%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU130+1 : 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 : n025.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 05:10:42 PM UTC 2026
% Result : Theorem 1.40s 1.76s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 6 unt; 0 def)
% Number of atoms : 65 ( 20 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 68 ( 23 ~; 30 |; 9 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 47 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(t28_xboole_1,conjecture,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(c_0_4,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53] :
( ( in(X49,X46)
| ~ in(X49,X48)
| X48 != set_intersection2(X46,X47) )
& ( in(X49,X47)
| ~ in(X49,X48)
| X48 != set_intersection2(X46,X47) )
& ( ~ in(X50,X46)
| ~ in(X50,X47)
| in(X50,X48)
| X48 != set_intersection2(X46,X47) )
& ( ~ in(esk2_3(X51,X52,X53),X53)
| ~ in(esk2_3(X51,X52,X53),X51)
| ~ in(esk2_3(X51,X52,X53),X52)
| X53 = set_intersection2(X51,X52) )
& ( in(esk2_3(X51,X52,X53),X51)
| in(esk2_3(X51,X52,X53),X53)
| X53 = set_intersection2(X51,X52) )
& ( in(esk2_3(X51,X52,X53),X52)
| in(esk2_3(X51,X52,X53),X53)
| X53 = set_intersection2(X51,X52) ) ),
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_5,plain,
! [X40,X41,X42,X43,X44] :
( ( ~ subset(X40,X41)
| ~ in(X42,X40)
| in(X42,X41) )
& ( in(esk1_2(X43,X44),X43)
| subset(X43,X44) )
& ( ~ in(esk1_2(X43,X44),X44)
| subset(X43,X44) ) ),
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_6,plain,
( in(esk2_3(X1,X2,X3),X2)
| in(esk2_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
inference(assume_negation,[status(cth)],[t28_xboole_1]) ).
cnf(c_0_8,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( set_intersection2(X1,X2) = X2
| in(esk2_3(X1,X2,X2),X2) ),
inference(ef,[status(thm)],[c_0_6]) ).
fof(c_0_10,negated_conjecture,
( subset(esk5_0,esk6_0)
& set_intersection2(esk5_0,esk6_0) != esk5_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_11,plain,
( X3 = set_intersection2(X1,X2)
| ~ in(esk2_3(X1,X2,X3),X3)
| ~ in(esk2_3(X1,X2,X3),X1)
| ~ in(esk2_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_12,plain,
( set_intersection2(X1,X2) = X2
| in(esk2_3(X1,X2,X2),X3)
| ~ subset(X2,X3) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
subset(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X36,X37] : set_intersection2(X36,X37) = set_intersection2(X37,X36),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_15,plain,
( set_intersection2(X1,X2) = X2
| ~ in(esk2_3(X1,X2,X2),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_9]),c_0_9]) ).
cnf(c_0_16,negated_conjecture,
( set_intersection2(X1,esk5_0) = esk5_0
| in(esk2_3(X1,esk5_0,esk5_0),esk6_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
set_intersection2(esk5_0,esk6_0) != esk5_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU130+1 : 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
% 0.15/0.33 % Computer : n025.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 02:45:13 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.40/1.76 % Version : CSE_E---1.7
% 1.40/1.76 % Problem : theBenchmark.p
% 1.40/1.76 % SZS status Theorem for theBenchmark.p
% 1.40/1.76 % SZS output start CNFRefutation
% See solution above
% 1.40/1.76 % Total time : 1.371s
%------------------------------------------------------------------------------