TSTP Solution File: SEU281+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU281+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 13:30:38 EDT 2022
% Result : Theorem 46.40s 46.72s
% Output : Refutation 46.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SEU281+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.30 % Computer : n028.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 600
% 0.11/0.30 % DateTime : Sun Jun 19 02:54:00 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.37/0.96 ============================== Prover9 ===============================
% 0.37/0.96 Prover9 (32) version 2009-11A, November 2009.
% 0.37/0.96 Process 25152 was started by sandbox2 on n028.cluster.edu,
% 0.37/0.96 Sun Jun 19 02:54:00 2022
% 0.37/0.96 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_24854_n028.cluster.edu".
% 0.37/0.96 ============================== end of head ===========================
% 0.37/0.96
% 0.37/0.96 ============================== INPUT =================================
% 0.37/0.96
% 0.37/0.96 % Reading from file /tmp/Prover9_24854_n028.cluster.edu
% 0.37/0.96
% 0.37/0.96 set(prolog_style_variables).
% 0.37/0.96 set(auto2).
% 0.37/0.96 % set(auto2) -> set(auto).
% 0.37/0.96 % set(auto) -> set(auto_inference).
% 0.37/0.96 % set(auto) -> set(auto_setup).
% 0.37/0.96 % set(auto_setup) -> set(predicate_elim).
% 0.37/0.96 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.37/0.96 % set(auto) -> set(auto_limits).
% 0.37/0.96 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.37/0.96 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.37/0.96 % set(auto) -> set(auto_denials).
% 0.37/0.96 % set(auto) -> set(auto_process).
% 0.37/0.96 % set(auto2) -> assign(new_constants, 1).
% 0.37/0.96 % set(auto2) -> assign(fold_denial_max, 3).
% 0.37/0.96 % set(auto2) -> assign(max_weight, "200.000").
% 0.37/0.96 % set(auto2) -> assign(max_hours, 1).
% 0.37/0.96 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.37/0.96 % set(auto2) -> assign(max_seconds, 0).
% 0.37/0.96 % set(auto2) -> assign(max_minutes, 5).
% 0.37/0.96 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.37/0.96 % set(auto2) -> set(sort_initial_sos).
% 0.37/0.96 % set(auto2) -> assign(sos_limit, -1).
% 0.37/0.96 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.37/0.96 % set(auto2) -> assign(max_megs, 400).
% 0.37/0.96 % set(auto2) -> assign(stats, some).
% 0.37/0.96 % set(auto2) -> clear(echo_input).
% 0.37/0.96 % set(auto2) -> set(quiet).
% 0.37/0.96 % set(auto2) -> clear(print_initial_clauses).
% 0.37/0.96 % set(auto2) -> clear(print_given).
% 0.37/0.96 assign(lrs_ticks,-1).
% 0.37/0.96 assign(sos_limit,10000).
% 0.37/0.96 assign(order,kbo).
% 0.37/0.96 set(lex_order_vars).
% 0.37/0.96 clear(print_given).
% 0.37/0.96
% 0.37/0.96 % formulas(sos). % not echoed (15 formulas)
% 0.37/0.96
% 0.37/0.96 ============================== end of input ==========================
% 0.37/0.96
% 0.37/0.96 % From the command line: assign(max_seconds, 300).
% 0.37/0.96
% 0.37/0.96 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.37/0.96
% 0.37/0.96 % Formulas that are not ordinary clauses:
% 0.37/0.96 1 (all A (ordinal(A) -> epsilon_transitive(A) & epsilon_connected(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption].
% 0.37/0.96 2 (all A (epsilon_transitive(A) & epsilon_connected(A) -> ordinal(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption].
% 0.37/0.96 3 (exists A (epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption].
% 0.37/0.96 4 (exists A (-empty(A) & epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption].
% 0.37/0.96 5 (all A (empty(A) -> function(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.37/0.96 6 (all A (empty(A) -> epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption].
% 0.37/0.96 7 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.37/0.96 8 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.37/0.96 9 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.37/0.96 10 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.37/0.96 11 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.37/0.96 12 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.37/0.96 13 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.37/0.96 14 (all A all B ((all C all D all E (C = D & (exists F exists G (ordered_pair(F,G) = D & in(F,A) & G = singleton(F))) & C = E & (exists H exists I (ordered_pair(H,I) = E & in(H,A) & I = singleton(H))) -> D = E)) -> (exists C all D (in(D,C) <-> (exists E (in(E,cartesian_product2(A,B)) & E = D & (exists J exists K (ordered_pair(J,K) = D & in(J,A) & K = singleton(J))))))))) # label(s1_tarski__e16_22__wellord2__2) # label(axiom) # label(non_clause). [assumption].
% 46.40/46.71 15 -(all A all B exists C all D (in(D,C) <-> in(D,cartesian_product2(A,B)) & (exists E exists F (ordered_pair(E,F) = D & in(E,A) & F = singleton(E))))) # label(s1_xboole_0__e16_22__wellord2__1) # label(negated_conjecture) # label(non_clause). [assumption].
% 46.40/46.71
% 46.40/46.71 ============================== end of process non-clausal formulas ===
% 46.40/46.71
% 46.40/46.71 ============================== PROCESS INITIAL CLAUSES ===============
% 46.40/46.71
% 46.40/46.71 ============================== PREDICATE ELIMINATION =================
% 46.40/46.71 16 -epsilon_transitive(A) | -epsilon_connected(A) | ordinal(A) # label(cc2_ordinal1) # label(axiom). [clausify(2)].
% 46.40/46.71 17 epsilon_transitive(c1) # label(rc1_ordinal1) # label(axiom). [clausify(3)].
% 46.40/46.71 18 epsilon_transitive(c2) # label(rc3_ordinal1) # label(axiom). [clausify(4)].
% 46.40/46.71 19 -ordinal(A) | epsilon_transitive(A) # label(cc1_ordinal1) # label(axiom). [clausify(1)].
% 46.40/46.71 20 -empty(A) | epsilon_transitive(A) # label(cc3_ordinal1) # label(axiom). [clausify(6)].
% 46.40/46.71 Derived: -epsilon_connected(c1) | ordinal(c1). [resolve(16,a,17,a)].
% 46.40/46.71 Derived: -epsilon_connected(c2) | ordinal(c2). [resolve(16,a,18,a)].
% 46.40/46.71 Derived: -epsilon_connected(A) | ordinal(A) | -empty(A). [resolve(16,a,20,b)].
% 46.40/46.71 21 -ordinal(A) | epsilon_connected(A) # label(cc1_ordinal1) # label(axiom). [clausify(1)].
% 46.40/46.71 22 ordinal(c1) # label(rc1_ordinal1) # label(axiom). [clausify(3)].
% 46.40/46.71 23 ordinal(c2) # label(rc3_ordinal1) # label(axiom). [clausify(4)].
% 46.40/46.71 Derived: epsilon_connected(c1). [resolve(21,a,22,a)].
% 46.40/46.71 Derived: epsilon_connected(c2). [resolve(21,a,23,a)].
% 46.40/46.71 24 -empty(A) | ordinal(A) # label(cc3_ordinal1) # label(axiom). [clausify(6)].
% 46.40/46.71 Derived: -empty(A) | epsilon_connected(A). [resolve(24,b,21,a)].
% 46.40/46.71 25 -epsilon_connected(c1) | ordinal(c1). [resolve(16,a,17,a)].
% 46.40/46.71 26 -epsilon_connected(c2) | ordinal(c2). [resolve(16,a,18,a)].
% 46.40/46.71 27 -epsilon_connected(A) | ordinal(A) | -empty(A). [resolve(16,a,20,b)].
% 46.40/46.71
% 46.40/46.71 ============================== end predicate elimination =============
% 46.40/46.71
% 46.40/46.71 Auto_denials: (non-Horn, no changes).
