TSTP Solution File: NUN054+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUN054+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.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 16:37:04 EDT 2022
% Result : Theorem 0.81s 1.11s
% Output : Refutation 0.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUN054+2 : TPTP v8.1.0. Released v7.3.0.
% 0.12/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 2 07:37:21 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.48/1.06 ============================== Prover9 ===============================
% 0.48/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.48/1.06 Process 10145 was started by sandbox2 on n022.cluster.edu,
% 0.48/1.06 Thu Jun 2 07:37:22 2022
% 0.48/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_9991_n022.cluster.edu".
% 0.48/1.06 ============================== end of head ===========================
% 0.48/1.06
% 0.48/1.06 ============================== INPUT =================================
% 0.48/1.06
% 0.48/1.06 % Reading from file /tmp/Prover9_9991_n022.cluster.edu
% 0.48/1.06
% 0.48/1.06 set(prolog_style_variables).
% 0.48/1.06 set(auto2).
% 0.48/1.06 % set(auto2) -> set(auto).
% 0.48/1.06 % set(auto) -> set(auto_inference).
% 0.48/1.06 % set(auto) -> set(auto_setup).
% 0.48/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.48/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.48/1.06 % set(auto) -> set(auto_limits).
% 0.48/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.48/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.48/1.06 % set(auto) -> set(auto_denials).
% 0.48/1.06 % set(auto) -> set(auto_process).
% 0.48/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.48/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.48/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.48/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.48/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.48/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.48/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.48/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.48/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.48/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.48/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.48/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.48/1.06 % set(auto2) -> assign(stats, some).
% 0.48/1.06 % set(auto2) -> clear(echo_input).
% 0.48/1.06 % set(auto2) -> set(quiet).
% 0.48/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.48/1.06 % set(auto2) -> clear(print_given).
% 0.48/1.06 assign(lrs_ticks,-1).
% 0.48/1.06 assign(sos_limit,10000).
% 0.48/1.06 assign(order,kbo).
% 0.48/1.06 set(lex_order_vars).
% 0.48/1.06 clear(print_given).
% 0.48/1.06
% 0.48/1.06 % formulas(sos). % not echoed (12 formulas)
% 0.48/1.06
% 0.48/1.06 ============================== end of input ==========================
% 0.48/1.06
% 0.48/1.06 % From the command line: assign(max_seconds, 300).
% 0.48/1.06
% 0.48/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.48/1.06
% 0.48/1.06 % Formulas that are not ordinary clauses:
% 0.48/1.06 1 (exists Y24 all X19 (-r1(X19) & X19 != Y24 | r1(X19) & X19 = Y24)) # label(axiom_1) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.06 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].
% 0.48/1.06 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].
% 0.48/1.06 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].
% 0.48/1.06 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].
% 0.48/1.06 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].
% 0.48/1.06 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].
% 0.48/1.06 8 (all X4 exists Y9 ((exists Y16 (r1(Y16) & r3(X4,Y16,Y9))) & Y9 = X4)) # label(axiom_4a) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.06 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].
% 0.48/1.06 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].
% 0.48/1.06 11 (all X7 all Y10 ((all Y20 (-r1(Y20) | Y20 != Y10)) | -r2(X7,Y10))) # label(axiom_7a) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.06 12 -(exists Y1 ((exists Y2 ((exists Y4 (r1(Y4) & r3(Y4,Y2,Y1))) & (exists Y5 (r1(Y5) & r2(Y5,Y2))))) & (exists Y3 (Y1 = Y3 & (exists Y6 (r1(Y6) & r2(Y6,Y3))))))) # label(zeroplusoneeqone) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.81/1.11
% 0.81/1.11 ============================== end of process non-clausal formulas ===
% 0.81/1.11
% 0.81/1.11 ============================== PROCESS INITIAL CLAUSES ===============
% 0.81/1.11
% 0.81/1.11 ============================== PREDICATE ELIMINATION =================
% 0.81/1.11 13 -r1(A) | -r3(A,B,C) | -r1(D) | -r2(D,B) | C != E | -r1(F) | -r2(F,E) # label(zeroplusoneeqone) # label(negated_conjecture). [clausify(12)].
% 0.81/1.11 14 r3(A,B,f7(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.81/1.11 15 r3(A,f13(A),f12(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.81/1.11 16 r3(A,f6(A,B),f5(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.81/1.11 17 r3(f11(A,B),A,f8(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.81/1.11 Derived: -r1(A) | -r1(B) | -r2(B,C) | f7(A,C) != D | -r1(E) | -r2(E,D). [resolve(13,b,14,a)].
% 0.81/1.11 Derived: -r1(A) | -r1(B) | -r2(B,f13(A)) | f12(A) != C | -r1(D) | -r2(D,C). [resolve(13,b,15,a)].
% 0.81/1.11 Derived: -r1(A) | -r1(B) | -r2(B,f6(A,C)) | f5(A,C) != D | -r1(E) | -r2(E,D). [resolve(13,b,16,a)].
