%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET607+3 : TPTP v9.2.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:08:07 PM UTC 2026
% Result : Theorem 42.05s 25.13s
% Output : CNFRefutation 42.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 6
% Syntax : Number of formulae : 125 ( 75 unt; 0 def)
% Number of atoms : 210 ( 43 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 132 ( 47 ~; 68 |; 11 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 358 ( 51 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(prove_th79,conjecture,
! [X1,X2] : union(X1,difference(X2,X1)) = union(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th79) ).
fof(c_0_6,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(c_0_7,plain,
! [X26,X27,X28] :
( ( member(X28,X26)
| ~ member(X28,difference(X26,X27)) )
& ( ~ member(X28,X27)
| ~ member(X28,difference(X26,X27)) )
& ( ~ member(X28,X26)
| member(X28,X27)
| member(X28,difference(X26,X27)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_8,plain,
! [X33,X34,X35,X36,X37] :
( ( ~ subset(X33,X34)
| ~ member(X35,X33)
| member(X35,X34) )
& ( member(esk1_2(X36,X37),X36)
| subset(X36,X37) )
& ( ~ member(esk1_2(X36,X37),X37)
| subset(X36,X37) ) ),
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)],[subset_defn])])])])])]) ).
cnf(c_0_9,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X23,X24,X25] :
( ( ~ member(X25,union(X23,X24))
| member(X25,X23)
| member(X25,X24) )
& ( ~ member(X25,X23)
| member(X25,union(X23,X24)) )
& ( ~ member(X25,X24)
| member(X25,union(X23,X24)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk1_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_16,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( subset(X1,difference(X2,X3))
| member(esk1_2(X1,difference(X2,X3)),X3)
| ~ member(esk1_2(X1,difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_18,plain,
! [X29,X30] :
( ( subset(X29,X30)
| X29 != X30 )
& ( subset(X30,X29)
| X29 != X30 )
& ( ~ subset(X29,X30)
| ~ subset(X30,X29)
| X29 = X30 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_19,plain,
( subset(difference(X1,X2),X3)
| member(esk1_2(difference(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_10]) ).
cnf(c_0_20,plain,
( subset(difference(X1,union(X2,X3)),X4)
| ~ member(esk1_2(difference(X1,union(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( subset(X1,difference(X1,X2))
| member(esk1_2(X1,difference(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_10]) ).
cnf(c_0_22,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
subset(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_24,plain,
( subset(difference(difference(X1,X2),X3),X4)
| ~ member(esk1_2(difference(difference(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_19]) ).
cnf(c_0_25,plain,
( subset(difference(X1,difference(X2,X3)),X4)
| member(esk1_2(difference(X1,difference(X2,X3)),X4),X3)
| ~ member(esk1_2(difference(X1,difference(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_26,plain,
( subset(difference(difference(X1,X2),X3),X4)
| member(esk1_2(difference(difference(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_19]) ).
cnf(c_0_27,plain,
subset(difference(X1,union(X2,X3)),difference(difference(X1,union(X2,X3)),X3)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_28,plain,
! [X31,X32] : union(X31,X32) = union(X32,X31),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_29,plain,
( difference(X1,X2) = X1
| ~ subset(X1,difference(X1,X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
subset(difference(X1,X1),X2),
inference(spm,[status(thm)],[c_0_15,c_0_19]) ).
cnf(c_0_31,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_32,plain,
( subset(difference(difference(X1,union(X2,X3)),X4),X5)
| ~ member(esk1_2(difference(difference(X1,union(X2,X3)),X4),X5),X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_33,plain,
( subset(difference(difference(X1,X2),difference(X1,X3)),X4)
| member(esk1_2(difference(difference(X1,X2),difference(X1,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,plain,
difference(difference(X1,union(X2,X3)),X3) = difference(X1,union(X2,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_27]),c_0_23])]) ).
cnf(c_0_35,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
difference(difference(X1,X1),X2) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,plain,
( member(X1,X2)
| ~ member(X1,difference(X3,X3)) ),
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_38,plain,
subset(difference(difference(X1,union(X2,X3)),difference(X1,X3)),X4),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
difference(difference(X1,union(X2,X3)),X2) = difference(X1,union(X2,X3)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
~ member(X1,difference(X2,X2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_36]),c_0_37]) ).
