TSTP Solution File: SEU264+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU264+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 13:30:28 EDT 2022
% Result : Theorem 0.77s 1.02s
% Output : Refutation 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU264+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n006.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 16:54:55 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.44/1.02 ============================== Prover9 ===============================
% 0.44/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.02 Process 6475 was started by sandbox on n006.cluster.edu,
% 0.44/1.02 Sun Jun 19 16:54:56 2022
% 0.44/1.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_6322_n006.cluster.edu".
% 0.44/1.02 ============================== end of head ===========================
% 0.44/1.02
% 0.44/1.02 ============================== INPUT =================================
% 0.44/1.02
% 0.44/1.02 % Reading from file /tmp/Prover9_6322_n006.cluster.edu
% 0.44/1.02
% 0.44/1.02 set(prolog_style_variables).
% 0.44/1.02 set(auto2).
% 0.44/1.02 % set(auto2) -> set(auto).
% 0.44/1.02 % set(auto) -> set(auto_inference).
% 0.44/1.02 % set(auto) -> set(auto_setup).
% 0.44/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.02 % set(auto) -> set(auto_limits).
% 0.44/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.02 % set(auto) -> set(auto_denials).
% 0.44/1.02 % set(auto) -> set(auto_process).
% 0.44/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.02 % set(auto2) -> assign(stats, some).
% 0.44/1.02 % set(auto2) -> clear(echo_input).
% 0.44/1.02 % set(auto2) -> set(quiet).
% 0.44/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.02 % set(auto2) -> clear(print_given).
% 0.44/1.02 assign(lrs_ticks,-1).
% 0.44/1.02 assign(sos_limit,10000).
% 0.44/1.02 assign(order,kbo).
% 0.44/1.02 set(lex_order_vars).
% 0.44/1.02 clear(print_given).
% 0.44/1.02
% 0.44/1.02 % formulas(sos). % not echoed (18 formulas)
% 0.44/1.02
% 0.44/1.02 ============================== end of input ==========================
% 0.44/1.02
% 0.44/1.02 % From the command line: assign(max_seconds, 300).
% 0.44/1.02
% 0.44/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.02
% 0.44/1.02 % Formulas that are not ordinary clauses:
% 0.44/1.02 1 (all A all B all C (element(C,powerset(cartesian_product2(A,B))) -> relation(C))) # label(cc1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 2 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 3 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 4 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 5 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 6 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 7 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 8 (all A all B all C (relation_of2_as_subset(C,A,B) -> element(C,powerset(cartesian_product2(A,B))))) # label(dt_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 9 (all A all B exists C relation_of2(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 10 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 11 (all A all B exists C relation_of2_as_subset(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 12 (all A all B all C (relation_of2_as_subset(C,A,B) <-> relation_of2(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 13 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 14 (all A all B all C (relation_of2_as_subset(C,A,B) -> subset(relation_dom(C),A) & subset(relation_rng(C),B))) # label(t12_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 15 (all A all B all C all D (relation_of2_as_subset(D,C,A) -> (subset(relation_rng(D),B) -> relation_of2_as_subset(D,C,B)))) # label(t14_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 16 (all A all B all C (subset(A,B) & subset(B,C) -> subset(A,C))) # label(t1_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 17 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 18 -(all A all B all C all D (relation_of2_as_subset(D,C,A) -> (subset(A,B) -> relation_of2_as_subset(D,C,B)))) # label(t16_relset_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.77/1.02
% 0.77/1.02 ============================== end of process non-clausal formulas ===
% 0.77/1.02
% 0.77/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.77/1.02
% 0.77/1.02 ============================== PREDICATE ELIMINATION =================
% 0.77/1.02 19 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom). [clausify(17)].
% 0.77/1.02 20 element(f2(A),A) # label(existence_m1_subset_1) # label(axiom). [clausify(10)].
% 0.77/1.02 Derived: subset(f2(powerset(A)),A). [resolve(19,a,20,a)].
% 0.77/1.02 21 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(17)].
% 0.77/1.02 22 -element(A,powerset(cartesian_product2(B,C))) | relation(A) # label(cc1_relset_1) # label(axiom). [clausify(1)].
% 0.77/1.02 Derived: relation(f2(powerset(cartesian_product2(A,B)))). [resolve(22,a,20,a)].
% 0.77/1.02 Derived: relation(A) | -subset(A,cartesian_product2(B,C)). [resolve(22,a,21,a)].
% 0.77/1.02 23 -relation_of2_as_subset(A,B,C) | element(A,powerset(cartesian_product2(B,C))) # label(dt_m2_relset_1) # label(axiom). [clausify(8)].
% 0.77/1.02 Derived: -relation_of2_as_subset(A,B,C) | subset(A,cartesian_product2(B,C)). [resolve(23,b,19,a)].
% 0.77/1.02 Derived: -relation_of2_as_subset(A,B,C) | relation(A). [resolve(23,b,22,a)].
% 0.77/1.02 24 relation_of2_as_subset(A,B,C) | -relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(12)].
