%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU139+2 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n010.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 : 300s
% DateTime : Tue May 5 05:10:44 PM UTC 2026
% Result : Theorem 0.31s 1.61s
% Output : CNFRefutation 0.75s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_74)
% Comments :
%------------------------------------------------------------------------------
fof(t4_xboole_0,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(t48_xboole_1,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(t26_xboole_1,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
fof(t19_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(t17_xboole_1,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d7_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(t3_xboole_0,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(t28_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(fc2_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(antisymmetry_r2_xboole_0,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(idempotence_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(t2_boole,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(irreflexivity_r2_xboole_0,axiom,
! [X1,X2] : ~ proper_subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(t60_xboole_1,conjecture,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(t33_xboole_1,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(t8_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(t45_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
fof(t1_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(t40_xboole_1,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(t39_xboole_1,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(t36_xboole_1,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(t7_xboole_1,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(d8_xboole_0,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(t12_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t37_xboole_1,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(l32_xboole_1,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t3_xboole_1,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(t1_boole,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
fof(t2_xboole_1,lemma,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(t4_boole,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(i_0_51,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t4_xboole_0]) ).
fof(i_0_52,plain,
! [X142,X143,X144,X145,X146,X147,X148,X149] :
( ( in(X145,X142)
| ~ in(X145,X144)
| X144 != set_intersection2(X142,X143) )
& ( in(X145,X143)
| ~ in(X145,X144)
| X144 != set_intersection2(X142,X143) )
& ( ~ in(X146,X142)
| ~ in(X146,X143)
| in(X146,X144)
| X144 != set_intersection2(X142,X143) )
& ( ~ in(esk4_3(X147,X148,X149),X149)
| ~ in(esk4_3(X147,X148,X149),X147)
| ~ in(esk4_3(X147,X148,X149),X148)
| X149 = set_intersection2(X147,X148) )
& ( in(esk4_3(X147,X148,X149),X147)
| in(esk4_3(X147,X148,X149),X149)
| X149 = set_intersection2(X147,X148) )
& ( in(esk4_3(X147,X148,X149),X148)
| in(esk4_3(X147,X148,X149),X149)
| X149 = set_intersection2(X147,X148) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_xboole_0])])])])])]) ).
fof(i_0_53,lemma,
! [X220,X221] : set_difference(X220,set_difference(X220,X221)) = set_intersection2(X220,X221),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(i_0_54,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(i_0_55,lemma,
! [X189,X190,X191] :
( ~ subset(X189,X190)
| subset(set_intersection2(X189,X191),set_intersection2(X190,X191)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t26_xboole_1])]) ).
fof(i_0_56,lemma,
! [X223,X224,X226,X227,X228] :
( ( disjoint(X223,X224)
| in(esk10_2(X223,X224),set_intersection2(X223,X224)) )
& ( ~ in(X228,set_intersection2(X226,X227))
| ~ disjoint(X226,X227) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_51])])])])]) ).
fof(i_0_57,lemma,
! [X182,X183,X184] :
( ~ subset(X182,X183)
| ~ subset(X182,X184)
| subset(X182,set_intersection2(X183,X184)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_xboole_1])]) ).
fof(i_0_58,lemma,
! [X180,X181] : subset(set_intersection2(X180,X181),X180),
inference(variable_rename,[status(thm)],[t17_xboole_1]) ).
fof(i_0_59,plain,
! [X119,X120] : set_intersection2(X119,X120) = set_intersection2(X120,X119),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(i_0_60,plain,
! [X160,X161] :
( ( ~ disjoint(X160,X161)
| set_intersection2(X160,X161) = empty_set )
& ( set_intersection2(X160,X161) != empty_set
| disjoint(X160,X161) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
fof(i_0_61,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t3_xboole_0]) ).
fof(i_0_62,lemma,
! [X192,X193] :
( ~ subset(X192,X193)
| set_intersection2(X192,X193) = X192 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(i_0_63,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_64,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_65,plain,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(i_0_66,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_67,plain,
! [X169] : set_intersection2(X169,X169) = X169,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
fof(i_0_68,plain,
! [X194] : set_intersection2(X194,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
fof(i_0_69,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(i_0_70,plain,
! [X1,X2] : ~ proper_subset(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(i_0_71,negated_conjecture,
~ ! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
inference(assume_negation,[status(cth)],[t60_xboole_1]) ).
fof(i_0_72,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
cnf(i_0_73,plain,
( X3 = set_intersection2(X1,X2)
| ~ in(esk4_3(X1,X2,X3),X3)
| ~ in(esk4_3(X1,X2,X3),X1)
| ~ in(esk4_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_52]) ).
cnf(i_0_74,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_53]) ).
fof(i_0_75,plain,
! [X151,X152,X153,X154,X155,X156,X157,X158] :
( ( in(X154,X151)
| ~ in(X154,X153)
| X153 != set_difference(X151,X152) )
& ( ~ in(X154,X152)
| ~ in(X154,X153)
| X153 != set_difference(X151,X152) )
& ( ~ in(X155,X151)
| in(X155,X152)
| in(X155,X153)
| X153 != set_difference(X151,X152) )
& ( ~ in(esk5_3(X156,X157,X158),X158)
| ~ in(esk5_3(X156,X157,X158),X156)
| in(esk5_3(X156,X157,X158),X157)
| X158 = set_difference(X156,X157) )
& ( in(esk5_3(X156,X157,X158),X156)
| in(esk5_3(X156,X157,X158),X158)
| X158 = set_difference(X156,X157) )
& ( ~ in(esk5_3(X156,X157,X158),X157)
| in(esk5_3(X156,X157,X158),X158)
| X158 = set_difference(X156,X157) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_54])])])])])]) ).
