TSTP Solution File: NUN057+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUN057+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 16:37:05 EDT 2022
% Result : Theorem 1.11s 1.41s
% Output : Refutation 1.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUN057+2 : TPTP v8.1.0. Released v7.3.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 2 04:19:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.67/0.98 ============================== Prover9 ===============================
% 0.67/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.67/0.98 Process 29538 was started by sandbox on n021.cluster.edu,
% 0.67/0.98 Thu Jun 2 04:19:17 2022
% 0.67/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29385_n021.cluster.edu".
% 0.67/0.98 ============================== end of head ===========================
% 0.67/0.98
% 0.67/0.98 ============================== INPUT =================================
% 0.67/0.98
% 0.67/0.98 % Reading from file /tmp/Prover9_29385_n021.cluster.edu
% 0.67/0.98
% 0.67/0.98 set(prolog_style_variables).
% 0.67/0.98 set(auto2).
% 0.67/0.98 % set(auto2) -> set(auto).
% 0.67/0.98 % set(auto) -> set(auto_inference).
% 0.67/0.98 % set(auto) -> set(auto_setup).
% 0.67/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.67/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.67/0.98 % set(auto) -> set(auto_limits).
% 0.67/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.67/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.67/0.98 % set(auto) -> set(auto_denials).
% 0.67/0.98 % set(auto) -> set(auto_process).
% 0.67/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.67/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.67/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.67/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.67/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.67/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.67/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.67/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.67/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.67/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.67/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.67/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.67/0.98 % set(auto2) -> assign(stats, some).
% 0.67/0.98 % set(auto2) -> clear(echo_input).
% 0.67/0.98 % set(auto2) -> set(quiet).
% 0.67/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.67/0.98 % set(auto2) -> clear(print_given).
% 0.67/0.98 assign(lrs_ticks,-1).
% 0.67/0.98 assign(sos_limit,10000).
% 0.67/0.98 assign(order,kbo).
% 0.67/0.98 set(lex_order_vars).
% 0.67/0.98 clear(print_given).
% 0.67/0.98
% 0.67/0.98 % formulas(sos). % not echoed (12 formulas)
% 0.67/0.98
% 0.67/0.98 ============================== end of input ==========================
% 0.67/0.98
% 0.67/0.98 % From the command line: assign(max_seconds, 300).
% 0.67/0.98
% 0.67/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.67/0.98
% 0.67/0.98 % Formulas that are not ordinary clauses:
% 0.67/0.98 1 (exists Y24 all X19 (-r1(X19) & X19 != Y24 | r1(X19) & X19 = Y24)) # label(axiom_1) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 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].
% 0.67/0.98 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].
% 0.67/0.98 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].
% 0.67/0.98 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].
% 0.67/0.98 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].
% 0.67/0.98 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].
% 0.67/0.98 8 (all X4 exists Y9 ((exists Y16 (r1(Y16) & r3(X4,Y16,Y9))) & Y9 = X4)) # label(axiom_4a) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 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].
% 0.67/0.98 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].
% 0.67/0.98 11 (all X7 all Y10 ((all Y20 (-r1(Y20) | Y20 != Y10)) | -r2(X7,Y10))) # label(axiom_7a) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 12 -(exists Y1 ((exists Y2 (Y1 = Y2 & (exists Y3 (r2(Y3,Y2) & (exists Y4 (r2(Y4,Y3) & (exists Y6 (r2(Y6,Y4) & (exists Y8 (r1(Y8) & r2(Y8,Y6))))))))))) & (exists Y5 (r3(Y5,Y5,Y1) & (exists Y7 (r2(Y7,Y5) & (exists Y9 (r1(Y9) & r2(Y9,Y7))))))))) # label(twoplustwoeqfour) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.11/1.41
% 1.11/1.41 ============================== end of process non-clausal formulas ===
% 1.11/1.41
% 1.11/1.41 ============================== PROCESS INITIAL CLAUSES ===============
% 1.11/1.41
% 1.11/1.41 ============================== PREDICATE ELIMINATION =================
% 1.11/1.41 13 -r4(A,B,C) | C = f3(A,B) # label(axiom_4) # label(axiom). [clausify(4)].
