%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN349+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 : n031.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 0.27s 1.62s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 24 ( 4 unt; 0 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 127 ( 46 ~; 62 |; 9 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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; 0 con; 1-2 aty)
% Number of variables : 44 ( 0 sgn 6 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_17_5,conjecture,
? [X1] :
! [X2] :
? [X3] :
! [X4] :
( ( big_f(X1,X4)
<=> big_f(X2,X4) )
=> ( ( ( big_f(X1,X4)
<=> big_f(X4,X3) )
<=> big_f(X3,X4) )
<=> big_f(X4,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_17_5) ).
fof(i_0_1,negated_conjecture,
~ ? [X1] :
! [X2] :
? [X3] :
! [X4] :
( ( big_f(X1,X4)
<=> big_f(X2,X4) )
=> ( ( ( big_f(X1,X4)
<=> big_f(X4,X3) )
<=> big_f(X3,X4) )
<=> big_f(X4,X2) ) ),
inference(assume_negation,[status(cth)],[church_46_17_5]) ).
fof(i_0_2,negated_conjecture,
! [X9,X11] :
( ( ~ big_f(X9,esk2_2(X9,X11))
| big_f(esk1_1(X9),esk2_2(X9,X11)) )
& ( ~ big_f(esk1_1(X9),esk2_2(X9,X11))
| big_f(X9,esk2_2(X9,X11)) )
& ( ~ big_f(X9,esk2_2(X9,X11))
| ~ big_f(esk2_2(X9,X11),X11)
| ~ big_f(X11,esk2_2(X9,X11))
| ~ big_f(esk2_2(X9,X11),esk1_1(X9)) )
& ( big_f(X9,esk2_2(X9,X11))
| big_f(esk2_2(X9,X11),X11)
| ~ big_f(X11,esk2_2(X9,X11))
| ~ big_f(esk2_2(X9,X11),esk1_1(X9)) )
& ( ~ big_f(X9,esk2_2(X9,X11))
| big_f(esk2_2(X9,X11),X11)
| big_f(X11,esk2_2(X9,X11))
| ~ big_f(esk2_2(X9,X11),esk1_1(X9)) )
& ( ~ big_f(esk2_2(X9,X11),X11)
| big_f(X9,esk2_2(X9,X11))
| big_f(X11,esk2_2(X9,X11))
| ~ big_f(esk2_2(X9,X11),esk1_1(X9)) )
& ( ~ big_f(X9,esk2_2(X9,X11))
| ~ big_f(esk2_2(X9,X11),X11)
| big_f(X11,esk2_2(X9,X11))
| big_f(esk2_2(X9,X11),esk1_1(X9)) )
& ( big_f(X9,esk2_2(X9,X11))
| big_f(esk2_2(X9,X11),X11)
| big_f(X11,esk2_2(X9,X11))
| big_f(esk2_2(X9,X11),esk1_1(X9)) )
& ( ~ big_f(X9,esk2_2(X9,X11))
| big_f(esk2_2(X9,X11),X11)
| ~ big_f(X11,esk2_2(X9,X11))
| big_f(esk2_2(X9,X11),esk1_1(X9)) )
& ( ~ big_f(esk2_2(X9,X11),X11)
| big_f(X9,esk2_2(X9,X11))
| ~ big_f(X11,esk2_2(X9,X11))
| big_f(esk2_2(X9,X11),esk1_1(X9)) ) ),
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(esk2_2(X1,X2),X2)
| ~ big_f(X2,esk2_2(X1,X2))
| ~ big_f(esk2_2(X1,X2),esk1_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_4,negated_conjecture,
( big_f(X1,esk2_2(X1,X2))
| big_f(esk2_2(X1,X2),X2)
| ~ big_f(X2,esk2_2(X1,X2))
| ~ big_f(esk2_2(X1,X2),esk1_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_5,negated_conjecture,
( big_f(esk2_2(X1,X2),X2)
| big_f(X2,esk2_2(X1,X2))
| ~ big_f(X1,esk2_2(X1,X2))
| ~ big_f(esk2_2(X1,X2),esk1_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_6,negated_conjecture,
( big_f(X1,esk2_2(X1,X2))
| big_f(X2,esk2_2(X1,X2))
