TSTP Solution File: NUN068+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUN068+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 16:37:11 EDT 2022
% Result : Theorem 1.10s 1.43s
% Output : Refutation 1.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUN068+2 : TPTP v8.1.0. Released v7.3.0.
% 0.13/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 2 08:18:45 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.46/1.04 ============================== Prover9 ===============================
% 0.46/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.04 Process 4747 was started by sandbox on n018.cluster.edu,
% 0.46/1.04 Thu Jun 2 08:18:45 2022
% 0.46/1.04 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4593_n018.cluster.edu".
% 0.46/1.04 ============================== end of head ===========================
% 0.46/1.04
% 0.46/1.04 ============================== INPUT =================================
% 0.46/1.04
% 0.46/1.04 % Reading from file /tmp/Prover9_4593_n018.cluster.edu
% 0.46/1.04
% 0.46/1.04 set(prolog_style_variables).
% 0.46/1.04 set(auto2).
% 0.46/1.04 % set(auto2) -> set(auto).
% 0.46/1.04 % set(auto) -> set(auto_inference).
% 0.46/1.04 % set(auto) -> set(auto_setup).
% 0.46/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.04 % set(auto) -> set(auto_limits).
% 0.46/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.04 % set(auto) -> set(auto_denials).
% 0.46/1.04 % set(auto) -> set(auto_process).
% 0.46/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.04 % set(auto2) -> assign(stats, some).
% 0.46/1.04 % set(auto2) -> clear(echo_input).
% 0.46/1.04 % set(auto2) -> set(quiet).
% 0.46/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.04 % set(auto2) -> clear(print_given).
% 0.46/1.04 assign(lrs_ticks,-1).
% 0.46/1.04 assign(sos_limit,10000).
% 0.46/1.04 assign(order,kbo).
% 0.46/1.04 set(lex_order_vars).
% 0.46/1.04 clear(print_given).
% 0.46/1.04
% 0.46/1.04 % formulas(sos). % not echoed (12 formulas)
% 0.46/1.04
% 0.46/1.04 ============================== end of input ==========================
% 0.46/1.04
% 0.46/1.04 % From the command line: assign(max_seconds, 300).
% 0.46/1.04
% 0.46/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.04
% 0.46/1.04 % Formulas that are not ordinary clauses:
% 0.46/1.04 1 (exists Y24 all X19 (-r1(X19) & X19 != Y24 | r1(X19) & X19 = Y24)) # label(axiom_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 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].
% 0.46/1.04 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].
% 0.46/1.04 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].
% 0.46/1.04 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].
% 0.46/1.04 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].
% 0.46/1.04 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].
% 0.46/1.04 8 (all X4 exists Y9 ((exists Y16 (r1(Y16) & r3(X4,Y16,Y9))) & Y9 = X4)) # label(axiom_4a) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 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].
% 0.46/1.04 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].
% 0.46/1.04 11 (all X7 all Y10 ((all Y20 (-r1(Y20) | Y20 != Y10)) | -r2(X7,Y10))) # label(axiom_7a) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 12 -(exists Y1 ((all Y2 ((all Y3 (-r1(Y3) | -r2(Y3,Y2))) | Y1 != Y2)) & (all Y4 (-r1(Y4) | Y1 != Y4)))) # label(nonzerosnononesexist) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.10/1.43
% 1.10/1.43 ============================== end of process non-clausal formulas ===
% 1.10/1.43
% 1.10/1.43 ============================== PROCESS INITIAL CLAUSES ===============
% 1.10/1.43
% 1.10/1.43 ============================== PREDICATE ELIMINATION =================
% 1.10/1.43 13 -r3(A,B,C) | C = f2(A,B) # label(axiom_3) # label(axiom). [clausify(3)].
% 1.10/1.43 14 r3(A,B,f7(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 1.10/1.43 15 r3(A,f13(A),f12(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 1.10/1.43 16 r3(A,f6(A,B),f5(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 1.10/1.43 17 r3(f11(A,B),A,f8(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 1.10/1.43 Derived: f7(A,B) = f2(A,B). [resolve(13,a,14,a)].
% 1.10/1.43 Derived: f12(A) = f2(A,f13(A)). [resolve(13,a,15,a)].
% 1.10/1.43 Derived: f5(A,B) = f2(A,f6(A,B)). [resolve(13,a,16,a)].
% 1.10/1.43 Derived: f8(A,B) = f2(f11(A,B),A). [resolve(13,a,17,a)].
% 1.10/1.43 18 A != f2(B,C) | r3(B,C,A) # label(axiom_3) # label(axiom). [clausify(3)].
% 1.10/1.43 19 -r4(A,B,C) | C = f3(A,B) # label(axiom_4) # label(axiom). [clausify(4)].
% 1.10/1.43 20 r4(A,B,f11(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 1.10/1.43 21 r4(A,f15(A),f14(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 1.10/1.43 22 r4(A,f10(A,B),f9(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 1.10/1.43 Derived: f11(A,B) = f3(A,B). [resolve(19,a,20,a)].
