%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU132+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 : 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 05:10:43 PM UTC 2026
% Result : Theorem 1.65s 1.83s
% Output : CNFRefutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 113 ( 23 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 126 ( 47 ~; 52 |; 16 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 83 ( 7 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t33_xboole_1,conjecture,
! [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(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(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(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(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(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
inference(assume_negation,[status(cth)],[t33_xboole_1]) ).
fof(c_0_6,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_7,plain,
! [X120,X121,X122,X123,X124,X125,X126,X127] :
( ( in(X123,X120)
| ~ in(X123,X122)
| X122 != set_intersection2(X120,X121) )
& ( in(X123,X121)
| ~ in(X123,X122)
| X122 != set_intersection2(X120,X121) )
& ( ~ in(X124,X120)
| ~ in(X124,X121)
| in(X124,X122)
| X122 != set_intersection2(X120,X121) )
& ( ~ in(esk4_3(X125,X126,X127),X127)
| ~ in(esk4_3(X125,X126,X127),X125)
| ~ in(esk4_3(X125,X126,X127),X126)
| X127 = set_intersection2(X125,X126) )
& ( in(esk4_3(X125,X126,X127),X125)
| in(esk4_3(X125,X126,X127),X127)
| X127 = set_intersection2(X125,X126) )
& ( in(esk4_3(X125,X126,X127),X126)
| in(esk4_3(X125,X126,X127),X127)
| X127 = set_intersection2(X125,X126) ) ),
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_8,lemma,
! [X167,X168] :
( ~ subset(X167,X168)
| set_intersection2(X167,X168) = X167 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(c_0_9,negated_conjecture,
( subset(esk9_0,esk10_0)
& ~ subset(set_difference(esk9_0,esk11_0),set_difference(esk10_0,esk11_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_10,plain,
! [X129,X130,X131,X132,X133,X134,X135,X136] :
( ( in(X132,X129)
| ~ in(X132,X131)
| X131 != set_difference(X129,X130) )
& ( ~ in(X132,X130)
| ~ in(X132,X131)
| X131 != set_difference(X129,X130) )
& ( ~ in(X133,X129)
| in(X133,X130)
| in(X133,X131)
| X131 != set_difference(X129,X130) )
& ( ~ in(esk5_3(X134,X135,X136),X136)
| ~ in(esk5_3(X134,X135,X136),X134)
| in(esk5_3(X134,X135,X136),X135)
| X136 = set_difference(X134,X135) )
& ( in(esk5_3(X134,X135,X136),X134)
| in(esk5_3(X134,X135,X136),X136)
| X136 = set_difference(X134,X135) )
& ( ~ in(esk5_3(X134,X135,X136),X135)
| in(esk5_3(X134,X135,X136),X136)
| X136 = set_difference(X134,X135) ) ),
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_6])])])])])]) ).
fof(c_0_11,plain,
! [X114,X115,X116,X117,X118] :
( ( ~ subset(X114,X115)
| ~ in(X116,X114)
| in(X116,X115) )
& ( in(esk3_2(X117,X118),X117)
| subset(X117,X118) )
& ( ~ in(esk3_2(X117,X118),X118)
| subset(X117,X118) ) ),
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(c_0_12,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
subset(esk9_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
~ subset(set_difference(esk9_0,esk11_0),set_difference(esk10_0,esk11_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
set_intersection2(esk9_0,esk10_0) = esk9_0,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
in(esk3_2(set_difference(esk9_0,esk11_0),set_difference(esk10_0,esk11_0)),set_difference(esk9_0,esk11_0)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,negated_conjecture,
( in(X1,esk10_0)
| ~ in(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
in(esk3_2(set_difference(esk9_0,esk11_0),set_difference(esk10_0,esk11_0)),esk9_0),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( in(X1,set_difference(X2,X3))
| in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
in(esk3_2(set_difference(esk9_0,esk11_0),set_difference(esk10_0,esk11_0)),esk10_0),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_28,plain,
( subset(X1,X2)
| ~ in(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,negated_conjecture,
( in(esk3_2(set_difference(esk9_0,esk11_0),set_difference(esk10_0,esk11_0)),set_difference(esk10_0,X1))
| in(esk3_2(set_difference(esk9_0,esk11_0),set_difference(esk10_0,esk11_0)),X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
( ~ in(X1,set_difference(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_31,negated_conjecture,
in(esk3_2(set_difference(esk9_0,esk11_0),set_difference(esk10_0,esk11_0)),esk11_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_16]) ).
cnf(c_0_32,negated_conjecture,
~ in(esk3_2(set_difference(esk9_0,esk11_0),set_difference(esk10_0,esk11_0)),set_difference(X1,esk11_0)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_21,c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU132+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n026.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:45:08 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.65/1.83 % Version : CSE_E---1.7
% 1.65/1.83 % Problem : theBenchmark.p
% 1.65/1.83 % SZS status Theorem for theBenchmark.p
% 1.65/1.83 % SZS output start CNFRefutation
% See solution above
% 1.65/1.83 % Total time : 1.372s
%------------------------------------------------------------------------------