TSTP Solution File: SET930+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET930+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 04:33:31 EDT 2022
% Result : Theorem 1.63s 1.94s
% Output : Refutation 1.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET930+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 9 21:24:20 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.41/0.98 ============================== Prover9 ===============================
% 0.41/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.41/0.98 Process 32257 was started by sandbox2 on n014.cluster.edu,
% 0.41/0.98 Sat Jul 9 21:24:21 2022
% 0.41/0.98 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_32104_n014.cluster.edu".
% 0.41/0.98 ============================== end of head ===========================
% 0.41/0.98
% 0.41/0.98 ============================== INPUT =================================
% 0.41/0.98
% 0.41/0.98 % Reading from file /tmp/Prover9_32104_n014.cluster.edu
% 0.41/0.98
% 0.41/0.98 set(prolog_style_variables).
% 0.41/0.98 set(auto2).
% 0.41/0.98 % set(auto2) -> set(auto).
% 0.41/0.98 % set(auto) -> set(auto_inference).
% 0.41/0.98 % set(auto) -> set(auto_setup).
% 0.41/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.41/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/0.98 % set(auto) -> set(auto_limits).
% 0.41/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/0.98 % set(auto) -> set(auto_denials).
% 0.41/0.98 % set(auto) -> set(auto_process).
% 0.41/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.41/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.41/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.41/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.41/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.41/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.41/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.41/0.98 % set(auto2) -> assign(stats, some).
% 0.41/0.98 % set(auto2) -> clear(echo_input).
% 0.41/0.98 % set(auto2) -> set(quiet).
% 0.41/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.41/0.98 % set(auto2) -> clear(print_given).
% 0.41/0.98 assign(lrs_ticks,-1).
% 0.41/0.98 assign(sos_limit,10000).
% 0.41/0.98 assign(order,kbo).
% 0.41/0.98 set(lex_order_vars).
% 0.41/0.98 clear(print_given).
% 0.41/0.98
% 0.41/0.98 % formulas(sos). % not echoed (9 formulas)
% 0.41/0.98
% 0.41/0.98 ============================== end of input ==========================
% 0.41/0.98
% 0.41/0.98 % From the command line: assign(max_seconds, 300).
% 0.41/0.98
% 0.41/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/0.98
% 0.41/0.98 % Formulas that are not ordinary clauses:
% 0.41/0.98 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 3 (all A all B all C (set_difference(unordered_pair(A,B),C) = singleton(A) <-> -in(A,C) & (in(B,C) | A = B))) # label(l39_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 4 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 5 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 6 (all A all B all C (set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) <-> -in(A,C) & -in(B,C))) # label(t72_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 7 (all A all B all C (set_difference(unordered_pair(A,B),C) = empty_set <-> in(A,C) & in(B,C))) # label(t73_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 8 -(all A all B all C -(set_difference(unordered_pair(A,B),C) != empty_set & set_difference(unordered_pair(A,B),C) != singleton(A) & set_difference(unordered_pair(A,B),C) != singleton(B) & set_difference(unordered_pair(A,B),C) != unordered_pair(A,B))) # label(t74_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.41/0.98
% 0.41/0.98 ============================== end of process non-clausal formulas ===
% 0.41/0.98
% 0.41/0.98 ============================== PROCESS INITIAL CLAUSES ===============
% 0.41/0.98
% 0.41/0.98 ============================== PREDICATE ELIMINATION =================
% 0.41/0.98
% 0.41/0.98 ============================== end predicate elimination =============
% 0.41/0.98
% 0.41/0.98 Auto_denials: (non-Horn, no changes).
% 0.41/0.98
% 0.41/0.98 Term ordering decisions:
% 0.41/0.98
% 0.41/0.98 % Assigning unary symbol singleton kb_weight 0 and highest precedence (12).
% 0.41/0.98 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. unordered_pair=1. set_difference=1. singleton=0.
% 0.41/0.98
% 0.41/0.98 ============================== end of process initial clauses ========
% 0.41/0.98
% 0.41/0.98 ============================== CLAUSES FOR SEARCH ====================
% 1.63/1.94
% 1.63/1.94 ============================== end of clauses for search =============
% 1.63/1.94
% 1.63/1.94 ============================== SEARCH ================================
% 1.63/1.94
% 1.63/1.94 % Starting search at 0.01 seconds.
% 1.63/1.94
% 1.63/1.94 Low Water (keep): wt=66.000, iters=3357
% 1.63/1.94
% 1.63/1.94 Low Water (keep): wt=64.000, iters=3351
% 1.63/1.94
% 1.63/1.94 Low Water (keep): wt=61.000, iters=3362
% 1.63/1.94
% 1.63/1.94 Low Water (keep): wt=58.000, iters=3341
% 1.63/1.94
% 1.63/1.94 Low Water (keep): wt=56.000, iters=3342
% 1.63/1.94
% 1.63/1.94 Low Water (keep): wt=54.000, iters=3340
% 1.63/1.94
% 1.63/1.94 Low Water (keep): wt=53.000, iters=3348
% 1.63/1.94
% 1.63/1.94 Low Water (keep): wt=52.000, iters=3341
% 1.63/1.94
% 1.63/1.94 ============================== PROOF =================================
% 1.63/1.94 % SZS status Theorem
% 1.63/1.94 % SZS output start Refutation
% 1.63/1.94
% 1.63/1.94 % Proof 1 at 0.96 (+ 0.01) seconds.
