%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET997+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n020.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 05:09:06 PM UTC 2026
% Result : Theorem 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 4 unt; 0 def)
% Number of atoms : 93 ( 18 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 121 ( 47 ~; 46 |; 19 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 42 ( 0 sgn 27 !; 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/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(t19_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ! [X3] :
~ ( in(X3,X1)
& ! [X4] :
~ ( in(X4,relation_dom(X2))
& X3 = apply(X2,X4) ) )
=> subset(X1,relation_rng(X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funct_1) ).
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(c_0_3,plain,
! [X66,X67,X68,X70,X71,X72,X74] :
( ( in(esk2_3(X66,X67,X68),relation_dom(X66))
| ~ in(X68,X67)
| X67 != relation_rng(X66)
| ~ relation(X66)
| ~ function(X66) )
& ( X68 = apply(X66,esk2_3(X66,X67,X68))
| ~ in(X68,X67)
| X67 != relation_rng(X66)
| ~ relation(X66)
| ~ function(X66) )
& ( ~ in(X71,relation_dom(X66))
| X70 != apply(X66,X71)
| in(X70,X67)
| X67 != relation_rng(X66)
| ~ relation(X66)
| ~ function(X66) )
& ( ~ in(esk3_2(X66,X72),X72)
| ~ in(X74,relation_dom(X66))
| esk3_2(X66,X72) != apply(X66,X74)
| X72 = relation_rng(X66)
| ~ relation(X66)
| ~ function(X66) )
& ( in(esk4_2(X66,X72),relation_dom(X66))
| in(esk3_2(X66,X72),X72)
| X72 = relation_rng(X66)
| ~ relation(X66)
| ~ function(X66) )
& ( esk3_2(X66,X72) = apply(X66,esk4_2(X66,X72))
| in(esk3_2(X66,X72),X72)
| X72 = relation_rng(X66)
| ~ relation(X66)
| ~ function(X66) ) ),
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,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ! [X3] :
~ ( in(X3,X1)
& ! [X4] :
~ ( in(X4,relation_dom(X2))
& X3 = apply(X2,X4) ) )
=> subset(X1,relation_rng(X2)) ) ),
inference(assume_negation,[status(cth)],[t19_funct_1]) ).
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]) ).
fof(c_0_6,negated_conjecture,
! [X96] :
( relation(esk15_0)
& function(esk15_0)
& ( in(esk16_1(X96),relation_dom(esk15_0))
| ~ in(X96,esk14_0) )
& ( X96 = apply(esk15_0,esk16_1(X96))
| ~ in(X96,esk14_0) )
& ~ subset(esk14_0,relation_rng(esk15_0)) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])]) ).
fof(c_0_7,plain,
! [X60,X61,X62,X63,X64] :
( ( ~ subset(X60,X61)
| ~ in(X62,X60)
| in(X62,X61) )
& ( in(esk1_2(X63,X64),X63)
| subset(X63,X64) )
& ( ~ in(esk1_2(X63,X64),X64)
| subset(X63,X64) ) ),
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_8,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_5])]) ).
cnf(c_0_9,negated_conjecture,
( X1 = apply(esk15_0,esk16_1(X1))
| ~ in(X1,esk14_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
( in(esk16_1(X1),relation_dom(esk15_0))
| ~ in(X1,esk14_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
( in(X1,relation_rng(esk15_0))
| ~ in(X1,esk14_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]),c_0_11])]),c_0_12]) ).
cnf(c_0_15,negated_conjecture,
( subset(X1,relation_rng(esk15_0))
| ~ in(esk1_2(X1,relation_rng(esk15_0)),esk14_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,negated_conjecture,
~ subset(esk14_0,relation_rng(esk15_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET997+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.16/0.33 % Computer : n020.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:41:05 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % 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 : 1.372s
%------------------------------------------------------------------------------