fof(i_0_76,plain,
! [X127,X128,X129,X130,X131,X132,X133,X134] :
( ( ~ in(X130,X129)
| in(X130,X127)
| in(X130,X128)
| X129 != set_union2(X127,X128) )
& ( ~ in(X131,X127)
| in(X131,X129)
| X129 != set_union2(X127,X128) )
& ( ~ in(X131,X128)
| in(X131,X129)
| X129 != set_union2(X127,X128) )
& ( ~ in(esk2_3(X132,X133,X134),X132)
| ~ in(esk2_3(X132,X133,X134),X134)
| X134 = set_union2(X132,X133) )
& ( ~ in(esk2_3(X132,X133,X134),X133)
| ~ in(esk2_3(X132,X133,X134),X134)
| X134 = set_union2(X132,X133) )
& ( in(esk2_3(X132,X133,X134),X134)
| in(esk2_3(X132,X133,X134),X132)
| in(esk2_3(X132,X133,X134),X133)
| X134 = set_union2(X132,X133) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_xboole_0])])])])])]) ).
cnf(i_0_77,plain,
( in(esk4_3(X1,X2,X3),X1)
| in(esk4_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_52]) ).
cnf(i_0_78,plain,
( in(esk4_3(X1,X2,X3),X2)
| in(esk4_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_52]) ).
cnf(i_0_79,lemma,
( subset(set_intersection2(X1,X3),set_intersection2(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_55]) ).
cnf(i_0_80,lemma,
( ~ in(X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_56]) ).
cnf(i_0_81,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_57]) ).
cnf(i_0_82,lemma,
( disjoint(X1,X2)
| in(esk10_2(X1,X2),set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_56]) ).
fof(i_0_83,plain,
! [X195,X196] :
( ( ~ in(esk8_2(X195,X196),X195)
| ~ in(esk8_2(X195,X196),X196)
| X195 = X196 )
& ( in(esk8_2(X195,X196),X195)
| in(esk8_2(X195,X196),X196)
| X195 = X196 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(i_0_84,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_52]) ).
cnf(i_0_85,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_52]) ).
cnf(i_0_86,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_52]) ).
cnf(i_0_87,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_58]) ).
fof(i_0_88,lemma,
! [X199,X200,X201] :
( ~ subset(X199,X200)
| subset(set_difference(X199,X201),set_difference(X200,X201)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_xboole_1])]) ).
fof(i_0_89,lemma,
! [X238,X239,X240] :
( ~ subset(X238,X239)
| ~ subset(X240,X239)
| subset(set_union2(X238,X240),X239) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])]) ).
cnf(i_0_90,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_59]) ).
fof(i_0_91,plain,
! [X136,X137,X138,X139,X140] :
( ( ~ subset(X136,X137)
| ~ in(X138,X136)
| in(X138,X137) )
& ( in(esk3_2(X139,X140),X139)
| subset(X139,X140) )
& ( ~ in(esk3_2(X139,X140),X140)
| subset(X139,X140) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])]) ).
cnf(i_0_92,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_60]) ).
fof(i_0_93,lemma,
! [X209,X210,X212,X213,X214] :
( ( in(esk9_2(X209,X210),X209)
| disjoint(X209,X210) )
& ( in(esk9_2(X209,X210),X210)
| disjoint(X209,X210) )
& ( ~ in(X214,X212)
| ~ in(X214,X213)
| ~ disjoint(X212,X213) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_61])])])])])]) ).
cnf(i_0_94,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_62]) ).
fof(i_0_95,lemma,
! [X218,X219] :
( ~ subset(X218,X219)
| X219 = set_union2(X218,set_difference(X219,X218)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t45_xboole_1])]) ).
cnf(i_0_96,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_60]) ).
fof(i_0_97,lemma,
! [X186,X187,X188] :
( ~ subset(X186,X187)
| ~ subset(X187,X188)
| subset(X186,X188) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
fof(i_0_98,lemma,
! [X216,X217] : set_difference(set_union2(X216,X217),X217) = set_difference(X216,X217),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
fof(i_0_99,lemma,
! [X206,X207] : set_union2(X206,set_difference(X207,X206)) = set_union2(X206,X207),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
fof(i_0_100,plain,
! [X164,X165] :
( empty(X164)
| ~ empty(set_union2(X164,X165)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_63])]) ).
fof(i_0_101,plain,
! [X166,X167] :
( empty(X166)
| ~ empty(set_union2(X167,X166)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_64])]) ).
fof(i_0_102,plain,
! [X121,X122] :
( ( subset(X121,X122)
| X121 != X122 )
& ( subset(X122,X121)
| X121 != X122 )
& ( ~ subset(X121,X122)
| ~ subset(X122,X121)
| X121 = X122 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
fof(i_0_103,plain,
! [X115,X116] :
( ~ proper_subset(X115,X116)
| ~ proper_subset(X116,X115) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_65])]) ).
fof(i_0_104,plain,
! [X113,X114] :
( ~ in(X113,X114)
| ~ in(X114,X113) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_66])]) ).
cnf(i_0_105,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_67]) ).
fof(i_0_106,lemma,
! [X202,X203] : subset(set_difference(X202,X203),X202),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
fof(i_0_107,lemma,
! [X234,X235] : subset(X234,set_union2(X234,X235)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(i_0_108,plain,
! [X162,X163] :
( ( subset(X162,X163)
| ~ proper_subset(X162,X163) )
& ( X162 != X163
| ~ proper_subset(X162,X163) )
& ( ~ subset(X162,X163)
| X162 = X163
| proper_subset(X162,X163) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).
