TSTP Solution File: SET886+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET886+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 04:33:11 EDT 2022
% Result : Theorem 0.44s 1.08s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET886+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n023.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 : Mon Jul 11 09:04:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.08 ============================== Prover9 ===============================
% 0.44/1.08 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.08 Process 17686 was started by sandbox2 on n023.cluster.edu,
% 0.44/1.08 Mon Jul 11 09:04:40 2022
% 0.44/1.08 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_17426_n023.cluster.edu".
% 0.44/1.08 ============================== end of head ===========================
% 0.44/1.08
% 0.44/1.08 ============================== INPUT =================================
% 0.44/1.08
% 0.44/1.08 % Reading from file /tmp/Prover9_17426_n023.cluster.edu
% 0.44/1.08
% 0.44/1.08 set(prolog_style_variables).
% 0.44/1.08 set(auto2).
% 0.44/1.08 % set(auto2) -> set(auto).
% 0.44/1.08 % set(auto) -> set(auto_inference).
% 0.44/1.08 % set(auto) -> set(auto_setup).
% 0.44/1.08 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.08 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.08 % set(auto) -> set(auto_limits).
% 0.44/1.08 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.08 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.08 % set(auto) -> set(auto_denials).
% 0.44/1.08 % set(auto) -> set(auto_process).
% 0.44/1.08 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.08 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.08 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.08 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.08 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.08 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.08 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.08 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.08 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.08 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.08 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.08 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.08 % set(auto2) -> assign(stats, some).
% 0.44/1.08 % set(auto2) -> clear(echo_input).
% 0.44/1.08 % set(auto2) -> set(quiet).
% 0.44/1.08 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.08 % set(auto2) -> clear(print_given).
% 0.44/1.08 assign(lrs_ticks,-1).
% 0.44/1.08 assign(sos_limit,10000).
% 0.44/1.08 assign(order,kbo).
% 0.44/1.08 set(lex_order_vars).
% 0.44/1.08 clear(print_given).
% 0.44/1.08
% 0.44/1.08 % formulas(sos). % not echoed (7 formulas)
% 0.44/1.08
% 0.44/1.08 ============================== end of input ==========================
% 0.44/1.08
% 0.44/1.08 % From the command line: assign(max_seconds, 300).
% 0.44/1.08
% 0.44/1.08 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.08
% 0.44/1.08 % Formulas that are not ordinary clauses:
% 0.44/1.08 1 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.08 2 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.08 3 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.08 4 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.08 5 (all A all B all C (subset(unordered_pair(A,B),singleton(C)) -> A = C)) # label(t26_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.08 6 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.08 7 -(all A all B all C (subset(unordered_pair(A,B),singleton(C)) -> unordered_pair(A,B) = singleton(C))) # label(t27_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.44/1.08
% 0.44/1.08 ============================== end of process non-clausal formulas ===
% 0.44/1.08
% 0.44/1.08 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.08
% 0.44/1.08 ============================== PREDICATE ELIMINATION =================
% 0.44/1.08
% 0.44/1.08 ============================== end predicate elimination =============
% 0.44/1.08
% 0.44/1.08 Auto_denials:
% 0.44/1.08 % copying label rc2_xboole_0 to answer in negative clause
% 0.44/1.08 % copying label t27_zfmisc_1 to answer in negative clause
% 0.44/1.08 % assign(max_proofs, 2). % (Horn set with more than one neg. clause)
% 0.44/1.08
% 0.44/1.08 Term ordering decisions:
% 0.44/1.08
% 0.44/1.08 % Assigning unary symbol singleton kb_weight 0 and highest precedence (10).
% 0.44/1.08 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. unordered_pair=1. singleton=0.
% 0.44/1.08
% 0.44/1.08 ============================== end of process initial clauses ========
% 0.44/1.08
% 0.44/1.08 ============================== CLAUSES FOR SEARCH ====================
% 0.44/1.08
% 0.44/1.08 ============================== end of clauses for search =============
% 0.44/1.08
% 0.44/1.08 ============================== SEARCH ================================
% 0.44/1.08
% 0.44/1.08 % Starting search at 0.01 seconds.
% 0.44/1.08
% 0.44/1.08 ============================== PROOF =================================
% 0.44/1.08 % SZS status Theorem
% 0.44/1.08 % SZS output start Refutation
% 0.44/1.08
% 0.44/1.08 % Proof 1 at 0.01 (+ 0.00) seconds: t27_zfmisc_1.
% 0.44/1.08 % Length of proof is 25.
% 0.44/1.08 % Level of proof is 9.
% 0.44/1.08 % Maximum clause weight is 10.000.
