TSTP Solution File: SET975+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET975+1 : TPTP v8.1.0. Released v3.2.0.
% 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 04:33:47 EDT 2022
% Result : Theorem 0.45s 1.04s
% Output : Refutation 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET975+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 13:11:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.45/1.03 ============================== Prover9 ===============================
% 0.45/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.03 Process 15996 was started by sandbox2 on n027.cluster.edu,
% 0.45/1.03 Sun Jul 10 13:11:48 2022
% 0.45/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_15843_n027.cluster.edu".
% 0.45/1.03 ============================== end of head ===========================
% 0.45/1.03
% 0.45/1.03 ============================== INPUT =================================
% 0.45/1.03
% 0.45/1.03 % Reading from file /tmp/Prover9_15843_n027.cluster.edu
% 0.45/1.03
% 0.45/1.03 set(prolog_style_variables).
% 0.45/1.03 set(auto2).
% 0.45/1.03 % set(auto2) -> set(auto).
% 0.45/1.03 % set(auto) -> set(auto_inference).
% 0.45/1.03 % set(auto) -> set(auto_setup).
% 0.45/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.03 % set(auto) -> set(auto_limits).
% 0.45/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.03 % set(auto) -> set(auto_denials).
% 0.45/1.03 % set(auto) -> set(auto_process).
% 0.45/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.03 % set(auto2) -> assign(stats, some).
% 0.45/1.03 % set(auto2) -> clear(echo_input).
% 0.45/1.03 % set(auto2) -> set(quiet).
% 0.45/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.03 % set(auto2) -> clear(print_given).
% 0.45/1.03 assign(lrs_ticks,-1).
% 0.45/1.03 assign(sos_limit,10000).
% 0.45/1.03 assign(order,kbo).
% 0.45/1.03 set(lex_order_vars).
% 0.45/1.03 clear(print_given).
% 0.45/1.03
% 0.45/1.03 % formulas(sos). % not echoed (9 formulas)
% 0.45/1.03
% 0.45/1.03 ============================== end of input ==========================
% 0.45/1.03
% 0.45/1.03 % From the command line: assign(max_seconds, 300).
% 0.45/1.03
% 0.45/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.03
% 0.45/1.03 % Formulas that are not ordinary clauses:
% 0.45/1.03 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 3 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 4 (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].
% 0.45/1.03 5 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 6 (all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(C,D)) <-> in(A,C) & in(B,D))) # label(l55_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 7 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 8 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 9 -(all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(singleton(C),D)) <-> A = C & in(B,D))) # label(t128_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/1.03
% 0.45/1.03 ============================== end of process non-clausal formulas ===
% 0.45/1.03
% 0.45/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/1.03
% 0.45/1.03 ============================== PREDICATE ELIMINATION =================
% 0.45/1.03
% 0.45/1.03 ============================== end predicate elimination =============
% 0.45/1.03
% 0.45/1.03 Auto_denials: (non-Horn, no changes).
% 0.45/1.03
% 0.45/1.03 Term ordering decisions:
% 0.45/1.03
% 0.45/1.03 % Assigning unary symbol singleton kb_weight 0 and highest precedence (14).
% 0.45/1.03 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. ordered_pair=1. cartesian_product2=1. unordered_pair=1. f1=1. singleton=0.
% 0.45/1.03
% 0.45/1.03 ============================== end of process initial clauses ========
% 0.45/1.03
% 0.45/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.45/1.03
% 0.45/1.03 ============================== end of clauses for search =============
% 0.45/1.04
% 0.45/1.04 ============================== SEARCH ================================
% 0.45/1.04
% 0.45/1.04 % Starting search at 0.01 seconds.
% 0.45/1.04
% 0.45/1.04 ============================== PROOF =================================
% 0.45/1.04 % SZS status Theorem
% 0.45/1.04 % SZS output start Refutation
% 0.45/1.04
% 0.45/1.04 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.45/1.04 % Length of proof is 33.
% 0.45/1.04 % Level of proof is 8.
% 0.45/1.04 % Maximum clause weight is 17.000.
% 0.45/1.04 % Given clauses 51.
% 0.45/1.04
% 0.45/1.04 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.04 3 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.04 4 (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].
% 0.45/1.04 6 (all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(C,D)) <-> in(A,C) & in(B,D))) # label(l55_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.04 9 -(all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(singleton(C),D)) <-> A = C & in(B,D))) # label(t128_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/1.04 11 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(2)].
% 0.45/1.04 12 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom). [clausify(4)].
% 0.45/1.04 13 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)). [copy(12),rewrite([11(4)])].
% 0.45/1.04 14 in(ordered_pair(c3,c4),cartesian_product2(singleton(c5),c6)) | c5 = c3 # label(t128_zfmisc_1) # label(negated_conjecture). [clausify(9)].
% 0.45/1.04 15 in(unordered_pair(singleton(c3),unordered_pair(c3,c4)),cartesian_product2(singleton(c5),c6)) | c5 = c3. [copy(14),rewrite([13(3)])].