fof(i_0_109,lemma,
! [X178,X179] :
( ~ subset(X178,X179)
| set_union2(X178,X179) = X179 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
cnf(i_0_110,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_68]) ).
fof(i_0_111,plain,
! [X176,X177] :
( ~ disjoint(X176,X177)
| disjoint(X177,X176) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(i_0_112,lemma,
! [X204,X205] :
( ( set_difference(X204,X205) != empty_set
| subset(X204,X205) )
& ( ~ subset(X204,X205)
| set_difference(X204,X205) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
fof(i_0_113,lemma,
! [X171,X172] :
( ( set_difference(X171,X172) != empty_set
| subset(X171,X172) )
& ( ~ subset(X171,X172)
| set_difference(X171,X172) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
fof(i_0_114,plain,
! [X232,X233] :
( ~ in(X232,X233)
| ~ empty(X233) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_115,plain,
! [X117,X118] : set_union2(X117,X118) = set_union2(X118,X117),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_116,plain,
! [X123,X124,X125] :
( ( X123 != empty_set
| ~ in(X124,X123) )
& ( in(esk1_1(X125),X125)
| X125 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_69])])])])]) ).
fof(i_0_117,plain,
! [X170] : ~ proper_subset(X170,X170),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[i_0_70])]) ).
fof(i_0_118,lemma,
! [X215] :
( ~ subset(X215,empty_set)
| X215 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
fof(i_0_119,plain,
! [X236,X237] :
( ~ empty(X236)
| X236 = X237
| ~ empty(X237) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_120,plain,
! [X168] : set_union2(X168,X168) = X168,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_121,plain,
! [X175] : subset(X175,X175),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_122,plain,
! [X208] : set_difference(X208,empty_set) = X208,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(i_0_123,plain,
! [X185] : set_union2(X185,empty_set) = X185,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(i_0_124,lemma,
! [X198] : subset(empty_set,X198),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
fof(i_0_125,plain,
! [X222] : set_difference(empty_set,X222) = empty_set,
inference(variable_rename,[status(thm)],[t4_boole]) ).
fof(i_0_126,negated_conjecture,
( subset(esk11_0,esk12_0)
& proper_subset(esk12_0,esk11_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_71])])]) ).
fof(i_0_127,plain,
! [X231] :
( ~ empty(X231)
| X231 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_128,plain,
~ empty(esk7_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_72])]) ).
fof(i_0_129,plain,
empty(esk6_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_130,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| ~ in(esk4_3(X1,X2,X3),X3)
| ~ in(esk4_3(X1,X2,X3),X2)
| ~ in(esk4_3(X1,X2,X3),X1) ),
inference(rw,[status(thm)],[i_0_73,c_0_74]),
[final] ).
cnf(i_0_131,plain,
( in(esk5_3(X1,X2,X3),X2)
| X3 = set_difference(X1,X2)
| ~ in(esk5_3(X1,X2,X3),X3)
| ~ in(esk5_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_132,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk2_3(X1,X2,X3),X1)
| ~ in(esk2_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_133,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk2_3(X1,X2,X3),X2)
| ~ in(esk2_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_134,plain,
( in(esk2_3(X1,X2,X3),X3)
| in(esk2_3(X1,X2,X3),X1)
| in(esk2_3(X1,X2,X3),X2)
| X3 = set_union2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_135,plain,
( in(esk5_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2)
| ~ in(esk5_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_136,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| in(esk4_3(X1,X2,X3),X3)
| in(esk4_3(X1,X2,X3),X1) ),
inference(rw,[status(thm)],[i_0_77,c_0_74]),
[final] ).
cnf(i_0_137,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| in(esk4_3(X1,X2,X3),X3)
| in(esk4_3(X1,X2,X3),X2) ),
inference(rw,[status(thm)],[i_0_78,c_0_74]),
[final] ).
cnf(i_0_138,plain,
( in(esk5_3(X1,X2,X3),X1)
| in(esk5_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_139,lemma,
( subset(set_difference(X1,set_difference(X1,X3)),set_difference(X2,set_difference(X2,X3)))
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_79,c_0_74]),c_0_74]),
[final] ).
cnf(i_0_140,lemma,
( ~ disjoint(X2,X3)
| ~ in(X1,set_difference(X2,set_difference(X2,X3))) ),
inference(rw,[status(thm)],[i_0_80,c_0_74]),
[final] ).
cnf(i_0_141,lemma,
( subset(X1,set_difference(X2,set_difference(X2,X3)))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_81,c_0_74]),
[final] ).
cnf(i_0_142,lemma,
( disjoint(X1,X2)
| in(esk10_2(X1,X2),set_difference(X1,set_difference(X1,X2))) ),
inference(rw,[status(thm)],[i_0_82,c_0_74]),
[final] ).
cnf(i_0_143,plain,
( X1 = X2
| ~ in(esk8_2(X1,X2),X1)
| ~ in(esk8_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_144,plain,
( in(X1,X4)
| X4 != set_difference(X2,set_difference(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_84,c_0_74]),
[final] ).
cnf(i_0_145,plain,
( in(X1,X2)
| X3 != set_difference(X2,set_difference(X2,X4))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_85,c_0_74]),
[final] ).
cnf(i_0_146,plain,
( in(X1,X2)
| X3 != set_difference(X4,set_difference(X4,X2))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_86,c_0_74]),
[final] ).
cnf(i_0_147,lemma,
subset(set_difference(X1,set_difference(X1,X2)),X1),
inference(rw,[status(thm)],[i_0_87,c_0_74]),
[final] ).
