%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN726+1 : TPTP v9.2.1. Released v2.5.0.
% 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 : n025.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 05:40:10 PM UTC 2026
% Result : Theorem 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 27 ( 9 unt; 0 def)
% Number of atoms : 97 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 100 ( 30 ~; 37 |; 20 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 80 ( 4 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm400,conjecture,
( ( ( ! [X1,X2,X3] :
( ( p(X1,X2)
& p(X2,X3) )
=> p(X1,X3) )
& ! [X1,X2,X3] :
( ( q(X1,X2)
& q(X2,X3) )
=> q(X1,X3) )
& ! [X1,X2] :
( q(X1,X2)
=> q(X2,X1) )
& ! [X1,X2] :
( p(X1,X2)
| q(X1,X2) ) )
=> ! [X1,X2] : p(X1,X2) )
| ! [X1,X2] : q(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm400) ).
fof(c_0_1,plain,
( epred1_0
<=> ( ! [X1,X2,X3] :
( ( p(X1,X2)
& p(X2,X3) )
=> p(X1,X3) )
& ! [X1,X2,X3] :
( ( q(X1,X2)
& q(X2,X3) )
=> q(X1,X3) )
& ! [X1,X2] :
( q(X1,X2)
=> q(X2,X1) )
& ! [X1,X2] :
( p(X1,X2)
| q(X1,X2) ) ) ),
introduced(definition) ).
fof(c_0_2,plain,
( epred1_0
=> ( ! [X1,X2,X3] :
( ( p(X1,X2)
& p(X2,X3) )
=> p(X1,X3) )
& ! [X1,X2,X3] :
( ( q(X1,X2)
& q(X2,X3) )
=> q(X1,X3) )
& ! [X1,X2] :
( q(X1,X2)
=> q(X2,X1) )
& ! [X1,X2] :
( p(X1,X2)
| q(X1,X2) ) ) ),
inference(split_equiv,[status(thm)],[c_0_1]) ).
fof(c_0_3,negated_conjecture,
~ ( ( epred1_0
=> ! [X1,X2] : p(X1,X2) )
| ! [X1,X2] : q(X1,X2) ),
inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm400]),c_0_1]) ).
fof(c_0_4,plain,
! [X22,X23,X24,X25,X26,X27,X28,X29,X30,X31] :
( ( ~ p(X22,X23)
| ~ p(X23,X24)
| p(X22,X24)
| ~ epred1_0 )
& ( ~ q(X25,X26)
| ~ q(X26,X27)
| q(X25,X27)
| ~ epred1_0 )
& ( ~ q(X28,X29)
| q(X29,X28)
| ~ epred1_0 )
& ( p(X30,X31)
| q(X30,X31)
| ~ epred1_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])]) ).
fof(c_0_5,negated_conjecture,
( epred1_0
& ~ p(esk1_0,esk2_0)
& ~ q(esk3_0,esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
cnf(c_0_6,plain,
( p(X1,X3)
| ~ p(X1,X2)
| ~ p(X2,X3)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
epred1_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( p(X1,X2)
| q(X1,X2)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,plain,
( p(X1,X2)
| ~ p(X3,X2)
| ~ p(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7])]) ).
cnf(c_0_10,plain,
( q(X1,X2)
| p(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_7])]) ).
cnf(c_0_11,plain,
( q(X2,X1)
| ~ q(X1,X2)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_12,negated_conjecture,
~ p(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,plain,
( q(X1,X2)
| p(X3,X2)
| ~ p(X3,X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( q(X1,X3)
| ~ q(X1,X2)
| ~ q(X2,X3)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_15,plain,
( q(X1,X2)
| ~ q(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_7])]) ).
cnf(c_0_16,negated_conjecture,
q(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_17,plain,
( q(X1,X2)
| q(X2,X3)
| p(X1,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_18,plain,
( q(X1,X2)
| ~ q(X3,X2)
| ~ q(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_7])]) ).
cnf(c_0_19,plain,
q(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( q(X1,esk2_0)
| q(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_21,plain,
( q(X1,esk1_0)
| ~ q(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
q(X1,esk1_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_20]),c_0_21]) ).
cnf(c_0_23,plain,
q(esk1_0,X1),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_24,negated_conjecture,
~ q(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_25,plain,
q(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_23]),c_0_22])]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN726+1 : TPTP v9.2.1. Released v2.5.0.
% 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 : n025.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
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 08:44:28 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Theorem for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.368s
%------------------------------------------------------------------------------