TSTP Solution File: SEU125+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU125+1 : TPTP v8.1.0. Released v3.3.0.
% 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 13:29:09 EDT 2022
% Result : Theorem 1.05s 1.33s
% Output : Refutation 1.05s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU125+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n027.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 : Sun Jun 19 19:36:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.78/1.03 ============================== Prover9 ===============================
% 0.78/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.78/1.03 Process 888 was started by sandbox on n027.cluster.edu,
% 0.78/1.03 Sun Jun 19 19:36:25 2022
% 0.78/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_620_n027.cluster.edu".
% 0.78/1.03 ============================== end of head ===========================
% 0.78/1.03
% 0.78/1.03 ============================== INPUT =================================
% 0.78/1.03
% 0.78/1.03 % Reading from file /tmp/Prover9_620_n027.cluster.edu
% 0.78/1.03
% 0.78/1.03 set(prolog_style_variables).
% 0.78/1.03 set(auto2).
% 0.78/1.03 % set(auto2) -> set(auto).
% 0.78/1.03 % set(auto) -> set(auto_inference).
% 0.78/1.03 % set(auto) -> set(auto_setup).
% 0.78/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.78/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.78/1.03 % set(auto) -> set(auto_limits).
% 0.78/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.78/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.78/1.03 % set(auto) -> set(auto_denials).
% 0.78/1.03 % set(auto) -> set(auto_process).
% 0.78/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.78/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.78/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.78/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.78/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.78/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.78/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.78/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.78/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.78/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.78/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.78/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.78/1.03 % set(auto2) -> assign(stats, some).
% 0.78/1.03 % set(auto2) -> clear(echo_input).
% 0.78/1.03 % set(auto2) -> set(quiet).
% 0.78/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.78/1.03 % set(auto2) -> clear(print_given).
% 0.78/1.03 assign(lrs_ticks,-1).
% 0.78/1.03 assign(sos_limit,10000).
% 0.78/1.03 assign(order,kbo).
% 0.78/1.03 set(lex_order_vars).
% 0.78/1.03 clear(print_given).
% 0.78/1.03
% 0.78/1.03 % formulas(sos). % not echoed (18 formulas)
% 0.78/1.03
% 0.78/1.03 ============================== end of input ==========================
% 0.78/1.03
% 0.78/1.03 % From the command line: assign(max_seconds, 300).
% 0.78/1.03
% 0.78/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.78/1.03
% 0.78/1.03 % Formulas that are not ordinary clauses:
% 0.78/1.03 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 2 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 3 (all A all B all C (C = set_union2(A,B) <-> (all D (in(D,C) <-> in(D,A) | in(D,B))))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 4 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 5 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 6 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 7 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 8 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 9 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 10 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 11 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 12 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 13 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 14 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 15 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 16 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.03 17 -(all A all B all C (subset(A,B) & subset(C,B) -> subset(set_union2(A,C),B))) # label(t8_xboole_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.05/1.33
% 1.05/1.33 ============================== end of process non-clausal formulas ===
% 1.05/1.33
% 1.05/1.33 ============================== PROCESS INITIAL CLAUSES ===============
% 1.05/1.33
% 1.05/1.33 ============================== PREDICATE ELIMINATION =================
% 1.05/1.33
% 1.05/1.33 ============================== end predicate elimination =============
% 1.05/1.33
% 1.05/1.33 Auto_denials: (non-Horn, no changes).
% 1.05/1.33
% 1.05/1.33 Term ordering decisions:
% 1.05/1.33 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. set_union2=1. f2=1. f1=1.
% 1.05/1.33
% 1.05/1.33 ============================== end of process initial clauses ========
% 1.05/1.33
% 1.05/1.33 ============================== CLAUSES FOR SEARCH ====================
% 1.05/1.33
% 1.05/1.33 ============================== end of clauses for search =============
% 1.05/1.33
% 1.05/1.33 ============================== SEARCH ================================
% 1.05/1.33
% 1.05/1.33 % Starting search at 0.01 seconds.