cnf(i_0_148,lemma,
( subset(set_difference(X1,X3),set_difference(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_149,lemma,
( subset(set_union2(X1,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_150,plain,
( in(esk8_2(X1,X2),X1)
| in(esk8_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_151,plain,
set_difference(X1,set_difference(X1,X2)) = set_difference(X2,set_difference(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_90,c_0_74]),c_0_74]),
[final] ).
cnf(i_0_152,plain,
( subset(X1,X2)
| ~ in(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_153,plain,
( disjoint(X1,X2)
| set_difference(X1,set_difference(X1,X2)) != empty_set ),
inference(rw,[status(thm)],[i_0_92,c_0_74]),
[final] ).
cnf(i_0_154,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_155,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_156,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_157,lemma,
( ~ in(X1,X2)
| ~ in(X1,X3)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_158,lemma,
( set_difference(X1,set_difference(X1,X2)) = X1
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_94,c_0_74]),
[final] ).
cnf(i_0_159,lemma,
( X2 = set_union2(X1,set_difference(X2,X1))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_160,plain,
( set_difference(X1,set_difference(X1,X2)) = empty_set
| ~ disjoint(X1,X2) ),
inference(rw,[status(thm)],[i_0_96,c_0_74]),
[final] ).
cnf(i_0_161,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_162,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_163,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_164,lemma,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_97]),
[final] ).
cnf(i_0_165,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_166,lemma,
( in(esk9_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_167,lemma,
( in(esk9_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_168,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_169,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_98]),
[final] ).
cnf(i_0_170,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_99]),
[final] ).
cnf(i_0_171,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_100]),
[final] ).
cnf(i_0_172,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_101]),
[final] ).
cnf(i_0_173,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_174,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_175,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_176,plain,
set_difference(X1,set_difference(X1,X1)) = X1,
inference(rw,[status(thm)],[i_0_105,c_0_74]),
[final] ).
cnf(i_0_177,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_178,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_179,plain,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_108]),
[final] ).
cnf(i_0_180,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_181,plain,
set_difference(X1,set_difference(X1,empty_set)) = empty_set,
inference(rw,[status(thm)],[i_0_110,c_0_74]),
[final] ).
cnf(i_0_182,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_183,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_108]),
[final] ).
cnf(i_0_184,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_112]),
[final] ).
cnf(i_0_185,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_113]),
[final] ).
cnf(i_0_186,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_112]),
[final] ).
cnf(i_0_187,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_113]),
[final] ).
cnf(i_0_188,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_189,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_115]),
[final] ).
cnf(i_0_190,plain,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_108]),
[final] ).
cnf(i_0_191,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_192,plain,
~ proper_subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_193,plain,
( in(esk1_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_194,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[i_0_118]),
[final] ).
cnf(i_0_195,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_196,plain,
( subset(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_197,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_119]),
[final] ).
cnf(i_0_198,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_120]),
[final] ).
cnf(i_0_199,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_121]),
[final] ).
cnf(i_0_200,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_122]),
[final] ).
cnf(i_0_201,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_123]),
[final] ).
cnf(i_0_202,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[i_0_124]),
[final] ).
cnf(i_0_203,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_204,negated_conjecture,
subset(esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_205,negated_conjecture,
proper_subset(esk12_0,esk11_0),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_206,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_127]),
[final] ).
cnf(i_0_207,plain,
~ empty(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_128]),
[final] ).
cnf(i_0_208,plain,
empty(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_129]),
[final] ).
cnf(i_0_209,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_210,axiom,
X1 = X1 ).
cnf(i_0_211,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_212,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_213,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_214,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_215,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_216,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_217,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_218,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_219,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_220,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_221,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_222,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_223,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_224,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_225,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_210_001,axiom,
X1 = X1 ).
cnf(i_0_211_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_212_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_213_004,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_214_005,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_215_006,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_216_007,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_217_008,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_218_009,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_219_010,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_220_011,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_221_012,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_222_013,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_223_014,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_224_015,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_225_016,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_226,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(equality_inference,[],[144]) ).
cnf(i_0_227,plain,
( ~ in(X1,set_difference(X2,set_difference(X2,X3)))
| in(X1,X3) ),
inference(equality_inference,[],[146]) ).
cnf(i_0_228,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X2,X3)) ),
inference(equality_inference,[],[154]) ).
cnf(i_0_229,plain,
( in(X1,X2)
| in(X1,set_difference(X3,X2))
| ~ in(X1,X3) ),
inference(equality_inference,[],[155]) ).
cnf(i_0_230,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(equality_inference,[],[156]) ).
cnf(i_0_231,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(equality_inference,[],[161]) ).
cnf(i_0_232,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(equality_inference,[],[162]) ).
cnf(i_0_233,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(equality_inference,[],[163]) ).
cnf(i_0_234,plain,
~ proper_subset(X1,X1),
inference(equality_inference,[],[190]) ).
cnf(i_0_235,plain,
~ in(X1,empty_set),
inference(equality_inference,[],[191]) ).
cnf(i_0_236,plain,
subset(X1,X1),
inference(equality_inference,[],[195]) ).
cnf(i_0_237,plain,
subset(X1,X1),
inference(equality_inference,[],[196]) ).
cnf(i_0_238,plain,
~ proper_subset(esk11_0,esk12_0),
inference(scs_inference,[],[i_0_205,i_0_174]) ).
cnf(i_0_239,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(rename_variables,[],[i_0_174]) ).
cnf(i_0_240,plain,
subset(esk12_0,esk11_0),
inference(scs_inference,[],[i_0_205,i_0_174,i_0_183]) ).
cnf(i_0_241,plain,
( ~ proper_subset(X1,X2)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_183]) ).
cnf(i_0_242,plain,
esk12_0 != esk11_0,
inference(scs_inference,[],[i_0_205,i_0_174,i_0_183,i_0_190]) ).
