TSTP Solution File: SET873+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET873+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 04:33:06 EDT 2022
% Result : Theorem 0.42s 0.99s
% Output : Refutation 0.42s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET873+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n024.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 : Sat Jul 9 20:09:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.42/0.99 ============================== Prover9 ===============================
% 0.42/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.99 Process 20959 was started by sandbox2 on n024.cluster.edu,
% 0.42/0.99 Sat Jul 9 20:09:44 2022
% 0.42/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_20716_n024.cluster.edu".
% 0.42/0.99 ============================== end of head ===========================
% 0.42/0.99
% 0.42/0.99 ============================== INPUT =================================
% 0.42/0.99
% 0.42/0.99 % Reading from file /tmp/Prover9_20716_n024.cluster.edu
% 0.42/0.99
% 0.42/0.99 set(prolog_style_variables).
% 0.42/0.99 set(auto2).
% 0.42/0.99 % set(auto2) -> set(auto).
% 0.42/0.99 % set(auto) -> set(auto_inference).
% 0.42/0.99 % set(auto) -> set(auto_setup).
% 0.42/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.99 % set(auto) -> set(auto_limits).
% 0.42/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.99 % set(auto) -> set(auto_denials).
% 0.42/0.99 % set(auto) -> set(auto_process).
% 0.42/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.99 % set(auto2) -> assign(stats, some).
% 0.42/0.99 % set(auto2) -> clear(echo_input).
% 0.42/0.99 % set(auto2) -> set(quiet).
% 0.42/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.99 % set(auto2) -> clear(print_given).
% 0.42/0.99 assign(lrs_ticks,-1).
% 0.42/0.99 assign(sos_limit,10000).
% 0.42/0.99 assign(order,kbo).
% 0.42/0.99 set(lex_order_vars).
% 0.42/0.99 clear(print_given).
% 0.42/0.99
% 0.42/0.99 % formulas(sos). % not echoed (11 formulas)
% 0.42/0.99
% 0.42/0.99 ============================== end of input ==========================
% 0.42/0.99
% 0.42/0.99 % From the command line: assign(max_seconds, 300).
% 0.42/0.99
% 0.42/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.99
% 0.42/0.99 % Formulas that are not ordinary clauses:
% 0.42/0.99 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 2 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 3 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 4 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 5 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 6 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 7 (all A all B (subset(set_union2(singleton(A),B),B) -> in(A,B))) # label(l21_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 8 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 9 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 10 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 11 -(all A all B (set_union2(singleton(A),singleton(B)) = singleton(A) -> A = B)) # label(t13_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.42/0.99
% 0.42/0.99 ============================== end of process non-clausal formulas ===
% 0.42/0.99
% 0.42/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.42/0.99
% 0.42/0.99 ============================== PREDICATE ELIMINATION =================
% 0.42/0.99
% 0.42/0.99 ============================== end predicate elimination =============
% 0.42/0.99
% 0.42/0.99 Auto_denials: (non-Horn, no changes).
% 0.42/0.99
% 0.42/0.99 Term ordering decisions:
% 0.42/0.99
% 0.42/0.99 % Assigning unary symbol singleton kb_weight 0 and highest precedence (11).
% 0.42/0.99 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. set_union2=1. f1=1. singleton=0.
% 0.42/0.99
% 0.42/0.99 ============================== end of process initial clauses ========
% 0.42/0.99
% 0.42/0.99 ============================== CLAUSES FOR SEARCH ====================
% 0.42/0.99
% 0.42/0.99 ============================== end of clauses for search =============
% 0.42/0.99
% 0.42/0.99 ============================== SEARCH ================================
% 0.42/0.99
% 0.42/0.99 % Starting search at 0.01 seconds.
% 0.42/0.99
% 0.42/0.99 ============================== PROOF =================================
% 0.42/0.99 % SZS status Theorem
% 0.42/0.99 % SZS output start Refutation
% 0.42/0.99
% 0.42/0.99 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.42/0.99 % Length of proof is 15.
% 0.42/0.99 % Level of proof is 4.
% 0.42/0.99 % Maximum clause weight is 10.000.
% 0.42/0.99 % Given clauses 12.
% 0.42/0.99
% 0.42/0.99 2 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 3 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 7 (all A all B (subset(set_union2(singleton(A),B),B) -> in(A,B))) # label(l21_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 10 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 11 -(all A all B (set_union2(singleton(A),singleton(B)) = singleton(A) -> A = B)) # label(t13_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.42/0.99 13 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(10)].
% 0.42/0.99 15 set_union2(A,B) = set_union2(B,A) # label(commutativity_k2_xboole_0) # label(axiom). [clausify(2)].
% 0.42/0.99 16 singleton(c3) = set_union2(singleton(c3),singleton(c4)) # label(t13_zfmisc_1) # label(negated_conjecture). [clausify(11)].
% 0.42/0.99 17 set_union2(singleton(c3),singleton(c4)) = singleton(c3). [copy(16),flip(a)].
% 0.42/0.99 20 c4 != c3 # label(t13_zfmisc_1) # label(negated_conjecture). [clausify(11)].
% 0.42/0.99 24 -subset(set_union2(singleton(A),B),B) | in(A,B) # label(l21_zfmisc_1) # label(axiom). [clausify(7)].
% 0.42/0.99 25 -subset(set_union2(A,singleton(B)),A) | in(B,A). [copy(24),rewrite([15(2)])].
% 0.42/0.99 26 singleton(A) != B | -in(C,B) | C = A # label(d1_tarski) # label(axiom). [clausify(3)].
% 0.42/0.99 34 in(c4,singleton(c3)). [para(17(a,1),25(a,1)),unit_del(a,13)].
% 0.42/0.99 36 $F. [ur(26,a,17,a(flip),c,20,a),rewrite([17(6)]),unit_del(a,34)].
% 0.42/0.99
% 0.42/0.99 % SZS output end Refutation
% 0.42/0.99 ============================== end of proof ==========================
% 0.42/0.99
% 0.42/0.99 ============================== STATISTICS ============================
% 0.42/0.99
% 0.42/0.99 Given=12. Generated=37. Kept=21. proofs=1.
% 0.42/0.99 Usable=12. Sos=8. Demods=3. Limbo=1, Disabled=15. Hints=0.
% 0.42/0.99 Megabytes=0.05.
% 0.42/0.99 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.42/0.99
% 0.42/0.99 ============================== end of statistics =====================
% 0.42/0.99
% 0.42/0.99 ============================== end of search =========================
% 0.42/0.99
% 0.42/0.99 THEOREM PROVED
% 0.42/0.99 % SZS status Theorem
% 0.42/0.99
% 0.42/0.99 Exiting with 1 proof.
% 0.42/0.99
% 0.42/0.99 Process 20959 exit (max_proofs) Sat Jul 9 20:09:44 2022
% 0.42/0.99 Prover9 interrupted
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