TSTP Solution File: SET957+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET957+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 : Tue Jul 19 04:33:41 EDT 2022
% Result : Theorem 2.14s 2.40s
% Output : Refutation 2.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET957+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n027.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 : Sun Jul 10 08:02:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.42/0.99 ============================== Prover9 ===============================
% 0.42/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.99 Process 29123 was started by sandbox on n027.cluster.edu,
% 0.42/0.99 Sun Jul 10 08:02:03 2022
% 0.42/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_28970_n027.cluster.edu".
% 0.42/0.99 ============================== end of head ===========================
% 0.42/0.99
% 0.42/0.99 ============================== INPUT =================================
% 0.42/0.99
% 0.42/0.99 % Reading from file /tmp/Prover9_28970_n027.cluster.edu
% 0.42/0.99
% 0.42/0.99 set(prolog_style_variables).
% 0.42/0.99 set(auto2).
% 0.42/0.99 % set(auto2) -> set(auto).
% 0.42/0.99 % set(auto) -> set(auto_inference).
% 0.42/0.99 % set(auto) -> set(auto_setup).
% 0.42/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.99 % set(auto) -> set(auto_limits).
% 0.42/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.99 % set(auto) -> set(auto_denials).
% 0.42/0.99 % set(auto) -> set(auto_process).
% 0.42/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.99 % set(auto2) -> assign(stats, some).
% 0.42/0.99 % set(auto2) -> clear(echo_input).
% 0.42/0.99 % set(auto2) -> set(quiet).
% 0.42/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.99 % set(auto2) -> clear(print_given).
% 0.42/0.99 assign(lrs_ticks,-1).
% 0.42/0.99 assign(sos_limit,10000).
% 0.42/0.99 assign(order,kbo).
% 0.42/0.99 set(lex_order_vars).
% 0.42/0.99 clear(print_given).
% 0.42/0.99
% 0.42/0.99 % formulas(sos). % not echoed (10 formulas)
% 0.42/0.99
% 0.42/0.99 ============================== end of input ==========================
% 0.42/0.99
% 0.42/0.99 % From the command line: assign(max_seconds, 300).
% 0.42/0.99
% 0.42/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.99
% 0.42/0.99 % Formulas that are not ordinary clauses:
% 0.42/0.99 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 3 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 4 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 5 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 6 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 7 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 8 (all A all B all C all D -(subset(A,cartesian_product2(B,C)) & in(D,A) & (all E all F -(in(E,B) & in(F,C) & D = ordered_pair(E,F))))) # label(t103_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 9 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 10 -(all A all B all C all D all E all F (subset(A,cartesian_product2(B,C)) & subset(D,cartesian_product2(E,F)) & (all G all H (in(ordered_pair(G,H),A) <-> in(ordered_pair(G,H),D))) -> A = D)) # label(t110_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.42/0.99
% 0.42/0.99 ============================== end of process non-clausal formulas ===
% 0.42/0.99
% 0.42/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.42/0.99
% 0.42/0.99 ============================== PREDICATE ELIMINATION =================
% 0.42/0.99
% 0.42/0.99 ============================== end predicate elimination =============
% 0.42/0.99
% 0.42/0.99 Auto_denials: (non-Horn, no changes).
% 0.42/0.99
% 0.42/0.99 Term ordering decisions:
% 0.42/0.99
% 0.42/0.99 % Assigning unary symbol singleton kb_weight 0 and highest precedence (19).
% 0.42/0.99 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. ordered_pair=1. cartesian_product2=1. unordered_pair=1. f3=1. f1=1. f2=1. singleton=0.
% 2.14/2.40
% 2.14/2.40 ============================== end of process initial clauses ========
% 2.14/2.40
% 2.14/2.40 ============================== CLAUSES FOR SEARCH ====================
% 2.14/2.40
% 2.14/2.40 ============================== end of clauses for search =============
% 2.14/2.40
% 2.14/2.40 ============================== SEARCH ================================
% 2.14/2.40
% 2.14/2.40 % Starting search at 0.01 seconds.
% 2.14/2.40
% 2.14/2.40 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 39 (0.00 of 0.27 sec).
% 2.14/2.40
% 2.14/2.40 ============================== PROOF =================================
% 2.14/2.40 % SZS status Theorem
% 2.14/2.40 % SZS output start Refutation
% 2.14/2.40
% 2.14/2.40 % Proof 1 at 1.41 (+ 0.01) seconds.