cnf(i_0_243,plain,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_190]) ).
cnf(i_0_244,plain,
disjoint(empty_set,empty_set),
inference(scs_inference,[],[i_0_205,i_0_176,i_0_174,i_0_183,i_0_190,i_0_153]) ).
cnf(i_0_245,plain,
set_difference(X1,set_difference(X1,X1)) = X1,
inference(rename_variables,[],[i_0_176]) ).
cnf(i_0_246,plain,
( set_difference(X1,set_difference(X1,X2)) != empty_set
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_247,plain,
subset(X1,set_difference(X1,empty_set)),
inference(scs_inference,[],[i_0_205,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185]) ).
cnf(i_0_248,plain,
( set_difference(X1,X2) != empty_set
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_185]) ).
cnf(i_0_249,plain,
~ in(X1,set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_205,i_0_198,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191]) ).
cnf(i_0_250,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_198]) ).
cnf(i_0_251,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_191]) ).
cnf(i_0_252,plain,
subset(set_union2(X1,X1),X1),
inference(scs_inference,[],[i_0_205,i_0_198,i_0_250,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195]) ).
cnf(i_0_253,plain,
( X1 != X2
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_195]) ).
cnf(i_0_254,plain,
subset(set_union2(X1,X2),set_union2(X2,X1)),
inference(scs_inference,[],[i_0_205,i_0_198,i_0_250,i_0_189,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196]) ).
cnf(i_0_255,plain,
( X1 != X2
| subset(X2,X1) ),
inference(rename_variables,[],[i_0_196]) ).
cnf(i_0_256,plain,
~ in(X1,set_difference(X2,set_difference(X2,empty_set))),
inference(scs_inference,[],[i_0_205,i_0_235,i_0_198,i_0_250,i_0_189,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227]) ).
cnf(i_0_257,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(rename_variables,[],[i_0_227]) ).
cnf(i_0_258,plain,
~ in(X1,set_difference(empty_set,X2)),
inference(scs_inference,[],[i_0_205,i_0_235,i_0_198,i_0_250,i_0_189,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231]) ).
cnf(i_0_259,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(rename_variables,[],[i_0_231]) ).
cnf(i_0_260,plain,
X1 = set_union2(X1,X1),
inference(scs_inference,[],[i_0_205,i_0_235,i_0_198,i_0_250,i_0_189,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211]) ).
cnf(i_0_261,plain,
disjoint(X1,empty_set),
inference(scs_inference,[],[i_0_205,i_0_235,i_0_198,i_0_250,i_0_189,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142]) ).
cnf(i_0_262,plain,
( in(esk10_2(X1,X2),set_difference(X1,set_difference(X1,X2)))
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_263,plain,
disjoint(set_union2(empty_set,empty_set),X1),
inference(scs_inference,[],[i_0_205,i_0_235,i_0_198,i_0_250,i_0_189,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166]) ).
cnf(i_0_264,plain,
( in(esk9_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_265,plain,
disjoint(empty_set,X1),
inference(scs_inference,[],[i_0_205,i_0_235,i_0_198,i_0_250,i_0_189,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182]) ).
cnf(i_0_266,plain,
( ~ disjoint(X1,X2)
| disjoint(X2,X1) ),
inference(rename_variables,[],[i_0_182]) ).
cnf(i_0_267,plain,
~ in(X1,esk6_0),
inference(scs_inference,[],[i_0_205,i_0_235,i_0_198,i_0_250,i_0_189,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188]) ).
cnf(i_0_268,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_188]) ).
cnf(i_0_269,plain,
subset(esk11_0,set_union2(esk12_0,X1)),
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_178,i_0_198,i_0_250,i_0_189,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164]) ).
cnf(i_0_270,plain,
subset(X1,set_union2(X1,X2)),
inference(rename_variables,[],[i_0_178]) ).
cnf(i_0_271,plain,
( ~ subset(X1,X2)
| subset(X3,X2)
| ~ subset(X3,X1) ),
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_272,plain,
esk11_0 = esk12_0,
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_178,i_0_198,i_0_250,i_0_189,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173]) ).
cnf(i_0_273,plain,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_173]) ).
cnf(i_0_274,plain,
~ proper_subset(set_union2(X1,X1),X1),
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_178,i_0_192,i_0_198,i_0_250,i_0_189,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173,i_0_224]) ).
cnf(i_0_275,plain,
~ proper_subset(X1,X1),
inference(rename_variables,[],[i_0_192]) ).
cnf(i_0_276,plain,
~ proper_subset(X1,set_union2(X1,X1)),
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_178,i_0_192,i_0_275,i_0_198,i_0_250,i_0_189,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173,i_0_224,i_0_225]) ).
cnf(i_0_277,plain,
~ proper_subset(X1,X1),
inference(rename_variables,[],[i_0_192]) ).
cnf(i_0_278,plain,
~ in(esk10_2(X1,empty_set),set_difference(set_difference(X2,set_difference(X2,empty_set)),empty_set)),
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_178,i_0_192,i_0_275,i_0_198,i_0_250,i_0_189,i_0_200,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173,i_0_224,i_0_225,i_0_146]) ).
cnf(i_0_279,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_200]) ).
cnf(i_0_280,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_235]) ).
cnf(i_0_281,plain,
( X1 != set_difference(X2,set_difference(X2,X3))
| ~ in(X4,X1)
| in(X4,X3) ),
inference(rename_variables,[],[i_0_146]) ).
cnf(i_0_282,plain,
~ in(X1,set_union2(set_difference(empty_set,X2),set_difference(empty_set,X2))),
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_280,i_0_178,i_0_192,i_0_275,i_0_198,i_0_250,i_0_189,i_0_200,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173,i_0_224,i_0_225,i_0_146,i_0_161]) ).
