TSTP Solution File: NUN066+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUN066+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 0.92s 1.18s
% Output : Refutation 0.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUN066+2 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n018.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 : Thu Jun 2 10:45:45 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.42/1.00 ============================== Prover9 ===============================
% 0.42/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.42/1.00 Process 31355 was started by sandbox on n018.cluster.edu,
% 0.42/1.00 Thu Jun 2 10:45:46 2022
% 0.42/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31202_n018.cluster.edu".
% 0.42/1.00 ============================== end of head ===========================
% 0.42/1.00
% 0.42/1.00 ============================== INPUT =================================
% 0.42/1.00
% 0.42/1.00 % Reading from file /tmp/Prover9_31202_n018.cluster.edu
% 0.42/1.00
% 0.42/1.00 set(prolog_style_variables).
% 0.42/1.00 set(auto2).
% 0.42/1.00 % set(auto2) -> set(auto).
% 0.42/1.00 % set(auto) -> set(auto_inference).
% 0.42/1.00 % set(auto) -> set(auto_setup).
% 0.42/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.42/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/1.00 % set(auto) -> set(auto_limits).
% 0.42/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/1.00 % set(auto) -> set(auto_denials).
% 0.42/1.00 % set(auto) -> set(auto_process).
% 0.42/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.42/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.42/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.42/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.42/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.42/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.42/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.42/1.00 % set(auto2) -> assign(stats, some).
% 0.42/1.00 % set(auto2) -> clear(echo_input).
% 0.42/1.00 % set(auto2) -> set(quiet).
% 0.42/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.42/1.00 % set(auto2) -> clear(print_given).
% 0.42/1.00 assign(lrs_ticks,-1).
% 0.42/1.00 assign(sos_limit,10000).
% 0.42/1.00 assign(order,kbo).
% 0.42/1.00 set(lex_order_vars).
% 0.42/1.00 clear(print_given).
% 0.42/1.00
% 0.42/1.00 % formulas(sos). % not echoed (12 formulas)
% 0.42/1.00
% 0.42/1.00 ============================== end of input ==========================
% 0.42/1.00
% 0.42/1.00 % From the command line: assign(max_seconds, 300).
% 0.42/1.00
% 0.42/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/1.00
% 0.42/1.00 % Formulas that are not ordinary clauses:
% 0.42/1.00 1 (exists Y24 all X19 (-r1(X19) & X19 != Y24 | r1(X19) & X19 = Y24)) # label(axiom_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 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].
% 0.42/1.00 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].
% 0.42/1.00 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].
% 0.42/1.00 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].
% 0.42/1.00 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].
% 0.42/1.00 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].
% 0.42/1.00 8 (all X4 exists Y9 ((exists Y16 (r1(Y16) & r3(X4,Y16,Y9))) & Y9 = X4)) # label(axiom_4a) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 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].
% 0.42/1.00 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].
% 0.42/1.00 11 (all X7 all Y10 ((all Y20 (-r1(Y20) | Y20 != Y10)) | -r2(X7,Y10))) # label(axiom_7a) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 12 -(exists Y1 ((all Y2 ((all Y3 ((all Y4 (-r1(Y4) | -r2(Y4,Y3))) | -r2(Y3,Y2))) | Y1 != Y2)) & (all Y5 (-r1(Y5) | Y1 != Y5)))) # label(nonzerononetwoexist) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.92/1.18
% 0.92/1.18 ============================== end of process non-clausal formulas ===
% 0.92/1.18
% 0.92/1.18 ============================== PROCESS INITIAL CLAUSES ===============
% 0.92/1.18
% 0.92/1.18 ============================== PREDICATE ELIMINATION =================
% 0.92/1.18 13 -r3(A,B,C) | C = f2(A,B) # label(axiom_3) # label(axiom). [clausify(3)].
% 0.92/1.18 14 r3(A,B,f7(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.92/1.18 15 r3(A,f13(A),f12(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.92/1.18 16 r3(A,f6(A,B),f5(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.92/1.18 17 r3(f11(A,B),A,f8(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.92/1.18 Derived: f7(A,B) = f2(A,B). [resolve(13,a,14,a)].
% 0.92/1.18 Derived: f12(A) = f2(A,f13(A)). [resolve(13,a,15,a)].
% 0.92/1.18 Derived: f5(A,B) = f2(A,f6(A,B)). [resolve(13,a,16,a)].
% 0.92/1.18 Derived: f8(A,B) = f2(f11(A,B),A). [resolve(13,a,17,a)].
% 0.92/1.18 18 A != f2(B,C) | r3(B,C,A) # label(axiom_3) # label(axiom). [clausify(3)].
% 0.92/1.18 19 -r4(A,B,C) | C = f3(A,B) # label(axiom_4) # label(axiom). [clausify(4)].
% 0.92/1.18 20 r4(A,B,f11(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.92/1.18 21 r4(A,f15(A),f14(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.92/1.18 22 r4(A,f10(A,B),f9(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.92/1.18 Derived: f11(A,B) = f3(A,B). [resolve(19,a,20,a)].