% 0.44/1.08 % Given clauses 17.
% 0.44/1.08
% 0.44/1.08 1 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.08 4 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.08 5 (all A all B all C (subset(unordered_pair(A,B),singleton(C)) -> A = C)) # label(t26_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.08 6 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.08 7 -(all A all B all C (subset(unordered_pair(A,B),singleton(C)) -> unordered_pair(A,B) = singleton(C))) # label(t27_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.44/1.08 9 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(4)].
% 0.44/1.08 10 singleton(A) = unordered_pair(A,A) # label(t69_enumset1) # label(axiom). [clausify(6)].
% 0.44/1.08 11 subset(unordered_pair(c3,c4),singleton(c5)) # label(t27_zfmisc_1) # label(negated_conjecture). [clausify(7)].
% 0.44/1.08 12 subset(unordered_pair(c3,c4),unordered_pair(c5,c5)). [copy(11),rewrite([10(5)])].
% 0.44/1.08 13 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(1)].
% 0.44/1.08 15 singleton(c5) != unordered_pair(c3,c4) # label(t27_zfmisc_1) # label(negated_conjecture) # answer(t27_zfmisc_1). [clausify(7)].
% 0.44/1.08 16 unordered_pair(c5,c5) != unordered_pair(c3,c4) # answer(t27_zfmisc_1). [copy(15),rewrite([10(2)])].
% 0.44/1.08 17 -subset(unordered_pair(A,B),singleton(C)) | C = A # label(t26_zfmisc_1) # label(axiom). [clausify(5)].
% 0.44/1.08 18 -subset(unordered_pair(A,B),unordered_pair(C,C)) | C = A. [copy(17),rewrite([10(2)])].
% 0.44/1.08 19 unordered_pair(c5,c5) = c_0. [new_symbol(16)].
% 0.44/1.08 20 unordered_pair(c3,c4) != c_0 # answer(t27_zfmisc_1). [back_rewrite(16),rewrite([19(3)]),flip(a)].
% 0.44/1.08 21 subset(unordered_pair(c3,c4),c_0). [back_rewrite(12),rewrite([19(6)])].
% 0.44/1.08 24 -subset(unordered_pair(A,B),c_0) | c5 = A. [para(19(a,1),18(a,2))].
% 0.44/1.08 26 -subset(unordered_pair(A,unordered_pair(c3,c4)),unordered_pair(c_0,c_0)) # answer(t27_zfmisc_1). [ur(18,b,20,a(flip)),rewrite([13(4)])].
% 0.44/1.08 28 c5 = c3. [hyper(24,a,21,a)].
% 0.44/1.08 29 -subset(unordered_pair(A,B),c_0) | c3 = B. [para(13(a,1),24(a,1)),rewrite([28(4)])].
% 0.44/1.08 32 unordered_pair(c3,c3) = c_0. [back_rewrite(19),rewrite([28(1),28(2)])].
% 0.44/1.08 33 c4 = c3. [hyper(29,a,21,a),flip(a)].
% 0.44/1.08 34 -subset(unordered_pair(A,c_0),unordered_pair(c_0,c_0)) # answer(t27_zfmisc_1). [back_rewrite(26),rewrite([33(2),32(3)])].
% 0.44/1.08 35 $F # answer(t27_zfmisc_1). [resolve(34,a,9,a)].
% 0.44/1.08
% 0.44/1.08 % SZS output end Refutation
% 0.44/1.08 ============================== end of proof ==========================
% 0.44/1.08 % Redundant proof: 36 $F # answer(t27_zfmisc_1). [back_rewrite(20),rewrite([33(2),32(3)]),xx(a)].
% 0.44/1.08
% 0.44/1.08 % Disable descendants (x means already disabled):
% 0.44/1.08 15x 16x 20x 25x 26x 34
% 0.44/1.08
% 0.44/1.08 ============================== STATISTICS ============================
% 0.44/1.08
% 0.44/1.08 Given=20. Generated=73. Kept=24. proofs=1.
% 0.44/1.08 Usable=13. Sos=0. Demods=5. Limbo=0, Disabled=19. Hints=0.
% 0.44/1.08 Megabytes=0.04.
% 0.44/1.08 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.44/1.08
% 0.44/1.08 ============================== end of statistics =====================
% 0.44/1.08
% 0.44/1.08 ============================== end of search =========================
% 0.44/1.08
% 0.44/1.08 SEARCH FAILED
% 0.44/1.08
% 0.44/1.08 Exiting with 1 proof.
% 0.44/1.08
% 0.44/1.08 Process 17686 exit (sos_empty) Mon Jul 11 09:04:40 2022
% 0.44/1.08 Prover9 interrupted
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