cnf(i_0_283,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_198]) ).
cnf(i_0_284,plain,
( X1 != set_difference(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_161]) ).
cnf(i_0_285,plain,
esk12_0 != set_union2(esk11_0,esk11_0),
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_280,i_0_178,i_0_192,i_0_275,i_0_198,i_0_250,i_0_283,i_0_189,i_0_200,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173,i_0_224,i_0_225,i_0_146,i_0_161,i_0_212]) ).
cnf(i_0_286,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_198]) ).
cnf(i_0_287,plain,
~ in(esk9_2(set_union2(empty_set,empty_set),X1),set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_280,i_0_178,i_0_192,i_0_275,i_0_198,i_0_250,i_0_283,i_0_286,i_0_189,i_0_200,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173,i_0_224,i_0_225,i_0_146,i_0_161,i_0_212,i_0_218]) ).
cnf(i_0_288,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_198]) ).
cnf(i_0_289,plain,
esk6_0 != esk7_0,
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_280,i_0_178,i_0_192,i_0_275,i_0_198,i_0_250,i_0_283,i_0_286,i_0_189,i_0_200,i_0_207,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173,i_0_224,i_0_225,i_0_146,i_0_161,i_0_212,i_0_218,i_0_223]) ).
cnf(i_0_290,plain,
esk6_0 = empty_set,
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_280,i_0_178,i_0_192,i_0_275,i_0_198,i_0_250,i_0_283,i_0_286,i_0_189,i_0_200,i_0_207,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173,i_0_224,i_0_225,i_0_146,i_0_161,i_0_212,i_0_218,i_0_223,i_0_150]) ).
cnf(i_0_291,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_235]) ).
cnf(i_0_292,plain,
( in(esk8_2(X1,X2),X1)
| in(esk8_2(X1,X2),X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_150]) ).
cnf(i_0_293,plain,
~ in(X1,set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_280,i_0_291,i_0_178,i_0_192,i_0_275,i_0_198,i_0_250,i_0_283,i_0_286,i_0_288,i_0_189,i_0_200,i_0_207,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173,i_0_224,i_0_225,i_0_146,i_0_161,i_0_212,i_0_218,i_0_223,i_0_150,i_0_154]) ).
cnf(i_0_294,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_198]) ).
cnf(i_0_295,plain,
( X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_154]) ).
cnf(i_0_296,plain,
subset(set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set)),X1),
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_280,i_0_291,i_0_178,i_0_192,i_0_275,i_0_198,i_0_250,i_0_283,i_0_286,i_0_288,i_0_189,i_0_200,i_0_207,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173,i_0_224,i_0_225,i_0_146,i_0_161,i_0_212,i_0_218,i_0_223,i_0_150,i_0_154,i_0_168]) ).
cnf(i_0_297,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_168]) ).
cnf(i_0_298,plain,
set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set)) = empty_set,
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_280,i_0_291,i_0_178,i_0_192,i_0_275,i_0_198,i_0_250,i_0_283,i_0_286,i_0_288,i_0_189,i_0_200,i_0_207,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173,i_0_224,i_0_225,i_0_146,i_0_161,i_0_212,i_0_218,i_0_223,i_0_150,i_0_154,i_0_168,i_0_194]) ).
cnf(i_0_299,plain,
( ~ subset(X1,empty_set)
| X1 = empty_set ),
inference(rename_variables,[],[i_0_194]) ).
cnf(i_0_300,plain,
( ~ in(X1,X2)
| ~ in(X1,set_union2(set_difference(X3,X2),set_difference(X3,X2))) ),
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_280,i_0_291,i_0_178,i_0_192,i_0_275,i_0_198,i_0_250,i_0_283,i_0_286,i_0_288,i_0_294,i_0_189,i_0_200,i_0_207,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173,i_0_224,i_0_225,i_0_146,i_0_161,i_0_212,i_0_218,i_0_223,i_0_150,i_0_154,i_0_168,i_0_194,i_0_156]) ).
cnf(i_0_301,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_198]) ).
cnf(i_0_302,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_156]) ).
cnf(i_0_303,plain,
( ~ in(set_union2(X1,X1),X2)
| ~ in(X1,set_union2(set_difference(X3,X2),set_difference(X3,X2))) ),
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_280,i_0_291,i_0_178,i_0_192,i_0_275,i_0_198,i_0_250,i_0_283,i_0_286,i_0_288,i_0_294,i_0_301,i_0_189,i_0_200,i_0_207,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173,i_0_224,i_0_225,i_0_146,i_0_161,i_0_212,i_0_218,i_0_223,i_0_150,i_0_154,i_0_168,i_0_194,i_0_156,i_0_217]) ).
cnf(i_0_304,plain,
( ~ in(esk2_3(esk11_0,esk11_0,esk12_0),set_union2(set_difference(X1,esk12_0),set_difference(X1,esk12_0)))
| in(esk2_3(esk11_0,esk11_0,esk12_0),esk11_0) ),
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_280,i_0_291,i_0_178,i_0_192,i_0_275,i_0_198,i_0_250,i_0_283,i_0_286,i_0_288,i_0_294,i_0_301,i_0_189,i_0_200,i_0_207,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173,i_0_224,i_0_225,i_0_146,i_0_161,i_0_212,i_0_218,i_0_223,i_0_150,i_0_154,i_0_168,i_0_194,i_0_156,i_0_217,i_0_134]) ).
cnf(i_0_305,plain,
( X1 = set_union2(X2,X3)
| in(esk2_3(X2,X3,X1),X1)
| in(esk2_3(X2,X3,X1),X2)
| in(esk2_3(X2,X3,X1),X3) ),
inference(rename_variables,[],[i_0_134]) ).