% 2.14/2.40 % Length of proof is 33.
% 2.14/2.40 % Level of proof is 14.
% 2.14/2.40 % Maximum clause weight is 59.000.
% 2.14/2.40 % Given clauses 1988.
% 2.14/2.40
% 2.14/2.40 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.40 3 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.40 8 (all A all B all C all D -(subset(A,cartesian_product2(B,C)) & in(D,A) & (all E all F -(in(E,B) & in(F,C) & D = ordered_pair(E,F))))) # label(t103_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.40 9 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.40 10 -(all A all B all C all D all E all F (subset(A,cartesian_product2(B,C)) & subset(D,cartesian_product2(E,F)) & (all G all H (in(ordered_pair(G,H),A) <-> in(ordered_pair(G,H),D))) -> A = D)) # label(t110_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.14/2.40 13 subset(c3,cartesian_product2(c4,c5)) # label(t110_zfmisc_1) # label(negated_conjecture). [clausify(10)].
% 2.14/2.40 14 subset(c6,cartesian_product2(c7,c8)) # label(t110_zfmisc_1) # label(negated_conjecture). [clausify(10)].
% 2.14/2.40 15 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(2)].
% 2.14/2.40 16 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom). [clausify(3)].
% 2.14/2.40 17 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)). [copy(16),rewrite([15(4)])].
% 2.14/2.40 18 in(f3(A,B),A) | in(f3(A,B),B) | B = A # label(t2_tarski) # label(axiom). [clausify(9)].
% 2.14/2.40 20 c6 != c3 # label(t110_zfmisc_1) # label(negated_conjecture). [clausify(10)].
% 2.14/2.40 24 -in(ordered_pair(A,B),c3) | in(ordered_pair(A,B),c6) # label(t110_zfmisc_1) # label(negated_conjecture). [clausify(10)].
% 2.14/2.40 25 -in(unordered_pair(singleton(A),unordered_pair(A,B)),c3) | in(unordered_pair(singleton(A),unordered_pair(A,B)),c6). [copy(24),rewrite([17(1),17(6)])].
% 2.14/2.40 26 in(ordered_pair(A,B),c3) | -in(ordered_pair(A,B),c6) # label(t110_zfmisc_1) # label(negated_conjecture). [clausify(10)].
% 2.14/2.40 27 in(unordered_pair(singleton(A),unordered_pair(A,B)),c3) | -in(unordered_pair(singleton(A),unordered_pair(A,B)),c6). [copy(26),rewrite([17(1),17(6)])].
% 2.14/2.40 28 -in(f3(A,B),A) | -in(f3(A,B),B) | B = A # label(t2_tarski) # label(axiom). [clausify(9)].
% 2.14/2.40 31 -subset(A,cartesian_product2(B,C)) | -in(D,A) | ordered_pair(f1(A,B,C,D),f2(A,B,C,D)) = D # label(t103_zfmisc_1) # label(axiom). [clausify(8)].
% 2.14/2.40 32 -subset(A,cartesian_product2(B,C)) | -in(D,A) | unordered_pair(singleton(f1(A,B,C,D)),unordered_pair(f1(A,B,C,D),f2(A,B,C,D))) = D. [copy(31),rewrite([17(6)])].
% 2.14/2.40 42 -in(A,c6) | unordered_pair(singleton(f1(c6,c7,c8,A)),unordered_pair(f1(c6,c7,c8,A),f2(c6,c7,c8,A))) = A. [resolve(32,a,14,a)].
% 2.14/2.40 43 -in(A,c3) | unordered_pair(singleton(f1(c3,c4,c5,A)),unordered_pair(f1(c3,c4,c5,A),f2(c3,c4,c5,A))) = A. [resolve(32,a,13,a)].
% 2.14/2.40 69 unordered_pair(singleton(f1(c6,c7,c8,f3(A,c6))),unordered_pair(f1(c6,c7,c8,f3(A,c6)),f2(c6,c7,c8,f3(A,c6)))) = f3(A,c6) | in(f3(A,c6),A) | c6 = A. [resolve(42,a,18,b)].
% 2.14/2.40 98 unordered_pair(singleton(f1(c3,c4,c5,f3(c3,A))),unordered_pair(f1(c3,c4,c5,f3(c3,A)),f2(c3,c4,c5,f3(c3,A)))) = f3(c3,A) | in(f3(c3,A),A) | c3 = A. [resolve(43,a,18,a),flip(c)].