% 46.40/46.71
% 46.40/46.71 Term ordering decisions:
% 46.40/46.71 Function symbol KB weights: c2=1. c3=1. c4=1. c5=1. c6=1. ordered_pair=1. cartesian_product2=1. f1=1. f2=1. f3=1. f4=1. f5=1. f6=1. f7=1. f8=1. singleton=1. f12=1. f13=1. f14=1. f9=1. f10=1. f11=1.
% 46.40/46.71
% 46.40/46.71 ============================== end of process initial clauses ========
% 46.40/46.71
% 46.40/46.71 ============================== CLAUSES FOR SEARCH ====================
% 46.40/46.71
% 46.40/46.71 ============================== end of clauses for search =============
% 46.40/46.71
% 46.40/46.71 ============================== SEARCH ================================
% 46.40/46.71
% 46.40/46.71 % Starting search at 0.02 seconds.
% 46.40/46.71
% 46.40/46.71 Low Water (keep): wt=81.000, iters=3334
% 46.40/46.71
% 46.40/46.71 Low Water (keep): wt=79.000, iters=3436
% 46.40/46.71
% 46.40/46.71 Low Water (keep): wt=76.000, iters=3392
% 46.40/46.71
% 46.40/46.71 Low Water (keep): wt=75.000, iters=3370
% 46.40/46.71
% 46.40/46.71 Low Water (keep): wt=74.000, iters=3338
% 46.40/46.71
% 46.40/46.71 Low Water (keep): wt=73.000, iters=3357
% 46.40/46.71
% 46.40/46.71 Low Water (keep): wt=72.000, iters=3407
% 46.40/46.71
% 46.40/46.71 Low Water (keep): wt=71.000, iters=3365
% 46.40/46.71
% 46.40/46.71 Low Water (keep): wt=70.000, iters=3341
% 46.40/46.71
% 46.40/46.71 Low Water (keep): wt=69.000, iters=3356
% 46.40/46.71
% 46.40/46.71 Low Water (keep): wt=68.000, iters=3438
% 46.40/46.71
% 46.40/46.71 Low Water (keep): wt=67.000, iters=3338
% 46.40/46.71
% 46.40/46.71 Low Water (keep): wt=66.000, iters=3335
% 46.40/46.71
% 46.40/46.71 Low Water (keep): wt=65.000, iters=3338
% 46.40/46.72
% 46.40/46.72 Low Water (keep): wt=64.000, iters=3543
% 46.40/46.72
% 46.40/46.72 Low Water (keep): wt=63.000, iters=3376
% 46.40/46.72
% 46.40/46.72 Low Water (keep): wt=62.000, iters=3363
% 46.40/46.72
% 46.40/46.72 Low Water (keep): wt=61.000, iters=3354
% 46.40/46.72
% 46.40/46.72 Low Water (keep): wt=60.000, iters=3355
% 46.40/46.72
% 46.40/46.72 Low Water (keep): wt=59.000, iters=3343
% 46.40/46.72
% 46.40/46.72 Low Water (keep): wt=58.000, iters=3335
% 46.40/46.72
% 46.40/46.72 Low Water (keep): wt=57.000, iters=3358
% 46.40/46.72
% 46.40/46.72 ============================== PROOF =================================
% 46.40/46.72 % SZS status Theorem
% 46.40/46.72 % SZS output start Refutation
% 46.40/46.72
% 46.40/46.72 % Proof 1 at 45.14 (+ 0.63) seconds.
% 46.40/46.72 % Length of proof is 172.
% 46.40/46.72 % Level of proof is 37.
% 46.40/46.72 % Maximum clause weight is 58.000.
% 46.40/46.72 % Given clauses 9009.
% 46.40/46.72
% 46.40/46.72 14 (all A all B ((all C all D all E (C = D & (exists F exists G (ordered_pair(F,G) = D & in(F,A) & G = singleton(F))) & C = E & (exists H exists I (ordered_pair(H,I) = E & in(H,A) & I = singleton(H))) -> D = E)) -> (exists C all D (in(D,C) <-> (exists E (in(E,cartesian_product2(A,B)) & E = D & (exists J exists K (ordered_pair(J,K) = D & in(J,A) & K = singleton(J))))))))) # label(s1_tarski__e16_22__wellord2__2) # label(axiom) # label(non_clause). [assumption].
% 46.40/46.72 15 -(all A all B exists C all D (in(D,C) <-> in(D,cartesian_product2(A,B)) & (exists E exists F (ordered_pair(E,F) = D & in(E,A) & F = singleton(E))))) # label(s1_xboole_0__e16_22__wellord2__1) # label(negated_conjecture) # label(non_clause). [assumption].
% 46.40/46.72 29 in(f12(A),A) | in(f13(A),c5) # label(s1_xboole_0__e16_22__wellord2__1) # label(negated_conjecture). [clausify(15)].
% 46.40/46.72 30 in(f12(A),A) | in(f12(A),cartesian_product2(c5,c6)) # label(s1_xboole_0__e16_22__wellord2__1) # label(negated_conjecture). [clausify(15)].
% 46.40/46.72 31 in(f12(A),A) | singleton(f13(A)) = f14(A) # label(s1_xboole_0__e16_22__wellord2__1) # label(negated_conjecture). [clausify(15)].
% 46.40/46.72 32 in(f12(A),A) | ordered_pair(f13(A),f14(A)) = f12(A) # label(s1_xboole_0__e16_22__wellord2__1) # label(negated_conjecture). [clausify(15)].
% 46.40/46.72 37 -in(f12(A),A) | -in(f12(A),cartesian_product2(c5,c6)) | ordered_pair(B,C) != f12(A) | -in(B,c5) | singleton(B) != C # label(s1_xboole_0__e16_22__wellord2__1) # label(negated_conjecture). [clausify(15)].
% 46.40/46.72 38 -in(f12(A),A) | -in(f12(A),cartesian_product2(c5,c6)) | f12(A) != ordered_pair(B,C) | -in(B,c5) | singleton(B) != C. [copy(37),flip(c)].
% 46.40/46.72 43 f2(A,B) = f1(A,B) | -in(C,f8(A,B)) | f9(A,B,C) = C # label(s1_tarski__e16_22__wellord2__2) # label(axiom). [clausify(14)].
% 46.40/46.72 44 f2(A,B) = f1(A,B) | -in(C,f8(A,B)) | in(f10(A,B,C),A) # label(s1_tarski__e16_22__wellord2__2) # label(axiom). [clausify(14)].
% 46.40/46.72 46 f3(A,B) = f1(A,B) | -in(C,f8(A,B)) | f9(A,B,C) = C # label(s1_tarski__e16_22__wellord2__2) # label(axiom). [clausify(14)].
% 46.40/46.72 47 f3(A,B) = f1(A,B) | -in(C,f8(A,B)) | in(f10(A,B,C),A) # label(s1_tarski__e16_22__wellord2__2) # label(axiom). [clausify(14)].
% 46.40/46.72 49 f3(A,B) != f2(A,B) | -in(C,f8(A,B)) | f9(A,B,C) = C # label(s1_tarski__e16_22__wellord2__2) # label(axiom). [clausify(14)].
% 46.40/46.72 50 f3(A,B) != f2(A,B) | -in(C,f8(A,B)) | in(f10(A,B,C),A) # label(s1_tarski__e16_22__wellord2__2) # label(axiom). [clausify(14)].
% 46.40/46.72 55 f2(A,B) = f1(A,B) | -in(C,f8(A,B)) | in(f9(A,B,C),cartesian_product2(A,B)) # label(s1_tarski__e16_22__wellord2__2) # label(axiom). [clausify(14)].
% 46.40/46.72 57 f3(A,B) = f1(A,B) | -in(C,f8(A,B)) | in(f9(A,B,C),cartesian_product2(A,B)) # label(s1_tarski__e16_22__wellord2__2) # label(axiom). [clausify(14)].