cnf(i_0_306,plain,
( ~ in(esk2_3(esk11_0,esk11_0,esk12_0),set_difference(X1,esk11_0))
| ~ in(esk2_3(esk11_0,esk11_0,esk12_0),set_union2(set_difference(X2,esk12_0),set_difference(X2,esk12_0))) ),
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_280,i_0_291,i_0_178,i_0_192,i_0_275,i_0_198,i_0_250,i_0_283,i_0_286,i_0_288,i_0_294,i_0_301,i_0_189,i_0_200,i_0_207,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173,i_0_224,i_0_225,i_0_146,i_0_161,i_0_212,i_0_218,i_0_223,i_0_150,i_0_154,i_0_168,i_0_194,i_0_156,i_0_217,i_0_134,i_0_230]) ).
cnf(i_0_307,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(rename_variables,[],[i_0_230]) ).
cnf(i_0_308,plain,
( in(esk2_3(esk11_0,esk11_0,esk12_0),set_union2(esk11_0,X1))
| ~ in(esk2_3(esk11_0,esk11_0,esk12_0),set_union2(set_difference(X2,esk12_0),set_difference(X2,esk12_0))) ),
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_280,i_0_291,i_0_178,i_0_192,i_0_275,i_0_198,i_0_250,i_0_283,i_0_286,i_0_288,i_0_294,i_0_301,i_0_189,i_0_200,i_0_207,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173,i_0_224,i_0_225,i_0_146,i_0_161,i_0_212,i_0_218,i_0_223,i_0_150,i_0_154,i_0_168,i_0_194,i_0_156,i_0_217,i_0_134,i_0_230,i_0_232]) ).
cnf(i_0_309,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X2,X3)) ),
inference(rename_variables,[],[i_0_232]) ).
cnf(i_0_310,plain,
( in(esk2_3(esk11_0,esk11_0,esk12_0),set_union2(X1,esk11_0))
| ~ in(esk2_3(esk11_0,esk11_0,esk12_0),set_union2(set_difference(X2,esk12_0),set_difference(X2,esk12_0))) ),
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_280,i_0_291,i_0_178,i_0_192,i_0_275,i_0_198,i_0_250,i_0_283,i_0_286,i_0_288,i_0_294,i_0_301,i_0_189,i_0_200,i_0_207,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173,i_0_224,i_0_225,i_0_146,i_0_161,i_0_212,i_0_218,i_0_223,i_0_150,i_0_154,i_0_168,i_0_194,i_0_156,i_0_217,i_0_134,i_0_230,i_0_232,i_0_233]) ).
cnf(i_0_311,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X3,X2)) ),
inference(rename_variables,[],[i_0_233]) ).
cnf(i_0_312,plain,
( ~ in(esk11_0,esk2_3(esk11_0,esk11_0,esk12_0))
| ~ in(esk2_3(esk11_0,esk11_0,esk12_0),set_union2(set_difference(X1,esk12_0),set_difference(X1,esk12_0))) ),
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_280,i_0_291,i_0_178,i_0_192,i_0_275,i_0_198,i_0_250,i_0_283,i_0_286,i_0_288,i_0_294,i_0_301,i_0_189,i_0_200,i_0_207,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173,i_0_224,i_0_225,i_0_146,i_0_161,i_0_212,i_0_218,i_0_223,i_0_150,i_0_154,i_0_168,i_0_194,i_0_156,i_0_217,i_0_134,i_0_230,i_0_232,i_0_233,i_0_175]) ).
cnf(i_0_313,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_175]) ).
cnf(i_0_314,plain,
( in(esk2_3(esk11_0,esk11_0,esk12_0),set_difference(set_union2(esk11_0,X1),empty_set))
| ~ in(esk2_3(esk11_0,esk11_0,esk12_0),set_union2(set_difference(X2,esk12_0),set_difference(X2,esk12_0))) ),
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_280,i_0_291,i_0_178,i_0_192,i_0_275,i_0_198,i_0_250,i_0_283,i_0_286,i_0_288,i_0_294,i_0_301,i_0_189,i_0_200,i_0_279,i_0_207,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173,i_0_224,i_0_225,i_0_146,i_0_161,i_0_212,i_0_218,i_0_223,i_0_150,i_0_154,i_0_168,i_0_194,i_0_156,i_0_217,i_0_134,i_0_230,i_0_232,i_0_233,i_0_175,i_0_165,i_0_162]) ).
cnf(i_0_315,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_200]) ).
cnf(i_0_316,plain,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(rename_variables,[],[i_0_162]) ).
cnf(i_0_317,plain,
( in(esk2_3(esk11_0,esk11_0,esk12_0),set_difference(set_union2(X1,esk11_0),empty_set))
| ~ in(esk2_3(esk11_0,esk11_0,esk12_0),set_union2(set_difference(X2,esk12_0),set_difference(X2,esk12_0))) ),
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_280,i_0_291,i_0_178,i_0_192,i_0_275,i_0_198,i_0_250,i_0_283,i_0_286,i_0_288,i_0_294,i_0_301,i_0_189,i_0_200,i_0_279,i_0_315,i_0_207,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173,i_0_224,i_0_225,i_0_146,i_0_161,i_0_212,i_0_218,i_0_223,i_0_150,i_0_154,i_0_168,i_0_194,i_0_156,i_0_217,i_0_134,i_0_230,i_0_232,i_0_233,i_0_175,i_0_165,i_0_162,i_0_163]) ).
cnf(i_0_318,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_200]) ).
cnf(i_0_319,plain,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3) ),
inference(rename_variables,[],[i_0_163]) ).