% 2.14/2.40 232 unordered_pair(singleton(f1(c6,c7,c8,f3(c3,c6))),unordered_pair(f1(c6,c7,c8,f3(c3,c6)),f2(c6,c7,c8,f3(c3,c6)))) = f3(c3,c6) | unordered_pair(singleton(f1(c3,c4,c5,f3(c3,c6))),unordered_pair(f1(c3,c4,c5,f3(c3,c6)),f2(c3,c4,c5,f3(c3,c6)))) = f3(c3,c6). [resolve(69,b,43,a),unit_del(b,20)].
% 2.14/2.40 1264 unordered_pair(singleton(f1(c3,c4,c5,f3(c3,c6))),unordered_pair(f1(c3,c4,c5,f3(c3,c6)),f2(c3,c4,c5,f3(c3,c6)))) = f3(c3,c6) | in(unordered_pair(singleton(f1(c6,c7,c8,f3(c3,c6))),unordered_pair(f1(c6,c7,c8,f3(c3,c6)),f2(c6,c7,c8,f3(c3,c6)))),c3) | -in(f3(c3,c6),c6). [para(232(a,1),27(b,1))].
% 2.14/2.40 4821 unordered_pair(singleton(f1(c3,c4,c5,f3(c3,c6))),unordered_pair(f1(c3,c4,c5,f3(c3,c6)),f2(c3,c4,c5,f3(c3,c6)))) = f3(c3,c6) | in(unordered_pair(singleton(f1(c6,c7,c8,f3(c3,c6))),unordered_pair(f1(c6,c7,c8,f3(c3,c6)),f2(c6,c7,c8,f3(c3,c6)))),c3). [resolve(1264,c,98,b),flip(d),merge(c),unit_del(c,20)].
% 2.14/2.40 4827 unordered_pair(singleton(f1(c3,c4,c5,f3(c3,c6))),unordered_pair(f1(c3,c4,c5,f3(c3,c6)),f2(c3,c4,c5,f3(c3,c6)))) = f3(c3,c6) | in(f3(c3,c6),c3). [para(232(a,1),4821(b,1)),merge(b)].
% 2.14/2.40 4833 unordered_pair(singleton(f1(c3,c4,c5,f3(c3,c6))),unordered_pair(f1(c3,c4,c5,f3(c3,c6)),f2(c3,c4,c5,f3(c3,c6)))) = f3(c3,c6). [resolve(4827,b,43,a),merge(b)].
% 2.14/2.40 4837 -in(f3(c3,c6),c3) | in(f3(c3,c6),c6). [para(4833(a,1),25(a,1)),rewrite([4833(29)])].
% 2.14/2.40 4839 in(f3(c3,c6),c3) | -in(f3(c3,c6),c6). [para(4833(a,1),27(b,1)),rewrite([4833(24)])].
% 2.14/2.40 4843 in(f3(c3,c6),c6). [resolve(4837,a,18,a),merge(b),unit_del(b,20)].
% 2.14/2.40 4844 in(f3(c3,c6),c3). [back_unit_del(4839),unit_del(b,4843)].
% 2.14/2.40 4848 $F. [resolve(4843,a,28,b),unit_del(a,4844),unit_del(b,20)].
% 2.14/2.40
% 2.14/2.40 % SZS output end Refutation
% 2.14/2.40 ============================== end of proof ==========================
% 2.14/2.40
% 2.14/2.40 ============================== STATISTICS ============================
% 2.14/2.40
% 2.14/2.40 Given=1988. Generated=13587. Kept=4832. proofs=1.
% 2.14/2.40 Usable=1977. Sos=2800. Demods=4. Limbo=3, Disabled=69. Hints=0.
% 2.14/2.40 Megabytes=15.51.
% 2.14/2.40 User_CPU=1.42, System_CPU=0.01, Wall_clock=1.
% 2.14/2.40
% 2.14/2.40 ============================== end of statistics =====================
% 2.14/2.40
% 2.14/2.40 ============================== end of search =========================
% 2.14/2.40
% 2.14/2.40 THEOREM PROVED
% 2.14/2.40 % SZS status Theorem
% 2.14/2.40
% 2.14/2.40 Exiting with 1 proof.
% 2.14/2.40
% 2.14/2.40 Process 29123 exit (max_proofs) Sun Jul 10 08:02:04 2022
% 2.14/2.40 Prover9 interrupted
%------------------------------------------------------------------------------