TSTP Solution File: SEU126+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU126+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 0.75s 1.09s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU126+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n018.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 Jun 20 10:32:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/1.02 ============================== Prover9 ===============================
% 0.43/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.02 Process 26138 was started by sandbox on n018.cluster.edu,
% 0.43/1.02 Mon Jun 20 10:32:36 2022
% 0.43/1.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25792_n018.cluster.edu".
% 0.43/1.02 ============================== end of head ===========================
% 0.43/1.02
% 0.43/1.02 ============================== INPUT =================================
% 0.43/1.02
% 0.43/1.02 % Reading from file /tmp/Prover9_25792_n018.cluster.edu
% 0.43/1.02
% 0.43/1.02 set(prolog_style_variables).
% 0.43/1.02 set(auto2).
% 0.43/1.02 % set(auto2) -> set(auto).
% 0.43/1.02 % set(auto) -> set(auto_inference).
% 0.43/1.02 % set(auto) -> set(auto_setup).
% 0.43/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.02 % set(auto) -> set(auto_limits).
% 0.43/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.02 % set(auto) -> set(auto_denials).
% 0.43/1.02 % set(auto) -> set(auto_process).
% 0.43/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.02 % set(auto2) -> assign(stats, some).
% 0.43/1.02 % set(auto2) -> clear(echo_input).
% 0.43/1.02 % set(auto2) -> set(quiet).
% 0.43/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.02 % set(auto2) -> clear(print_given).
% 0.43/1.02 assign(lrs_ticks,-1).
% 0.43/1.02 assign(sos_limit,10000).
% 0.43/1.02 assign(order,kbo).
% 0.43/1.02 set(lex_order_vars).
% 0.43/1.02 clear(print_given).
% 0.43/1.02
% 0.43/1.02 % formulas(sos). % not echoed (33 formulas)
% 0.43/1.02
% 0.43/1.02 ============================== end of input ==========================
% 0.43/1.02
% 0.43/1.02 % From the command line: assign(max_seconds, 300).
% 0.43/1.02
% 0.43/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.02
% 0.43/1.02 % Formulas that are not ordinary clauses:
% 0.43/1.02 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 2 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 3 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 4 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 5 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 6 (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].
% 0.43/1.02 7 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 8 (all A all B all C (C = set_intersection2(A,B) <-> (all D (in(D,C) <-> in(D,A) & in(D,B))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 9 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 10 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 11 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 12 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 13 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 14 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 15 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 16 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.09 17 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.09 18 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.09 19 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.09 20 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.09 21 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.09 22 (all A all B all C (subset(A,B) & subset(B,C) -> subset(A,C))) # label(t1_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.75/1.09 23 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.75/1.09 24 (all A all B (-(-disjoint(A,B) & (all C -(in(C,A) & in(C,B)))) & -((exists C (in(C,A) & in(C,B))) & disjoint(A,B)))) # label(t3_xboole_0) # label(lemma) # label(non_clause). [assumption].
% 0.75/1.09 25 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.75/1.09 26 (all A all B (-(-disjoint(A,B) & (all C -in(C,set_intersection2(A,B)))) & -((exists C in(C,set_intersection2(A,B))) & disjoint(A,B)))) # label(t4_xboole_0) # label(lemma) # label(non_clause). [assumption].
% 0.75/1.09 27 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.09 28 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.09 29 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.75/1.09 30 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.09 31 (all A all B all C (subset(A,B) & subset(C,B) -> subset(set_union2(A,C),B))) # label(t8_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.75/1.09 32 -(all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.09
% 0.75/1.09 ============================== end of process non-clausal formulas ===
% 0.75/1.09
% 0.75/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.75/1.09
% 0.75/1.09 ============================== PREDICATE ELIMINATION =================
% 0.75/1.09
% 0.75/1.09 ============================== end predicate elimination =============
% 0.75/1.09
% 0.75/1.09 Auto_denials: (non-Horn, no changes).
% 0.75/1.09
% 0.75/1.09 Term ordering decisions:
% 0.75/1.09
% 0.75/1.09 % Assigning unary symbol f1 kb_weight 0 and highest precedence (18).
% 0.75/1.09 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. set_union2=1. set_intersection2=1. f3=1. f5=1. f6=1. f2=1. f4=1. f1=0.