% 1.05/1.33
% 1.05/1.33 ============================== PROOF =================================
% 1.05/1.33 % SZS status Theorem
% 1.05/1.33 % SZS output start Refutation
% 1.05/1.33
% 1.05/1.33 % Proof 1 at 0.29 (+ 0.02) seconds.
% 1.05/1.33 % Length of proof is 17.
% 1.05/1.33 % Level of proof is 4.
% 1.05/1.33 % Maximum clause weight is 14.000.
% 1.05/1.33 % Given clauses 315.
% 1.05/1.33
% 1.05/1.33 3 (all A all B all C (C = set_union2(A,B) <-> (all D (in(D,C) <-> in(D,A) | in(D,B))))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.33 4 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.33 17 -(all A all B all C (subset(A,B) & subset(C,B) -> subset(set_union2(A,C),B))) # label(t8_xboole_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.05/1.33 21 subset(c3,c4) # label(t8_xboole_1) # label(negated_conjecture). [clausify(17)].
% 1.05/1.33 22 subset(c5,c4) # label(t8_xboole_1) # label(negated_conjecture). [clausify(17)].
% 1.05/1.33 26 subset(A,B) | in(f2(A,B),A) # label(d3_tarski) # label(axiom). [clausify(4)].
% 1.05/1.33 30 -subset(set_union2(c3,c5),c4) # label(t8_xboole_1) # label(negated_conjecture). [clausify(17)].
% 1.05/1.33 36 subset(A,B) | -in(f2(A,B),B) # label(d3_tarski) # label(axiom). [clausify(4)].
% 1.05/1.33 37 -subset(A,B) | -in(C,A) | in(C,B) # label(d3_tarski) # label(axiom). [clausify(4)].
% 1.05/1.33 40 set_union2(A,B) != C | -in(D,C) | in(D,A) | in(D,B) # label(d2_xboole_0) # label(axiom). [clausify(3)].
% 1.05/1.33 58 in(f2(set_union2(c3,c5),c4),set_union2(c3,c5)). [resolve(30,a,26,a)].
% 1.05/1.33 67 -in(f2(set_union2(c3,c5),c4),c4). [ur(36,a,30,a)].
% 1.05/1.33 69 -in(A,c5) | in(A,c4). [resolve(37,a,22,a)].
% 1.05/1.33 70 -in(A,c3) | in(A,c4). [resolve(37,a,21,a)].
% 1.05/1.33 376 -in(f2(set_union2(c3,c5),c4),c3). [ur(70,b,67,a)].
% 1.05/1.33 377 -in(f2(set_union2(c3,c5),c4),c5). [ur(69,b,67,a)].
% 1.05/1.33 2737 $F. [ur(40,b,58,a,c,376,a,d,377,a),xx(a)].
% 1.05/1.33
% 1.05/1.33 % SZS output end Refutation
% 1.05/1.33 ============================== end of proof ==========================
% 1.05/1.33
% 1.05/1.33 ============================== STATISTICS ============================
% 1.05/1.33
% 1.05/1.33 Given=315. Generated=13578. Kept=2718. proofs=1.
% 1.05/1.33 Usable=269. Sos=1932. Demods=6. Limbo=2, Disabled=540. Hints=0.
% 1.05/1.33 Megabytes=1.88.
% 1.05/1.33 User_CPU=0.29, System_CPU=0.02, Wall_clock=0.
% 1.05/1.33
% 1.05/1.33 ============================== end of statistics =====================
% 1.05/1.33
% 1.05/1.33 ============================== end of search =========================
% 1.05/1.33
% 1.05/1.33 THEOREM PROVED
% 1.05/1.33 % SZS status Theorem
% 1.05/1.33
% 1.05/1.33 Exiting with 1 proof.
% 1.05/1.33
% 1.05/1.33 Process 888 exit (max_proofs) Sun Jun 19 19:36:25 2022
% 1.05/1.33 Prover9 interrupted
%------------------------------------------------------------------------------