TSTP Solution File: SEU263+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU263+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 0.41s 1.08s
% Output : Refutation 0.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU263+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 20:45:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.41/1.06 ============================== Prover9 ===============================
% 0.41/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.41/1.06 Process 21777 was started by sandbox on n025.cluster.edu,
% 0.41/1.06 Sun Jun 19 20:45:59 2022
% 0.41/1.06 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_21624_n025.cluster.edu".
% 0.41/1.06 ============================== end of head ===========================
% 0.41/1.06
% 0.41/1.06 ============================== INPUT =================================
% 0.41/1.06
% 0.41/1.06 % Reading from file /tmp/Prover9_21624_n025.cluster.edu
% 0.41/1.06
% 0.41/1.06 set(prolog_style_variables).
% 0.41/1.06 set(auto2).
% 0.41/1.06 % set(auto2) -> set(auto).
% 0.41/1.06 % set(auto) -> set(auto_inference).
% 0.41/1.06 % set(auto) -> set(auto_setup).
% 0.41/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.41/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/1.06 % set(auto) -> set(auto_limits).
% 0.41/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/1.06 % set(auto) -> set(auto_denials).
% 0.41/1.06 % set(auto) -> set(auto_process).
% 0.41/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.41/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.41/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.41/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.41/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.41/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.41/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.41/1.06 % set(auto2) -> assign(stats, some).
% 0.41/1.06 % set(auto2) -> clear(echo_input).
% 0.41/1.06 % set(auto2) -> set(quiet).
% 0.41/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.41/1.06 % set(auto2) -> clear(print_given).
% 0.41/1.06 assign(lrs_ticks,-1).
% 0.41/1.06 assign(sos_limit,10000).
% 0.41/1.06 assign(order,kbo).
% 0.41/1.06 set(lex_order_vars).
% 0.41/1.06 clear(print_given).
% 0.41/1.06
% 0.41/1.06 % formulas(sos). % not echoed (20 formulas)
% 0.41/1.06
% 0.41/1.06 ============================== end of input ==========================
% 0.41/1.06
% 0.41/1.06 % From the command line: assign(max_seconds, 300).
% 0.41/1.06
% 0.41/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/1.06
% 0.41/1.06 % Formulas that are not ordinary clauses:
% 0.41/1.06 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].
% 0.41/1.06 2 (all A all B all C (relation_of2(C,A,B) <-> subset(C,cartesian_product2(A,B)))) # label(d1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 3 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 4 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 5 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 6 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 7 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 8 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 9 (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].
% 0.41/1.06 10 (all A all B exists C relation_of2(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 11 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 12 (all A all B exists C relation_of2_as_subset(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 13 (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].
% 0.41/1.06 14 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 15 (all A all B all C all D (subset(A,B) & subset(C,D) -> subset(cartesian_product2(A,C),cartesian_product2(B,D)))) # label(t119_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 16 (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].
% 0.41/1.06 17 (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].
% 0.41/1.06 18 (all A (relation(A) -> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))))) # label(t21_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 19 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 20 -(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(negated_conjecture) # label(non_clause). [assumption].
% 0.41/1.06
% 0.41/1.06 ============================== end of process non-clausal formulas ===
% 0.41/1.06
% 0.41/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.41/1.06
% 0.41/1.06 ============================== PREDICATE ELIMINATION =================
% 0.41/1.06 21 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom). [clausify(19)].
% 0.41/1.06 22 element(f2(A),A) # label(existence_m1_subset_1) # label(axiom). [clausify(11)].
% 0.41/1.06 Derived: subset(f2(powerset(A)),A). [resolve(21,a,22,a)].
% 0.41/1.06 23 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(19)].
% 0.41/1.06 24 -element(A,powerset(cartesian_product2(B,C))) | relation(A) # label(cc1_relset_1) # label(axiom). [clausify(1)].
% 0.41/1.06 Derived: relation(f2(powerset(cartesian_product2(A,B)))). [resolve(24,a,22,a)].
% 0.41/1.06 Derived: relation(A) | -subset(A,cartesian_product2(B,C)). [resolve(24,a,23,a)].
% 0.41/1.06 25 -relation_of2_as_subset(A,B,C) | element(A,powerset(cartesian_product2(B,C))) # label(dt_m2_relset_1) # label(axiom). [clausify(9)].
% 0.41/1.06 Derived: -relation_of2_as_subset(A,B,C) | subset(A,cartesian_product2(B,C)). [resolve(25,b,21,a)].
% 0.41/1.06 Derived: -relation_of2_as_subset(A,B,C) | relation(A). [resolve(25,b,24,a)].
% 0.41/1.06 26 -relation_of2_as_subset(c4,c3,c2) # label(t14_relset_1) # label(negated_conjecture). [clausify(20)].