% 0.75/1.09
% 0.75/1.09 ============================== end of process initial clauses ========
% 0.75/1.09
% 0.75/1.09 ============================== CLAUSES FOR SEARCH ====================
% 0.75/1.09
% 0.75/1.09 ============================== end of clauses for search =============
% 0.75/1.09
% 0.75/1.09 ============================== SEARCH ================================
% 0.75/1.09
% 0.75/1.09 % Starting search at 0.02 seconds.
% 0.75/1.09
% 0.75/1.09 ============================== PROOF =================================
% 0.75/1.09 % SZS status Theorem
% 0.75/1.09 % SZS output start Refutation
% 0.75/1.09
% 0.75/1.09 % Proof 1 at 0.07 (+ 0.00) seconds.
% 0.75/1.09 % Length of proof is 16.
% 0.75/1.09 % Level of proof is 5.
% 0.75/1.09 % Maximum clause weight is 23.000.
% 0.75/1.09 % Given clauses 81.
% 0.75/1.09
% 0.75/1.09 2 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.09 6 (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].
% 0.75/1.09 7 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.09 32 -(all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.09 37 subset(c3,c4) # label(t12_xboole_1) # label(negated_conjecture). [clausify(32)].
% 0.75/1.09 42 set_union2(A,B) = set_union2(B,A) # label(commutativity_k2_xboole_0) # label(axiom). [clausify(2)].
% 0.75/1.09 51 set_union2(A,B) = C | in(f2(A,B,C),C) | in(f2(A,B,C),A) | in(f2(A,B,C),B) # label(d2_xboole_0) # label(axiom). [clausify(6)].
% 0.75/1.09 54 set_union2(c3,c4) != c4 # label(t12_xboole_1) # label(negated_conjecture). [clausify(32)].
% 0.75/1.09 71 -subset(A,B) | -in(C,A) | in(C,B) # label(d3_tarski) # label(axiom). [clausify(7)].
% 0.75/1.09 81 set_union2(A,B) = C | -in(f2(A,B,C),C) | -in(f2(A,B,C),B) # label(d2_xboole_0) # label(axiom). [clausify(6)].
% 0.75/1.09 93 set_union2(A,B) = B | -in(f2(A,B,B),B). [factor(81,b,c)].
% 0.75/1.09 155 -in(A,c3) | in(A,c4). [resolve(71,a,37,a)].
% 0.75/1.09 488 -in(f2(c3,c4,c4),c4). [ur(93,a,54,a)].
% 0.75/1.09 567 in(f2(c3,A,B),c4) | set_union2(A,c3) = B | in(f2(c3,A,B),B) | in(f2(c3,A,B),A). [resolve(155,a,51,c),rewrite([42(6)])].
% 0.75/1.09 579 in(f2(c3,A,c4),c4) | set_union2(A,c3) = c4 | in(f2(c3,A,c4),A). [factor(567,a,c)].
% 0.75/1.09 589 $F. [factor(579,a,c),rewrite([42(9)]),unit_del(a,488),unit_del(b,54)].
% 0.75/1.09
% 0.75/1.09 % SZS output end Refutation
% 0.75/1.09 ============================== end of proof ==========================
% 0.75/1.09
% 0.75/1.09 ============================== STATISTICS ============================
% 0.75/1.09
% 0.75/1.09 Given=81. Generated=1726. Kept=555. proofs=1.
% 0.75/1.09 Usable=75. Sos=431. Demods=7. Limbo=10, Disabled=89. Hints=0.
% 0.75/1.09 Megabytes=0.45.
% 0.75/1.09 User_CPU=0.08, System_CPU=0.00, Wall_clock=0.
% 0.75/1.09
% 0.75/1.09 ============================== end of statistics =====================
% 0.75/1.09
% 0.75/1.09 ============================== end of search =========================
% 0.75/1.09
% 0.75/1.09 THEOREM PROVED
% 0.75/1.09 % SZS status Theorem
% 0.75/1.09
% 0.75/1.09 Exiting with 1 proof.
% 0.75/1.09
% 0.75/1.09 Process 26138 exit (max_proofs) Mon Jun 20 10:32:36 2022
% 0.75/1.09 Prover9 interrupted
%------------------------------------------------------------------------------