cnf(c_0_41,plain,
( X1 = difference(X2,X2)
| ~ subset(X1,difference(X2,X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_30]) ).
cnf(c_0_42,plain,
subset(difference(X1,union(X2,difference(X1,X2))),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_35]) ).
cnf(c_0_43,plain,
subset(X1,difference(X1,difference(X2,X2))),
inference(spm,[status(thm)],[c_0_40,c_0_21]) ).
cnf(c_0_44,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_45,plain,
( subset(X1,difference(X1,difference(X2,X3)))
| ~ member(esk1_2(X1,difference(X1,difference(X2,X3))),X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_21]) ).
cnf(c_0_46,plain,
( subset(difference(X1,difference(X1,X2)),X3)
| member(esk1_2(difference(X1,difference(X1,X2)),X3),X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_47,plain,
difference(X1,union(X2,difference(X1,X2))) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,plain,
difference(X1,difference(X2,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_43]),c_0_23])]) ).
cnf(c_0_49,plain,
( subset(difference(difference(difference(X1,X2),X3),X4),X5)
| member(esk1_2(difference(difference(difference(X1,X2),X3),X4),X5),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_26]) ).
cnf(c_0_50,plain,
( subset(union(X1,X2),X3)
| member(esk1_2(union(X1,X2),X3),X1)
| member(esk1_2(union(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_10]) ).
cnf(c_0_51,plain,
( subset(difference(difference(X1,X2),X3),difference(X1,X4))
| member(esk1_2(difference(difference(X1,X2),X3),difference(X1,X4)),X4) ),
inference(spm,[status(thm)],[c_0_17,c_0_26]) ).
cnf(c_0_52,plain,
subset(X1,difference(X1,difference(X2,X1))),
inference(spm,[status(thm)],[c_0_45,c_0_10]) ).
cnf(c_0_53,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),union(X3,difference(X1,X3))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_48]) ).
cnf(c_0_54,plain,
( subset(difference(difference(difference(X1,X2),X3),difference(X1,X4)),X5)
| member(esk1_2(difference(difference(difference(X1,X2),X3),difference(X1,X4)),X5),X4) ),
inference(spm,[status(thm)],[c_0_25,c_0_49]) ).
cnf(c_0_55,plain,
subset(difference(difference(X1,X2),X3),difference(difference(difference(X1,X2),X3),X2)),
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_56,plain,
( subset(union(X1,X2),X2)
| member(esk1_2(union(X1,X2),X2),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_50]) ).
cnf(c_0_57,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_58,plain,
subset(difference(difference(X1,X2),X3),difference(X1,X3)),
inference(spm,[status(thm)],[c_0_15,c_0_51]) ).
cnf(c_0_59,plain,
difference(X1,difference(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_52]),c_0_23])]) ).
cnf(c_0_60,plain,
subset(X1,difference(X1,difference(X2,union(X3,difference(X1,X3))))),
inference(spm,[status(thm)],[c_0_45,c_0_53]) ).
cnf(c_0_61,plain,
subset(difference(difference(difference(X1,X2),X3),difference(X1,X3)),X4),
inference(spm,[status(thm)],[c_0_24,c_0_54]) ).
cnf(c_0_62,plain,
difference(difference(difference(X1,X2),X3),X2) = difference(difference(X1,X2),X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_55]),c_0_23])]) ).
cnf(c_0_63,plain,
subset(union(difference(X1,X1),X2),X2),
inference(spm,[status(thm)],[c_0_40,c_0_56]) ).
cnf(c_0_64,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_57,c_0_10]) ).
cnf(c_0_65,plain,
subset(difference(X1,X2),difference(X1,difference(X3,difference(X1,X2)))),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_66,plain,
difference(X1,difference(X2,union(X3,difference(X1,X3)))) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_60]),c_0_23])]) ).
cnf(c_0_67,plain,
subset(difference(difference(X1,difference(X1,X2)),X2),X3),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_68,plain,
union(difference(X1,X1),X2) = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_63]),c_0_64])]) ).
cnf(c_0_69,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_70,plain,
( subset(difference(difference(union(X1,X2),X3),X4),X5)
| member(esk1_2(difference(difference(union(X1,X2),X3),X4),X5),X1)
| member(esk1_2(difference(difference(union(X1,X2),X3),X4),X5),X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_26]) ).
