TSTP Solution File: SEU131+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU131+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 13:29:12 EDT 2022
% Result : Theorem 1.76s 2.03s
% Output : Refutation 1.76s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SEU131+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jun 19 07:12:24 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.74/1.04 ============================== Prover9 ===============================
% 0.74/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.74/1.04 Process 2167 was started by sandbox on n019.cluster.edu,
% 0.74/1.04 Sun Jun 19 07:12:25 2022
% 0.74/1.04 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_2005_n019.cluster.edu".
% 0.74/1.04 ============================== end of head ===========================
% 0.74/1.04
% 0.74/1.04 ============================== INPUT =================================
% 0.74/1.04
% 0.74/1.04 % Reading from file /tmp/Prover9_2005_n019.cluster.edu
% 0.74/1.04
% 0.74/1.04 set(prolog_style_variables).
% 0.74/1.04 set(auto2).
% 0.74/1.04 % set(auto2) -> set(auto).
% 0.74/1.04 % set(auto) -> set(auto_inference).
% 0.74/1.04 % set(auto) -> set(auto_setup).
% 0.74/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.74/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.74/1.04 % set(auto) -> set(auto_limits).
% 0.74/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.74/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.74/1.04 % set(auto) -> set(auto_denials).
% 0.74/1.04 % set(auto) -> set(auto_process).
% 0.74/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.74/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.74/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.74/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.74/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.74/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.74/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.74/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.74/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.74/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.74/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.74/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.74/1.04 % set(auto2) -> assign(stats, some).
% 0.74/1.04 % set(auto2) -> clear(echo_input).
% 0.74/1.04 % set(auto2) -> set(quiet).
% 0.74/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.74/1.04 % set(auto2) -> clear(print_given).
% 0.74/1.04 assign(lrs_ticks,-1).
% 0.74/1.04 assign(sos_limit,10000).
% 0.74/1.04 assign(order,kbo).
% 0.74/1.04 set(lex_order_vars).
% 0.74/1.04 clear(print_given).
% 0.74/1.04
% 0.74/1.04 % formulas(sos). % not echoed (16 formulas)
% 0.74/1.04
% 0.74/1.04 ============================== end of input ==========================
% 0.74/1.04
% 0.74/1.04 % From the command line: assign(max_seconds, 300).
% 0.74/1.04
% 0.74/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.74/1.04
% 0.74/1.04 % Formulas that are not ordinary clauses:
% 0.74/1.04 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 2 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 3 (all A all B all C (C = set_difference(A,B) <-> (all D (in(D,C) <-> in(D,A) & -in(D,B))))) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 4 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 5 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 6 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 7 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 8 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 9 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 10 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 11 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 12 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 13 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 14 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 15 -(all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.74/1.04
% 0.74/1.04 ============================== end of process non-clausal formulas ===
% 0.74/1.04
% 0.74/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.74/1.04
% 0.74/1.04 ============================== PREDICATE ELIMINATION =================
% 0.74/1.04
% 0.74/1.04 ============================== end predicate elimination =============
% 1.76/2.03
% 1.76/2.03 Auto_denials: (non-Horn, no changes).
% 1.76/2.03
% 1.76/2.03 Term ordering decisions:
% 1.76/2.03 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. set_difference=1. f1=1. f3=1. f2=1.
% 1.76/2.03
% 1.76/2.03 ============================== end of process initial clauses ========
% 1.76/2.03
% 1.76/2.03 ============================== CLAUSES FOR SEARCH ====================
% 1.76/2.03
% 1.76/2.03 ============================== end of clauses for search =============
% 1.76/2.03
% 1.76/2.03 ============================== SEARCH ================================
% 1.76/2.03
% 1.76/2.03 % Starting search at 0.01 seconds.
% 1.76/2.03
% 1.76/2.03 ============================== PROOF =================================
% 1.76/2.03 % SZS status Theorem
% 1.76/2.03 % SZS output start Refutation
% 1.76/2.03
% 1.76/2.03 % Proof 1 at 0.99 (+ 0.02) seconds.
% 1.76/2.03 % Length of proof is 28.
% 1.76/2.03 % Level of proof is 10.
% 1.76/2.03 % Maximum clause weight is 22.000.
% 1.76/2.03 % Given clauses 117.
% 1.76/2.03
% 1.76/2.03 2 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 1.76/2.03 3 (all A all B all C (C = set_difference(A,B) <-> (all D (in(D,C) <-> in(D,A) & -in(D,B))))) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 1.76/2.03 13 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 1.76/2.03 15 -(all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.76/2.03 16 empty(empty_set) # label(fc1_xboole_0) # label(axiom). [assumption].