% 1.11/1.41 14 r4(A,B,f11(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 1.11/1.41 15 r4(A,f15(A),f14(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 1.11/1.41 16 r4(A,f10(A,B),f9(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 1.11/1.41 Derived: f11(A,B) = f3(A,B). [resolve(13,a,14,a)].
% 1.11/1.41 Derived: f14(A) = f3(A,f15(A)). [resolve(13,a,15,a)].
% 1.11/1.41 Derived: f9(A,B) = f3(A,f10(A,B)). [resolve(13,a,16,a)].
% 1.11/1.41 17 A != f3(B,C) | r4(B,C,A) # label(axiom_4) # label(axiom). [clausify(4)].
% 1.11/1.41
% 1.11/1.41 ============================== end predicate elimination =============
% 1.11/1.41
% 1.11/1.41 Auto_denials: (non-Horn, no changes).
% 1.11/1.41
% 1.11/1.41 Term ordering decisions:
% 1.11/1.41 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.
% 1.11/1.41
% 1.11/1.41 ============================== end of process initial clauses ========
% 1.11/1.41
% 1.11/1.41 ============================== CLAUSES FOR SEARCH ====================
% 1.11/1.41
% 1.11/1.41 ============================== end of clauses for search =============
% 1.11/1.41
% 1.11/1.41 ============================== SEARCH ================================
% 1.11/1.41
% 1.11/1.41 % Starting search at 0.06 seconds.
% 1.11/1.41
% 1.11/1.41 ============================== PROOF =================================
% 1.11/1.41 % SZS status Theorem
% 1.11/1.41 % SZS output start Refutation
% 1.11/1.41
% 1.11/1.41 % Proof 1 at 0.44 (+ 0.01) seconds.
% 1.11/1.41 % Length of proof is 44.
% 1.11/1.41 % Level of proof is 7.
% 1.11/1.41 % Maximum clause weight is 29.000.
% 1.11/1.41 % Given clauses 174.
% 1.11/1.41
% 1.11/1.41 1 (exists Y24 all X19 (-r1(X19) & X19 != Y24 | r1(X19) & X19 = Y24)) # label(axiom_1) # label(axiom) # label(non_clause). [assumption].
% 1.11/1.41 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].
% 1.11/1.41 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].
% 1.11/1.41 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].
% 1.11/1.41 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].
% 1.11/1.41 8 (all X4 exists Y9 ((exists Y16 (r1(Y16) & r3(X4,Y16,Y9))) & Y9 = X4)) # label(axiom_4a) # label(axiom) # label(non_clause). [assumption].
% 1.11/1.41 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].
% 1.11/1.41 12 -(exists Y1 ((exists Y2 (Y1 = Y2 & (exists Y3 (r2(Y3,Y2) & (exists Y4 (r2(Y4,Y3) & (exists Y6 (r2(Y6,Y4) & (exists Y8 (r1(Y8) & r2(Y8,Y6))))))))))) & (exists Y5 (r3(Y5,Y5,Y1) & (exists Y7 (r2(Y7,Y5) & (exists Y9 (r1(Y9) & r2(Y9,Y7))))))))) # label(twoplustwoeqfour) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.11/1.41 18 r1(f13(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 1.11/1.41 19 r1(f15(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 1.11/1.41 21 f12(A) = A # label(axiom_4a) # label(axiom). [clausify(8)].
% 1.11/1.41 22 r2(A,f6(B,A)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 1.11/1.41 23 r2(A,f10(B,A)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 1.11/1.41 25 r3(A,B,f7(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 1.11/1.41 26 r3(A,f13(A),f12(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 1.11/1.41 27 r3(A,f13(A),A). [copy(26),rewrite([21(2)])].
% 1.11/1.41 28 f5(A,B) = f4(A,B) # label(axiom_1a) # label(axiom). [clausify(5)].
% 1.11/1.41 29 r2(f7(A,B),f4(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 1.11/1.41 32 r3(A,f6(A,B),f5(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 1.11/1.41 33 r3(A,f6(A,B),f4(A,B)). [copy(32),rewrite([28(2)])].
% 1.11/1.41 39 A != B | -r2(C,B) | -r2(D,C) | -r2(E,D) | -r1(F) | -r2(F,E) | -r3(V6,V6,A) | -r2(V7,V6) | -r1(V8) | -r2(V8,V7) # label(twoplustwoeqfour) # label(negated_conjecture). [clausify(12)].