% 1.63/1.94 % Length of proof is 51.
% 1.63/1.94 % Level of proof is 12.
% 1.63/1.94 % Maximum clause weight is 21.000.
% 1.63/1.94 % Given clauses 458.
% 1.63/1.94
% 1.63/1.94 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.94 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.94 3 (all A all B all C (set_difference(unordered_pair(A,B),C) = singleton(A) <-> -in(A,C) & (in(B,C) | A = B))) # label(l39_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.94 6 (all A all B all C (set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) <-> -in(A,C) & -in(B,C))) # label(t72_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.94 7 (all A all B all C (set_difference(unordered_pair(A,B),C) = empty_set <-> in(A,C) & in(B,C))) # label(t73_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.94 8 -(all A all B all C -(set_difference(unordered_pair(A,B),C) != empty_set & set_difference(unordered_pair(A,B),C) != singleton(A) & set_difference(unordered_pair(A,B),C) != singleton(B) & set_difference(unordered_pair(A,B),C) != unordered_pair(A,B))) # label(t74_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.63/1.94 11 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(2)].
% 1.63/1.94 12 set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) | in(A,C) | in(B,C) # label(t72_zfmisc_1) # label(axiom). [clausify(6)].
% 1.63/1.94 14 -in(A,B) | -in(B,A) # label(antisymmetry_r2_hidden) # label(axiom). [clausify(1)].
% 1.63/1.94 15 set_difference(unordered_pair(c3,c4),c5) != empty_set # label(t74_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 1.63/1.94 16 singleton(c3) != set_difference(unordered_pair(c3,c4),c5) # label(t74_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 1.63/1.94 17 set_difference(unordered_pair(c3,c4),c5) != singleton(c3). [copy(16),flip(a)].
% 1.63/1.94 18 singleton(c4) != set_difference(unordered_pair(c3,c4),c5) # label(t74_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 1.63/1.94 19 set_difference(unordered_pair(c3,c4),c5) != singleton(c4). [copy(18),flip(a)].
% 1.63/1.94 20 set_difference(unordered_pair(c3,c4),c5) != unordered_pair(c3,c4) # label(t74_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 1.63/1.94 21 singleton(A) != set_difference(unordered_pair(A,B),C) | -in(A,C) # label(l39_zfmisc_1) # label(axiom). [clausify(3)].
% 1.63/1.94 22 set_difference(unordered_pair(A,B),C) != singleton(A) | -in(A,C). [copy(21),flip(a)].
% 1.63/1.94 23 set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) | -in(A,C) # label(t72_zfmisc_1) # label(axiom). [clausify(6)].
% 1.63/1.94 25 set_difference(unordered_pair(A,B),C) != empty_set | in(A,C) # label(t73_zfmisc_1) # label(axiom). [clausify(7)].
% 1.63/1.94 27 set_difference(unordered_pair(A,B),C) = empty_set | -in(A,C) | -in(B,C) # label(t73_zfmisc_1) # label(axiom). [clausify(7)].
% 1.63/1.94 30 singleton(A) = set_difference(unordered_pair(A,B),C) | in(A,C) | -in(B,C) # label(l39_zfmisc_1) # label(axiom). [clausify(3)].
% 1.63/1.94 31 set_difference(unordered_pair(A,B),C) = singleton(A) | in(A,C) | -in(B,C). [copy(30),flip(a)].
% 1.63/1.94 32 singleton(A) = set_difference(unordered_pair(A,B),C) | in(A,C) | B != A # label(l39_zfmisc_1) # label(axiom). [clausify(3)].
% 1.63/1.94 33 set_difference(unordered_pair(A,B),C) = singleton(A) | in(A,C) | B != A. [copy(32),flip(a)].
% 1.63/1.94 34 set_difference(unordered_pair(A,A),B) = unordered_pair(A,A) | in(A,B). [factor(12,b,c)].
% 1.63/1.94 35 -in(A,A). [factor(14,a,b)].
% 1.63/1.94 36 set_difference(unordered_pair(A,A),B) = empty_set | -in(A,B). [factor(27,b,c)].
% 1.63/1.94 38 set_difference(unordered_pair(A,B),C) != singleton(A) | set_difference(unordered_pair(A,D),C) = unordered_pair(A,D) | in(D,C). [resolve(22,b,12,c),rewrite([11(5),11(7)])].
% 1.63/1.94 47 set_difference(unordered_pair(A,A),B) = singleton(A) | in(A,B). [xx_res(33,c)].
% 1.63/1.94 53 set_difference(unordered_pair(A,A),A) = unordered_pair(A,A). [resolve(35,a,34,b)].