% 46.40/46.72 59 f3(A,B) != f2(A,B) | -in(C,f8(A,B)) | in(f9(A,B,C),cartesian_product2(A,B)) # label(s1_tarski__e16_22__wellord2__2) # label(axiom). [clausify(14)].
% 46.40/46.72 64 f2(A,B) = f1(A,B) | -in(C,f8(A,B)) | singleton(f10(A,B,C)) = f11(A,B,C) # label(s1_tarski__e16_22__wellord2__2) # label(axiom). [clausify(14)].
% 46.40/46.72 67 f3(A,B) = f1(A,B) | -in(C,f8(A,B)) | singleton(f10(A,B,C)) = f11(A,B,C) # label(s1_tarski__e16_22__wellord2__2) # label(axiom). [clausify(14)].
% 46.40/46.72 70 f3(A,B) != f2(A,B) | -in(C,f8(A,B)) | singleton(f10(A,B,C)) = f11(A,B,C) # label(s1_tarski__e16_22__wellord2__2) # label(axiom). [clausify(14)].
% 46.40/46.72 71 f2(A,B) = f1(A,B) | -in(C,f8(A,B)) | ordered_pair(f10(A,B,C),f11(A,B,C)) = C # label(s1_tarski__e16_22__wellord2__2) # label(axiom). [clausify(14)].
% 46.40/46.72 73 f3(A,B) = f1(A,B) | -in(C,f8(A,B)) | ordered_pair(f10(A,B,C),f11(A,B,C)) = C # label(s1_tarski__e16_22__wellord2__2) # label(axiom). [clausify(14)].
% 46.40/46.72 75 f3(A,B) != f2(A,B) | -in(C,f8(A,B)) | ordered_pair(f10(A,B,C),f11(A,B,C)) = C # label(s1_tarski__e16_22__wellord2__2) # label(axiom). [clausify(14)].
% 46.40/46.72 86 f2(A,B) = f1(A,B) | in(C,f8(A,B)) | -in(D,cartesian_product2(A,B)) | D != C | ordered_pair(E,F) != C | -in(E,A) | singleton(E) != F # label(s1_tarski__e16_22__wellord2__2) # label(axiom). [clausify(14)].
% 46.40/46.72 87 f3(A,B) = f1(A,B) | in(C,f8(A,B)) | -in(D,cartesian_product2(A,B)) | D != C | ordered_pair(E,F) != C | -in(E,A) | singleton(E) != F # label(s1_tarski__e16_22__wellord2__2) # label(axiom). [clausify(14)].
% 46.40/46.72 88 f3(A,B) != f2(A,B) | in(C,f8(A,B)) | -in(D,cartesian_product2(A,B)) | D != C | ordered_pair(E,F) != C | -in(E,A) | singleton(E) != F # label(s1_tarski__e16_22__wellord2__2) # label(axiom). [clausify(14)].
% 46.40/46.72 122 -in(f12(A),cartesian_product2(c5,c6)) | f12(A) != ordered_pair(B,C) | -in(B,c5) | singleton(B) != C | ordered_pair(f13(A),f14(A)) = f12(A). [resolve(38,a,32,a)].
% 46.40/46.72 123 -in(f12(A),cartesian_product2(c5,c6)) | f12(A) != ordered_pair(B,C) | -in(B,c5) | singleton(B) != C | singleton(f13(A)) = f14(A). [resolve(38,a,31,a)].
% 46.40/46.72 151 f2(A,B) = f1(A,B) | f9(A,B,f12(f8(A,B))) = f12(f8(A,B)) | ordered_pair(f13(f8(A,B)),f14(f8(A,B))) = f12(f8(A,B)). [resolve(43,b,32,a)].
% 46.40/46.72 152 f2(A,B) = f1(A,B) | f9(A,B,f12(f8(A,B))) = f12(f8(A,B)) | singleton(f13(f8(A,B))) = f14(f8(A,B)). [resolve(43,b,31,a)].
% 46.40/46.72 155 f2(A,B) = f1(A,B) | in(f10(A,B,f12(f8(A,B))),A) | ordered_pair(f13(f8(A,B)),f14(f8(A,B))) = f12(f8(A,B)). [resolve(44,b,32,a)].
% 46.40/46.72 156 f2(A,B) = f1(A,B) | in(f10(A,B,f12(f8(A,B))),A) | singleton(f13(f8(A,B))) = f14(f8(A,B)). [resolve(44,b,31,a)].
% 46.40/46.72 163 f3(A,B) = f1(A,B) | f9(A,B,f12(f8(A,B))) = f12(f8(A,B)) | ordered_pair(f13(f8(A,B)),f14(f8(A,B))) = f12(f8(A,B)). [resolve(46,b,32,a)].
% 46.40/46.72 164 f3(A,B) = f1(A,B) | f9(A,B,f12(f8(A,B))) = f12(f8(A,B)) | singleton(f13(f8(A,B))) = f14(f8(A,B)). [resolve(46,b,31,a)].
% 46.40/46.72 167 f3(A,B) = f1(A,B) | in(f10(A,B,f12(f8(A,B))),A) | ordered_pair(f13(f8(A,B)),f14(f8(A,B))) = f12(f8(A,B)). [resolve(47,b,32,a)].
% 46.40/46.72 168 f3(A,B) = f1(A,B) | in(f10(A,B,f12(f8(A,B))),A) | singleton(f13(f8(A,B))) = f14(f8(A,B)). [resolve(47,b,31,a)].
% 46.40/46.72 175 f3(A,B) != f2(A,B) | f9(A,B,f12(f8(A,B))) = f12(f8(A,B)) | ordered_pair(f13(f8(A,B)),f14(f8(A,B))) = f12(f8(A,B)). [resolve(49,b,32,a)].
% 46.40/46.72 176 f3(A,B) != f2(A,B) | f9(A,B,f12(f8(A,B))) = f12(f8(A,B)) | singleton(f13(f8(A,B))) = f14(f8(A,B)). [resolve(49,b,31,a)].
% 46.40/46.72 179 f3(A,B) != f2(A,B) | in(f10(A,B,f12(f8(A,B))),A) | ordered_pair(f13(f8(A,B)),f14(f8(A,B))) = f12(f8(A,B)). [resolve(50,b,32,a)].
% 46.40/46.72 180 f3(A,B) != f2(A,B) | in(f10(A,B,f12(f8(A,B))),A) | singleton(f13(f8(A,B))) = f14(f8(A,B)). [resolve(50,b,31,a)].
% 46.40/46.72 201 f2(A,B) = f1(A,B) | in(f9(A,B,f12(f8(A,B))),cartesian_product2(A,B)) | in(f12(f8(A,B)),cartesian_product2(c5,c6)). [resolve(55,b,30,a)].
% 46.40/46.72 209 f3(A,B) = f1(A,B) | in(f9(A,B,f12(f8(A,B))),cartesian_product2(A,B)) | in(f12(f8(A,B)),cartesian_product2(c5,c6)). [resolve(57,b,30,a)].
% 46.40/46.72 217 f3(A,B) != f2(A,B) | in(f9(A,B,f12(f8(A,B))),cartesian_product2(A,B)) | in(f12(f8(A,B)),cartesian_product2(c5,c6)). [resolve(59,b,30,a)].
% 46.40/46.72 235 f2(A,B) = f1(A,B) | singleton(f10(A,B,f12(f8(A,B)))) = f11(A,B,f12(f8(A,B))) | ordered_pair(f13(f8(A,B)),f14(f8(A,B))) = f12(f8(A,B)). [resolve(64,b,32,a)].
% 46.40/46.72 236 f2(A,B) = f1(A,B) | singleton(f10(A,B,f12(f8(A,B)))) = f11(A,B,f12(f8(A,B))) | singleton(f13(f8(A,B))) = f14(f8(A,B)). [resolve(64,b,31,a)].