% 1.11/1.41 40 -r1(A) | A = c1 # label(axiom_1) # label(axiom). [clausify(1)].
% 1.11/1.41 41 -r1(A) | c1 = A. [copy(40),flip(b)].
% 1.11/1.41 44 -r2(A,B) | B = f1(A) # label(axiom_2) # label(axiom). [clausify(2)].
% 1.11/1.41 45 -r2(A,B) | f1(A) = B. [copy(44),flip(b)].
% 1.11/1.41 48 -r3(A,B,C) | C = f2(A,B) # label(axiom_3) # label(axiom). [clausify(3)].
% 1.11/1.41 49 -r3(A,B,C) | f2(A,B) = C. [copy(48),flip(b)].
% 1.11/1.41 68 A != B | -r2(C,B) | -r2(D,C) | -r2(E,D) | -r1(F) | -r2(F,E) | -r3(D,D,A) | -r1(V6) | -r2(V6,E). [factor(39,d,h)].
% 1.11/1.41 130 A != B | -r2(C,B) | -r2(D,C) | -r2(E,D) | -r1(F) | -r2(F,E) | -r3(D,D,A). [factor(68,e,h),merge(h)].
% 1.11/1.41 964 f15(A) = c1. [resolve(41,a,19,a),flip(a)].
% 1.11/1.41 965 f13(A) = c1. [resolve(41,a,18,a),flip(a)].
% 1.11/1.41 1133 r1(c1). [back_rewrite(19),rewrite([964(1)])].
% 1.11/1.41 1134 r3(A,c1,A). [back_rewrite(27),rewrite([965(1)])].
% 1.11/1.41 1139 f10(A,B) = f1(B). [resolve(45,a,23,a),flip(a)].
% 1.11/1.41 1140 f6(A,B) = f1(B). [resolve(45,a,22,a),flip(a)].
% 1.11/1.41 1148 r2(A,f1(A)). [back_rewrite(23),rewrite([1139(1)])].
% 1.11/1.41 1149 r3(A,f1(B),f4(A,B)). [back_rewrite(33),rewrite([1140(1)])].
% 1.11/1.41 1151 f7(A,B) = f2(A,B). [resolve(49,a,25,a),flip(a)].
% 1.11/1.41 1261 r2(f2(A,B),f4(A,B)). [back_rewrite(29),rewrite([1151(1)])].
% 1.11/1.41 1279 f2(A,c1) = A. [resolve(1134,a,49,a)].
% 1.11/1.41 1371 f2(A,f1(B)) = f4(A,B). [resolve(1149,a,49,a)].
% 1.11/1.41 1391 -r2(f1(f1(c1)),f4(f1(f1(c1)),c1)). [ur(130,a,xx,b,1261,a,d,1148,a,e,1133,a,f,1148,a,g,1149,a),rewrite([1371(9)])].
% 1.11/1.41 1392 r2(A,f4(A,c1)). [para(1279(a,1),1261(a,1))].
% 1.11/1.41 1393 $F. [resolve(1392,a,1391,a)].
% 1.11/1.41
% 1.11/1.41 % SZS output end Refutation
% 1.11/1.41 ============================== end of proof ==========================
% 1.11/1.41
% 1.11/1.41 ============================== STATISTICS ============================
% 1.11/1.41
% 1.11/1.41 Given=174. Generated=5665. Kept=1366. proofs=1.
% 1.11/1.41 Usable=164. Sos=219. Demods=19. Limbo=2, Disabled=1015. Hints=0.
% 1.11/1.41 Megabytes=1.09.
% 1.11/1.41 User_CPU=0.44, System_CPU=0.01, Wall_clock=0.
% 1.11/1.41
% 1.11/1.41 ============================== end of statistics =====================
% 1.11/1.41
% 1.11/1.41 ============================== end of search =========================
% 1.11/1.41
% 1.11/1.41 THEOREM PROVED
% 1.11/1.41 % SZS status Theorem
% 1.11/1.41
% 1.11/1.41 Exiting with 1 proof.
% 1.11/1.41
% 1.11/1.41 Process 29538 exit (max_proofs) Thu Jun 2 04:19:17 2022
% 1.11/1.41 Prover9 interrupted
%------------------------------------------------------------------------------