TSTP Solution File: SEU156+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU156+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 13:29:27 EDT 2022
% Result : Theorem 0.82s 1.08s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU156+3 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.32 % Computer : n012.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sun Jun 19 01:45:08 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.41/1.06 ============================== Prover9 ===============================
% 0.41/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.41/1.06 Process 32259 was started by sandbox2 on n012.cluster.edu,
% 0.41/1.06 Sun Jun 19 01:45:09 2022
% 0.41/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_32106_n012.cluster.edu".
% 0.41/1.06 ============================== end of head ===========================
% 0.41/1.06
% 0.41/1.06 ============================== INPUT =================================
% 0.41/1.06
% 0.41/1.06 % Reading from file /tmp/Prover9_32106_n012.cluster.edu
% 0.41/1.06
% 0.41/1.06 set(prolog_style_variables).
% 0.41/1.06 set(auto2).
% 0.41/1.06 % set(auto2) -> set(auto).
% 0.41/1.06 % set(auto) -> set(auto_inference).
% 0.41/1.06 % set(auto) -> set(auto_setup).
% 0.41/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.41/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/1.06 % set(auto) -> set(auto_limits).
% 0.41/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/1.06 % set(auto) -> set(auto_denials).
% 0.41/1.06 % set(auto) -> set(auto_process).
% 0.41/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.41/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.41/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.41/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.41/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.41/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.41/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.41/1.06 % set(auto2) -> assign(stats, some).
% 0.41/1.06 % set(auto2) -> clear(echo_input).
% 0.41/1.06 % set(auto2) -> set(quiet).
% 0.41/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.41/1.06 % set(auto2) -> clear(print_given).
% 0.41/1.06 assign(lrs_ticks,-1).
% 0.41/1.06 assign(sos_limit,10000).
% 0.41/1.06 assign(order,kbo).
% 0.41/1.06 set(lex_order_vars).
% 0.41/1.06 clear(print_given).
% 0.41/1.06
% 0.41/1.06 % formulas(sos). % not echoed (12 formulas)
% 0.41/1.06
% 0.41/1.06 ============================== end of input ==========================
% 0.41/1.06
% 0.41/1.06 % From the command line: assign(max_seconds, 300).
% 0.41/1.06
% 0.41/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/1.06
% 0.41/1.06 % Formulas that are not ordinary clauses:
% 0.41/1.06 1 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 2 (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].
% 0.41/1.06 3 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 4 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 5 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 6 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 7 (all A all B all C all D -(unordered_pair(A,B) = unordered_pair(C,D) & A != C & A != D)) # label(t10_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 8 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 9 (all A all B (subset(singleton(A),singleton(B)) -> A = B)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 10 (all A all B all C (singleton(A) = unordered_pair(B,C) -> A = B)) # label(t8_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 11 (all A all B all C (singleton(A) = unordered_pair(B,C) -> B = C)) # label(t9_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 12 -(all A all B all C all D (ordered_pair(A,B) = ordered_pair(C,D) -> A = C & B = D)) # label(t33_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.41/1.06
% 0.41/1.06 ============================== end of process non-clausal formulas ===
% 0.41/1.06
% 0.41/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.41/1.06
% 0.41/1.06 ============================== PREDICATE ELIMINATION =================
% 0.41/1.06
% 0.41/1.06 ============================== end predicate elimination =============
% 0.41/1.06
% 0.41/1.06 Auto_denials: (non-Horn, no changes).
% 0.41/1.06
% 0.41/1.06 Term ordering decisions:
% 0.41/1.06
% 0.41/1.06 % Assigning unary symbol singleton kb_weight 0 and highest precedence (12).
% 0.82/1.08 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. unordered_pair=1. ordered_pair=1. singleton=0.
% 0.82/1.08
% 0.82/1.08 ============================== end of process initial clauses ========
% 0.82/1.08
% 0.82/1.08 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.08
% 0.82/1.08 ============================== end of clauses for search =============
% 0.82/1.08
% 0.82/1.08 ============================== SEARCH ================================
% 0.82/1.08
% 0.82/1.08 % Starting search at 0.01 seconds.
% 0.82/1.08
% 0.82/1.08 ============================== PROOF =================================
% 0.82/1.08 % SZS status Theorem
% 0.82/1.08 % SZS output start Refutation
% 0.82/1.08
% 0.82/1.08 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.82/1.08 % Length of proof is 35.
% 0.82/1.08 % Level of proof is 12.
% 0.82/1.08 % Maximum clause weight is 15.000.
% 0.82/1.08 % Given clauses 45.
% 0.82/1.08
% 0.82/1.08 1 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 2 (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].
% 0.82/1.08 7 (all A all B all C all D -(unordered_pair(A,B) = unordered_pair(C,D) & A != C & A != D)) # label(t10_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 8 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 11 (all A all B all C (singleton(A) = unordered_pair(B,C) -> B = C)) # label(t9_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 12 -(all A all B all C all D (ordered_pair(A,B) = ordered_pair(C,D) -> A = C & B = D)) # label(t33_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.82/1.08 15 singleton(A) = unordered_pair(A,A) # label(t69_enumset1) # label(axiom). [clausify(8)].
% 0.82/1.08 16 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(1)].
% 0.82/1.08 17 ordered_pair(c5,c6) = ordered_pair(c3,c4) # label(t33_zfmisc_1) # label(negated_conjecture). [clausify(12)].