% 46.40/46.72 247 f3(A,B) = f1(A,B) | singleton(f10(A,B,f12(f8(A,B)))) = f11(A,B,f12(f8(A,B))) | ordered_pair(f13(f8(A,B)),f14(f8(A,B))) = f12(f8(A,B)). [resolve(67,b,32,a)].
% 46.40/46.72 248 f3(A,B) = f1(A,B) | singleton(f10(A,B,f12(f8(A,B)))) = f11(A,B,f12(f8(A,B))) | singleton(f13(f8(A,B))) = f14(f8(A,B)). [resolve(67,b,31,a)].
% 46.40/46.72 259 f3(A,B) != f2(A,B) | singleton(f10(A,B,f12(f8(A,B)))) = f11(A,B,f12(f8(A,B))) | ordered_pair(f13(f8(A,B)),f14(f8(A,B))) = f12(f8(A,B)). [resolve(70,b,32,a)].
% 46.40/46.72 260 f3(A,B) != f2(A,B) | singleton(f10(A,B,f12(f8(A,B)))) = f11(A,B,f12(f8(A,B))) | singleton(f13(f8(A,B))) = f14(f8(A,B)). [resolve(70,b,31,a)].
% 46.40/46.72 263 f2(A,B) = f1(A,B) | ordered_pair(f10(A,B,f12(f8(A,B))),f11(A,B,f12(f8(A,B)))) = f12(f8(A,B)) | ordered_pair(f13(f8(A,B)),f14(f8(A,B))) = f12(f8(A,B)). [resolve(71,b,32,a)].
% 46.40/46.72 264 f2(A,B) = f1(A,B) | ordered_pair(f10(A,B,f12(f8(A,B))),f11(A,B,f12(f8(A,B)))) = f12(f8(A,B)) | singleton(f13(f8(A,B))) = f14(f8(A,B)). [resolve(71,b,31,a)].
% 46.40/46.72 271 f3(A,B) = f1(A,B) | ordered_pair(f10(A,B,f12(f8(A,B))),f11(A,B,f12(f8(A,B)))) = f12(f8(A,B)) | ordered_pair(f13(f8(A,B)),f14(f8(A,B))) = f12(f8(A,B)). [resolve(73,b,32,a)].
% 46.40/46.72 272 f3(A,B) = f1(A,B) | ordered_pair(f10(A,B,f12(f8(A,B))),f11(A,B,f12(f8(A,B)))) = f12(f8(A,B)) | singleton(f13(f8(A,B))) = f14(f8(A,B)). [resolve(73,b,31,a)].
% 46.40/46.72 279 f3(A,B) != f2(A,B) | ordered_pair(f10(A,B,f12(f8(A,B))),f11(A,B,f12(f8(A,B)))) = f12(f8(A,B)) | ordered_pair(f13(f8(A,B)),f14(f8(A,B))) = f12(f8(A,B)). [resolve(75,b,32,a)].
% 46.40/46.72 280 f3(A,B) != f2(A,B) | ordered_pair(f10(A,B,f12(f8(A,B))),f11(A,B,f12(f8(A,B)))) = f12(f8(A,B)) | singleton(f13(f8(A,B))) = f14(f8(A,B)). [resolve(75,b,31,a)].
% 46.40/46.72 377 f2(c5,c6) = f1(c5,c6) | in(A,f8(c5,c6)) | f12(B) != A | ordered_pair(C,D) != A | -in(C,c5) | singleton(C) != D | in(f12(B),B). [resolve(86,c,30,b)].
% 46.40/46.72 384 f2(c5,A) = f1(c5,A) | in(B,f8(c5,A)) | -in(C,cartesian_product2(c5,A)) | C != B | ordered_pair(f13(D),E) != B | singleton(f13(D)) != E | in(f12(D),D). [resolve(86,f,29,b)].
% 46.40/46.72 407 f3(c5,c6) = f1(c5,c6) | in(A,f8(c5,c6)) | f12(B) != A | ordered_pair(C,D) != A | -in(C,c5) | singleton(C) != D | in(f12(B),B). [resolve(87,c,30,b)].
% 46.40/46.72 414 f3(c5,A) = f1(c5,A) | in(B,f8(c5,A)) | -in(C,cartesian_product2(c5,A)) | C != B | ordered_pair(f13(D),E) != B | singleton(f13(D)) != E | in(f12(D),D). [resolve(87,f,29,b)].
% 46.40/46.72 437 f3(c5,c6) != f2(c5,c6) | in(A,f8(c5,c6)) | f12(B) != A | ordered_pair(C,D) != A | -in(C,c5) | singleton(C) != D | in(f12(B),B). [resolve(88,c,30,b)].
% 46.40/46.72 444 f3(c5,A) != f2(c5,A) | in(B,f8(c5,A)) | -in(C,cartesian_product2(c5,A)) | C != B | ordered_pair(f13(D),E) != B | singleton(f13(D)) != E | in(f12(D),D). [resolve(88,f,29,b)].
% 46.40/46.72 3796 f2(c5,A) = f1(c5,A) | ordered_pair(f13(f8(c5,A)),f14(f8(c5,A))) = f12(f8(c5,A)) | -in(f12(B),cartesian_product2(c5,c6)) | f12(B) != ordered_pair(f10(c5,A,f12(f8(c5,A))),C) | singleton(f10(c5,A,f12(f8(c5,A)))) != C | ordered_pair(f13(B),f14(B)) = f12(B). [resolve(155,b,122,c)].
% 46.40/46.72 3864 f2(c5,A) = f1(c5,A) | ordered_pair(f13(f8(c5,A)),f14(f8(c5,A))) = f12(f8(c5,A)) | -in(f12(f8(c5,A)),cartesian_product2(c5,c6)) | ordered_pair(f10(c5,A,f12(f8(c5,A))),B) != f12(f8(c5,A)) | singleton(f10(c5,A,f12(f8(c5,A)))) != B. [factor(3796,b,f),flip(d)].
% 46.40/46.72 3978 f2(A,B) = f1(A,B) | singleton(f13(f8(A,B))) = f14(f8(A,B)) | in(f12(f8(A,B)),cartesian_product2(A,B)) | in(f12(f8(A,B)),cartesian_product2(c5,c6)). [para(152(b,1),201(b,1)),merge(c)].
% 46.40/46.72 3997 f2(c5,c6) = f1(c5,c6) | singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)) | in(f12(f8(c5,c6)),cartesian_product2(c5,c6)). [factor(3978,c,d)].
% 46.40/46.72 4004 f2(c5,c6) = f1(c5,c6) | singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)) | f12(f8(c5,c6)) != ordered_pair(A,B) | -in(A,c5) | singleton(A) != B. [resolve(3997,c,123,a),merge(f)].
% 46.40/46.72 4323 f3(A,B) = f1(A,B) | singleton(f13(f8(A,B))) = f14(f8(A,B)) | in(f12(f8(A,B)),cartesian_product2(A,B)) | in(f12(f8(A,B)),cartesian_product2(c5,c6)). [para(164(b,1),209(b,1)),merge(c)].
% 46.40/46.72 4324 f3(c5,c6) = f1(c5,c6) | singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)) | in(f12(f8(c5,c6)),cartesian_product2(c5,c6)). [factor(4323,c,d)].
% 46.40/46.72 4332 f3(c5,c6) = f1(c5,c6) | singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)) | f12(f8(c5,c6)) != ordered_pair(A,B) | -in(A,c5) | singleton(A) != B. [resolve(4324,c,123,a),merge(f)].
% 46.40/46.72 4418 f3(c5,A) = f1(c5,A) | ordered_pair(f13(f8(c5,A)),f14(f8(c5,A))) = f12(f8(c5,A)) | -in(f12(B),cartesian_product2(c5,c6)) | f12(B) != ordered_pair(f10(c5,A,f12(f8(c5,A))),C) | singleton(f10(c5,A,f12(f8(c5,A)))) != C | ordered_pair(f13(B),f14(B)) = f12(B). [resolve(167,b,122,c)].
