%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN350+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 : n014.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 05:36:53 PM UTC 2026
% Result : Theorem 0.26s 1.62s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 2 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 66 ( 25 ~; 26 |; 7 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 6 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_18_2,conjecture,
! [X1] :
? [X2,X3] :
! [X4] :
( ( big_f(X1,X4)
<=> big_f(X4,X1) )
=> ( big_f(X1,X4)
<=> ( big_f(X3,X4)
& ( big_f(X2,X4)
=> big_f(X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_18_2) ).
fof(i_0_1,negated_conjecture,
~ ! [X1] :
? [X2,X3] :
! [X4] :
( ( big_f(X1,X4)
<=> big_f(X4,X1) )
=> ( big_f(X1,X4)
<=> ( big_f(X3,X4)
& ( big_f(X2,X4)
=> big_f(X2,X3) ) ) ) ),
inference(assume_negation,[status(cth)],[church_46_18_2]) ).
fof(i_0_2,negated_conjecture,
! [X10,X11] :
( ( ~ big_f(esk1_0,esk2_2(X10,X11))
| big_f(esk2_2(X10,X11),esk1_0) )
& ( ~ big_f(esk2_2(X10,X11),esk1_0)
| big_f(esk1_0,esk2_2(X10,X11)) )
& ( big_f(X10,esk2_2(X10,X11))
| ~ big_f(X11,esk2_2(X10,X11))
| ~ big_f(esk1_0,esk2_2(X10,X11)) )
& ( ~ big_f(X10,X11)
| ~ big_f(X11,esk2_2(X10,X11))
| ~ big_f(esk1_0,esk2_2(X10,X11)) )
& ( big_f(X11,esk2_2(X10,X11))
| big_f(esk1_0,esk2_2(X10,X11)) )
& ( ~ big_f(X10,esk2_2(X10,X11))
| big_f(X10,X11)
| big_f(esk1_0,esk2_2(X10,X11)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1])])])]) ).
cnf(i_0_3,negated_conjecture,
( big_f(X1,esk2_2(X1,X2))
| ~ big_f(X2,esk2_2(X1,X2))
| ~ big_f(esk1_0,esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_4,negated_conjecture,
( ~ big_f(X1,X2)
| ~ big_f(X2,esk2_2(X1,X2))
| ~ big_f(esk1_0,esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_5,negated_conjecture,
( big_f(X1,X2)
| big_f(esk1_0,esk2_2(X1,X2))
| ~ big_f(X1,esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_6,negated_conjecture,
( big_f(esk2_2(X1,X2),esk1_0)
| ~ big_f(esk1_0,esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_7,negated_conjecture,
( big_f(esk1_0,esk2_2(X1,X2))
| ~ big_f(esk2_2(X1,X2),esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_8,negated_conjecture,
( big_f(X1,esk2_2(X2,X1))
| big_f(esk1_0,esk2_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_9,plain,
( ~ big_f(esk1_0,esk2_2(X1,X2))
| big_f(esk1_0,esk2_2(X1,X2)) ),
inference(scs_inference,[],[i_0_6,i_0_7]) ).
cnf(i_0_10,plain,
( ~ big_f(esk2_2(X1,X2),esk2_2(X2,esk2_2(X1,X2)))
| ~ big_f(esk1_0,esk2_2(X2,esk2_2(X1,X2)))
| big_f(esk1_0,esk2_2(X1,X2)) ),
inference(scs_inference,[],[i_0_8,i_0_4]) ).
cnf(i_0_11,plain,
( big_f(X1,X1)
| big_f(esk1_0,esk2_2(X1,X1)) ),
inference(scs_inference,[],[i_0_5,i_0_8]) ).
cnf(i_0_12,plain,
( big_f(X1,X1)
| big_f(esk2_2(X1,X1),esk1_0) ),
inference(scs_inference,[],[i_0_11,i_0_6]) ).
cnf(i_0_13,plain,
( big_f(X1,X1)
| ~ big_f(esk1_0,esk2_2(esk2_2(X1,X1),esk1_0)) ),
inference(scs_inference,[],[i_0_12,i_0_4]) ).
cnf(i_0_14,plain,
( ~ big_f(X1,esk2_2(X1,X1))
| ~ big_f(esk1_0,esk2_2(esk2_2(X1,X1),esk1_0))
| ~ big_f(esk1_0,esk2_2(X1,X1)) ),
inference(scs_inference,[],[i_0_13,i_0_4]) ).
cnf(i_0_15,plain,
~ big_f(esk1_0,esk2_2(esk2_2(esk1_0,esk1_0),esk1_0)),
inference(scs_inference,[],[i_0_14,i_0_8]) ).
cnf(i_0_16,plain,
$false,
inference(scs_inference,[],[i_0_15,i_0_8]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN350+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 : n014.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 08:29:21 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.26/1.62 % Version : CSE_E---1.7
% 0.26/1.62 % Problem : theBenchmark.p
% 0.26/1.62 % SZS status Theorem for theBenchmark.p
% 0.26/1.62 % SZS output start CNFRefutation
% See solution above
% 0.26/1.64 % Total time : 1.271s
%------------------------------------------------------------------------------