%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU062+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 : n024.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 05:10:34 PM UTC 2026
% Result : Theorem 1.11s 1.61s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 3 unt; 0 def)
% Number of atoms : 49 ( 9 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 53 ( 21 ~; 17 |; 7 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t143_funct_1,conjecture,
! [X1,X2] :
( relation(X2)
=> ( ! [X3] :
~ ( in(X3,X1)
& relation_inverse_image(X2,singleton(X3)) = empty_set )
=> subset(X1,relation_rng(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_funct_1) ).
fof(t142_funct_1,axiom,
! [X1,X2] :
( relation(X2)
=> ( in(X1,relation_rng(X2))
<=> relation_inverse_image(X2,singleton(X1)) != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_funct_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_3,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> ( ! [X3] :
~ ( in(X3,X1)
& relation_inverse_image(X2,singleton(X3)) = empty_set )
=> subset(X1,relation_rng(X2)) ) ),
inference(assume_negation,[status(cth)],[t143_funct_1]) ).
fof(c_0_4,plain,
! [X84,X85] :
( ( ~ in(X84,relation_rng(X85))
| relation_inverse_image(X85,singleton(X84)) != empty_set
| ~ relation(X85) )
& ( relation_inverse_image(X85,singleton(X84)) = empty_set
| in(X84,relation_rng(X85))
| ~ relation(X85) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t142_funct_1])])]) ).
fof(c_0_5,negated_conjecture,
! [X88] :
( relation(esk14_0)
& ( ~ in(X88,esk13_0)
| relation_inverse_image(esk14_0,singleton(X88)) != empty_set )
& ~ subset(esk13_0,relation_rng(esk14_0)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
cnf(c_0_6,plain,
( relation_inverse_image(X1,singleton(X2)) = empty_set
| in(X2,relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X59,X60,X61,X62,X63] :
( ( ~ subset(X59,X60)
| ~ in(X61,X59)
| in(X61,X60) )
& ( in(esk1_2(X62,X63),X62)
| subset(X62,X63) )
& ( ~ in(esk1_2(X62,X63),X63)
| subset(X62,X63) ) ),
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_9,negated_conjecture,
( ~ in(X1,esk13_0)
| relation_inverse_image(esk14_0,singleton(X1)) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
( relation_inverse_image(esk14_0,singleton(X1)) = empty_set
| in(X1,relation_rng(esk14_0)) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_11,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( in(X1,relation_rng(esk14_0))
| ~ in(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( subset(X1,relation_rng(esk14_0))
| ~ in(esk1_2(X1,relation_rng(esk14_0)),esk13_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
~ subset(esk13_0,relation_rng(esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU062+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 21:42:12 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.11/1.61 % Version : CSE_E---1.7
% 1.11/1.61 % Problem : theBenchmark.p
% 1.11/1.61 % SZS status Theorem for theBenchmark.p
% 1.11/1.61 % SZS output start CNFRefutation
% See solution above
% 1.11/1.61 % Total time : 1.361s
%------------------------------------------------------------------------------