% 0.92/1.18 Derived: f14(A) = f3(A,f15(A)). [resolve(19,a,21,a)].
% 0.92/1.18 Derived: f9(A,B) = f3(A,f10(A,B)). [resolve(19,a,22,a)].
% 0.92/1.18 23 A != f3(B,C) | r4(B,C,A) # label(axiom_4) # label(axiom). [clausify(4)].
% 0.92/1.18
% 0.92/1.18 ============================== end predicate elimination =============
% 0.92/1.18
% 0.92/1.18 Auto_denials: (non-Horn, no changes).
% 0.92/1.18
% 0.92/1.18 Term ordering decisions:
% 0.92/1.18 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. f23=1.
% 0.92/1.18
% 0.92/1.18 ============================== end of process initial clauses ========
% 0.92/1.18
% 0.92/1.18 ============================== CLAUSES FOR SEARCH ====================
% 0.92/1.18
% 0.92/1.18 ============================== end of clauses for search =============
% 0.92/1.18
% 0.92/1.18 ============================== SEARCH ================================
% 0.92/1.18
% 0.92/1.18 % Starting search at 0.02 seconds.
% 0.92/1.18
% 0.92/1.18 ============================== PROOF =================================
% 0.92/1.18 % SZS status Theorem
% 0.92/1.18 % SZS output start Refutation
% 0.92/1.18
% 0.92/1.18 % Proof 1 at 0.19 (+ 0.01) seconds.
% 0.92/1.18 % Length of proof is 59.
% 0.92/1.18 % Level of proof is 11.
% 0.92/1.18 % Maximum clause weight is 12.000.
% 0.92/1.18 % Given clauses 294.
% 0.92/1.18
% 0.92/1.18 1 (exists Y24 all X19 (-r1(X19) & X19 != Y24 | r1(X19) & X19 = Y24)) # label(axiom_1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.18 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].
% 0.92/1.18 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].
% 0.92/1.18 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].
% 0.92/1.18 8 (all X4 exists Y9 ((exists Y16 (r1(Y16) & r3(X4,Y16,Y9))) & Y9 = X4)) # label(axiom_4a) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.18 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].
% 0.92/1.18 11 (all X7 all Y10 ((all Y20 (-r1(Y20) | Y20 != Y10)) | -r2(X7,Y10))) # label(axiom_7a) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.18 12 -(exists Y1 ((all Y2 ((all Y3 ((all Y4 (-r1(Y4) | -r2(Y4,Y3))) | -r2(Y3,Y2))) | Y1 != Y2)) & (all Y5 (-r1(Y5) | Y1 != Y5)))) # label(nonzerononetwoexist) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.92/1.18 25 r1(f15(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.92/1.18 27 f12(A) = A # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.92/1.18 29 r2(A,f10(B,A)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.92/1.18 31 r1(f22(A)) | r1(f23(A)) # label(nonzerononetwoexist) # label(negated_conjecture). [clausify(12)].
% 0.92/1.18 36 r1(f22(A)) | A = f23(A) # label(nonzerononetwoexist) # label(negated_conjecture). [clausify(12)].
% 0.92/1.18 37 r1(f22(A)) | f23(A) = A. [copy(36),flip(b)].
% 0.92/1.18 38 A = f20(A) | r1(f23(A)) # label(nonzerononetwoexist) # label(negated_conjecture). [clausify(12)].
% 0.92/1.18 39 f20(A) = A | r1(f23(A)). [copy(38),flip(a)].
% 0.92/1.18 42 r2(f22(A),f21(A)) | r1(f23(A)) # label(nonzerononetwoexist) # label(negated_conjecture). [clausify(12)].
% 0.92/1.18 43 r2(f21(A),f20(A)) | r1(f23(A)) # label(nonzerononetwoexist) # label(negated_conjecture). [clausify(12)].
% 0.92/1.18 44 A = f20(A) | A = f23(A) # label(nonzerononetwoexist) # label(negated_conjecture). [clausify(12)].
% 0.92/1.18 45 f20(A) = A | f23(A) = A. [copy(44),flip(a),flip(b)].
% 0.92/1.18 47 r2(f22(A),f21(A)) | A = f23(A) # label(nonzerononetwoexist) # label(negated_conjecture). [clausify(12)].
% 0.92/1.18 48 r2(f22(A),f21(A)) | f23(A) = A. [copy(47),flip(b)].
% 0.92/1.18 49 r2(f21(A),f20(A)) | A = f23(A) # label(nonzerononetwoexist) # label(negated_conjecture). [clausify(12)].
% 0.92/1.18 50 r2(f21(A),f20(A)) | f23(A) = A. [copy(49),flip(b)].
% 0.92/1.18 51 -r1(A) | A != B | -r2(C,B) # label(axiom_7a) # label(axiom). [clausify(11)].
% 0.92/1.18 52 -r1(A) | A = c1 # label(axiom_1) # label(axiom). [clausify(1)].
% 0.92/1.18 53 -r1(A) | c1 = A. [copy(52),flip(b)].
% 0.92/1.18 54 A != c1 | r1(A) # label(axiom_1) # label(axiom). [clausify(1)].