% 0.41/1.06 27 relation_of2_as_subset(c4,c3,c1) # label(t14_relset_1) # label(negated_conjecture). [clausify(20)].
% 0.41/1.06 28 relation_of2_as_subset(f3(A,B),A,B) # label(existence_m2_relset_1) # label(axiom). [clausify(12)].
% 0.41/1.06 29 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(13)].
% 0.41/1.06 Derived: relation_of2(c4,c3,c1). [resolve(29,a,27,a)].
% 0.41/1.06 Derived: relation_of2(f3(A,B),A,B). [resolve(29,a,28,a)].
% 0.41/1.06 30 relation_of2_as_subset(A,B,C) | -relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(13)].
% 0.41/1.06 Derived: -relation_of2(c4,c3,c2). [resolve(30,a,26,a)].
% 0.41/1.06 31 -relation_of2_as_subset(A,B,C) | subset(relation_dom(A),B) # label(t12_relset_1) # label(axiom). [clausify(16)].
% 0.41/1.06 Derived: subset(relation_dom(c4),c3). [resolve(31,a,27,a)].
% 0.41/1.06 Derived: subset(relation_dom(f3(A,B)),A). [resolve(31,a,28,a)].
% 0.41/1.06 Derived: subset(relation_dom(A),B) | -relation_of2(A,B,C). [resolve(31,a,30,a)].
% 0.41/1.06 32 -relation_of2_as_subset(A,B,C) | subset(relation_rng(A),C) # label(t12_relset_1) # label(axiom). [clausify(16)].
% 0.41/1.06 Derived: subset(relation_rng(c4),c1). [resolve(32,a,27,a)].
% 0.41/1.06 Derived: subset(relation_rng(f3(A,B)),B). [resolve(32,a,28,a)].
% 0.41/1.06 Derived: subset(relation_rng(A),B) | -relation_of2(A,C,B). [resolve(32,a,30,a)].
% 0.41/1.06 33 -relation_of2_as_subset(A,B,C) | subset(A,cartesian_product2(B,C)). [resolve(25,b,21,a)].
% 0.41/1.06 Derived: subset(c4,cartesian_product2(c3,c1)). [resolve(33,a,27,a)].
% 0.41/1.06 Derived: subset(f3(A,B),cartesian_product2(A,B)). [resolve(33,a,28,a)].
% 0.41/1.06 Derived: subset(A,cartesian_product2(B,C)) | -relation_of2(A,B,C). [resolve(33,a,30,a)].
% 0.41/1.06 34 -relation_of2_as_subset(A,B,C) | relation(A). [resolve(25,b,24,a)].
% 0.41/1.06 Derived: relation(c4). [resolve(34,a,27,a)].
% 0.41/1.06 Derived: relation(f3(A,B)). [resolve(34,a,28,a)].
% 0.41/1.06 Derived: relation(A) | -relation_of2(A,B,C). [resolve(34,a,30,a)].
% 0.41/1.06 35 -relation_of2(A,B,C) | subset(A,cartesian_product2(B,C)) # label(d1_relset_1) # label(axiom). [clausify(2)].
% 0.41/1.06 36 relation_of2(f1(A,B),A,B) # label(existence_m1_relset_1) # label(axiom). [clausify(10)].
% 0.41/1.06 Derived: subset(f1(A,B),cartesian_product2(A,B)). [resolve(35,a,36,a)].
% 0.41/1.06 37 relation_of2(A,B,C) | -subset(A,cartesian_product2(B,C)) # label(d1_relset_1) # label(axiom). [clausify(2)].
% 0.41/1.08 38 relation_of2(c4,c3,c1). [resolve(29,a,27,a)].
% 0.41/1.08 39 relation_of2(f3(A,B),A,B). [resolve(29,a,28,a)].
% 0.41/1.08 40 -relation_of2(c4,c3,c2). [resolve(30,a,26,a)].
% 0.41/1.08 Derived: -subset(c4,cartesian_product2(c3,c2)). [resolve(40,a,37,a)].
% 0.41/1.08 41 subset(relation_dom(A),B) | -relation_of2(A,B,C). [resolve(31,a,30,a)].
% 0.41/1.08 Derived: subset(relation_dom(f1(A,B)),A). [resolve(41,b,36,a)].
% 0.41/1.08 Derived: subset(relation_dom(A),B) | -subset(A,cartesian_product2(B,C)). [resolve(41,b,37,a)].
% 0.41/1.08 Derived: subset(relation_dom(c4),c3). [resolve(41,b,38,a)].
% 0.41/1.08 Derived: subset(relation_dom(f3(A,B)),A). [resolve(41,b,39,a)].
% 0.41/1.08 42 subset(relation_rng(A),B) | -relation_of2(A,C,B). [resolve(32,a,30,a)].
