%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU039+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n021.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 05:10:32 PM UTC 2026
% Result : Theorem 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 11 unt; 0 def)
% Number of atoms : 185 ( 43 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 246 ( 97 ~; 101 |; 31 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 85 ( 2 sgn 54 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d5_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(t73_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( ( in(X2,relation_dom(X3))
& in(X2,X1) )
=> in(apply(X3,X2),relation_rng(relation_dom_restriction(X3,X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_funct_1) ).
fof(t72_funct_1,axiom,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,X1)
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_funct_1) ).
fof(fc4_funct_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1) )
=> ( relation(relation_dom_restriction(X1,X2))
& function(relation_dom_restriction(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(dt_k7_relat_1,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(t68_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( X2 = relation_dom_restriction(X3,X1)
<=> ( relation_dom(X2) = set_intersection2(relation_dom(X3),X1)
& ! [X4] :
( in(X4,relation_dom(X2))
=> apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_funct_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(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(c_0_8,plain,
! [X95,X96,X97,X99,X100,X101,X103] :
( ( in(esk2_3(X95,X96,X97),relation_dom(X95))
| ~ in(X97,X96)
| X96 != relation_rng(X95)
| ~ relation(X95)
| ~ function(X95) )
& ( X97 = apply(X95,esk2_3(X95,X96,X97))
| ~ in(X97,X96)
| X96 != relation_rng(X95)
| ~ relation(X95)
| ~ function(X95) )
& ( ~ in(X100,relation_dom(X95))
| X99 != apply(X95,X100)
| in(X99,X96)
| X96 != relation_rng(X95)
| ~ relation(X95)
| ~ function(X95) )
& ( ~ in(esk3_2(X95,X101),X101)
| ~ in(X103,relation_dom(X95))
| esk3_2(X95,X101) != apply(X95,X103)
| X101 = relation_rng(X95)
| ~ relation(X95)
| ~ function(X95) )
& ( in(esk4_2(X95,X101),relation_dom(X95))
| in(esk3_2(X95,X101),X101)
| X101 = relation_rng(X95)
| ~ relation(X95)
| ~ function(X95) )
& ( esk3_2(X95,X101) = apply(X95,esk4_2(X95,X101))
| in(esk3_2(X95,X101),X101)
| X101 = relation_rng(X95)
| ~ relation(X95)
| ~ function(X95) ) ),
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)],[d5_funct_1])])])])])]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( ( in(X2,relation_dom(X3))
& in(X2,X1) )
=> in(apply(X3,X2),relation_rng(relation_dom_restriction(X3,X1))) ) ),
inference(assume_negation,[status(cth)],[t73_funct_1]) ).
cnf(c_0_10,plain,
( in(X3,X4)
| ~ in(X1,relation_dom(X2))
| X3 != apply(X2,X1)
| X4 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X153,X154,X155] :
( ~ relation(X155)
| ~ function(X155)
| ~ in(X154,X153)
| apply(relation_dom_restriction(X155,X153),X154) = apply(X155,X154) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t72_funct_1])]) ).
fof(c_0_12,plain,
! [X114,X115] :
( ( relation(relation_dom_restriction(X114,X115))
| ~ relation(X114)
| ~ function(X114) )
& ( function(relation_dom_restriction(X114,X115))
| ~ relation(X114)
| ~ function(X114) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_funct_1])])]) ).
fof(c_0_13,plain,
! [X105,X106] :
( ~ relation(X105)
| relation(relation_dom_restriction(X105,X106)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_relat_1])]) ).
fof(c_0_14,negated_conjecture,
( relation(esk19_0)
& function(esk19_0)
& in(esk18_0,relation_dom(esk19_0))
& in(esk18_0,esk17_0)
& ~ in(apply(esk19_0,esk18_0),relation_rng(relation_dom_restriction(esk19_0,esk17_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_15,plain,
( in(apply(X1,X2),relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_10])]) ).