% 0.45/1.04 16 in(ordered_pair(c3,c4),cartesian_product2(singleton(c5),c6)) | in(c4,c6) # label(t128_zfmisc_1) # label(negated_conjecture). [clausify(9)].
% 0.45/1.04 17 in(unordered_pair(singleton(c3),unordered_pair(c3,c4)),cartesian_product2(singleton(c5),c6)) | in(c4,c6). [copy(16),rewrite([13(3)])].
% 0.45/1.04 23 -in(ordered_pair(c3,c4),cartesian_product2(singleton(c5),c6)) | c5 != c3 | -in(c4,c6) # label(t128_zfmisc_1) # label(negated_conjecture). [clausify(9)].
% 0.45/1.04 24 -in(unordered_pair(singleton(c3),unordered_pair(c3,c4)),cartesian_product2(singleton(c5),c6)) | c5 != c3 | -in(c4,c6). [copy(23),rewrite([13(3)])].
% 0.45/1.04 25 singleton(A) != B | -in(C,B) | C = A # label(d1_tarski) # label(axiom). [clausify(3)].
% 0.45/1.04 26 singleton(A) != B | in(C,B) | C != A # label(d1_tarski) # label(axiom). [clausify(3)].
% 0.45/1.04 27 -in(ordered_pair(A,B),cartesian_product2(C,D)) | in(A,C) # label(l55_zfmisc_1) # label(axiom). [clausify(6)].
% 0.45/1.04 28 -in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | in(A,C). [copy(27),rewrite([13(1)])].
% 0.45/1.04 29 -in(ordered_pair(A,B),cartesian_product2(C,D)) | in(B,D) # label(l55_zfmisc_1) # label(axiom). [clausify(6)].
% 0.45/1.04 30 -in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | in(B,D). [copy(29),rewrite([13(1)])].
% 0.45/1.04 31 in(ordered_pair(A,B),cartesian_product2(C,D)) | -in(A,C) | -in(B,D) # label(l55_zfmisc_1) # label(axiom). [clausify(6)].
% 0.45/1.04 32 in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | -in(A,C) | -in(B,D). [copy(31),rewrite([13(1)])].
% 0.45/1.04 43 in(A,singleton(B)) | A != B. [xx_res(26,a)].
% 0.45/1.04 48 in(c3,singleton(c5)) | c5 = c3. [resolve(28,a,15,a)].
% 0.45/1.04 49 in(c4,c6). [resolve(30,a,17,a),merge(b)].
% 0.45/1.04 50 -in(unordered_pair(singleton(c3),unordered_pair(c3,c4)),cartesian_product2(singleton(c5),c6)) | c5 != c3. [back_unit_del(24),unit_del(c,49)].
% 0.45/1.04 72 in(unordered_pair(singleton(A),unordered_pair(A,c4)),cartesian_product2(B,c6)) | -in(A,B). [resolve(49,a,32,c)].
% 0.45/1.04 79 in(A,singleton(A)). [xx_res(43,b)].
% 0.45/1.04 100 c5 = c3 | singleton(c5) != singleton(A) | c3 = A. [resolve(48,a,25,b),flip(b)].
% 0.45/1.04 119 c5 = c3. [xx_res(100,b),flip(b),merge(b)].
% 0.45/1.04 120 -in(unordered_pair(singleton(c3),unordered_pair(c3,c4)),cartesian_product2(singleton(c3),c6)). [back_rewrite(50),rewrite([119(7),119(12)]),xx(b)].
% 0.45/1.04 143 in(unordered_pair(singleton(A),unordered_pair(A,c4)),cartesian_product2(singleton(A),c6)). [resolve(72,b,79,a)].
% 0.45/1.04 144 $F. [resolve(143,a,120,a)].
% 0.45/1.04
% 0.45/1.04 % SZS output end Refutation
% 0.45/1.04 ============================== end of proof ==========================
% 0.45/1.04
% 0.45/1.04 ============================== STATISTICS ============================
% 0.45/1.04
% 0.45/1.04 Given=51. Generated=284. Kept=126. proofs=1.
% 0.45/1.04 Usable=44. Sos=55. Demods=3. Limbo=1, Disabled=41. Hints=0.
% 0.45/1.04 Megabytes=0.16.
% 0.45/1.04 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.45/1.04
% 0.45/1.04 ============================== end of statistics =====================
% 0.45/1.04
% 0.45/1.04 ============================== end of search =========================
% 0.45/1.04
% 0.45/1.04 THEOREM PROVED
% 0.45/1.04 % SZS status Theorem
% 0.45/1.04
% 0.45/1.04 Exiting with 1 proof.
% 0.45/1.04
% 0.45/1.04 Process 15996 exit (max_proofs) Sun Jul 10 13:11:48 2022
% 0.45/1.04 Prover9 interrupted
%------------------------------------------------------------------------------