% 0.41/1.08 Derived: subset(relation_rng(f1(A,B)),B). [resolve(42,b,36,a)].
% 0.41/1.08 Derived: subset(relation_rng(A),B) | -subset(A,cartesian_product2(C,B)). [resolve(42,b,37,a)].
% 0.41/1.08 Derived: subset(relation_rng(c4),c1). [resolve(42,b,38,a)].
% 0.41/1.08 Derived: subset(relation_rng(f3(A,B)),B). [resolve(42,b,39,a)].
% 0.41/1.08 43 subset(A,cartesian_product2(B,C)) | -relation_of2(A,B,C). [resolve(33,a,30,a)].
% 0.41/1.08 Derived: subset(c4,cartesian_product2(c3,c1)). [resolve(43,b,38,a)].
% 0.41/1.08 Derived: subset(f3(A,B),cartesian_product2(A,B)). [resolve(43,b,39,a)].
% 0.41/1.08 44 relation(A) | -relation_of2(A,B,C). [resolve(34,a,30,a)].
% 0.41/1.08 Derived: relation(f1(A,B)). [resolve(44,b,36,a)].
% 0.41/1.08 Derived: relation(A) | -subset(A,cartesian_product2(B,C)). [resolve(44,b,37,a)].
% 0.41/1.08 Derived: relation(c4). [resolve(44,b,38,a)].
% 0.41/1.08 Derived: relation(f3(A,B)). [resolve(44,b,39,a)].
% 0.41/1.08 45 relation(f2(powerset(cartesian_product2(A,B)))). [resolve(24,a,22,a)].
% 0.41/1.08 46 -relation(A) | subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) # label(t21_relat_1) # label(axiom). [clausify(18)].
% 0.41/1.08 Derived: subset(f2(powerset(cartesian_product2(A,B))),cartesian_product2(relation_dom(f2(powerset(cartesian_product2(A,B)))),relation_rng(f2(powerset(cartesian_product2(A,B)))))). [resolve(45,a,46,a)].
% 0.41/1.08 47 relation(A) | -subset(A,cartesian_product2(B,C)). [resolve(24,a,23,a)].
% 0.41/1.08 Derived: -subset(A,cartesian_product2(B,C)) | subset(A,cartesian_product2(relation_dom(A),relation_rng(A))). [resolve(47,a,46,a)].
% 0.41/1.08 48 relation(c4). [resolve(34,a,27,a)].
% 0.41/1.08 Derived: subset(c4,cartesian_product2(relation_dom(c4),relation_rng(c4))). [resolve(48,a,46,a)].
% 0.41/1.08 49 relation(f3(A,B)). [resolve(34,a,28,a)].
% 0.41/1.08 Derived: subset(f3(A,B),cartesian_product2(relation_dom(f3(A,B)),relation_rng(f3(A,B)))). [resolve(49,a,46,a)].
% 0.41/1.08 50 relation(f1(A,B)). [resolve(44,b,36,a)].
% 0.41/1.08 Derived: subset(f1(A,B),cartesian_product2(relation_dom(f1(A,B)),relation_rng(f1(A,B)))). [resolve(50,a,46,a)].
% 0.41/1.08 51 relation(A) | -subset(A,cartesian_product2(B,C)). [resolve(44,b,37,a)].
% 0.41/1.08 52 relation(c4). [resolve(44,b,38,a)].
% 0.41/1.08 53 relation(f3(A,B)). [resolve(44,b,39,a)].
% 0.41/1.08
% 0.41/1.08 ============================== end predicate elimination =============
% 0.41/1.08
% 0.41/1.08 Auto_denials: (no changes).
% 0.41/1.08
% 0.41/1.08 Term ordering decisions:
% 0.41/1.08 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. cartesian_product2=1. f1=1. f3=1. relation_rng=1. relation_dom=1. powerset=1. f2=1.
% 0.41/1.08
% 0.41/1.08 ============================== end of process initial clauses ========
% 0.41/1.08
% 0.41/1.08 ============================== CLAUSES FOR SEARCH ====================
% 0.41/1.08
% 0.41/1.08 ============================== end of clauses for search =============
% 0.41/1.08
% 0.41/1.08 ============================== SEARCH ================================
% 0.41/1.08
% 0.41/1.08 % Starting search at 0.01 seconds.
% 0.41/1.08
% 0.41/1.08 ============================== PROOF =================================
% 0.41/1.08 % SZS status Theorem
% 0.41/1.08 % SZS output start Refutation
% 0.41/1.08
% 0.41/1.08 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.41/1.08 % Length of proof is 29.
% 0.41/1.08 % Level of proof is 6.
% 0.41/1.08 % Maximum clause weight is 13.000.
% 0.41/1.08 % Given clauses 20.
% 0.41/1.08
% 0.41/1.08 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].
