%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN377+1 : TPTP v9.2.1. Released v2.0.0.
% 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 : n001.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 05:36:58 PM UTC 2026
% Result : Theorem 0.27s 1.62s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 3 unt; 0 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 107 ( 39 ~; 55 |; 7 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 36 ( 20 sgn 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2128,conjecture,
( ! [X1] :
( big_p(X1)
<=> ! [X2] : big_p(X2) )
<=> ( ? [X1] : big_p(X1)
<=> ! [X2] : big_p(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2128) ).
fof(i_0_1,negated_conjecture,
~ ( ! [X1] :
( big_p(X1)
<=> ! [X2] : big_p(X2) )
<=> ( ? [X1] : big_p(X1)
<=> ! [X2] : big_p(X2) ) ),
inference(assume_negation,[status(cth)],[x2128]) ).
fof(i_0_2,negated_conjecture,
! [X9,X10,X13,X14,X15,X17,X18,X19] :
( ( ~ big_p(X10)
| ~ big_p(esk3_0)
| ~ big_p(esk1_0)
| ~ big_p(esk2_0) )
& ( big_p(esk4_0)
| big_p(X13)
| ~ big_p(esk1_0)
| ~ big_p(esk2_0) )
& ( ~ big_p(X10)
| ~ big_p(esk3_0)
| big_p(esk1_0)
| big_p(X9) )
& ( big_p(esk4_0)
| big_p(X13)
| big_p(esk1_0)
| big_p(X9) )
& ( ~ big_p(X18)
| big_p(X19)
| ~ big_p(X14)
| big_p(X15) )
& ( ~ big_p(esk6_0)
| big_p(esk7_0)
| ~ big_p(X14)
| big_p(X15) )
& ( ~ big_p(X18)
| big_p(X19)
| ~ big_p(esk5_0)
| big_p(X17) )
& ( ~ big_p(esk6_0)
| big_p(esk7_0)
| ~ big_p(esk5_0)
| big_p(X17) ) ),
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)],[i_0_1])])])])])]) ).
cnf(i_0_3,negated_conjecture,
( big_p(X2)
| big_p(X4)
| ~ big_p(X1)
| ~ big_p(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_4,negated_conjecture,
( ~ big_p(X1)
| ~ big_p(esk3_0)
| ~ big_p(esk1_0)
| ~ big_p(esk2_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_5,negated_conjecture,
( big_p(X2)
| big_p(X3)
| ~ big_p(X1)
| ~ big_p(esk5_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_6,negated_conjecture,
( big_p(esk7_0)
| big_p(X2)
| ~ big_p(esk6_0)
| ~ big_p(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_7,negated_conjecture,
( big_p(esk1_0)
| big_p(X2)
| ~ big_p(X1)
| ~ big_p(esk3_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_8,negated_conjecture,
( big_p(esk7_0)
| big_p(X1)
| ~ big_p(esk6_0)
| ~ big_p(esk5_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_9,negated_conjecture,
( big_p(esk4_0)
| big_p(X1)
| ~ big_p(esk1_0)
| ~ big_p(esk2_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_10,negated_conjecture,
( big_p(esk4_0)
| big_p(X1)
| big_p(esk1_0)
| big_p(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_11,plain,
( ~ big_p(esk3_0)
| ~ big_p(esk2_0)
| ~ big_p(esk1_0) ),
nference(factoring_inference,[],[4]) ).
cnf(i_0_12,plain,
( big_p(esk4_0)
| big_p(esk1_0) ),
nference(factoring_inference,[],[10]) ).
cnf(i_0_13,plain,
( big_p(X1)
| big_p(X2)
| big_p(esk1_0) ),
inference(scs_inference,[],[i_0_12,i_0_3]) ).
cnf(i_0_14,plain,
big_p(esk1_0),
nference(factoring_inference,[],[13]) ).
cnf(i_0_15,plain,
( big_p(X1)
| big_p(X2) ),
inference(scs_inference,[],[i_0_14,i_0_3]) ).
cnf(i_0_16,plain,
( ~ big_p(esk3_0)
| ~ big_p(esk2_0) ),
inference(scs_inference,[],[i_0_14,i_0_11]) ).
cnf(i_0_17,plain,
~ big_p(esk2_0),
inference(scs_inference,[],[i_0_15,i_0_16]) ).
cnf(i_0_18,plain,
$false,
inference(scs_inference,[],[i_0_17,i_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN377+1 : TPTP v9.2.1. Released v2.0.0.
% 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
% 0.17/0.33 % Computer : n001.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 08:31:33 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 0.27/1.62 % Version : CSE_E---1.7
% 0.27/1.62 % Problem : theBenchmark.p
% 0.27/1.62 % SZS status Theorem for theBenchmark.p
% 0.27/1.62 % SZS output start CNFRefutation
% See solution above
% 0.27/1.64 % Total time : 1.273s
%------------------------------------------------------------------------------