% 1.76/2.03 21 subset(A,B) | in(f1(A,B),A) # label(d3_tarski) # label(axiom). [clausify(2)].
% 1.76/2.03 22 set_difference(c3,c4) = empty_set | subset(c3,c4) # label(l32_xboole_1) # label(negated_conjecture). [clausify(15)].
% 1.76/2.03 24 set_difference(A,B) = C | in(f2(A,B,C),C) | in(f2(A,B,C),A) # label(d4_xboole_0) # label(axiom). [clausify(3)].
% 1.76/2.03 26 -in(A,B) | -empty(B) # label(t7_boole) # label(axiom). [clausify(13)].
% 1.76/2.03 28 set_difference(c3,c4) != empty_set | -subset(c3,c4) # label(l32_xboole_1) # label(negated_conjecture). [clausify(15)].
% 1.76/2.03 32 subset(A,B) | -in(f1(A,B),B) # label(d3_tarski) # label(axiom). [clausify(2)].
% 1.76/2.03 33 -subset(A,B) | -in(C,A) | in(C,B) # label(d3_tarski) # label(axiom). [clausify(2)].
% 1.76/2.03 36 set_difference(A,B) != C | in(D,C) | -in(D,A) | in(D,B) # label(d4_xboole_0) # label(axiom). [clausify(3)].
% 1.76/2.03 37 set_difference(A,B) = C | in(f2(A,B,C),C) | -in(f2(A,B,C),B) # label(d4_xboole_0) # label(axiom). [clausify(3)].
% 1.76/2.03 49 -in(A,empty_set). [ur(26,b,16,a)].
% 1.76/2.03 54 set_difference(c3,c4) != empty_set | in(f1(c3,c4),c3). [resolve(28,b,21,a)].
% 1.76/2.03 64 -in(A,c3) | in(A,c4) | set_difference(c3,c4) = empty_set. [resolve(33,a,22,b)].
% 1.76/2.03 65 -in(A,B) | in(A,C) | in(f1(B,C),B). [resolve(33,a,21,a)].
% 1.76/2.03 152 in(f2(c3,A,B),c4) | set_difference(c3,c4) = empty_set | set_difference(c3,A) = B | in(f2(c3,A,B),B). [resolve(64,a,24,c)].
% 1.76/2.03 157 in(f2(c3,c4,empty_set),c4) | set_difference(c3,c4) = empty_set. [factor(152,b,c),unit_del(c,49)].
% 1.76/2.03 228 set_difference(c3,c4) = empty_set. [resolve(157,a,37,c),merge(b),unit_del(b,49)].
% 1.76/2.03 229 in(f1(c3,c4),c3). [back_rewrite(54),rewrite([228(3)]),xx(a)].
% 1.76/2.03 230 -subset(c3,c4). [back_rewrite(28),rewrite([228(3)]),xx(a)].
% 1.76/2.03 235 in(f1(c3,c4),A) | in(f1(c3,A),c3). [resolve(229,a,65,a)].
% 1.76/2.03 1399 -in(f1(c3,c4),c4). [ur(32,a,230,a)].
% 1.76/2.03 1458 in(f1(c3,c4),A) | set_difference(c3,B) != C | in(f1(c3,A),C) | in(f1(c3,A),B). [resolve(235,b,36,c)].
% 1.76/2.03 1465 empty_set != A | in(f1(c3,c4),A). [factor(1458,a,d),rewrite([228(8)]),unit_del(a,1399)].
% 1.76/2.03 3793 $F. [resolve(1465,a,228,a(flip)),rewrite([228(6)]),unit_del(a,49)].
% 1.76/2.03
% 1.76/2.03 % SZS output end Refutation
% 1.76/2.03 ============================== end of proof ==========================
% 1.76/2.03
% 1.76/2.03 ============================== STATISTICS ============================
% 1.76/2.03
% 1.76/2.03 Given=117. Generated=7733. Kept=3777. proofs=1.
% 1.76/2.03 Usable=106. Sos=3637. Demods=5. Limbo=0, Disabled=57. Hints=0.
% 1.76/2.03 Megabytes=9.29.
% 1.76/2.03 User_CPU=0.99, System_CPU=0.02, Wall_clock=1.
% 1.76/2.03
% 1.76/2.03 ============================== end of statistics =====================
% 1.76/2.03
% 1.76/2.03 ============================== end of search =========================
% 1.76/2.03
% 1.76/2.03 THEOREM PROVED
% 1.76/2.03 % SZS status Theorem
% 1.76/2.03
% 1.76/2.03 Exiting with 1 proof.
% 1.76/2.03
% 1.76/2.03 Process 2167 exit (max_proofs) Sun Jun 19 07:12:26 2022
% 1.76/2.03 Prover9 interrupted
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