% 46.40/46.72 4486 f3(c5,A) = f1(c5,A) | ordered_pair(f13(f8(c5,A)),f14(f8(c5,A))) = f12(f8(c5,A)) | -in(f12(f8(c5,A)),cartesian_product2(c5,c6)) | ordered_pair(f10(c5,A,f12(f8(c5,A))),B) != f12(f8(c5,A)) | singleton(f10(c5,A,f12(f8(c5,A)))) != B. [factor(4418,b,f),flip(d)].
% 46.40/46.72 8932 f2(c5,c6) = f1(c5,c6) | in(A,f8(c5,c6)) | f12(B) != A | ordered_pair(f13(C),D) != A | singleton(f13(C)) != D | in(f12(B),B) | in(f12(C),C). [resolve(377,e,29,b)].
% 46.40/46.72 8939 f2(c5,c6) = f1(c5,c6) | in(A,f8(c5,c6)) | f12(B) != A | ordered_pair(f13(B),C) != A | singleton(f13(B)) != C | in(f12(B),B). [factor(8932,f,g)].
% 46.40/46.72 8952 f2(c5,c6) = f1(c5,c6) | in(f12(f8(A,B)),f8(c5,c6)) | singleton(f13(f8(A,B))) != f14(f8(A,B)) | in(f12(f8(A,B)),f8(A,B)) | f2(A,B) = f1(A,B) | singleton(f10(A,B,f12(f8(A,B)))) = f11(A,B,f12(f8(A,B))). [resolve(8939,d,235,c),xx(c)].
% 46.40/46.72 8956 f2(c5,c6) = f1(c5,c6) | in(f12(f8(A,B)),f8(c5,c6)) | singleton(f13(f8(A,B))) != f14(f8(A,B)) | in(f12(f8(A,B)),f8(A,B)) | f2(A,B) = f1(A,B) | f9(A,B,f12(f8(A,B))) = f12(f8(A,B)). [resolve(8939,d,151,c),xx(c)].
% 46.40/46.72 8969 f2(c5,c6) = f1(c5,c6) | in(f12(f8(c5,c6)),f8(c5,c6)) | singleton(f13(f8(c5,c6))) != f14(f8(c5,c6)) | singleton(f10(c5,c6,f12(f8(c5,c6)))) = f11(c5,c6,f12(f8(c5,c6))). [factor(8952,a,e),merge(d)].
% 46.40/46.72 8973 f2(c5,c6) = f1(c5,c6) | in(f12(f8(c5,c6)),f8(c5,c6)) | singleton(f13(f8(c5,c6))) != f14(f8(c5,c6)) | f9(c5,c6,f12(f8(c5,c6))) = f12(f8(c5,c6)). [factor(8956,a,e),merge(d)].
% 46.40/46.72 9037 f3(c5,c6) = f1(c5,c6) | in(A,f8(c5,c6)) | f12(B) != A | ordered_pair(f13(C),D) != A | singleton(f13(C)) != D | in(f12(B),B) | in(f12(C),C). [resolve(407,e,29,b)].
% 46.40/46.72 9044 f3(c5,c6) = f1(c5,c6) | in(A,f8(c5,c6)) | f12(B) != A | ordered_pair(f13(B),C) != A | singleton(f13(B)) != C | in(f12(B),B). [factor(9037,f,g)].
% 46.40/46.72 9046 f3(c5,c6) = f1(c5,c6) | in(f12(f8(A,B)),f8(c5,c6)) | singleton(f13(f8(A,B))) != f14(f8(A,B)) | in(f12(f8(A,B)),f8(A,B)) | f3(A,B) = f1(A,B) | singleton(f10(A,B,f12(f8(A,B)))) = f11(A,B,f12(f8(A,B))). [resolve(9044,d,247,c),xx(c)].
% 46.40/46.72 9051 f3(c5,c6) = f1(c5,c6) | in(f12(f8(A,B)),f8(c5,c6)) | singleton(f13(f8(A,B))) != f14(f8(A,B)) | in(f12(f8(A,B)),f8(A,B)) | f3(A,B) = f1(A,B) | f9(A,B,f12(f8(A,B))) = f12(f8(A,B)). [resolve(9044,d,163,c),xx(c)].
% 46.40/46.72 9063 f3(c5,c6) = f1(c5,c6) | in(f12(f8(c5,c6)),f8(c5,c6)) | singleton(f13(f8(c5,c6))) != f14(f8(c5,c6)) | singleton(f10(c5,c6,f12(f8(c5,c6)))) = f11(c5,c6,f12(f8(c5,c6))). [factor(9046,a,e),merge(d)].
% 46.40/46.72 9067 f3(c5,c6) = f1(c5,c6) | in(f12(f8(c5,c6)),f8(c5,c6)) | singleton(f13(f8(c5,c6))) != f14(f8(c5,c6)) | f9(c5,c6,f12(f8(c5,c6))) = f12(f8(c5,c6)). [factor(9051,a,e),merge(d)].
% 46.40/46.72 9152 f3(c5,c6) != f2(c5,c6) | in(A,f8(c5,c6)) | f12(B) != A | ordered_pair(f13(C),D) != A | singleton(f13(C)) != D | in(f12(B),B) | in(f12(C),C). [resolve(437,e,29,b)].
% 46.40/46.72 9239 f2(c5,c6) = f1(c5,c6) | singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)) | ordered_pair(f10(c5,A,f12(f8(c5,A))),B) != f12(f8(c5,c6)) | singleton(f10(c5,A,f12(f8(c5,A)))) != B | f2(c5,A) = f1(c5,A) | singleton(f13(f8(c5,A))) = f14(f8(c5,A)). [resolve(4004,d,156,b),flip(c)].
% 46.40/46.72 9263 f2(c5,c6) = f1(c5,c6) | singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)) | ordered_pair(f10(c5,c6,f12(f8(c5,c6))),A) != f12(f8(c5,c6)) | singleton(f10(c5,c6,f12(f8(c5,c6)))) != A. [factor(9239,a,e),merge(e)].
% 46.40/46.72 9292 f3(c5,c6) = f1(c5,c6) | singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)) | ordered_pair(f10(c5,A,f12(f8(c5,A))),B) != f12(f8(c5,c6)) | singleton(f10(c5,A,f12(f8(c5,A)))) != B | f3(c5,A) = f1(c5,A) | singleton(f13(f8(c5,A))) = f14(f8(c5,A)). [resolve(4332,d,168,b),flip(c)].
% 46.40/46.72 9317 f3(c5,c6) = f1(c5,c6) | singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)) | ordered_pair(f10(c5,c6,f12(f8(c5,c6))),A) != f12(f8(c5,c6)) | singleton(f10(c5,c6,f12(f8(c5,c6)))) != A. [factor(9292,a,e),merge(e)].
% 46.40/46.72 10819 f3(c5,c6) != f2(c5,c6) | in(f12(A),f8(c5,c6)) | f12(A) != ordered_pair(f13(B),C) | singleton(f13(B)) != C | in(f12(A),A) | in(f12(B),B). [xx_res(9152,c),flip(c)].
% 46.40/46.72 10821 f3(c5,c6) != f2(c5,c6) | in(f12(A),f8(c5,c6)) | ordered_pair(f13(A),B) != f12(A) | singleton(f13(A)) != B | in(f12(A),A). [factor(10819,e,f),flip(c)].
% 46.40/46.72 11931 f2(c5,c6) = f1(c5,c6) | singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)) | singleton(f10(c5,c6,f12(f8(c5,c6)))) != f11(c5,c6,f12(f8(c5,c6))). [resolve(9263,c,264,b),merge(d),merge(e)].
% 46.40/46.72 11937 f2(c5,c6) = f1(c5,c6) | singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)). [resolve(11931,c,236,b),merge(c),merge(d)].