% 0.81/1.11 Derived: -r1(f11(A,B)) | -r1(C) | -r2(C,A) | f8(A,B) != D | -r1(E) | -r2(E,D). [resolve(13,b,17,a)].
% 0.81/1.11 18 -r3(A,B,C) | C = f2(A,B) # label(axiom_3) # label(axiom). [clausify(3)].
% 0.81/1.11 Derived: f7(A,B) = f2(A,B). [resolve(18,a,14,a)].
% 0.81/1.11 Derived: f12(A) = f2(A,f13(A)). [resolve(18,a,15,a)].
% 0.81/1.11 Derived: f5(A,B) = f2(A,f6(A,B)). [resolve(18,a,16,a)].
% 0.81/1.11 Derived: f8(A,B) = f2(f11(A,B),A). [resolve(18,a,17,a)].
% 0.81/1.11 19 A != f2(B,C) | r3(B,C,A) # label(axiom_3) # label(axiom). [clausify(3)].
% 0.81/1.11 Derived: A != f2(B,C) | -r1(B) | -r1(D) | -r2(D,C) | A != E | -r1(F) | -r2(F,E). [resolve(19,b,13,b)].
% 0.81/1.11 20 -r4(A,B,C) | C = f3(A,B) # label(axiom_4) # label(axiom). [clausify(4)].
% 0.81/1.11 21 r4(A,B,f11(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.81/1.11 22 r4(A,f15(A),f14(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.81/1.11 23 r4(A,f10(A,B),f9(A,B)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.81/1.11 Derived: f11(A,B) = f3(A,B). [resolve(20,a,21,a)].
% 0.81/1.11 Derived: f14(A) = f3(A,f15(A)). [resolve(20,a,22,a)].
% 0.81/1.11 Derived: f9(A,B) = f3(A,f10(A,B)). [resolve(20,a,23,a)].
% 0.81/1.11 24 A != f3(B,C) | r4(B,C,A) # label(axiom_4) # label(axiom). [clausify(4)].
% 0.81/1.11
% 0.81/1.11 ============================== end predicate elimination =============
% 0.81/1.11
% 0.81/1.11 Auto_denials: (non-Horn, no changes).
% 0.81/1.11
% 0.81/1.11 Term ordering decisions:
% 0.81/1.11 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.
% 0.81/1.11
% 0.81/1.11 ============================== end of process initial clauses ========
% 0.81/1.11
% 0.81/1.11 ============================== CLAUSES FOR SEARCH ====================
% 0.81/1.11
% 0.81/1.11 ============================== end of clauses for search =============
% 0.81/1.11
% 0.81/1.11 ============================== SEARCH ================================
% 0.81/1.11
% 0.81/1.11 % Starting search at 0.02 seconds.
% 0.81/1.11
% 0.81/1.11 ============================== PROOF =================================
% 0.81/1.11 % SZS status Theorem
% 0.81/1.11 % SZS output start Refutation
% 0.81/1.11
% 0.81/1.11 % Proof 1 at 0.06 (+ 0.00) seconds.
% 0.81/1.11 % Length of proof is 47.
% 0.81/1.11 % Level of proof is 8.
% 0.81/1.11 % Maximum clause weight is 20.000.
% 0.81/1.11 % Given clauses 62.
% 0.81/1.11
% 0.81/1.11 1 (exists Y24 all X19 (-r1(X19) & X19 != Y24 | r1(X19) & X19 = Y24)) # label(axiom_1) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.11 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].
% 0.81/1.11 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].
% 0.81/1.11 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].
% 0.81/1.11 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].
% 0.81/1.11 8 (all X4 exists Y9 ((exists Y16 (r1(Y16) & r3(X4,Y16,Y9))) & Y9 = X4)) # label(axiom_4a) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.11 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].
% 0.81/1.11 12 -(exists Y1 ((exists Y2 ((exists Y4 (r1(Y4) & r3(Y4,Y2,Y1))) & (exists Y5 (r1(Y5) & r2(Y5,Y2))))) & (exists Y3 (Y1 = Y3 & (exists Y6 (r1(Y6) & r2(Y6,Y3))))))) # label(zeroplusoneeqone) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.81/1.11 13 -r1(A) | -r3(A,B,C) | -r1(D) | -r2(D,B) | C != E | -r1(F) | -r2(F,E) # label(zeroplusoneeqone) # label(negated_conjecture). [clausify(12)].
% 0.81/1.11 14 r3(A,B,f7(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.81/1.11 15 r3(A,f13(A),f12(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.81/1.11 16 r3(A,f6(A,B),f5(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.81/1.11 18 -r3(A,B,C) | C = f2(A,B) # label(axiom_3) # label(axiom). [clausify(3)].
% 0.81/1.11 19 A != f2(B,C) | r3(B,C,A) # label(axiom_3) # label(axiom). [clausify(3)].
% 0.81/1.11 25 r1(f13(A)) # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.81/1.11 26 r1(f15(A)) # label(axiom_5a) # label(axiom). [clausify(9)].