% 0.41/1.08 2 (all A all B all C (relation_of2(C,A,B) <-> subset(C,cartesian_product2(A,B)))) # label(d1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.08 9 (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].
% 0.83/1.08 13 (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].
% 0.83/1.08 15 (all A all B all C all D (subset(A,B) & subset(C,D) -> subset(cartesian_product2(A,C),cartesian_product2(B,D)))) # label(t119_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.08 16 (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].
% 0.83/1.08 17 (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].
% 0.83/1.08 18 (all A (relation(A) -> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))))) # label(t21_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.08 20 -(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(negated_conjecture) # label(non_clause). [assumption].
% 0.83/1.08 24 -element(A,powerset(cartesian_product2(B,C))) | relation(A) # label(cc1_relset_1) # label(axiom). [clausify(1)].
% 0.83/1.08 25 -relation_of2_as_subset(A,B,C) | element(A,powerset(cartesian_product2(B,C))) # label(dt_m2_relset_1) # label(axiom). [clausify(9)].
% 0.83/1.08 26 -relation_of2_as_subset(c4,c3,c2) # label(t14_relset_1) # label(negated_conjecture). [clausify(20)].
% 0.83/1.08 27 relation_of2_as_subset(c4,c3,c1) # label(t14_relset_1) # label(negated_conjecture). [clausify(20)].
% 0.83/1.08 30 relation_of2_as_subset(A,B,C) | -relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(13)].
% 0.83/1.08 31 -relation_of2_as_subset(A,B,C) | subset(relation_dom(A),B) # label(t12_relset_1) # label(axiom). [clausify(16)].
% 0.83/1.08 34 -relation_of2_as_subset(A,B,C) | relation(A). [resolve(25,b,24,a)].
% 0.83/1.08 37 relation_of2(A,B,C) | -subset(A,cartesian_product2(B,C)) # label(d1_relset_1) # label(axiom). [clausify(2)].
% 0.83/1.08 40 -relation_of2(c4,c3,c2). [resolve(30,a,26,a)].
% 0.83/1.08 46 -relation(A) | subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) # label(t21_relat_1) # label(axiom). [clausify(18)].
% 0.83/1.08 48 relation(c4). [resolve(34,a,27,a)].
% 0.83/1.08 55 subset(relation_rng(c4),c2) # label(t14_relset_1) # label(negated_conjecture). [clausify(20)].
% 0.83/1.08 56 -subset(A,B) | -subset(B,C) | subset(A,C) # label(t1_xboole_1) # label(axiom). [clausify(17)].
% 0.83/1.08 57 -subset(A,B) | -subset(C,D) | subset(cartesian_product2(A,C),cartesian_product2(B,D)) # label(t119_zfmisc_1) # label(axiom). [clausify(15)].
% 0.83/1.08 59 subset(relation_dom(c4),c3). [resolve(31,a,27,a)].
% 0.83/1.08 66 -subset(c4,cartesian_product2(c3,c2)). [resolve(40,a,37,a)].
% 0.83/1.08 73 subset(c4,cartesian_product2(relation_dom(c4),relation_rng(c4))). [resolve(48,a,46,a)].
% 0.83/1.08 91 subset(cartesian_product2(relation_dom(c4),relation_rng(c4)),cartesian_product2(c3,c2)). [ur(57,a,59,a,b,55,a)].
% 0.83/1.08 362 -subset(cartesian_product2(relation_dom(c4),relation_rng(c4)),cartesian_product2(c3,c2)). [ur(56,a,73,a,c,66,a)].
% 0.83/1.08 363 $F. [resolve(362,a,91,a)].
% 0.83/1.08
% 0.83/1.08 % SZS output end Refutation
% 0.83/1.08 ============================== end of proof ==========================
% 0.83/1.08
% 0.83/1.08 ============================== STATISTICS ============================
% 0.83/1.08
% 0.83/1.08 Given=20. Generated=378. Kept=309. proofs=1.
% 0.83/1.08 Usable=20. Sos=256. Demods=0. Limbo=32, Disabled=61. Hints=0.
% 0.83/1.08 Megabytes=0.31.
% 0.83/1.08 User_CPU=0.02, System_CPU=0.00, Wall_clock=1.
% 0.83/1.08
% 0.83/1.08 ============================== end of statistics =====================
% 0.83/1.08
% 0.83/1.08 ============================== end of search =========================
% 0.83/1.08
% 0.83/1.08 THEOREM PROVED
% 0.83/1.08 % SZS status Theorem
% 0.83/1.08
% 0.83/1.08 Exiting with 1 proof.
% 0.83/1.08
% 0.83/1.08 Process 21777 exit (max_proofs) Sun Jun 19 20:46:00 2022
% 0.83/1.08 Prover9 interrupted
%------------------------------------------------------------------------------