TSTP Solution File: SET927+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET927+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : Tue Jul 19 04:33:29 EDT 2022
% Result : Theorem 0.73s 1.01s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET927+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 04:58:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/1.01 ============================== Prover9 ===============================
% 0.43/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.01 Process 29400 was started by sandbox2 on n022.cluster.edu,
% 0.43/1.01 Mon Jul 11 04:58:41 2022
% 0.43/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_29247_n022.cluster.edu".
% 0.43/1.01 ============================== end of head ===========================
% 0.43/1.01
% 0.43/1.01 ============================== INPUT =================================
% 0.43/1.01
% 0.43/1.01 % Reading from file /tmp/Prover9_29247_n022.cluster.edu
% 0.43/1.01
% 0.43/1.01 set(prolog_style_variables).
% 0.43/1.01 set(auto2).
% 0.43/1.01 % set(auto2) -> set(auto).
% 0.43/1.01 % set(auto) -> set(auto_inference).
% 0.43/1.01 % set(auto) -> set(auto_setup).
% 0.43/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.01 % set(auto) -> set(auto_limits).
% 0.43/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.01 % set(auto) -> set(auto_denials).
% 0.43/1.01 % set(auto) -> set(auto_process).
% 0.43/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.01 % set(auto2) -> assign(stats, some).
% 0.43/1.01 % set(auto2) -> clear(echo_input).
% 0.43/1.01 % set(auto2) -> set(quiet).
% 0.43/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.01 % set(auto2) -> clear(print_given).
% 0.43/1.01 assign(lrs_ticks,-1).
% 0.43/1.01 assign(sos_limit,10000).
% 0.43/1.01 assign(order,kbo).
% 0.43/1.01 set(lex_order_vars).
% 0.43/1.01 clear(print_given).
% 0.43/1.01
% 0.43/1.01 % formulas(sos). % not echoed (6 formulas)
% 0.43/1.01
% 0.43/1.01 ============================== end of input ==========================
% 0.43/1.01
% 0.43/1.01 % From the command line: assign(max_seconds, 300).
% 0.43/1.01
% 0.43/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/1.01
% 0.73/1.01 % Formulas that are not ordinary clauses:
% 0.73/1.01 1 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.01 2 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.01 3 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.01 4 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.01 5 (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].
% 0.73/1.01 6 -(all A all B all C (set_difference(unordered_pair(A,B),C) = singleton(A) <-> -in(A,C) & (in(B,C) | A = B))) # label(t70_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.01
% 0.73/1.01 ============================== end of process non-clausal formulas ===
% 0.73/1.01
% 0.73/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.01
% 0.73/1.01 ============================== PREDICATE ELIMINATION =================
% 0.73/1.01
% 0.73/1.01 ============================== end predicate elimination =============
% 0.73/1.01
% 0.73/1.01 Auto_denials: (non-Horn, no changes).
% 0.73/1.01
% 0.73/1.01 Term ordering decisions:
% 0.73/1.01
% 0.73/1.01 % Assigning unary symbol singleton kb_weight 0 and highest precedence (11).
% 0.73/1.01 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. unordered_pair=1. set_difference=1. singleton=0.
% 0.73/1.01
% 0.73/1.01 ============================== end of process initial clauses ========
% 0.73/1.01
% 0.73/1.01 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.01
% 0.73/1.01 ============================== end of clauses for search =============
% 0.73/1.01
% 0.73/1.01 ============================== SEARCH ================================
% 0.73/1.01
% 0.73/1.01 % Starting search at 0.01 seconds.
% 0.73/1.01
% 0.73/1.01 ============================== PROOF =================================
% 0.73/1.01 % SZS status Theorem
% 0.73/1.01 % SZS output start Refutation
% 0.73/1.01
% 0.73/1.01 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.73/1.01 % Length of proof is 34.
% 0.73/1.01 % Level of proof is 11.
% 0.73/1.01 % Maximum clause weight is 22.000.
% 0.73/1.01 % Given clauses 40.
% 0.73/1.02
% 0.73/1.02 1 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 5 (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].
% 0.73/1.02 6 -(all A all B all C (set_difference(unordered_pair(A,B),C) = singleton(A) <-> -in(A,C) & (in(B,C) | A = B))) # label(t70_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.02 8 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(1)].
% 0.73/1.02 9 singleton(c3) = set_difference(unordered_pair(c3,c4),c5) | in(c4,c5) | c4 = c3 # label(t70_zfmisc_1) # label(negated_conjecture). [clausify(6)].
% 0.73/1.02 10 set_difference(unordered_pair(c3,c4),c5) = singleton(c3) | in(c4,c5) | c4 = c3. [copy(9),flip(a)].
% 0.73/1.02 13 singleton(A) != set_difference(unordered_pair(A,B),C) | -in(A,C) # label(l39_zfmisc_1) # label(axiom). [clausify(5)].
% 0.73/1.02 14 set_difference(unordered_pair(A,B),C) != singleton(A) | -in(A,C). [copy(13),flip(a)].
% 0.73/1.02 15 singleton(c3) = set_difference(unordered_pair(c3,c4),c5) | -in(c3,c5) # label(t70_zfmisc_1) # label(negated_conjecture). [clausify(6)].