% 1.10/1.43 Derived: f14(A) = f3(A,f15(A)). [resolve(19,a,21,a)].
% 1.10/1.43 Derived: f9(A,B) = f3(A,f10(A,B)). [resolve(19,a,22,a)].
% 1.10/1.43 23 A != f3(B,C) | r4(B,C,A) # label(axiom_4) # label(axiom). [clausify(4)].
% 1.10/1.43
% 1.10/1.43 ============================== end predicate elimination =============
% 1.10/1.43
% 1.10/1.43 Auto_denials: (non-Horn, no changes).
% 1.10/1.43
% 1.10/1.43 Term ordering decisions:
% 1.10/1.43 Function symbol KB weights: c1=1. f2=1. f3=1. f4=1. f5=1. f6=1. f7=1. f8=1. f9=1. f10=1. f11=1. f1=1. f12=1. f13=1. f14=1. f15=1. f16=1. f17=1. f18=1. f19=1. f20=1. f21=1. f22=1.
% 1.10/1.43
% 1.10/1.43 ============================== end of process initial clauses ========
% 1.10/1.43
% 1.10/1.43 ============================== CLAUSES FOR SEARCH ====================
% 1.10/1.43
% 1.10/1.43 ============================== end of clauses for search =============
% 1.10/1.43
% 1.10/1.43 ============================== SEARCH ================================
% 1.10/1.43
% 1.10/1.43 % Starting search at 0.02 seconds.
% 1.10/1.43
% 1.10/1.43 ============================== PROOF =================================
% 1.10/1.43 % SZS status Theorem
% 1.10/1.43 % SZS output start Refutation
% 1.10/1.43
% 1.10/1.43 % Proof 1 at 0.38 (+ 0.02) seconds.
% 1.10/1.43 % Length of proof is 53.
% 1.10/1.43 % Level of proof is 11.
% 1.10/1.43 % Maximum clause weight is 12.000.
% 1.10/1.43 % Given clauses 474.
% 1.10/1.43
% 1.10/1.43 1 (exists Y24 all X19 (-r1(X19) & X19 != Y24 | r1(X19) & X19 = Y24)) # label(axiom_1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 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].
% 1.10/1.43 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].
% 1.10/1.43 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].
% 1.10/1.43 8 (all X4 exists Y9 ((exists Y16 (r1(Y16) & r3(X4,Y16,Y9))) & Y9 = X4)) # label(axiom_4a) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 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].
% 1.10/1.43 11 (all X7 all Y10 ((all Y20 (-r1(Y20) | Y20 != Y10)) | -r2(X7,Y10))) # label(axiom_7a) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 12 -(exists Y1 ((all Y2 ((all Y3 (-r1(Y3) | -r2(Y3,Y2))) | Y1 != Y2)) & (all Y4 (-r1(Y4) | Y1 != Y4)))) # label(nonzerosnononesexist) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.10/1.43 25 r1(f15(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 1.10/1.43 27 f12(A) = A # label(axiom_4a) # label(axiom). [clausify(8)].
% 1.10/1.43 29 r2(A,f10(B,A)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 1.10/1.43 31 r1(f21(A)) | r1(f22(A)) # label(nonzerosnononesexist) # label(negated_conjecture). [clausify(12)].
% 1.10/1.43 36 r1(f21(A)) | A = f22(A) # label(nonzerosnononesexist) # label(negated_conjecture). [clausify(12)].
% 1.10/1.43 37 r1(f21(A)) | f22(A) = A. [copy(36),flip(b)].
% 1.10/1.43 38 A = f20(A) | r1(f22(A)) # label(nonzerosnononesexist) # label(negated_conjecture). [clausify(12)].
% 1.10/1.43 39 f20(A) = A | r1(f22(A)). [copy(38),flip(a)].
% 1.10/1.43 42 r2(f21(A),f20(A)) | r1(f22(A)) # label(nonzerosnononesexist) # label(negated_conjecture). [clausify(12)].
% 1.10/1.43 43 A = f20(A) | A = f22(A) # label(nonzerosnononesexist) # label(negated_conjecture). [clausify(12)].
% 1.10/1.43 44 f20(A) = A | f22(A) = A. [copy(43),flip(a),flip(b)].
% 1.10/1.43 46 r2(f21(A),f20(A)) | A = f22(A) # label(nonzerosnononesexist) # label(negated_conjecture). [clausify(12)].
% 1.10/1.43 47 r2(f21(A),f20(A)) | f22(A) = A. [copy(46),flip(b)].
% 1.10/1.43 48 -r1(A) | A != B | -r2(C,B) # label(axiom_7a) # label(axiom). [clausify(11)].
% 1.10/1.43 49 -r1(A) | A = c1 # label(axiom_1) # label(axiom). [clausify(1)].
