%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN353+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 : n006.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 05:36:54 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 1
% Syntax : Number of formulae : 44 ( 7 unt; 0 def)
% Number of atoms : 182 ( 0 equ)
% Maximal formula atoms : 47 ( 4 avg)
% Number of connectives : 196 ( 58 ~; 86 |; 24 &)
% ( 8 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-3 aty)
% Number of variables : 95 ( 8 sgn 7 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_18_5,conjecture,
! [X1] :
? [X2,X3,X4] :
! [X5] :
( ( big_f(X2,X3,X4)
=> ( big_f(X1,X1,X5)
=> ( big_f(X3,X4,X2)
| big_f(X4,X2,X3) ) ) )
=> ( ( ( big_f(X4,X2,X3)
=> ( big_f(X2,X3,X4)
& big_f(X3,X4,X2) ) )
<=> big_f(X3,X2,X5) )
=> ( ( ( big_f(X3,X4,X2)
=> ( big_f(X2,X3,X4)
& big_f(X4,X2,X3) ) )
<=> big_f(X2,X5,X3) )
=> ( ( ( ( big_f(X4,X2,X3)
=> ~ big_f(X3,X4,X2) )
=> big_f(X2,X3,X4) )
<=> big_f(X5,X3,X2) )
=> ( ( big_f(X2,X3,X4)
& big_f(X3,X4,X2)
& big_f(X4,X2,X3) )
<=> big_f(X5,X5,X5) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_18_5) ).
fof(c_0_1,negated_conjecture,
~ ! [X1] :
? [X2,X3,X4] :
! [X5] :
( ( big_f(X2,X3,X4)
=> ( big_f(X1,X1,X5)
=> ( big_f(X3,X4,X2)
| big_f(X4,X2,X3) ) ) )
=> ( ( ( big_f(X4,X2,X3)
=> ( big_f(X2,X3,X4)
& big_f(X3,X4,X2) ) )
<=> big_f(X3,X2,X5) )
=> ( ( ( big_f(X3,X4,X2)
=> ( big_f(X2,X3,X4)
& big_f(X4,X2,X3) ) )
<=> big_f(X2,X5,X3) )
=> ( ( ( ( big_f(X4,X2,X3)
=> ~ big_f(X3,X4,X2) )
=> big_f(X2,X3,X4) )
<=> big_f(X5,X3,X2) )
=> ( ( big_f(X2,X3,X4)
& big_f(X3,X4,X2)
& big_f(X4,X2,X3) )
<=> big_f(X5,X5,X5) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[church_46_18_5])]) ).
fof(c_0_2,negated_conjecture,
! [X12,X13,X14] :
( ( ~ big_f(X12,X13,X14)
| ~ big_f(esk1_0,esk1_0,esk2_3(X12,X13,X14))
| big_f(X13,X14,X12)
| big_f(X14,X12,X13) )
& ( big_f(X14,X12,X13)
| big_f(X13,X12,esk2_3(X12,X13,X14)) )
& ( ~ big_f(X12,X13,X14)
| ~ big_f(X13,X14,X12)
| big_f(X13,X12,esk2_3(X12,X13,X14)) )
& ( big_f(X12,X13,X14)
| ~ big_f(X14,X12,X13)
| ~ big_f(X13,X12,esk2_3(X12,X13,X14)) )
& ( big_f(X13,X14,X12)
| ~ big_f(X14,X12,X13)
| ~ big_f(X13,X12,esk2_3(X12,X13,X14)) )
& ( big_f(X13,X14,X12)
| big_f(X12,esk2_3(X12,X13,X14),X13) )
& ( ~ big_f(X12,X13,X14)
| ~ big_f(X14,X12,X13)
| big_f(X12,esk2_3(X12,X13,X14),X13) )
& ( big_f(X12,X13,X14)
| ~ big_f(X13,X14,X12)
| ~ big_f(X12,esk2_3(X12,X13,X14),X13) )
& ( big_f(X14,X12,X13)
| ~ big_f(X13,X14,X12)
| ~ big_f(X12,esk2_3(X12,X13,X14),X13) )
& ( ~ big_f(X14,X12,X13)
| ~ big_f(X13,X14,X12)
| big_f(esk2_3(X12,X13,X14),X13,X12) )
& ( ~ big_f(X12,X13,X14)
| big_f(esk2_3(X12,X13,X14),X13,X12) )
& ( big_f(X14,X12,X13)
| big_f(X12,X13,X14)
| ~ big_f(esk2_3(X12,X13,X14),X13,X12) )
& ( big_f(X13,X14,X12)
| big_f(X12,X13,X14)
| ~ big_f(esk2_3(X12,X13,X14),X13,X12) )
& ( ~ big_f(X12,X13,X14)
| ~ big_f(X13,X14,X12)
| ~ big_f(X14,X12,X13)