| ~ big_f(esk2_2(X1,X2),X2)
| ~ big_f(esk2_2(X1,X2),esk1_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_7,negated_conjecture,
( big_f(esk2_2(X1,X2),X2)
| big_f(esk2_2(X1,X2),esk1_1(X1))
| ~ big_f(X1,esk2_2(X1,X2))
| ~ big_f(X2,esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_8,negated_conjecture,
( big_f(X1,esk2_2(X1,X2))
| big_f(esk2_2(X1,X2),esk1_1(X1))
| ~ big_f(esk2_2(X1,X2),X2)
| ~ big_f(X2,esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_9,negated_conjecture,
( big_f(X2,esk2_2(X1,X2))
| big_f(esk2_2(X1,X2),esk1_1(X1))
| ~ big_f(X1,esk2_2(X1,X2))
| ~ big_f(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_10,negated_conjecture,
( big_f(X1,esk2_2(X1,X2))
| big_f(esk2_2(X1,X2),X2)
| big_f(X2,esk2_2(X1,X2))
| big_f(esk2_2(X1,X2),esk1_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_11,negated_conjecture,
( big_f(X1,esk2_2(X1,X2))
| ~ big_f(esk1_1(X1),esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_12,negated_conjecture,
( big_f(esk1_1(X1),esk2_2(X1,X2))
| ~ big_f(X1,esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_13,plain,
( ~ big_f(esk1_1(X1),esk2_2(X1,X2))
| big_f(esk1_1(X1),esk2_2(X1,X2)) ),
inference(scs_inference,[],[i_0_11,i_0_12]) ).
cnf(i_0_14,plain,
( big_f(X1,esk2_2(X1,X2))
| ~ big_f(X1,esk2_2(X1,X2)) ),
inference(scs_inference,[],[i_0_11,i_0_12]) ).
cnf(i_0_15,plain,
( big_f(X1,esk2_2(X1,esk1_1(X1)))
| ~ big_f(esk2_2(X1,esk1_1(X1)),esk1_1(X1)) ),
inference(scs_inference,[],[i_0_11,i_0_6]) ).
cnf(i_0_16,plain,
( big_f(X1,esk2_2(X1,esk1_1(X1)))
| big_f(esk1_1(X1),esk2_2(X1,esk1_1(X1)))
| big_f(esk2_2(X1,esk1_1(X1)),esk1_1(X1)) ),
inference(scs_inference,[],[i_0_15,i_0_10]) ).
cnf(i_0_17,plain,
( big_f(esk2_2(X1,esk1_1(X1)),esk1_1(X1))
| big_f(X1,esk2_2(X1,esk1_1(X1))) ),
inference(scs_inference,[],[i_0_16,i_0_11]) ).
cnf(i_0_18,plain,
big_f(X1,esk2_2(X1,esk1_1(X1))),
inference(scs_inference,[],[i_0_17,i_0_15]) ).
cnf(i_0_19,plain,
big_f(esk1_1(X1),esk2_2(X1,esk1_1(X1))),
inference(scs_inference,[],[i_0_18,i_0_12]) ).
cnf(i_0_20,plain,
( ~ big_f(X1,esk2_2(X1,X2))
| big_f(esk1_1(X1),esk2_2(X1,X2)) ),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_21,plain,
~ big_f(esk2_2(X1,esk1_1(X1)),esk1_1(X1)),
inference(scs_inference,[],[i_0_18,i_0_12,i_0_3]) ).
cnf(i_0_22,plain,
( ~ big_f(X1,esk2_2(X1,X2))
| ~ big_f(esk2_2(X1,X2),X2)
| ~ big_f(X2,esk2_2(X1,X2))
| ~ big_f(esk2_2(X1,X2),esk1_1(X1)) ),
inference(rename_variables,[],[i_0_3]) ).
cnf(i_0_23,plain,
$false,
inference(scs_inference,[],[i_0_18,i_0_12,i_0_3,i_0_7]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN349+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 : n031.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 08:31:24 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 : 1.271s
%------------------------------------------------------------------------------