% 0.81/1.11 28 f12(A) = A # label(axiom_4a) # label(axiom). [clausify(8)].
% 0.81/1.11 29 r2(A,f6(B,A)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.81/1.11 30 r2(A,f10(B,A)) # label(axiom_2a) # label(axiom). [clausify(6)].
% 0.81/1.11 32 f5(A,B) = f4(A,B) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.81/1.11 33 r2(f7(A,B),f4(A,B)) # label(axiom_1a) # label(axiom). [clausify(5)].
% 0.81/1.11 40 -r1(A) | A = c1 # label(axiom_1) # label(axiom). [clausify(1)].
% 0.81/1.11 41 -r1(A) | c1 = A. [copy(40),flip(b)].
% 0.81/1.11 44 -r2(A,B) | B = f1(A) # label(axiom_2) # label(axiom). [clausify(2)].
% 0.81/1.11 45 -r2(A,B) | f1(A) = B. [copy(44),flip(b)].
% 0.81/1.11 54 f7(A,B) = f2(A,B). [resolve(18,a,14,a)].
% 0.81/1.11 55 f12(A) = f2(A,f13(A)). [resolve(18,a,15,a)].
% 0.81/1.11 56 f2(A,f13(A)) = A. [copy(55),rewrite([28(1)]),flip(a)].
% 0.81/1.11 57 f5(A,B) = f2(A,f6(A,B)). [resolve(18,a,16,a)].
% 0.81/1.11 58 f2(A,f6(A,B)) = f4(A,B). [copy(57),rewrite([32(1)]),flip(a)].
% 0.81/1.11 60 A != f2(B,C) | -r1(B) | -r1(D) | -r2(D,C) | A != E | -r1(F) | -r2(F,E). [resolve(19,b,13,b)].
% 0.81/1.11 61 f2(A,B) != C | -r1(A) | -r1(D) | -r2(D,B) | C != E | -r1(F) | -r2(F,E). [copy(60),flip(a)].
% 0.81/1.11 76 r2(f2(A,B),f4(A,B)). [back_rewrite(33),rewrite([54(1)])].
% 0.81/1.11 78 -r1(A) | -r1(B) | -r2(B,C) | -r1(D) | -r2(D,f2(A,C)). [factor(61,a,e),xx(a)].
% 0.81/1.11 89 -r1(A) | -r2(A,B) | -r1(C) | -r2(C,f2(A,B)). [factor(78,a,b)].
% 0.81/1.11 94 -r1(A) | -r2(A,B) | -r2(A,f2(A,B)). [factor(89,a,c)].
% 0.81/1.11 110 f15(A) = c1. [resolve(41,a,26,a),flip(a)].
% 0.81/1.11 111 f13(A) = c1. [resolve(41,a,25,a),flip(a)].
% 0.81/1.11 118 r1(c1). [back_rewrite(26),rewrite([110(1)])].
% 0.81/1.11 119 f2(A,c1) = A. [back_rewrite(56),rewrite([111(1)])].
% 0.81/1.11 123 f10(A,B) = f1(B). [resolve(45,a,30,a),flip(a)].
% 0.81/1.11 124 f6(A,B) = f1(B). [resolve(45,a,29,a),flip(a)].
% 0.81/1.11 129 r2(A,f1(A)). [back_rewrite(30),rewrite([123(1)])].
% 0.81/1.11 136 f2(A,f1(B)) = f4(A,B). [back_rewrite(58),rewrite([124(1)])].
% 0.81/1.11 309 -r2(c1,f4(c1,c1)). [ur(94,a,118,a,b,129,a),rewrite([136(5)])].
% 0.81/1.11 324 r2(A,f4(A,c1)). [para(119(a,1),76(a,1))].
% 0.81/1.11 325 $F. [resolve(324,a,309,a)].
% 0.81/1.11
% 0.81/1.11 % SZS output end Refutation
% 0.81/1.11 ============================== end of proof ==========================
% 0.81/1.11
% 0.81/1.11 ============================== STATISTICS ============================
% 0.81/1.11
% 0.81/1.11 Given=62. Generated=843. Kept=290. proofs=1.
% 0.81/1.11 Usable=57. Sos=189. Demods=18. Limbo=0, Disabled=87. Hints=0.
% 0.81/1.11 Megabytes=0.32.
% 0.81/1.11 User_CPU=0.06, System_CPU=0.00, Wall_clock=0.
% 0.81/1.11
% 0.81/1.11 ============================== end of statistics =====================
% 0.81/1.11
% 0.81/1.11 ============================== end of search =========================
% 0.81/1.11
% 0.81/1.11 THEOREM PROVED
% 0.81/1.11 % SZS status Theorem
% 0.81/1.11
% 0.81/1.11 Exiting with 1 proof.
% 0.81/1.11
% 0.81/1.11 Process 10145 exit (max_proofs) Thu Jun 2 07:37:22 2022
% 0.81/1.11 Prover9 interrupted
%------------------------------------------------------------------------------