| ~ big_f(esk2_3(X12,X13,X14),esk2_3(X12,X13,X14),esk2_3(X12,X13,X14)) )
& ( big_f(X12,X13,X14)
| big_f(esk2_3(X12,X13,X14),esk2_3(X12,X13,X14),esk2_3(X12,X13,X14)) )
& ( big_f(X13,X14,X12)
| big_f(esk2_3(X12,X13,X14),esk2_3(X12,X13,X14),esk2_3(X12,X13,X14)) )
& ( big_f(X14,X12,X13)
| big_f(esk2_3(X12,X13,X14),esk2_3(X12,X13,X14),esk2_3(X12,X13,X14)) ) ),
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(X2,X3,X1)
| big_f(X3,X1,X2)
| ~ big_f(X1,X2,X3)
| ~ big_f(esk1_0,esk1_0,esk2_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4,negated_conjecture,
( big_f(X1,X2,X3)
| big_f(X3,X2,esk2_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5,negated_conjecture,
( big_f(esk1_0,X1,esk1_0)
| big_f(X1,esk1_0,esk1_0)
| ~ big_f(esk1_0,esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_6,negated_conjecture,
( big_f(X1,X2,X3)
| big_f(X2,X3,X1)
| ~ big_f(esk2_3(X2,X3,X1),X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_7,negated_conjecture,
( big_f(esk2_3(esk1_0,esk1_0,X1),esk1_0,esk1_0)
| big_f(esk1_0,esk2_3(esk1_0,esk1_0,X1),esk1_0)
| big_f(X1,esk1_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_5,c_0_4]) ).
cnf(c_0_8,negated_conjecture,
( big_f(X1,X2,X3)
| ~ big_f(X3,X1,X2)
| ~ big_f(X2,esk2_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_9,negated_conjecture,
( big_f(esk1_0,esk2_3(esk1_0,esk1_0,X1),esk1_0)
| big_f(X1,esk1_0,esk1_0)
| big_f(esk1_0,esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,negated_conjecture,
( big_f(esk1_0,esk1_0,X1)
| big_f(X1,esk1_0,esk1_0)
| ~ big_f(esk1_0,X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,negated_conjecture,
( big_f(X1,X2,X3)
| big_f(X3,esk2_3(X3,X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_12,negated_conjecture,
( big_f(X1,X2,X3)
| big_f(X3,X1,X2)
| ~ big_f(esk2_3(X3,X1,X2),X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_13,negated_conjecture,
( big_f(esk2_3(esk1_0,esk1_0,X1),esk1_0,esk1_0)
| big_f(esk1_0,esk1_0,esk2_3(esk1_0,esk1_0,X1))
| big_f(esk1_0,X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,negated_conjecture,
( big_f(X1,X2,X3)
| ~ big_f(X2,X3,X1)
| ~ big_f(X1,X3,esk2_3(X3,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_15,negated_conjecture,
( big_f(esk1_0,esk1_0,esk2_3(esk1_0,esk1_0,X1))
| big_f(esk1_0,X1,esk1_0)
| big_f(esk1_0,esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
( big_f(esk1_0,esk1_0,X1)
| big_f(esk1_0,X1,esk1_0)
| ~ big_f(X1,esk1_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,negated_conjecture,
( big_f(esk2_3(X2,X3,X1),X3,X2)
| ~ big_f(X1,X2,X3)
| ~ big_f(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_18,negated_conjecture,
( big_f(X1,X2,X3)
| ~ big_f(X2,X3,X1)
| ~ big_f(X1,esk2_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_19,negated_conjecture,
( big_f(esk1_0,esk2_3(esk1_0,esk1_0,X1),esk1_0)
| big_f(esk1_0,esk1_0,esk2_3(esk1_0,esk1_0,X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_4]),c_0_11]) ).