cnf(c_0_71,plain,
subset(difference(X1,union(X2,difference(X3,X2))),difference(X1,X3)),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_72,plain,
difference(difference(X1,difference(X1,X2)),X2) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_41,c_0_67]) ).
cnf(c_0_73,plain,
union(X1,difference(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_68]) ).
cnf(c_0_74,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_69]) ).
cnf(c_0_75,plain,
( subset(X1,union(X2,difference(X3,X4)))
| member(esk1_2(X1,union(X2,difference(X3,X4))),X4)
| ~ member(esk1_2(X1,union(X2,difference(X3,X4))),X3) ),
inference(spm,[status(thm)],[c_0_57,c_0_13]) ).
cnf(c_0_76,plain,
subset(difference(difference(X1,X2),X1),X3),
inference(spm,[status(thm)],[c_0_15,c_0_26]) ).
cnf(c_0_77,plain,
( subset(difference(difference(union(X1,X2),X2),X3),X4)
| member(esk1_2(difference(difference(union(X1,X2),X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_70]) ).
cnf(c_0_78,plain,
subset(difference(X1,X2),difference(X1,difference(X3,difference(X3,X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_79,plain,
( subset(X1,union(union(X2,X3),X4))
| ~ member(esk1_2(X1,union(union(X2,X3),X4)),X3) ),
inference(spm,[status(thm)],[c_0_74,c_0_16]) ).
cnf(c_0_80,plain,
( subset(difference(X1,X2),union(X3,difference(X1,X4)))
| member(esk1_2(difference(X1,X2),union(X3,difference(X1,X4))),X4) ),
inference(spm,[status(thm)],[c_0_75,c_0_19]) ).
cnf(c_0_81,plain,
difference(difference(difference(X1,X2),X1),X3) = difference(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_29,c_0_76]) ).
cnf(c_0_82,plain,
subset(difference(difference(union(X1,X2),X2),X1),X3),
inference(spm,[status(thm)],[c_0_15,c_0_77]) ).
cnf(c_0_83,plain,
subset(X1,difference(X1,difference(X2,difference(X2,difference(X3,X1))))),
inference(spm,[status(thm)],[c_0_78,c_0_59]) ).
cnf(c_0_84,plain,
subset(difference(X1,X2),union(union(X3,X4),difference(X1,X4))),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_85,plain,
difference(X1,difference(difference(X2,X3),X2)) = X1,
inference(spm,[status(thm)],[c_0_48,c_0_81]) ).
cnf(c_0_86,plain,
difference(difference(union(X1,X2),X2),X1) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_41,c_0_82]) ).
cnf(c_0_87,plain,
difference(X1,difference(X2,difference(X2,difference(X3,X1)))) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_83]),c_0_23])]) ).
cnf(c_0_88,plain,
( subset(difference(union(X1,X2),X3),X4)
| member(esk1_2(difference(union(X1,X2),X3),X4),X1)
| member(esk1_2(difference(union(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_19]) ).
cnf(c_0_89,plain,
subset(X1,union(union(X2,X3),difference(X1,X3))),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_90,plain,
union(difference(difference(union(X1,X2),X2),X1),X3) = X3,
inference(spm,[status(thm)],[c_0_68,c_0_86]) ).
cnf(c_0_91,plain,
difference(difference(X1,X2),difference(X3,difference(X3,X2))) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_87,c_0_59]) ).
cnf(c_0_92,plain,
difference(X1,difference(difference(X2,X1),X3)) = X1,
inference(spm,[status(thm)],[c_0_59,c_0_62]) ).
cnf(c_0_93,plain,
( subset(X1,union(X2,union(X3,X4)))
| ~ member(esk1_2(X1,union(X2,union(X3,X4))),X4) ),
inference(spm,[status(thm)],[c_0_57,c_0_16]) ).
cnf(c_0_94,plain,
( subset(difference(union(X1,X2),X3),union(X2,X4))
| member(esk1_2(difference(union(X1,X2),X3),union(X2,X4)),X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_88]) ).
cnf(c_0_95,plain,
subset(X1,union(difference(X1,X2),union(X3,X2))),
inference(spm,[status(thm)],[c_0_89,c_0_35]) ).
