -r3(A,B,C) | C = f2(A,B) # label(axiom_3) # label(axiom). [clausify(3)].
% 0.82/1.09 47 -r3(A,B,C) | f2(A,B) = C. [copy(46),flip(b)].
% 0.82/1.09 51 A = f20(B,A) | -r3(c2,A,C) | C != B # label(infiniteNumbers) # label(negated_conjecture). [clausify(12)].
% 0.82/1.09 52 f20(A,B) = B | -r3(c2,B,C) | C != A. [copy(51),flip(a)].
% 0.82/1.09 59 f13(A) = c1. [resolve(19,a,14,a)].
% 0.82/1.09 63 f17(A) = c1 | f19(A) = A. [resolve(19,a,17,a)].
% 0.82/1.09 64 f17(A) = c1 | r2(f18(A),f19(A)). [resolve(19,a,18,a)].
% 0.82/1.09 65 A != c1 | A != B | -r2(C,B). [resolve(20,b,13,a)].
% 0.82/1.09 66 c1 != A | A != B | -r2(C,B). [copy(65),flip(a)].
% 0.82/1.09 67 -r3(c2,A,B) | B != C | f20(C,A) != D | -r2(E,D). [resolve(21,a,13,a)].
% 0.82/1.09 75 r3(A,c1,A). [back_rewrite(33),rewrite([59(1)])].
% 0.82/1.09 77 -r2(A,c1). [factor(66,a,b),xx(a)].
% 0.82/1.09 80 f17(A) = A | r2(f18(A),A). [para(40(b,1),41(b,2)),merge(b)].
% 0.82/1.09 84 f6(A,B) = f1(B). [resolve(43,a,28,a),flip(a)].
% 0.82/1.09 87 r3(A,f1(B),f4(A,B)). [back_rewrite(38),rewrite([84(1)])].
% 0.82/1.09 89 f7(A,B) = f2(A,B). [resolve(47,a,31,a),flip(a)].
% 0.82/1.09 92 r3(A,B,f2(A,B)). [back_rewrite(31),rewrite([89(1)])].
% 0.82/1.09 103 f17(A) = c1 | r2(f18(A),A). [para(63(b,1),64(b,2)),merge(b)].
% 0.82/1.09 110 f2(A,c1) = A. [resolve(75,a,47,a)].
% 0.82/1.09 112 f1(A) != c1. [ur(45,b,77,a)].
% 0.82/1.09 151 f20(A,B) = B | f2(c2,B) != A. [resolve(92,a,52,b)].
% 0.82/1.09 158 f2(A,f1(B)) = f4(A,B). [resolve(87,a,47,a)].
% 0.82/1.09 160 -r2(A,f20(f4(c2,B),f1(B))). [ur(67,a,87,a,b,110,a(flip),c,110,a(flip)),rewrite([110(4),110(6)])].
% 0.82/1.09 238 f17(f20(f4(c2,A),f1(A))) = c1. [resolve(160,a,103,b)].
% 0.82/1.09 239 f20(f4(c2,A),f1(A)) = c1. [resolve(160,a,80,b),rewrite([238(5)]),flip(a)].
% 0.82/1.09 643 $F. [resolve(151,b,158,a),rewrite([239(4)]),flip(a),unit_del(a,112)].
% 0.82/1.09
% 0.82/1.09 % SZS output end Refutation
% 0.82/1.09 ============================== end of proof ==========================
% 0.82/1.09
% 0.82/1.09 ============================== STATISTICS ============================
% 0.82/1.09
% 0.82/1.09 Given=186. Generated=3325. Kept=604. proofs=1.
% 0.82/1.09 Usable=163. Sos=366. Demods=38. Limbo=0, Disabled=124. Hints=0.
% 0.82/1.09 Megabytes=0.59.
% 0.82/1.09 User_CPU=0.12, System_CPU=0.00, Wall_clock=0.
% 0.82/1.09
% 0.82/1.09 ============================== end of statistics =====================
% 0.82/1.09
% 0.82/1.09 ============================== end of search =========================
% 0.82/1.09
% 0.82/1.09 THEOREM PROVED
% 0.82/1.09 % SZS status Theorem
% 0.82/1.09
% 0.82/1.09 Exiting with 1 proof.
% 0.82/1.09
% 0.82/1.09 Process 8160 exit (max_proofs) Thu Jun 2 02:48:53 2022
% 0.82/1.09 Prover9 interrupted
%------------------------------------------------------------------------------