cnf(c_0_16,plain,
( apply(relation_dom_restriction(X1,X3),X2) = apply(X1,X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( function(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_19,plain,
! [X147,X148,X149,X150] :
( ( relation_dom(X148) = set_intersection2(relation_dom(X149),X147)
| X148 != relation_dom_restriction(X149,X147)
| ~ relation(X149)
| ~ function(X149)
| ~ relation(X148)
| ~ function(X148) )
& ( ~ in(X150,relation_dom(X148))
| apply(X148,X150) = apply(X149,X150)
| X148 != relation_dom_restriction(X149,X147)
| ~ relation(X149)
| ~ function(X149)
| ~ relation(X148)
| ~ function(X148) )
& ( in(esk16_3(X147,X148,X149),relation_dom(X148))
| relation_dom(X148) != set_intersection2(relation_dom(X149),X147)
| X148 = relation_dom_restriction(X149,X147)
| ~ relation(X149)
| ~ function(X149)
| ~ relation(X148)
| ~ function(X148) )
& ( apply(X148,esk16_3(X147,X148,X149)) != apply(X149,esk16_3(X147,X148,X149))
| relation_dom(X148) != set_intersection2(relation_dom(X149),X147)
| X148 = relation_dom_restriction(X149,X147)
| ~ relation(X149)
| ~ function(X149)
| ~ relation(X148)
| ~ function(X148) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t68_funct_1])])])])]) ).
cnf(c_0_20,negated_conjecture,
~ in(apply(esk19_0,esk18_0),relation_rng(relation_dom_restriction(esk19_0,esk17_0))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( in(apply(X1,X2),relation_rng(relation_dom_restriction(X1,X3)))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3)))
| ~ in(X2,X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]) ).
cnf(c_0_22,negated_conjecture,
relation(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,negated_conjecture,
function(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,negated_conjecture,
in(esk18_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,plain,
( relation_dom(X1) = set_intersection2(relation_dom(X2),X3)
| X1 != relation_dom_restriction(X2,X3)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_26,plain,
! [X84,X85] : set_intersection2(X84,X85) = set_intersection2(X85,X84),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_27,plain,
! [X86,X87,X88,X89,X90,X91,X92,X93] :
( ( in(X89,X86)
| ~ in(X89,X88)
| X88 != set_intersection2(X86,X87) )
& ( in(X89,X87)
| ~ in(X89,X88)
| X88 != set_intersection2(X86,X87) )
& ( ~ in(X90,X86)
| ~ in(X90,X87)
| in(X90,X88)
| X88 != set_intersection2(X86,X87) )
& ( ~ in(esk1_3(X91,X92,X93),X93)
| ~ in(esk1_3(X91,X92,X93),X91)
| ~ in(esk1_3(X91,X92,X93),X92)
| X93 = set_intersection2(X91,X92) )
& ( in(esk1_3(X91,X92,X93),X91)
| in(esk1_3(X91,X92,X93),X93)
| X93 = set_intersection2(X91,X92) )
& ( in(esk1_3(X91,X92,X93),X92)
| in(esk1_3(X91,X92,X93),X93)
| X93 = set_intersection2(X91,X92) ) ),
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])])])])])]) ).
cnf(c_0_28,negated_conjecture,
~ in(esk18_0,relation_dom(relation_dom_restriction(esk19_0,esk17_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23]),c_0_24])]) ).
cnf(c_0_29,plain,
( relation_dom(relation_dom_restriction(X1,X2)) = set_intersection2(relation_dom(X1),X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_25]),c_0_17]),c_0_18]) ).
cnf(c_0_30,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,negated_conjecture,
~ in(esk18_0,set_intersection2(esk17_0,relation_dom(esk19_0))),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_22]),c_0_23])]),c_0_30]) ).
cnf(c_0_33,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_34,negated_conjecture,
in(esk18_0,relation_dom(esk19_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU039+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.15/0.32 % Computer : n021.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:43:10 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.28/1.72 % Version : CSE_E---1.7
% 1.28/1.72 % Problem : theBenchmark.p
% 1.28/1.72 % SZS status Theorem for theBenchmark.p
% 1.28/1.72 % SZS output start CNFRefutation
% See solution above
% 1.28/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------