cnf(i_0_320,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_200]) ).
cnf(i_0_321,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_200]) ).
cnf(i_0_322,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_235]) ).
cnf(i_0_323,plain,
( ~ in(esk2_3(esk11_0,esk11_0,esk12_0),set_union2(set_difference(X1,esk12_0),set_difference(X1,esk12_0)))
| ~ in(esk10_2(X2,empty_set),X2)
| in(esk3_2(set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set)),empty_set),set_difference(set_difference(X3,empty_set),empty_set))
| ~ in(esk3_2(set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set)),empty_set),X3) ),
inference(scs_inference,[],[i_0_204,i_0_205,i_0_235,i_0_280,i_0_291,i_0_178,i_0_192,i_0_275,i_0_198,i_0_250,i_0_283,i_0_286,i_0_288,i_0_294,i_0_301,i_0_189,i_0_200,i_0_279,i_0_315,i_0_318,i_0_320,i_0_207,i_0_208,i_0_176,i_0_181,i_0_174,i_0_183,i_0_190,i_0_153,i_0_185,i_0_191,i_0_195,i_0_196,i_0_227,i_0_231,i_0_211,i_0_142,i_0_166,i_0_182,i_0_188,i_0_164,i_0_173,i_0_224,i_0_225,i_0_146,i_0_161,i_0_212,i_0_218,i_0_223,i_0_150,i_0_154,i_0_168,i_0_194,i_0_156,i_0_217,i_0_134,i_0_230,i_0_232,i_0_233,i_0_175,i_0_165,i_0_162,i_0_163,i_0_226,i_0_228,i_0_229,i_0_132,i_0_133,i_0_157,i_0_144,i_0_155]) ).
cnf(i_0_324,plain,
disjoint(X1,set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(scs_inference,[],[i_0_293,i_0_167]) ).
cnf(i_0_325,plain,
~ in(X1,set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(rename_variables,[],[i_0_293]) ).
cnf(i_0_326,plain,
( in(esk9_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_167]) ).
cnf(i_0_327,plain,
subset(set_union2(X1,empty_set),X1),
inference(scs_inference,[],[i_0_293,i_0_201,i_0_167,i_0_195]) ).
cnf(i_0_328,plain,
( X1 != X2
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_195]) ).
cnf(i_0_329,plain,
disjoint(set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set)),X1),
inference(scs_inference,[],[i_0_293,i_0_325,i_0_201,i_0_167,i_0_195,i_0_166]) ).
cnf(i_0_330,plain,
~ in(X1,set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(rename_variables,[],[i_0_293]) ).
cnf(i_0_331,plain,
( in(esk9_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_332,plain,
disjoint(X1,set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_293,i_0_325,i_0_263,i_0_201,i_0_167,i_0_195,i_0_166,i_0_182]) ).
cnf(i_0_333,plain,
( ~ disjoint(X1,X2)
| disjoint(X2,X1) ),
inference(rename_variables,[],[i_0_182]) ).
cnf(i_0_334,plain,
subset(set_difference(X1,set_difference(X1,X2)),set_difference(X2,set_difference(X2,X1))),
inference(scs_inference,[],[i_0_293,i_0_325,i_0_263,i_0_201,i_0_151,i_0_167,i_0_195,i_0_166,i_0_182,i_0_196]) ).
cnf(i_0_335,plain,
( X1 != X2
| subset(X2,X1) ),
inference(rename_variables,[],[i_0_196]) ).
cnf(i_0_336,plain,
~ in(X1,set_difference(X2,set_difference(X2,set_difference(empty_set,X3)))),
inference(scs_inference,[],[i_0_293,i_0_325,i_0_258,i_0_263,i_0_201,i_0_151,i_0_167,i_0_195,i_0_166,i_0_182,i_0_196,i_0_227]) ).
cnf(i_0_337,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(rename_variables,[],[i_0_227]) ).
cnf(i_0_338,plain,
~ in(X1,set_difference(set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set)),X2)),
inference(scs_inference,[],[i_0_293,i_0_325,i_0_330,i_0_258,i_0_263,i_0_201,i_0_151,i_0_167,i_0_195,i_0_166,i_0_182,i_0_196,i_0_227,i_0_231]) ).
cnf(i_0_339,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(rename_variables,[],[i_0_231]) ).
cnf(i_0_340,plain,
subset(set_difference(X1,set_difference(X1,empty_set)),X2),
inference(scs_inference,[],[i_0_293,i_0_325,i_0_330,i_0_256,i_0_258,i_0_263,i_0_201,i_0_151,i_0_167,i_0_195,i_0_166,i_0_182,i_0_196,i_0_227,i_0_231,i_0_168]) ).
cnf(i_0_341,plain,
~ in(X1,set_difference(X2,set_difference(X2,empty_set))),
inference(rename_variables,[],[i_0_256]) ).
cnf(i_0_342,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_168]) ).
cnf(i_0_343,plain,
$false,
inference(scs_inference,[],[i_0_272,i_0_242,i_0_293,i_0_325,i_0_330,i_0_256,i_0_258,i_0_263,i_0_201,i_0_151,i_0_167,i_0_195,i_0_166,i_0_182,i_0_196,i_0_227,i_0_231,i_0_168,i_0_211]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU139+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32 % Computer : n010.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 02:44:21 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 % start to proof: theBenchmark
% 0.31/1.61 % Version : CSE_E---1.7
% 0.31/1.61 % Problem : theBenchmark.p
% 0.31/1.61 % SZS status Theorem for theBenchmark.p
% 0.31/1.61 % SZS output start CNFRefutation
% See solution above
% 0.75/2.05 % Total time : 1.271s
%------------------------------------------------------------------------------