% 0.77/1.02 25 relation_of2(f1(A,B),A,B) # label(existence_m1_relset_1) # label(axiom). [clausify(9)].
% 0.77/1.02 26 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(12)].
% 0.77/1.02 Derived: relation_of2_as_subset(f1(A,B),A,B). [resolve(24,b,25,a)].
% 0.77/1.02
% 0.77/1.02 ============================== end predicate elimination =============
% 0.77/1.02
% 0.77/1.02 Auto_denials:
% 0.77/1.02 % copying label t16_relset_1 to answer in negative clause
% 0.77/1.02
% 0.77/1.02 Term ordering decisions:
% 0.77/1.02 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. cartesian_product2=1. f1=1. f3=1. relation_rng=1. powerset=1. relation_dom=1. f2=1.
% 0.77/1.02
% 0.77/1.02 ============================== end of process initial clauses ========
% 0.77/1.02
% 0.77/1.02 ============================== CLAUSES FOR SEARCH ====================
% 0.77/1.02
% 0.77/1.02 ============================== end of clauses for search =============
% 0.77/1.02
% 0.77/1.02 ============================== SEARCH ================================
% 0.77/1.02
% 0.77/1.02 % Starting search at 0.01 seconds.
% 0.77/1.02
% 0.77/1.02 ============================== PROOF =================================
% 0.77/1.02 % SZS status Theorem
% 0.77/1.02 % SZS output start Refutation
% 0.77/1.02
% 0.77/1.02 % Proof 1 at 0.01 (+ 0.00) seconds: t16_relset_1.
% 0.77/1.02 % Length of proof is 14.
% 0.77/1.02 % Level of proof is 4.
% 0.77/1.02 % Maximum clause weight is 12.000.
% 0.77/1.02 % Given clauses 14.
% 0.77/1.02
% 0.77/1.02 14 (all A all B all C (relation_of2_as_subset(C,A,B) -> subset(relation_dom(C),A) & subset(relation_rng(C),B))) # label(t12_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 15 (all A all B all C all D (relation_of2_as_subset(D,C,A) -> (subset(relation_rng(D),B) -> relation_of2_as_subset(D,C,B)))) # label(t14_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 16 (all A all B all C (subset(A,B) & subset(B,C) -> subset(A,C))) # label(t1_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.02 18 -(all A all B all C all D (relation_of2_as_subset(D,C,A) -> (subset(A,B) -> relation_of2_as_subset(D,C,B)))) # label(t16_relset_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.77/1.02 28 subset(c1,c2) # label(t16_relset_1) # label(negated_conjecture). [clausify(18)].
% 0.77/1.02 29 relation_of2_as_subset(c4,c3,c1) # label(t16_relset_1) # label(negated_conjecture). [clausify(18)].
% 0.77/1.02 31 -relation_of2_as_subset(c4,c3,c2) # label(t16_relset_1) # label(negated_conjecture) # answer(t16_relset_1). [clausify(18)].
% 0.77/1.02 33 -relation_of2_as_subset(A,B,C) | subset(relation_rng(A),C) # label(t12_relset_1) # label(axiom). [clausify(14)].
% 0.77/1.02 34 -subset(A,B) | -subset(B,C) | subset(A,C) # label(t1_xboole_1) # label(axiom). [clausify(16)].
% 0.77/1.02 35 -relation_of2_as_subset(A,B,C) | -subset(relation_rng(A),D) | relation_of2_as_subset(A,B,D) # label(t14_relset_1) # label(axiom). [clausify(15)].
% 0.77/1.02 42 subset(relation_rng(c4),c1). [ur(33,a,29,a)].
% 0.77/1.02 46 -subset(relation_rng(c4),c2) # answer(t16_relset_1). [ur(35,a,29,a,c,31,a)].
% 0.77/1.02 63 -subset(relation_rng(c4),c1) # answer(t16_relset_1). [ur(34,b,28,a,c,46,a)].
% 0.77/1.02 64 $F # answer(t16_relset_1). [resolve(63,a,42,a)].
% 0.77/1.02
% 0.77/1.02 % SZS output end Refutation
% 0.77/1.02 ============================== end of proof ==========================
% 0.77/1.02
% 0.77/1.02 ============================== STATISTICS ============================
% 0.77/1.02
% 0.77/1.02 Given=14. Generated=46. Kept=37. proofs=1.
% 0.77/1.02 Usable=14. Sos=17. Demods=0. Limbo=4, Disabled=24. Hints=0.
% 0.77/1.02 Megabytes=0.07.
% 0.77/1.02 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.77/1.02
% 0.77/1.02 ============================== end of statistics =====================
% 0.77/1.02
% 0.77/1.02 ============================== end of search =========================
% 0.77/1.02
% 0.77/1.02 THEOREM PROVED
% 0.77/1.02 % SZS status Theorem
% 0.77/1.02
% 0.77/1.02 Exiting with 1 proof.
% 0.77/1.02
% 0.77/1.02 Process 6475 exit (max_proofs) Sun Jun 19 16:54:56 2022
% 0.77/1.02 Prover9 interrupted
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