% 0.73/1.02 16 set_difference(unordered_pair(c3,c4),c5) = singleton(c3) | -in(c3,c5). [copy(15),flip(a)].
% 0.73/1.02 17 singleton(A) != set_difference(unordered_pair(A,B),C) | in(B,C) | B = A # label(l39_zfmisc_1) # label(axiom). [clausify(5)].
% 0.73/1.02 18 set_difference(unordered_pair(A,B),C) != singleton(A) | in(B,C) | B = A. [copy(17),flip(a)].
% 0.73/1.02 19 singleton(A) = set_difference(unordered_pair(A,B),C) | in(A,C) | -in(B,C) # label(l39_zfmisc_1) # label(axiom). [clausify(5)].
% 0.73/1.02 20 set_difference(unordered_pair(A,B),C) = singleton(A) | in(A,C) | -in(B,C). [copy(19),flip(a)].
% 0.73/1.02 21 singleton(A) = set_difference(unordered_pair(A,B),C) | in(A,C) | B != A # label(l39_zfmisc_1) # label(axiom). [clausify(5)].
% 0.73/1.02 22 set_difference(unordered_pair(A,B),C) = singleton(A) | in(A,C) | B != A. [copy(21),flip(a)].
% 0.73/1.02 23 singleton(c3) != set_difference(unordered_pair(c3,c4),c5) | in(c3,c5) | -in(c4,c5) # label(t70_zfmisc_1) # label(negated_conjecture). [clausify(6)].
% 0.73/1.02 24 set_difference(unordered_pair(c3,c4),c5) != singleton(c3) | in(c3,c5) | -in(c4,c5). [copy(23),flip(a)].
% 0.73/1.02 25 singleton(c3) != set_difference(unordered_pair(c3,c4),c5) | in(c3,c5) | c4 != c3 # label(t70_zfmisc_1) # label(negated_conjecture). [clausify(6)].
% 0.73/1.02 26 set_difference(unordered_pair(c3,c4),c5) != singleton(c3) | in(c3,c5) | c4 != c3. [copy(25),flip(a)].
% 0.73/1.02 31 set_difference(unordered_pair(A,c4),c5) = singleton(A) | in(A,c5) | set_difference(unordered_pair(c3,c4),c5) = singleton(c3) | c4 = c3. [resolve(20,c,10,b)].
% 0.73/1.02 32 set_difference(unordered_pair(c3,c4),c5) = singleton(c3) | in(c3,c5) | c4 = c3. [factor(31,a,c)].
% 0.73/1.02 34 set_difference(unordered_pair(A,A),B) = singleton(A) | in(A,B). [xx_res(22,c)].
% 0.73/1.02 39 set_difference(unordered_pair(c3,c3),c5) = singleton(c3) | set_difference(unordered_pair(c3,c4),c5) = singleton(c3). [resolve(34,b,16,b)].
% 0.73/1.02 40 set_difference(unordered_pair(A,A),B) = singleton(A) | set_difference(unordered_pair(A,C),B) != singleton(A). [resolve(34,b,14,b)].
% 0.73/1.02 45 set_difference(unordered_pair(c3,c4),c5) = singleton(c3) | c4 = c3. [resolve(32,b,16,b),merge(c)].
% 0.73/1.02 47 c4 = c3 | in(c4,c5). [resolve(45,a,18,a),merge(c)].
% 0.73/1.02 51 c4 = c3 | set_difference(unordered_pair(c3,c4),c5) != singleton(c3) | in(c3,c5). [resolve(47,b,24,c)].
% 0.73/1.02 67 c4 = c3 | in(c3,c5). [resolve(51,b,45,a),merge(c)].
% 0.73/1.02 70 c4 = c3 | set_difference(unordered_pair(A,c3),c5) != singleton(c3). [resolve(67,b,14,b),rewrite([8(5)])].
% 0.73/1.02 86 set_difference(unordered_pair(c3,c3),c5) = singleton(c3). [resolve(40,b,39,b),merge(b)].
% 0.73/1.02 88 c4 = c3. [resolve(86,a,70,b)].
% 0.73/1.02 89 -in(c3,c5). [ur(14,a,86,a)].
% 0.73/1.02 91 $F. [back_rewrite(26),rewrite([88(2),86(5),88(9)]),xx(a),xx(c),unit_del(a,89)].
% 0.73/1.02
% 0.73/1.02 % SZS output end Refutation
% 0.73/1.02 ============================== end of proof ==========================
% 0.73/1.02
% 0.73/1.02 ============================== STATISTICS ============================
% 0.73/1.02
% 0.73/1.02 Given=40. Generated=185. Kept=76. proofs=1.
% 0.73/1.02 Usable=18. Sos=6. Demods=4. Limbo=3, Disabled=61. Hints=0.
% 0.73/1.02 Megabytes=0.11.
% 0.73/1.02 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.73/1.02
% 0.73/1.02 ============================== end of statistics =====================
% 0.73/1.02
% 0.73/1.02 ============================== end of search =========================
% 0.73/1.02
% 0.73/1.02 THEOREM PROVED
% 0.73/1.02 % SZS status Theorem
% 0.73/1.02
% 0.73/1.02 Exiting with 1 proof.
% 0.73/1.02
% 0.73/1.02 Process 29400 exit (max_proofs) Mon Jul 11 04:58:41 2022
% 0.73/1.02 Prover9 interrupted
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