% 1.63/1.94 55 set_difference(unordered_pair(A,B),A) = unordered_pair(A,B) | in(B,A). [resolve(35,a,12,b)].
% 1.63/1.94 78 unordered_pair(A,A) != empty_set. [para(53(a,1),25(a,1)),unit_del(b,35)].
% 1.63/1.94 81 unordered_pair(A,A) = singleton(A). [resolve(47,b,35,a),rewrite([53(2)])].
% 1.63/1.94 82 set_difference(singleton(A),B) = singleton(A) | set_difference(unordered_pair(A,C),B) = singleton(C) | in(C,B). [resolve(47,b,31,c),rewrite([81(1),11(5)])].
% 1.63/1.94 83 set_difference(singleton(A),B) = singleton(A) | set_difference(unordered_pair(A,C),B) = empty_set | -in(C,B). [resolve(47,b,27,c),rewrite([81(1),11(5)])].
% 1.63/1.94 89 singleton(A) != empty_set. [back_rewrite(78),rewrite([81(1)])].
% 1.63/1.94 92 set_difference(singleton(A),B) = singleton(A) | in(A,B). [back_rewrite(47),rewrite([81(1)])].
% 1.63/1.94 93 set_difference(singleton(A),B) = empty_set | -in(A,B). [back_rewrite(36),rewrite([81(1)])].
% 1.63/1.94 96 set_difference(singleton(A),B) != singleton(A) | set_difference(unordered_pair(A,C),B) = unordered_pair(A,C) | in(C,B). [para(81(a,1),38(a,1,1))].
% 1.63/1.94 130 set_difference(unordered_pair(A,B),A) = unordered_pair(A,B) | set_difference(unordered_pair(B,C),A) != singleton(B). [resolve(55,b,22,b)].
% 1.63/1.94 397 set_difference(singleton(A),B) = singleton(A) | set_difference(unordered_pair(A,C),B) = empty_set | set_difference(singleton(C),B) = singleton(C). [resolve(83,c,92,b)].
% 1.63/1.94 460 set_difference(unordered_pair(A,B),A) = unordered_pair(A,B) | set_difference(singleton(B),A) != singleton(B). [para(81(a,1),130(b,1,1))].
% 1.63/1.94 510 set_difference(singleton(A),B) = singleton(A) | set_difference(unordered_pair(A,C),B) = singleton(C) | set_difference(singleton(C),B) = empty_set. [resolve(82,c,93,b)].
% 1.63/1.94 5139 set_difference(singleton(c3),c5) = singleton(c3) | set_difference(singleton(c4),c5) = singleton(c4). [resolve(397,b,15,a)].
% 1.63/1.94 5271 set_difference(singleton(c3),c5) = singleton(c3) | set_difference(singleton(c4),c5) = empty_set. [resolve(510,b,19,a)].
% 1.63/1.94 5306 set_difference(singleton(c3),c5) = singleton(c3). [para(5271(b,1),5139(b,1)),flip(c),merge(b),unit_del(b,89)].
% 1.63/1.94 5307 set_difference(unordered_pair(c3,c5),c5) = unordered_pair(c3,c5). [resolve(5306,a,460,b),rewrite([11(3),11(8)])].
% 1.63/1.94 5308 set_difference(unordered_pair(A,c3),c5) = unordered_pair(A,c3) | in(A,c5). [resolve(5306,a,96,a),rewrite([11(2),11(6)])].
% 1.63/1.94 5309 -in(c3,c5). [ur(23,a,5307,a)].
% 1.63/1.94 5347 -in(c4,c5). [ur(31,a,17,a,b,5309,a)].
% 1.63/1.94 5351 $F. [resolve(5347,a,5308,b),rewrite([11(3),11(8)]),unit_del(a,20)].
% 1.63/1.94
% 1.63/1.94 % SZS output end Refutation
% 1.63/1.94 ============================== end of proof ==========================
% 1.63/1.94
% 1.63/1.94 ============================== STATISTICS ============================
% 1.63/1.94
% 1.63/1.94 Given=458. Generated=14525. Kept=5336. proofs=1.
% 1.63/1.94 Usable=443. Sos=4733. Demods=7. Limbo=0, Disabled=179. Hints=0.
% 1.63/1.94 Megabytes=9.50.
% 1.63/1.94 User_CPU=0.96, System_CPU=0.01, Wall_clock=1.
% 1.63/1.94
% 1.63/1.94 ============================== end of statistics =====================
% 1.63/1.94
% 1.63/1.94 ============================== end of search =========================
% 1.63/1.94
% 1.63/1.94 THEOREM PROVED
% 1.63/1.94 % SZS status Theorem
% 1.63/1.94
% 1.63/1.94 Exiting with 1 proof.
% 1.63/1.94
% 1.63/1.94 Process 32257 exit (max_proofs) Sat Jul 9 21:24:22 2022
% 1.63/1.94 Prover9 interrupted
%------------------------------------------------------------------------------