% 46.40/46.72 11946 f2(c5,c6) = f1(c5,c6) | in(f12(f8(c5,c6)),f8(c5,c6)) | f9(c5,c6,f12(f8(c5,c6))) = f12(f8(c5,c6)). [resolve(11937,b,8973,c),merge(b)].
% 46.40/46.72 11947 f2(c5,c6) = f1(c5,c6) | in(f12(f8(c5,c6)),f8(c5,c6)) | singleton(f10(c5,c6,f12(f8(c5,c6)))) = f11(c5,c6,f12(f8(c5,c6))). [resolve(11937,b,8969,c),merge(b)].
% 46.40/46.72 12007 f2(c5,c6) = f1(c5,c6) | f9(c5,c6,f12(f8(c5,c6))) = f12(f8(c5,c6)). [resolve(11946,b,43,b),merge(c),merge(d)].
% 46.40/46.72 12037 f2(c5,c6) = f1(c5,c6) | in(f12(f8(c5,c6)),cartesian_product2(c5,c6)). [para(12007(b,1),201(b,1)),merge(b),merge(d)].
% 46.40/46.72 12099 f2(c5,c6) = f1(c5,c6) | in(A,f8(c5,c6)) | f12(f8(c5,c6)) != A | ordered_pair(f13(B),C) != A | singleton(f13(B)) != C | in(f12(B),B). [resolve(12037,b,384,c),merge(b)].
% 46.40/46.72 12131 f2(c5,c6) = f1(c5,c6) | -in(f12(f8(c5,c6)),f8(c5,c6)) | f12(f8(c5,c6)) != ordered_pair(A,B) | -in(A,c5) | singleton(A) != B. [resolve(12037,b,38,b)].
% 46.40/46.72 12334 f2(c5,c6) = f1(c5,c6) | singleton(f10(c5,c6,f12(f8(c5,c6)))) = f11(c5,c6,f12(f8(c5,c6))). [resolve(11947,b,64,b),merge(c),merge(d)].
% 46.40/46.72 12365 f3(c5,c6) = f1(c5,c6) | singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)) | singleton(f10(c5,c6,f12(f8(c5,c6)))) != f11(c5,c6,f12(f8(c5,c6))). [resolve(9317,c,272,b),merge(d),merge(e)].
% 46.40/46.72 12370 f3(c5,c6) = f1(c5,c6) | singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)). [resolve(12365,c,248,b),merge(c),merge(d)].
% 46.40/46.72 12376 f3(c5,c6) = f1(c5,c6) | in(f12(f8(c5,c6)),f8(c5,c6)) | f9(c5,c6,f12(f8(c5,c6))) = f12(f8(c5,c6)). [resolve(12370,b,9067,c),merge(b)].
% 46.40/46.72 12377 f3(c5,c6) = f1(c5,c6) | in(f12(f8(c5,c6)),f8(c5,c6)) | singleton(f10(c5,c6,f12(f8(c5,c6)))) = f11(c5,c6,f12(f8(c5,c6))). [resolve(12370,b,9063,c),merge(b)].
% 46.40/46.72 12432 f3(c5,c6) = f1(c5,c6) | f9(c5,c6,f12(f8(c5,c6))) = f12(f8(c5,c6)). [resolve(12376,b,46,b),merge(c),merge(d)].
% 46.40/46.72 12458 f3(c5,c6) = f1(c5,c6) | in(f12(f8(c5,c6)),cartesian_product2(c5,c6)). [para(12432(b,1),209(b,1)),merge(b),merge(d)].
% 46.40/46.72 12513 f3(c5,c6) = f1(c5,c6) | in(A,f8(c5,c6)) | f12(f8(c5,c6)) != A | ordered_pair(f13(B),C) != A | singleton(f13(B)) != C | in(f12(B),B). [resolve(12458,b,414,c),merge(b)].
% 46.40/46.72 12545 f3(c5,c6) = f1(c5,c6) | -in(f12(f8(c5,c6)),f8(c5,c6)) | f12(f8(c5,c6)) != ordered_pair(A,B) | -in(A,c5) | singleton(A) != B. [resolve(12458,b,38,b)].
% 46.40/46.72 12735 f3(c5,c6) = f1(c5,c6) | singleton(f10(c5,c6,f12(f8(c5,c6)))) = f11(c5,c6,f12(f8(c5,c6))). [resolve(12377,b,67,b),merge(c),merge(d)].
% 46.40/46.72 20898 f2(c5,c6) = f1(c5,c6) | ordered_pair(f13(f8(c5,c6)),f14(f8(c5,c6))) = f12(f8(c5,c6)) | ordered_pair(f10(c5,c6,f12(f8(c5,c6))),A) != f12(f8(c5,c6)) | singleton(f10(c5,c6,f12(f8(c5,c6)))) != A. [resolve(3864,c,12037,b),merge(e)].
% 46.40/46.72 20904 f2(c5,c6) = f1(c5,c6) | ordered_pair(f13(f8(c5,c6)),f14(f8(c5,c6))) = f12(f8(c5,c6)) | singleton(f10(c5,c6,f12(f8(c5,c6)))) != f11(c5,c6,f12(f8(c5,c6))). [resolve(20898,c,263,b),merge(d),merge(e)].
% 46.40/46.72 20910 f2(c5,c6) = f1(c5,c6) | ordered_pair(f13(f8(c5,c6)),f14(f8(c5,c6))) = f12(f8(c5,c6)). [resolve(20904,c,12334,b),merge(c)].
% 46.40/46.72 20914 f2(c5,c6) = f1(c5,c6) | in(f12(f8(c5,c6)),f8(c5,c6)) | singleton(f13(f8(c5,c6))) != f14(f8(c5,c6)). [resolve(20910,b,12099,d),xx(d),merge(b),merge(e)].
% 46.40/46.72 20954 f2(c5,c6) = f1(c5,c6) | in(f12(f8(c5,c6)),f8(c5,c6)). [resolve(20914,c,11937,b),merge(c)].
% 46.40/46.72 21017 f2(c5,c6) = f1(c5,c6) | f12(f8(c5,c6)) != ordered_pair(A,B) | -in(A,c5) | singleton(A) != B. [resolve(20954,b,12131,b),merge(b)].
% 46.40/46.72 21094 f2(c5,c6) = f1(c5,c6) | ordered_pair(f10(c5,c6,f12(f8(c5,c6))),f11(c5,c6,f12(f8(c5,c6)))) = f12(f8(c5,c6)). [resolve(20954,b,71,b),merge(b)].
% 46.40/46.72 21106 f2(c5,c6) = f1(c5,c6) | in(f10(c5,c6,f12(f8(c5,c6))),c5). [resolve(20954,b,44,b),merge(b)].
% 46.40/46.72 21308 f2(c5,c6) = f1(c5,c6) | ordered_pair(f10(c5,c6,f12(f8(c5,c6))),A) != f12(f8(c5,c6)) | singleton(f10(c5,c6,f12(f8(c5,c6)))) != A. [resolve(21017,c,21106,b),flip(b),merge(d)].
% 46.40/46.72 21418 f2(c5,c6) = f1(c5,c6) | singleton(f10(c5,c6,f12(f8(c5,c6)))) != f11(c5,c6,f12(f8(c5,c6))). [resolve(21308,b,21094,b),merge(c)].
% 46.40/46.72 21422 f2(c5,c6) = f1(c5,c6). [resolve(21418,b,12334,b),merge(b)].
% 46.40/46.72 21771 f3(c5,c6) != f1(c5,c6) | in(f12(A),f8(c5,c6)) | ordered_pair(f13(A),B) != f12(A) | singleton(f13(A)) != B | in(f12(A),A). [back_rewrite(10821),rewrite([21422(6)])].
% 46.40/46.72 22169 f3(c5,c6) != f1(c5,c6) | in(f10(c5,c6,f12(f8(c5,c6))),c5) | singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)). [para(21422(a,1),180(a,2))].
