%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET991+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 : n029.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 05:09:05 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 65 ( 14 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 86 ( 33 ~; 34 |; 12 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 21 ( 0 sgn 14 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t12_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(X2))
=> in(apply(X2,X1),relation_rng(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_1) ).
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(c_0_2,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(X2))
=> in(apply(X2,X1),relation_rng(X2)) ) ),
inference(assume_negation,[status(cth)],[t12_funct_1]) ).
fof(c_0_3,plain,
! [X92,X93,X94,X96,X97,X98,X100] :
( ( in(esk12_3(X92,X93,X94),relation_dom(X92))
| ~ in(X94,X93)
| X93 != relation_rng(X92)
| ~ relation(X92)
| ~ function(X92) )
& ( X94 = apply(X92,esk12_3(X92,X93,X94))
| ~ in(X94,X93)
| X93 != relation_rng(X92)
| ~ relation(X92)
| ~ function(X92) )
& ( ~ in(X97,relation_dom(X92))
| X96 != apply(X92,X97)
| in(X96,X93)
| X93 != relation_rng(X92)
| ~ relation(X92)
| ~ function(X92) )
& ( ~ in(esk13_2(X92,X98),X98)
| ~ in(X100,relation_dom(X92))
| esk13_2(X92,X98) != apply(X92,X100)
| X98 = relation_rng(X92)
| ~ relation(X92)
| ~ function(X92) )
& ( in(esk14_2(X92,X98),relation_dom(X92))
| in(esk13_2(X92,X98),X98)
| X98 = relation_rng(X92)
| ~ relation(X92)
| ~ function(X92) )
& ( esk13_2(X92,X98) = apply(X92,esk14_2(X92,X98))
| in(esk13_2(X92,X98),X98)
| X98 = relation_rng(X92)
| ~ relation(X92)
| ~ function(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)],[d5_funct_1])])])])])]) ).
fof(c_0_4,negated_conjecture,
( relation(esk11_0)
& function(esk11_0)
& in(esk10_0,relation_dom(esk11_0))
& ~ in(apply(esk11_0,esk10_0),relation_rng(esk11_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])]) ).
cnf(c_0_5,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_3]) ).
cnf(c_0_6,negated_conjecture,
~ in(apply(esk11_0,esk10_0),relation_rng(esk11_0)),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( in(apply(X1,X2),relation_rng(X1))
| ~ in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_5])]) ).
cnf(c_0_8,negated_conjecture,
in(esk10_0,relation_dom(esk11_0)),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,negated_conjecture,
function(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,negated_conjecture,
relation(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]),c_0_9]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET991+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n029.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 02:41:14 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------