%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN332+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 : 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 05:36:49 PM UTC 2026
% Result : Theorem 1.29s 1.74s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 3 unt; 0 def)
% Number of atoms : 86 ( 0 equ)
% Maximal formula atoms : 34 ( 5 avg)
% Number of connectives : 97 ( 27 ~; 33 |; 15 &)
% ( 11 <=>; 10 =>; 0 <=; 1 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 31 ( 2 sgn 4 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_14_4,conjecture,
? [X1,X2] :
! [X3] :
( ( ( big_f(X1,X2)
& big_f(X2,X1) )
<~> big_f(X1,X3) )
=> ( ( big_f(X1,X3)
<=> big_f(X3,X1) )
=> ( ( big_f(X1,X3)
<=> big_f(X2,X3) )
=> ( ( ( big_f(X2,X1)
=> big_f(X1,X2) )
<=> big_f(X3,X3) )
=> ( ( big_f(X1,X2)
<=> big_f(X2,X1) )
<=> big_f(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_14_4) ).
fof(c_0_1,negated_conjecture,
~ ? [X1,X2] :
! [X3] :
( ~ ( ( big_f(X1,X2)
& big_f(X2,X1) )
<=> big_f(X1,X3) )
=> ( ( big_f(X1,X3)
<=> big_f(X3,X1) )
=> ( ( big_f(X1,X3)
<=> big_f(X2,X3) )
=> ( ( ( big_f(X2,X1)
=> big_f(X1,X2) )
<=> big_f(X3,X3) )
=> ( ( big_f(X1,X2)
<=> big_f(X2,X1) )
<=> big_f(X3,X2) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[church_46_14_4])]) ).
fof(c_0_2,negated_conjecture,
! [X7,X8] :
( ( ~ big_f(X7,X8)
| ~ big_f(X8,X7)
| ~ big_f(X7,esk1_2(X7,X8)) )
& ( big_f(X7,X8)
| big_f(X7,esk1_2(X7,X8)) )
& ( big_f(X8,X7)
| big_f(X7,esk1_2(X7,X8)) )
& ( ~ big_f(X7,esk1_2(X7,X8))
| big_f(esk1_2(X7,X8),X7) )
& ( ~ big_f(esk1_2(X7,X8),X7)
| big_f(X7,esk1_2(X7,X8)) )
& ( ~ big_f(X7,esk1_2(X7,X8))
| big_f(X8,esk1_2(X7,X8)) )
& ( ~ big_f(X8,esk1_2(X7,X8))
| big_f(X7,esk1_2(X7,X8)) )
& ( big_f(X8,X7)
| big_f(esk1_2(X7,X8),esk1_2(X7,X8)) )
& ( ~ big_f(X7,X8)
| big_f(esk1_2(X7,X8),esk1_2(X7,X8)) )
& ( ~ big_f(esk1_2(X7,X8),esk1_2(X7,X8))
| ~ big_f(X8,X7)
| big_f(X7,X8) )
& ( ~ big_f(X7,X8)
| ~ big_f(X8,X7)
| ~ big_f(esk1_2(X7,X8),X8) )
& ( big_f(X7,X8)
| big_f(X8,X7)
| ~ big_f(esk1_2(X7,X8),X8) )
& ( ~ big_f(X7,X8)
| big_f(X8,X7)
| big_f(esk1_2(X7,X8),X8) )
& ( ~ big_f(X8,X7)
| big_f(X7,X8)
| big_f(esk1_2(X7,X8),X8) ) ),
inference(distribute,[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_f(X1,X2)
| big_f(X2,X1)
| ~ big_f(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4,negated_conjecture,
( big_f(esk1_2(X1,X2),X1)
| ~ big_f(X1,esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5,negated_conjecture,
( big_f(X1,X2)
| big_f(X1,esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_6,negated_conjecture,
( big_f(X1,X2)
| ~ big_f(esk1_2(X1,X2),esk1_2(X1,X2))
| ~ big_f(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_7,negated_conjecture,
big_f(X1,X1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_4]),c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( big_f(X2,esk1_2(X1,X2))
| ~ big_f(X1,esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_9,negated_conjecture,
( big_f(X1,X2)
| big_f(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_10,negated_conjecture,
( big_f(X1,X2)
| ~ big_f(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7])]) ).
cnf(c_0_11,negated_conjecture,
( big_f(X1,esk1_2(X2,X1))
| big_f(X1,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
( big_f(esk1_2(X1,X2),X2)
| big_f(X2,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,negated_conjecture,
( ~ big_f(X1,X2)
| ~ big_f(X2,X1)
| ~ big_f(X1,esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_14,negated_conjecture,
big_f(X1,X2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_12]),c_0_10]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_14]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SYN332+1 : TPTP v9.2.1. Released v2.0.0.
% 0.13/0.13 % 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
% 0.17/0.34 % Computer : n020.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 08:29:04 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.21/0.36 % start to proof: theBenchmark
% 1.29/1.74 % Version : CSE_E---1.7
% 1.29/1.74 % Problem : theBenchmark.p
% 1.29/1.74 % SZS status Theorem for theBenchmark.p
% 1.29/1.74 % SZS output start CNFRefutation
% See solution above
% 1.29/1.74 % Total time : 1.376s
%------------------------------------------------------------------------------