% 46.40/46.72 22170 f3(c5,c6) != f1(c5,c6) | in(f9(c5,c6,f12(f8(c5,c6))),cartesian_product2(c5,c6)) | in(f12(f8(c5,c6)),cartesian_product2(c5,c6)). [para(21422(a,1),217(a,2))].
% 46.40/46.72 22172 f3(c5,c6) != f1(c5,c6) | f9(c5,c6,f12(f8(c5,c6))) = f12(f8(c5,c6)) | ordered_pair(f13(f8(c5,c6)),f14(f8(c5,c6))) = f12(f8(c5,c6)). [para(21422(a,1),175(a,2))].
% 46.40/46.72 22173 f3(c5,c6) != f1(c5,c6) | f9(c5,c6,f12(f8(c5,c6))) = f12(f8(c5,c6)) | singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)). [para(21422(a,1),176(a,2))].
% 46.40/46.72 22174 f3(c5,c6) != f1(c5,c6) | in(f10(c5,c6,f12(f8(c5,c6))),c5) | ordered_pair(f13(f8(c5,c6)),f14(f8(c5,c6))) = f12(f8(c5,c6)). [para(21422(a,1),179(a,2))].
% 46.40/46.72 22179 f3(c5,c6) != f1(c5,c6) | singleton(f10(c5,c6,f12(f8(c5,c6)))) = f11(c5,c6,f12(f8(c5,c6))) | ordered_pair(f13(f8(c5,c6)),f14(f8(c5,c6))) = f12(f8(c5,c6)). [para(21422(a,1),259(a,2))].
% 46.40/46.72 22180 f3(c5,c6) != f1(c5,c6) | singleton(f10(c5,c6,f12(f8(c5,c6)))) = f11(c5,c6,f12(f8(c5,c6))) | singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)). [para(21422(a,1),260(a,2))].
% 46.40/46.72 22182 f3(c5,c6) != f1(c5,c6) | ordered_pair(f10(c5,c6,f12(f8(c5,c6))),f11(c5,c6,f12(f8(c5,c6)))) = f12(f8(c5,c6)) | ordered_pair(f13(f8(c5,c6)),f14(f8(c5,c6))) = f12(f8(c5,c6)). [para(21422(a,1),279(a,2))].
% 46.40/46.72 22183 f3(c5,c6) != f1(c5,c6) | ordered_pair(f10(c5,c6,f12(f8(c5,c6))),f11(c5,c6,f12(f8(c5,c6)))) = f12(f8(c5,c6)) | singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)). [para(21422(a,1),280(a,2))].
% 46.40/46.72 22376 f3(c5,c6) = f1(c5,c6) | ordered_pair(f13(f8(c5,c6)),f14(f8(c5,c6))) = f12(f8(c5,c6)) | ordered_pair(f10(c5,c6,f12(f8(c5,c6))),A) != f12(f8(c5,c6)) | singleton(f10(c5,c6,f12(f8(c5,c6)))) != A. [resolve(4486,c,12458,b),merge(e)].
% 46.40/46.72 22381 f3(c5,c6) = f1(c5,c6) | ordered_pair(f13(f8(c5,c6)),f14(f8(c5,c6))) = f12(f8(c5,c6)) | singleton(f10(c5,c6,f12(f8(c5,c6)))) != f11(c5,c6,f12(f8(c5,c6))). [resolve(22376,c,271,b),merge(d),merge(e)].
% 46.40/46.72 22384 f3(c5,c6) = f1(c5,c6) | ordered_pair(f13(f8(c5,c6)),f14(f8(c5,c6))) = f12(f8(c5,c6)). [resolve(22381,c,12735,b),merge(c)].
% 46.40/46.72 22388 f3(c5,c6) = f1(c5,c6) | in(f12(f8(c5,c6)),f8(c5,c6)) | singleton(f13(f8(c5,c6))) != f14(f8(c5,c6)). [resolve(22384,b,12513,d),xx(d),merge(b),merge(e)].
% 46.40/46.72 22424 f3(c5,c6) = f1(c5,c6) | in(f12(f8(c5,c6)),f8(c5,c6)). [resolve(22388,c,12370,b),merge(c)].
% 46.40/46.72 22467 f3(c5,c6) = f1(c5,c6) | f12(f8(c5,c6)) != ordered_pair(A,B) | -in(A,c5) | singleton(A) != B. [resolve(22424,b,12545,b),merge(b)].
% 46.40/46.72 22553 f3(c5,c6) = f1(c5,c6) | ordered_pair(f10(c5,c6,f12(f8(c5,c6))),f11(c5,c6,f12(f8(c5,c6)))) = f12(f8(c5,c6)). [resolve(22424,b,73,b),merge(b)].
% 46.40/46.72 22561 f3(c5,c6) = f1(c5,c6) | in(f10(c5,c6,f12(f8(c5,c6))),c5). [resolve(22424,b,47,b),merge(b)].
% 46.40/46.72 22758 f3(c5,c6) = f1(c5,c6) | ordered_pair(f10(c5,c6,f12(f8(c5,c6))),A) != f12(f8(c5,c6)) | singleton(f10(c5,c6,f12(f8(c5,c6)))) != A. [resolve(22467,c,22561,b),flip(b),merge(d)].
% 46.40/46.72 22873 f3(c5,c6) = f1(c5,c6) | singleton(f10(c5,c6,f12(f8(c5,c6)))) != f11(c5,c6,f12(f8(c5,c6))). [resolve(22758,b,22553,b),merge(c)].
% 46.40/46.72 22876 f3(c5,c6) = f1(c5,c6). [resolve(22873,b,12735,b),merge(b)].
% 46.40/46.72 23013 ordered_pair(f10(c5,c6,f12(f8(c5,c6))),f11(c5,c6,f12(f8(c5,c6)))) = f12(f8(c5,c6)) | singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)). [back_rewrite(22183),rewrite([22876(3)]),xx(a)].
% 46.40/46.72 23014 ordered_pair(f10(c5,c6,f12(f8(c5,c6))),f11(c5,c6,f12(f8(c5,c6)))) = f12(f8(c5,c6)) | ordered_pair(f13(f8(c5,c6)),f14(f8(c5,c6))) = f12(f8(c5,c6)). [back_rewrite(22182),rewrite([22876(3)]),xx(a)].
% 46.40/46.72 23016 singleton(f10(c5,c6,f12(f8(c5,c6)))) = f11(c5,c6,f12(f8(c5,c6))) | singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)). [back_rewrite(22180),rewrite([22876(3)]),xx(a)].
% 46.40/46.72 23017 singleton(f10(c5,c6,f12(f8(c5,c6)))) = f11(c5,c6,f12(f8(c5,c6))) | ordered_pair(f13(f8(c5,c6)),f14(f8(c5,c6))) = f12(f8(c5,c6)). [back_rewrite(22179),rewrite([22876(3)]),xx(a)].
% 46.40/46.72 23022 in(f10(c5,c6,f12(f8(c5,c6))),c5) | ordered_pair(f13(f8(c5,c6)),f14(f8(c5,c6))) = f12(f8(c5,c6)). [back_rewrite(22174),rewrite([22876(3)]),xx(a)].
% 46.40/46.72 23023 f9(c5,c6,f12(f8(c5,c6))) = f12(f8(c5,c6)) | singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)). [back_rewrite(22173),rewrite([22876(3)]),xx(a)].
% 46.40/46.72 23024 f9(c5,c6,f12(f8(c5,c6))) = f12(f8(c5,c6)) | ordered_pair(f13(f8(c5,c6)),f14(f8(c5,c6))) = f12(f8(c5,c6)). [back_rewrite(22172),rewrite([22876(3)]),xx(a)].
% 46.40/46.72 23026 in(f9(c5,c6,f12(f8(c5,c6))),cartesian_product2(c5,c6)) | in(f12(f8(c5,c6)),cartesian_product2(c5,c6)). [back_rewrite(22170),rewrite([22876(3)]),xx(a)].