cnf(c_0_96,plain,
union(difference(union(X1,difference(X2,difference(X2,X1))),X1),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_35]) ).
cnf(c_0_97,plain,
difference(difference(X1,X2),difference(X2,X3)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_92,c_0_59]) ).
cnf(c_0_98,plain,
subset(difference(union(X1,X2),X3),union(X2,union(X4,X1))),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_99,plain,
subset(union(X1,union(X2,union(X3,X1))),union(X2,union(X3,X1))),
inference(spm,[status(thm)],[c_0_93,c_0_56]) ).
cnf(c_0_100,plain,
subset(union(X1,difference(X2,difference(X2,X1))),union(X3,X1)),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_101,plain,
union(difference(difference(X1,X2),X1),X3) = X3,
inference(spm,[status(thm)],[c_0_68,c_0_81]) ).
cnf(c_0_102,plain,
subset(difference(union(X1,difference(X1,X2)),X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_97]),c_0_35]) ).
cnf(c_0_103,plain,
subset(union(X1,X2),union(X2,union(X3,X1))),
inference(spm,[status(thm)],[c_0_98,c_0_85]) ).
cnf(c_0_104,plain,
union(X1,union(X2,union(X3,X1))) = union(X2,union(X3,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_99]),c_0_64])]) ).
cnf(c_0_105,plain,
subset(union(X1,difference(X2,difference(X2,X1))),X1),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_106,plain,
subset(X1,union(X1,X2)),
inference(spm,[status(thm)],[c_0_64,c_0_35]) ).
cnf(c_0_107,plain,
subset(difference(X1,difference(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_12,c_0_46]) ).
cnf(c_0_108,plain,
difference(union(X1,difference(X1,X2)),X1) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_41,c_0_102]) ).
cnf(c_0_109,plain,
subset(union(X1,X2),union(X2,union(X1,X3))),
inference(spm,[status(thm)],[c_0_103,c_0_35]) ).
cnf(c_0_110,plain,
union(X1,union(X2,union(X1,X3))) = union(X2,union(X1,X3)),
inference(spm,[status(thm)],[c_0_104,c_0_35]) ).
cnf(c_0_111,plain,
union(X1,difference(X2,difference(X2,X1))) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_105]),c_0_106])]) ).
cnf(c_0_112,plain,
union(X1,union(union(X2,X1),X3)) = union(union(X2,X1),X3),
inference(spm,[status(thm)],[c_0_104,c_0_35]) ).
cnf(c_0_113,plain,
subset(union(X1,difference(X1,X2)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_48]) ).
fof(c_0_114,negated_conjecture,
~ ! [X1,X2] : union(X1,difference(X2,X1)) = union(X1,X2),
inference(assume_negation,[status(cth)],[prove_th79]) ).
cnf(c_0_115,plain,
subset(union(X1,X2),union(X1,union(X2,X3))),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_116,plain,
union(X1,union(X2,difference(X1,X2))) = union(X2,difference(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_47]),c_0_48]),c_0_35]) ).
cnf(c_0_117,plain,
subset(union(X1,X2),union(union(X3,X2),X1)),
inference(spm,[status(thm)],[c_0_103,c_0_112]) ).
cnf(c_0_118,plain,
union(X1,difference(X1,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_113]),c_0_106])]) ).
fof(c_0_119,negated_conjecture,
union(esk3_0,difference(esk4_0,esk3_0)) != union(esk3_0,esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_114])])]) ).
cnf(c_0_120,plain,
subset(union(X1,X2),union(X2,difference(X1,X2))),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_121,plain,
subset(union(X1,difference(X2,X3)),union(X2,X1)),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_122,negated_conjecture,
union(esk3_0,difference(esk4_0,esk3_0)) != union(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_123,plain,
union(X1,difference(X2,X1)) = union(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_120]),c_0_121])]) ).
cnf(c_0_124,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_123]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET607+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n006.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:29:16 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 42.05/25.13 % Version : CSE_E---1.7
% 42.05/25.13 % Problem : theBenchmark.p
% 42.05/25.13 % SZS status Theorem for theBenchmark.p
% 42.05/25.13 % SZS output start CNFRefutation
% See solution above
% 42.23/25.31 % Total time : 18.406s
%------------------------------------------------------------------------------