%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU140+2 : TPTP v9.2.1. Released v3.3.0.
% 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 : n026.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 05:10:45 PM UTC 2026
% Result : Theorem 1.30s 1.73s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 57 ( 22 unt; 0 def)
% Number of atoms : 170 ( 42 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 191 ( 78 ~; 60 |; 41 &)
% ( 10 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 128 ( 8 sgn 81 !; 4 ?)
% 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/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(t48_xboole_1,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(t63_xboole_1,conjecture,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
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/sandbox/benchmark/theBenchmark.p',d4_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/sandbox/benchmark/theBenchmark.p',t3_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/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(l32_xboole_1,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(t36_xboole_1,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(c_0_11,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(c_0_12,lemma,
! [X226,X227,X229,X230,X231] :
( ( disjoint(X226,X227)
| in(esk10_2(X226,X227),set_intersection2(X226,X227)) )
& ( ~ in(X231,set_intersection2(X229,X230))
| ~ disjoint(X229,X230) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])]) ).
fof(c_0_13,lemma,
! [X223,X224] : set_difference(X223,set_difference(X223,X224)) = set_intersection2(X223,X224),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(c_0_14,negated_conjecture,
~ ! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
inference(assume_negation,[status(cth)],[t63_xboole_1]) ).
cnf(c_0_15,lemma,
( ~ in(X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,negated_conjecture,
( subset(esk11_0,esk12_0)
& disjoint(esk12_0,esk13_0)
& ~ disjoint(esk11_0,esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_18,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_19,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(c_0_20,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]) ).
cnf(c_0_21,lemma,
( ~ disjoint(X2,X3)
| ~ in(X1,set_difference(X2,set_difference(X2,X3))) ),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
disjoint(esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,plain,
! [X126,X127,X128] :
( ( X126 != empty_set
| ~ in(X127,X126) )
& ( in(esk1_1(X128),X128)
| X128 = 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)],[c_0_18])])])])]) ).
fof(c_0_24,plain,
! [X145,X146,X147,X148,X149,X150,X151,X152] :
( ( in(X148,X145)
| ~ in(X148,X147)
| X147 != set_intersection2(X145,X146) )
& ( in(X148,X146)
| ~ in(X148,X147)
| X147 != set_intersection2(X145,X146) )
& ( ~ in(X149,X145)
| ~ in(X149,X146)
| in(X149,X147)
| X147 != set_intersection2(X145,X146) )
& ( ~ in(esk4_3(X150,X151,X152),X152)
| ~ in(esk4_3(X150,X151,X152),X150)
| ~ in(esk4_3(X150,X151,X152),X151)
| X152 = set_intersection2(X150,X151) )
& ( in(esk4_3(X150,X151,X152),X150)
| in(esk4_3(X150,X151,X152),X152)
| X152 = set_intersection2(X150,X151) )
& ( in(esk4_3(X150,X151,X152),X151)
| in(esk4_3(X150,X151,X152),X152)
| X152 = set_intersection2(X150,X151) ) ),
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(c_0_25,plain,
! [X154,X155,X156,X157,X158,X159,X160,X161] :
( ( in(X157,X154)
| ~ in(X157,X156)
| X156 != set_difference(X154,X155) )
& ( ~ in(X157,X155)
| ~ in(X157,X156)
| X156 != set_difference(X154,X155) )
& ( ~ in(X158,X154)
| in(X158,X155)
| in(X158,X156)
| X156 != set_difference(X154,X155) )
& ( ~ in(esk5_3(X159,X160,X161),X161)
| ~ in(esk5_3(X159,X160,X161),X159)
| in(esk5_3(X159,X160,X161),X160)
| X161 = set_difference(X159,X160) )
& ( in(esk5_3(X159,X160,X161),X159)
| in(esk5_3(X159,X160,X161),X161)
| X161 = set_difference(X159,X160) )
& ( ~ in(esk5_3(X159,X160,X161),X160)
| in(esk5_3(X159,X160,X161),X161)
| X161 = set_difference(X159,X160) ) ),
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)],[c_0_19])])])])])]) ).
fof(c_0_26,lemma,
! [X212,X213,X215,X216,X217] :
( ( in(esk9_2(X212,X213),X212)
| disjoint(X212,X213) )
& ( in(esk9_2(X212,X213),X213)
| disjoint(X212,X213) )
& ( ~ in(X217,X215)
| ~ in(X217,X216)
| ~ disjoint(X215,X216) ) ),
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)],[c_0_20])])])])])]) ).
fof(c_0_27,lemma,
! [X174,X175] :
( ( set_difference(X174,X175) != empty_set
| subset(X174,X175) )
& ( ~ subset(X174,X175)
| set_difference(X174,X175) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
cnf(c_0_28,negated_conjecture,
~ in(X1,set_difference(esk12_0,set_difference(esk12_0,esk13_0))),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
( in(esk1_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,negated_conjecture,
~ disjoint(esk11_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_33,lemma,
( in(esk9_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_34,plain,
! [X124,X125] :
( ( subset(X124,X125)
| X124 != X125 )
& ( subset(X125,X124)
| X124 != X125 )
& ( ~ subset(X124,X125)
| ~ subset(X125,X124)
| X124 = X125 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(c_0_35,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,negated_conjecture,
set_difference(esk12_0,set_difference(esk12_0,esk13_0)) = empty_set,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_37,lemma,
! [X205,X206] : subset(set_difference(X205,X206),X205),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
cnf(c_0_38,plain,
( in(X1,X2)
| X3 != set_difference(X4,set_difference(X4,X2))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_30,c_0_16]) ).
cnf(c_0_39,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_40,negated_conjecture,
subset(esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_41,plain,
! [X211] : set_difference(X211,empty_set) = X211,
inference(variable_rename,[status(thm)],[t3_boole]) ).
cnf(c_0_42,plain,
( ~ in(X1,set_difference(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_43,negated_conjecture,
in(esk9_2(esk11_0,esk13_0),esk13_0),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_44,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_45,lemma,
subset(esk12_0,set_difference(esk12_0,esk13_0)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_46,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_47,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_48,negated_conjecture,
set_difference(esk11_0,esk12_0) = empty_set,
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_49,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,lemma,
( in(esk9_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_51,negated_conjecture,
~ in(esk9_2(esk11_0,esk13_0),set_difference(X1,esk13_0)),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_52,lemma,
set_difference(esk12_0,esk13_0) = esk12_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]) ).
cnf(c_0_53,negated_conjecture,
( in(X1,esk12_0)
| ~ in(X1,esk11_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_54,negated_conjecture,
in(esk9_2(esk11_0,esk13_0),esk11_0),
inference(spm,[status(thm)],[c_0_32,c_0_50]) ).
cnf(c_0_55,lemma,
~ in(esk9_2(esk11_0,esk13_0),esk12_0),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU140+2 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.15/0.34 % Computer : n026.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 02:45:38 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.30/1.73 % Version : CSE_E---1.7
% 1.30/1.73 % Problem : theBenchmark.p
% 1.30/1.73 % SZS status Theorem for theBenchmark.p
% 1.30/1.73 % SZS output start CNFRefutation
% See solution above
% 1.30/1.73 % Total time : 1.373s
%------------------------------------------------------------------------------