% 0.92/1.18 55 c1 != A | r1(A). [copy(54),flip(a)].
% 0.92/1.18 56 -r2(A,B) | B = f1(A) # label(axiom_2) # label(axiom). [clausify(2)].
% 0.92/1.18 57 -r2(A,B) | f1(A) = B. [copy(56),flip(b)].
% 0.92/1.18 60 -r2(A,B) | B != C | -r2(D,C) | D = A # label(axiom_3a) # label(axiom). [clausify(7)].
% 0.92/1.18 78 f20(A) = A | r1(A). [para(45(b,1),39(b,1)),merge(b)].
% 0.92/1.18 88 -r1(f10(A,B)). [ur(51,b,27,a,c,29,a),rewrite([27(2)])].
% 0.92/1.18 90 f15(A) != f10(B,C). [ur(51,a,25,a,c,29,a)].
% 0.92/1.18 97 f22(A) = c1 | f23(A) = A. [resolve(53,a,37,a),flip(a)].
% 0.92/1.18 99 f23(A) = c1 | r1(f22(A)). [resolve(53,a,31,b),flip(a)].
% 0.92/1.18 100 f15(A) = c1. [resolve(53,a,25,a),flip(a)].
% 0.92/1.18 104 f10(A,B) != c1. [back_rewrite(90),rewrite([100(1)]),flip(a)].
% 0.92/1.18 111 f1(f21(A)) = f20(A) | f23(A) = A. [resolve(57,a,50,a)].
% 0.92/1.18 112 f1(f22(A)) = f21(A) | f23(A) = A. [resolve(57,a,48,a)].
% 0.92/1.18 114 f1(f21(A)) = f20(A) | r1(f23(A)). [resolve(57,a,43,a)].
% 0.92/1.18 115 f1(f22(A)) = f21(A) | r1(f23(A)). [resolve(57,a,42,a)].
% 0.92/1.18 117 f10(A,B) = f1(B). [resolve(57,a,29,a),flip(a)].
% 0.92/1.18 119 f1(A) != c1. [back_rewrite(104),rewrite([117(1)])].
% 0.92/1.18 120 -r1(f1(A)). [back_rewrite(88),rewrite([117(1)])].
% 0.92/1.18 123 r2(A,f1(A)). [back_rewrite(29),rewrite([117(1)])].
% 0.92/1.18 140 f20(f1(A)) = f1(A). [resolve(120,a,78,b)].
% 0.92/1.18 168 f1(f1(A)) != f1(c1). [ur(60,a,123,a,c,123,a,d,119,a),flip(a)].
% 0.92/1.18 199 f23(A) = c1 | f22(A) = c1. [resolve(99,b,53,a),flip(b)].
% 0.92/1.18 309 f22(A) = c1 | r1(f23(A)). [resolve(199,a,55,a(flip))].
% 0.92/1.18 319 f22(A) = c1 | r1(A). [para(97(b,1),309(b,1)),merge(b)].
% 0.92/1.18 325 f23(A) = A | f1(f21(A)) != f1(c1). [para(112(a,1),168(a,1,1))].
% 0.92/1.18 359 f22(f1(A)) = c1. [resolve(319,b,120,a)].
% 0.92/1.18 1252 f23(A) = A | f20(A) != f1(c1). [para(111(a,1),325(b,1)),merge(b)].
% 0.92/1.18 1280 f23(f1(c1)) = f1(c1). [resolve(1252,b,140,a)].
% 0.92/1.18 1287 f1(f21(f1(c1))) = f1(c1). [para(1280(a,1),114(b,1)),rewrite([140(7)]),unit_del(b,120)].
% 0.92/1.18 1288 f21(f1(c1)) = f1(c1). [para(1280(a,1),115(b,1)),rewrite([359(3)]),flip(a),unit_del(b,120)].
% 0.92/1.18 1289 $F. [back_rewrite(1287),rewrite([1288(3)]),unit_del(a,168)].
% 0.92/1.18
% 0.92/1.18 % SZS output end Refutation
% 0.92/1.18 ============================== end of proof ==========================
% 0.92/1.18
% 0.92/1.18 ============================== STATISTICS ============================
% 0.92/1.18
% 0.92/1.18 Given=294. Generated=6111. Kept=1253. proofs=1.
% 0.92/1.18 Usable=273. Sos=876. Demods=37. Limbo=1, Disabled=149. Hints=0.
% 0.92/1.18 Megabytes=1.30.
% 0.92/1.18 User_CPU=0.19, System_CPU=0.01, Wall_clock=0.
% 0.92/1.18
% 0.92/1.18 ============================== end of statistics =====================
% 0.92/1.18
% 0.92/1.18 ============================== end of search =========================
% 0.92/1.18
% 0.92/1.18 THEOREM PROVED
% 0.92/1.18 % SZS status Theorem
% 0.92/1.18
% 0.92/1.18 Exiting with 1 proof.
% 0.92/1.18
% 0.92/1.18 Process 31355 exit (max_proofs) Thu Jun 2 10:45:46 2022
% 0.92/1.18 Prover9 interrupted
%------------------------------------------------------------------------------