cnf(c_0_20,negated_conjecture,
( big_f(X1,X2,X3)
| ~ big_f(X3,X1,X2)
| ~ big_f(X2,X1,esk2_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_21,negated_conjecture,
( big_f(esk1_0,esk1_0,esk2_3(esk1_0,esk1_0,X1))
| big_f(esk1_0,esk1_0,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_15]) ).
cnf(c_0_22,negated_conjecture,
( big_f(esk1_0,esk1_0,X1)
| ~ big_f(X1,esk1_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,negated_conjecture,
( big_f(esk2_3(esk1_0,esk1_0,X1),esk1_0,esk1_0)
| big_f(esk1_0,esk1_0,esk2_3(esk1_0,esk1_0,X1)) ),
inference(spm,[status(thm)],[c_0_10,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
big_f(esk1_0,esk1_0,esk2_3(esk1_0,esk1_0,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,negated_conjecture,
( big_f(esk1_0,X1,esk1_0)
| ~ big_f(X1,esk1_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_24]) ).
cnf(c_0_26,negated_conjecture,
( big_f(esk2_3(X1,X2,X3),X2,X1)
| ~ big_f(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_27,negated_conjecture,
( big_f(esk1_0,esk2_3(esk1_0,esk1_0,X1),esk1_0)
| ~ big_f(esk1_0,esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,negated_conjecture,
( big_f(X1,esk1_0,esk1_0)
| ~ big_f(esk1_0,X1,esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_27]),c_0_10]) ).
cnf(c_0_29,negated_conjecture,
( big_f(esk2_3(esk1_0,esk1_0,X1),esk1_0,esk1_0)
| big_f(esk1_0,X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_11]) ).
cnf(c_0_30,negated_conjecture,
big_f(esk1_0,esk2_3(esk1_0,esk1_0,X1),esk1_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_24]),c_0_25]) ).
cnf(c_0_31,negated_conjecture,
( big_f(esk1_0,X1,esk1_0)
| big_f(esk1_0,esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
big_f(esk1_0,esk1_0,X1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_30]),c_0_31]) ).
cnf(c_0_33,negated_conjecture,
( big_f(X1,X2,X3)
| big_f(X2,X3,X1)
| ~ big_f(X3,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_3,c_0_32])]) ).
cnf(c_0_34,negated_conjecture,
( big_f(X1,esk2_3(X1,X2,X3),X2)
| big_f(X2,X1,esk2_3(X1,X2,X3)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_17]),c_0_4]),c_0_11]) ).
cnf(c_0_35,negated_conjecture,
( big_f(X1,esk2_3(X1,X2,X3),X2)
| ~ big_f(X1,X2,X3)
| ~ big_f(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_36,negated_conjecture,
( big_f(X1,esk2_3(X1,X2,X3),X2)
| ~ big_f(X3,X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_34]),c_0_35]) ).
cnf(c_0_37,negated_conjecture,
( big_f(X1,X2,X3)
| ~ big_f(X2,X3,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_36]),c_0_33]) ).
cnf(c_0_38,negated_conjecture,
big_f(X1,X2,esk2_3(X2,X1,X3)),
inference(spm,[status(thm)],[c_0_37,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
big_f(esk2_3(X1,X2,X3),X2,X1),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,negated_conjecture,
( big_f(X1,X2,X3)
| ~ big_f(X3,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_38])]) ).
cnf(c_0_41,negated_conjecture,
( ~ big_f(X1,X2,X3)
| ~ big_f(X2,X3,X1)
| ~ big_f(X3,X1,X2)
| ~ big_f(esk2_3(X1,X2,X3),esk2_3(X1,X2,X3),esk2_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_42,negated_conjecture,
big_f(X1,X2,X3),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_39])]),c_0_40]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_42]),c_0_42]),c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN353+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 : n006.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 08:29:46 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------