% 1.10/1.43 50 -r1(A) | c1 = A. [copy(49),flip(b)].
% 1.10/1.43 51 A != c1 | r1(A) # label(axiom_1) # label(axiom). [clausify(1)].
% 1.10/1.43 52 c1 != A | r1(A). [copy(51),flip(a)].
% 1.10/1.43 53 -r2(A,B) | B = f1(A) # label(axiom_2) # label(axiom). [clausify(2)].
% 1.10/1.43 54 -r2(A,B) | f1(A) = B. [copy(53),flip(b)].
% 1.10/1.43 57 -r2(A,B) | B != C | -r2(D,C) | D = A # label(axiom_3a) # label(axiom). [clausify(7)].
% 1.10/1.43 75 f20(A) = A | r1(A). [para(44(b,1),39(b,1)),merge(b)].
% 1.10/1.43 83 -r1(f10(A,B)). [ur(48,b,27,a,c,29,a),rewrite([27(2)])].
% 1.10/1.43 85 f15(A) != f10(B,C). [ur(48,a,25,a,c,29,a)].
% 1.10/1.43 92 f21(A) = c1 | f22(A) = A. [resolve(50,a,37,a),flip(a)].
% 1.10/1.43 94 f22(A) = c1 | r1(f21(A)). [resolve(50,a,31,b),flip(a)].
% 1.10/1.43 95 f15(A) = c1. [resolve(50,a,25,a),flip(a)].
% 1.10/1.43 99 f10(A,B) != c1. [back_rewrite(85),rewrite([95(1)]),flip(a)].
% 1.10/1.43 110 f10(A,B) = f1(B). [resolve(54,a,29,a),flip(a)].
% 1.10/1.43 112 f1(A) != c1. [back_rewrite(99),rewrite([110(1)])].
% 1.10/1.43 113 -r1(f1(A)). [back_rewrite(83),rewrite([110(1)])].
% 1.10/1.43 116 r2(A,f1(A)). [back_rewrite(29),rewrite([110(1)])].
% 1.10/1.43 131 f20(f1(A)) = f1(A). [resolve(113,a,75,b)].
% 1.10/1.43 155 -r2(c1,f1(f1(A))). [ur(57,b,27,a,c,116,a,d,112,a),rewrite([27(4)])].
% 1.10/1.43 183 r2(f21(f1(A)),f1(A)) | r1(f22(f1(A))). [para(131(a,1),42(a,2))].
% 1.10/1.43 184 r2(f21(f1(A)),f1(A)) | f22(f1(A)) = f1(A). [para(131(a,1),47(a,2))].
% 1.10/1.43 189 f22(A) = c1 | f21(A) = c1. [resolve(94,b,50,a),flip(b)].
% 1.10/1.43 344 f21(A) = c1 | r1(f22(A)). [resolve(189,a,52,a(flip))].
% 1.10/1.43 352 f21(A) = c1 | r1(A). [para(92(b,1),344(b,1)),merge(b)].
% 1.10/1.43 359 f21(f1(A)) = c1. [resolve(352,b,113,a)].
% 1.10/1.43 368 r2(c1,f1(A)) | f22(f1(A)) = f1(A). [back_rewrite(184),rewrite([359(2)])].
% 1.10/1.43 369 r2(c1,f1(A)) | r1(f22(f1(A))). [back_rewrite(183),rewrite([359(2)])].
% 1.10/1.43 466 r1(f22(f1(f1(A)))). [resolve(369,a,155,a)].
% 1.10/1.43 478 f22(f1(f1(A))) = c1. [resolve(466,a,50,a),flip(a)].
% 1.10/1.43 2775 $F. [resolve(368,a,155,a),rewrite([478(3)]),flip(a),unit_del(a,112)].
% 1.10/1.43
% 1.10/1.43 % SZS output end Refutation
% 1.10/1.43 ============================== end of proof ==========================
% 1.10/1.43
% 1.10/1.43 ============================== STATISTICS ============================
% 1.10/1.43
% 1.10/1.43 Given=474. Generated=12479. Kept=2740. proofs=1.
% 1.10/1.43 Usable=450. Sos=2091. Demods=37. Limbo=6, Disabled=237. Hints=0.
% 1.10/1.43 Megabytes=2.59.
% 1.10/1.43 User_CPU=0.38, System_CPU=0.02, Wall_clock=1.
% 1.10/1.43
% 1.10/1.43 ============================== end of statistics =====================
% 1.10/1.43
% 1.10/1.43 ============================== end of search =========================
% 1.10/1.43
% 1.10/1.43 THEOREM PROVED
% 1.10/1.43 % SZS status Theorem
% 1.10/1.43
% 1.10/1.43 Exiting with 1 proof.
% 1.10/1.43
% 1.10/1.43 Process 4747 exit (max_proofs) Thu Jun 2 08:18:46 2022
% 1.10/1.43 Prover9 interrupted
%------------------------------------------------------------------------------