% 0.82/1.08 18 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom). [clausify(2)].
% 0.82/1.08 19 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),unordered_pair(A,A)). [copy(18),rewrite([15(3)])].
% 0.82/1.08 23 c5 != c3 | c6 != c4 # label(t33_zfmisc_1) # label(negated_conjecture). [clausify(12)].
% 0.82/1.08 28 singleton(A) != unordered_pair(B,C) | C = B # label(t9_zfmisc_1) # label(axiom). [clausify(11)].
% 0.82/1.08 29 unordered_pair(A,B) != unordered_pair(C,C) | B = A. [copy(28),rewrite([15(1)]),flip(a)].
% 0.82/1.08 30 unordered_pair(A,B) != unordered_pair(C,D) | A = C | B = C # label(t10_zfmisc_1) # label(axiom). [clausify(7)].
% 0.82/1.08 31 unordered_pair(unordered_pair(c5,c5),unordered_pair(c5,c6)) = unordered_pair(unordered_pair(c3,c3),unordered_pair(c3,c4)). [back_rewrite(17),rewrite([19(3),16(7),19(10),16(14)])].
% 0.82/1.08 36 unordered_pair(A,B) != unordered_pair(C,C) | A = B. [para(16(a,1),29(a,1))].
% 0.82/1.08 37 unordered_pair(A,B) != unordered_pair(C,D) | A = D | B = D. [para(16(a,1),30(a,2))].
% 0.82/1.08 38 unordered_pair(A,B) != unordered_pair(C,C) | C = B. [factor(37,b,c),flip(a)].
% 0.82/1.08 39 unordered_pair(c5,c5) = unordered_pair(c3,c3) | unordered_pair(c5,c6) = unordered_pair(c3,c3). [resolve(31,a,30,a)].
% 0.82/1.08 49 unordered_pair(c5,c6) = unordered_pair(c3,c3) | unordered_pair(c5,c6) = unordered_pair(c3,c4). [resolve(37,a,31,a(flip)),flip(a),flip(b)].
% 0.82/1.08 52 unordered_pair(c5,c5) = unordered_pair(c3,c3) | c6 = c3. [resolve(39,b,38,a),flip(b)].
% 0.82/1.08 53 unordered_pair(c5,c5) = unordered_pair(c3,c3) | c6 = c5. [resolve(39,b,36,a),flip(b)].
% 0.82/1.08 65 c6 = c3 | c5 = c3. [resolve(52,a,38,a),flip(b)].
% 0.82/1.08 82 c6 = c5 | c5 = c3. [resolve(53,a,38,a),flip(b)].
% 0.82/1.08 99 c5 = c3. [para(82(a,1),65(a,1)),merge(b),merge(c)].
% 0.82/1.08 105 unordered_pair(c3,c6) = unordered_pair(c3,c3) | unordered_pair(c3,c6) = unordered_pair(c3,c4). [back_rewrite(49),rewrite([99(1),99(8)])].
% 0.82/1.08 112 unordered_pair(unordered_pair(c3,c3),unordered_pair(c3,c6)) = unordered_pair(unordered_pair(c3,c3),unordered_pair(c3,c4)). [back_rewrite(31),rewrite([99(1),99(2),99(4)])].
% 0.82/1.08 113 c6 != c4. [back_rewrite(23),rewrite([99(1)]),xx(a)].
% 0.82/1.08 115 unordered_pair(c4,c6) != unordered_pair(A,A). [ur(36,b,113,a),rewrite([16(3)])].
% 0.82/1.08 132 unordered_pair(unordered_pair(A,A),unordered_pair(c4,c6)) != unordered_pair(B,B). [ur(29,b,115,a)].
% 0.82/1.08 179 unordered_pair(c3,c6) = unordered_pair(c3,c3) | c6 = c3. [resolve(105,b,37,a(flip)),flip(b),flip(c),unit_del(c,113)].
% 0.82/1.08 199 c6 = c3. [resolve(179,a,38,a),flip(b),merge(b)].
% 0.82/1.08 237 unordered_pair(unordered_pair(A,A),unordered_pair(c3,c4)) != unordered_pair(B,B). [back_rewrite(132),rewrite([199(3),16(4)])].
% 0.82/1.08 254 $F. [back_rewrite(112),rewrite([199(5)]),flip(a),unit_del(a,237)].
% 0.82/1.08
% 0.82/1.08 % SZS output end Refutation
% 0.82/1.08 ============================== end of proof ==========================
% 0.82/1.08
% 0.82/1.08 ============================== STATISTICS ============================
% 0.82/1.08
% 0.82/1.08 Given=45. Generated=754. Kept=236. proofs=1.
% 0.82/1.08 Usable=21. Sos=10. Demods=5. Limbo=55, Disabled=163. Hints=0.
% 0.82/1.08 Megabytes=0.20.
% 0.82/1.08 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.82/1.08
% 0.82/1.08 ============================== end of statistics =====================
% 0.82/1.08
% 0.82/1.08 ============================== end of search =========================
% 0.82/1.08
% 0.82/1.08 THEOREM PROVED
% 0.82/1.08 % SZS status Theorem
% 0.82/1.08
% 0.82/1.08 Exiting with 1 proof.
% 0.82/1.08
% 0.82/1.08 Process 32259 exit (max_proofs) Sun Jun 19 01:45:09 2022
% 0.82/1.08 Prover9 interrupted
%------------------------------------------------------------------------------