% 46.40/46.72 23027 in(f10(c5,c6,f12(f8(c5,c6))),c5) | singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)). [back_rewrite(22169),rewrite([22876(3)]),xx(a)].
% 46.40/46.72 23322 in(f12(A),f8(c5,c6)) | ordered_pair(f13(A),B) != f12(A) | singleton(f13(A)) != B | in(f12(A),A). [back_rewrite(21771),rewrite([22876(3)]),xx(a)].
% 46.40/46.72 24744 singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)) | in(f12(f8(c5,c6)),cartesian_product2(c5,c6)). [para(23023(a,1),23026(a,1)),merge(c)].
% 46.40/46.72 24976 singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)) | f12(f8(c5,c6)) != ordered_pair(A,B) | -in(A,c5) | singleton(A) != B. [resolve(24744,b,123,a),merge(e)].
% 46.40/46.72 25034 ordered_pair(f13(f8(c5,c6)),f14(f8(c5,c6))) = f12(f8(c5,c6)) | -in(f12(A),cartesian_product2(c5,c6)) | f12(A) != ordered_pair(f10(c5,c6,f12(f8(c5,c6))),B) | singleton(f10(c5,c6,f12(f8(c5,c6)))) != B | ordered_pair(f13(A),f14(A)) = f12(A). [resolve(23022,a,122,c)].
% 46.40/46.72 25048 ordered_pair(f13(f8(c5,c6)),f14(f8(c5,c6))) = f12(f8(c5,c6)) | -in(f12(f8(c5,c6)),cartesian_product2(c5,c6)) | ordered_pair(f10(c5,c6,f12(f8(c5,c6))),A) != f12(f8(c5,c6)) | singleton(f10(c5,c6,f12(f8(c5,c6)))) != A. [factor(25034,a,e),flip(c)].
% 46.40/46.72 25250 singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)) | ordered_pair(f10(c5,c6,f12(f8(c5,c6))),A) != f12(f8(c5,c6)) | singleton(f10(c5,c6,f12(f8(c5,c6)))) != A. [resolve(24976,c,23027,a),flip(b),merge(d)].
% 46.40/46.72 25355 f9(c5,c6,f12(f8(c5,c6))) = f12(f8(c5,c6)) | in(f12(f8(c5,c6)),f8(c5,c6)) | singleton(f13(f8(c5,c6))) != f14(f8(c5,c6)). [resolve(23024,b,23322,b),merge(d)].
% 46.40/46.72 25550 singleton(f10(c5,c6,f12(f8(c5,c6)))) = f11(c5,c6,f12(f8(c5,c6))) | in(f12(f8(c5,c6)),f8(c5,c6)) | singleton(f13(f8(c5,c6))) != f14(f8(c5,c6)). [resolve(23017,b,23322,b),merge(d)].
% 46.40/46.72 25692 singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)) | singleton(f10(c5,c6,f12(f8(c5,c6)))) != f11(c5,c6,f12(f8(c5,c6))). [resolve(25250,b,23013,a),merge(c)].
% 46.40/46.72 25693 singleton(f13(f8(c5,c6))) = f14(f8(c5,c6)). [resolve(25692,b,23016,a),merge(b)].
% 46.40/46.72 25703 singleton(f10(c5,c6,f12(f8(c5,c6)))) = f11(c5,c6,f12(f8(c5,c6))) | in(f12(f8(c5,c6)),f8(c5,c6)). [back_rewrite(25550),rewrite([25693(29)]),xx(c)].
% 46.40/46.72 25735 f9(c5,c6,f12(f8(c5,c6))) = f12(f8(c5,c6)) | in(f12(f8(c5,c6)),f8(c5,c6)). [back_rewrite(25355),rewrite([25693(25)]),xx(c)].
% 46.40/46.72 26208 f9(c5,c6,f12(f8(c5,c6))) = f12(f8(c5,c6)). [resolve(25735,b,49,b),rewrite([22876(15),21422(18)]),xx(b),merge(b)].
% 46.40/46.72 26411 in(f12(f8(c5,c6)),cartesian_product2(c5,c6)). [back_rewrite(23026),rewrite([26208(7)]),merge(b)].
% 46.40/46.72 26422 ordered_pair(f13(f8(c5,c6)),f14(f8(c5,c6))) = f12(f8(c5,c6)) | ordered_pair(f10(c5,c6,f12(f8(c5,c6))),A) != f12(f8(c5,c6)) | singleton(f10(c5,c6,f12(f8(c5,c6)))) != A. [back_unit_del(25048),unit_del(b,26411)].
% 46.40/46.72 26717 in(A,f8(c5,c6)) | f12(f8(c5,c6)) != A | ordered_pair(f13(B),C) != A | singleton(f13(B)) != C | in(f12(B),B). [resolve(26411,a,444,c),rewrite([22876(3),21422(6)]),xx(a)].
% 46.40/46.72 26981 singleton(f10(c5,c6,f12(f8(c5,c6)))) = f11(c5,c6,f12(f8(c5,c6))). [resolve(25703,b,70,b),rewrite([22876(19),21422(22)]),xx(b),merge(b)].
% 46.40/46.72 26984 ordered_pair(f13(f8(c5,c6)),f14(f8(c5,c6))) = f12(f8(c5,c6)) | ordered_pair(f10(c5,c6,f12(f8(c5,c6))),A) != f12(f8(c5,c6)) | f11(c5,c6,f12(f8(c5,c6))) != A. [back_rewrite(26422),rewrite([26981(35)])].
% 46.40/46.72 27541 ordered_pair(f13(f8(c5,c6)),f14(f8(c5,c6))) = f12(f8(c5,c6)). [resolve(26984,b,23014,a),xx(b),merge(b)].
% 46.40/46.72 27542 in(f12(f8(c5,c6)),f8(c5,c6)). [resolve(27541,a,26717,c),rewrite([25693(22)]),xx(b),xx(c),merge(b)].
% 46.40/46.72 27714 ordered_pair(f10(c5,c6,f12(f8(c5,c6))),f11(c5,c6,f12(f8(c5,c6)))) = f12(f8(c5,c6)). [resolve(27542,a,75,b),rewrite([22876(3),21422(6)]),xx(a)].
% 46.40/46.72 27719 in(f10(c5,c6,f12(f8(c5,c6))),c5). [resolve(27542,a,50,b),rewrite([22876(3),21422(6)]),xx(a)].
% 46.40/46.72 27932 $F. [ur(38,a,27542,a,b,26411,a,d,27719,a,e,26981,a),rewrite([27714(19)]),xx(a)].
% 46.40/46.72
% 46.40/46.72 % SZS output end Refutation
% 46.40/46.72 ============================== end of proof ==========================
% 46.40/46.72
% 46.40/46.72 ============================== STATISTICS ============================
% 46.40/46.72
% 46.40/46.72 Given=9009. Generated=1260402. Kept=27903. proofs=1.
% 46.40/46.72 Usable=5938. Sos=6126. Demods=7. Limbo=1, Disabled=15921. Hints=0.
% 46.40/46.72 Megabytes=46.48.
% 46.40/46.72 User_CPU=45.14, System_CPU=0.63, Wall_clock=46.
% 46.40/46.72
% 46.40/46.72 ============================== end of statistics =====================
% 46.40/46.72
% 46.40/46.72 ============================== end of search =========================
% 46.40/46.72
% 46.40/46.72 THEOREM PROVED
% 46.40/46.72 % SZS status Theorem
% 46.40/46.72
% 46.40/46.72 Exiting with 1 proof.
% 46.40/46.72
% 46.40/46.72 Process 25152 exit (max_proofs) Sun Jun 19 02:54:46 2022
% 46.40/46.72 Prover9 interrupted
%------------------------------------------------------------------------------