%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN374+1 : TPTP v9.2.1. Released v2.0.0.
% 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 : n022.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 05:36:57 PM UTC 2026
% Result : Theorem 1.24s 1.71s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 3 unt; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 88 ( 28 ~; 47 |; 7 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 35 ( 18 sgn 10 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2125,conjecture,
( ? [X1] :
! [X2] :
( big_p(X1)
<=> big_p(X2) )
<=> ( ? [X1] : big_p(X1)
<=> ! [X2] : big_p(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2125) ).
fof(c_0_1,negated_conjecture,
~ ( ? [X1] :
! [X2] :
( big_p(X1)
<=> big_p(X2) )
<=> ( ? [X1] : big_p(X1)
<=> ! [X2] : big_p(X2) ) ),
inference(assume_negation,[status(cth)],[x2125]) ).
fof(c_0_2,negated_conjecture,
! [X7,X9,X12,X14,X15,X16] :
( ( ~ big_p(X9)
| ~ big_p(esk2_0)
| ~ big_p(X7)
| ~ big_p(esk1_1(X7)) )
& ( big_p(esk3_0)
| big_p(X12)
| ~ big_p(X7)
| ~ big_p(esk1_1(X7)) )
& ( ~ big_p(X9)
| ~ big_p(esk2_0)
| big_p(X7)
| big_p(esk1_1(X7)) )
& ( big_p(esk3_0)
| big_p(X12)
| big_p(X7)
| big_p(esk1_1(X7)) )
& ( ~ big_p(X15)
| big_p(X16)
| ~ big_p(esk4_0)
| big_p(X14) )
& ( ~ big_p(esk5_0)
| big_p(esk6_0)
| ~ big_p(esk4_0)
| big_p(X14) )
& ( ~ big_p(X15)
| big_p(X16)
| ~ big_p(X14)
| big_p(esk4_0) )
& ( ~ big_p(esk5_0)
| big_p(esk6_0)
| ~ big_p(X14)
| big_p(esk4_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_1])])])])]) ).
cnf(c_0_3,negated_conjecture,
( big_p(esk3_0)
| big_p(X1)
| big_p(X2)
| big_p(esk1_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4,negated_conjecture,
( big_p(X2)
| big_p(esk4_0)
| ~ big_p(X1)
| ~ big_p(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5,negated_conjecture,
( big_p(esk1_1(X1))
| big_p(esk3_0)
| big_p(X1) ),
inference(ef,[status(thm)],[c_0_3]) ).
cnf(c_0_6,negated_conjecture,
( big_p(esk3_0)
| big_p(esk4_0)
| ~ big_p(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_5]),c_0_4]),c_0_4]) ).
cnf(c_0_7,negated_conjecture,
( big_p(esk4_0)
| big_p(esk3_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_5]),c_0_6]) ).
cnf(c_0_8,negated_conjecture,
( big_p(esk4_0)
| big_p(X1)
| ~ big_p(X2) ),
inference(spm,[status(thm)],[c_0_4,c_0_7]) ).
cnf(c_0_9,negated_conjecture,
( ~ big_p(X1)
| ~ big_p(esk2_0)
| ~ big_p(X2)
| ~ big_p(esk1_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_10,negated_conjecture,
( big_p(esk4_0)
| big_p(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( big_p(X2)
| big_p(X3)
| ~ big_p(X1)
| ~ big_p(esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_12,negated_conjecture,
big_p(esk4_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_10]),c_0_10]),c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( big_p(X1)
| big_p(X2)
| ~ big_p(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12])]) ).
cnf(c_0_14,negated_conjecture,
( big_p(X1)
| big_p(X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
big_p(X1),
inference(ef,[status(thm)],[c_0_14]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_15]),c_0_15]),c_0_15]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN374+1 : TPTP v9.2.1. Released v2.0.0.
% 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 : n022.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 08:30:51 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.24/1.71 % Version : CSE_E---1.7
% 1.24/1.71 % Problem : theBenchmark.p
% 1.24/1.71 % SZS status Theorem for theBenchmark.p
% 1.24/1.71 % SZS output start CNFRefutation
% See solution above
% 1.24/1.71 % Total time : 1.369s
%------------------------------------------------------------------------------