%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN084+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 : n001.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 05:36:06 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 33 ( 6 unt; 0 def)
% Number of atoms : 221 ( 0 equ)
% Maximal formula atoms : 114 ( 6 avg)
% Number of connectives : 291 ( 103 ~; 148 |; 34 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 5 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 23 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel62,conjecture,
( ! [X1] :
( ( big_p(a)
& ( big_p(X1)
=> big_p(f(X1)) ) )
=> big_p(f(f(X1))) )
<=> ! [X2] :
( ( ~ big_p(a)
| big_p(X2)
| big_p(f(f(X2))) )
& ( ~ big_p(a)
| ~ big_p(f(X2))
| big_p(f(f(X2))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel62) ).
fof(c_0_1,negated_conjecture,
~ ( ! [X1] :
( ( big_p(a)
& ( big_p(X1)
=> big_p(f(X1)) ) )
=> big_p(f(f(X1))) )
<=> ! [X2] :
( ( ~ big_p(a)
| big_p(X2)
| big_p(f(f(X2))) )
& ( ~ big_p(a)
| ~ big_p(f(X2))
| big_p(f(f(X2))) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[pel62])]) ).
fof(c_0_2,negated_conjecture,
! [X7,X8] :
( ( big_p(a)
| big_p(a)
| big_p(a) )
& ( big_p(f(esk2_0))
| big_p(a)
| big_p(a) )
& ( ~ big_p(f(f(esk2_0)))
| big_p(a)
| big_p(a) )
& ( big_p(a)
| ~ big_p(esk2_0)
| big_p(a) )
& ( big_p(f(esk2_0))
| ~ big_p(esk2_0)
| big_p(a) )
& ( ~ big_p(f(f(esk2_0)))
| ~ big_p(esk2_0)
| big_p(a) )
& ( big_p(a)
| ~ big_p(f(f(esk2_0)))
| big_p(a) )
& ( big_p(f(esk2_0))
| ~ big_p(f(f(esk2_0)))
| big_p(a) )
& ( ~ big_p(f(f(esk2_0)))
| ~ big_p(f(f(esk2_0)))
| big_p(a) )
& ( big_p(a)
| big_p(a)
| ~ big_p(esk1_0)
| big_p(f(esk1_0)) )
& ( big_p(f(esk2_0))
| big_p(a)
| ~ big_p(esk1_0)
| big_p(f(esk1_0)) )
& ( ~ big_p(f(f(esk2_0)))
| big_p(a)
| ~ big_p(esk1_0)
| big_p(f(esk1_0)) )
& ( big_p(a)
| ~ big_p(esk2_0)
| ~ big_p(esk1_0)
| big_p(f(esk1_0)) )
& ( big_p(f(esk2_0))
| ~ big_p(esk2_0)
| ~ big_p(esk1_0)
| big_p(f(esk1_0)) )
& ( ~ big_p(f(f(esk2_0)))
| ~ big_p(esk2_0)
| ~ big_p(esk1_0)
| big_p(f(esk1_0)) )
& ( big_p(a)
| ~ big_p(f(f(esk2_0)))
| ~ big_p(esk1_0)
| big_p(f(esk1_0)) )
& ( big_p(f(esk2_0))
| ~ big_p(f(f(esk2_0)))
| ~ big_p(esk1_0)
| big_p(f(esk1_0)) )
& ( ~ big_p(f(f(esk2_0)))
| ~ big_p(f(f(esk2_0)))
| ~ big_p(esk1_0)
| big_p(f(esk1_0)) )
& ( big_p(a)
| big_p(a)
| ~ big_p(f(f(esk1_0))) )
& ( big_p(f(esk2_0))
| big_p(a)
| ~ big_p(f(f(esk1_0))) )
& ( ~ big_p(f(f(esk2_0)))
| big_p(a)
| ~ big_p(f(f(esk1_0))) )
& ( big_p(a)
| ~ big_p(esk2_0)
| ~ big_p(f(f(esk1_0))) )
& ( big_p(f(esk2_0))
| ~ big_p(esk2_0)
| ~ big_p(f(f(esk1_0))) )
& ( ~ big_p(f(f(esk2_0)))
| ~ big_p(esk2_0)
| ~ big_p(f(f(esk1_0))) )
& ( big_p(a)
| ~ big_p(f(f(esk2_0)))
| ~ big_p(f(f(esk1_0))) )
& ( big_p(f(esk2_0))
| ~ big_p(f(f(esk2_0)))
| ~ big_p(f(f(esk1_0))) )
& ( ~ big_p(f(f(esk2_0)))
| ~ big_p(f(f(esk2_0)))
| ~ big_p(f(f(esk1_0))) )
& ( ~ big_p(a)
| big_p(X8)
| big_p(f(f(X8)))
| big_p(X7)
| ~ big_p(a)
| big_p(f(f(X7))) )
& ( ~ big_p(a)
| ~ big_p(f(X8))
| big_p(f(f(X8)))
| big_p(X7)
| ~ big_p(a)
| big_p(f(f(X7))) )
& ( ~ big_p(a)
| big_p(X8)
| big_p(f(f(X8)))
| ~ big_p(f(X7))
| ~ big_p(a)
| big_p(f(f(X7))) )
& ( ~ big_p(a)
| ~ big_p(f(X8))
| big_p(f(f(X8)))
| ~ big_p(f(X7))
| ~ big_p(a)
| big_p(f(f(X7))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[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_p(X1)
| big_p(f(f(X1)))
| big_p(X2)
| big_p(f(f(X2)))
| ~ big_p(a)
| ~ big_p(a) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4,negated_conjecture,
( big_p(a)
| big_p(a)
| big_p(a) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5,negated_conjecture,
( big_p(X2)
| big_p(X1)
| big_p(f(f(X2)))
| big_p(f(f(X1)))
| ~ big_p(a) ),
inference(cn,[status(thm)],[c_0_3]) ).
cnf(c_0_6,negated_conjecture,
big_p(a),
inference(cn,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
( big_p(f(f(X1)))
| big_p(f(f(X2)))
| ~ big_p(a)
| ~ big_p(f(X1))
| ~ big_p(f(X2))
| ~ big_p(a) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_8,negated_conjecture,
( ~ big_p(f(f(esk2_0)))
| ~ big_p(f(f(esk2_0)))
| ~ big_p(f(f(esk1_0))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_9,negated_conjecture,
( big_p(f(f(X1)))
| big_p(f(f(X2)))
| big_p(X1)
| big_p(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_5,c_0_6])]) ).
cnf(c_0_10,negated_conjecture,
( big_p(f(f(X2)))
| big_p(f(f(X1)))
| ~ big_p(a)
| ~ big_p(f(X2))
| ~ big_p(f(X1)) ),
inference(cn,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( ~ big_p(f(f(esk1_0)))
| ~ big_p(f(f(esk2_0))) ),
inference(cn,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( big_p(f(f(X1)))
| big_p(X1) ),
inference(ef,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
( big_p(f(f(X1)))
| big_p(f(f(X2)))
| ~ big_p(f(X2))
| ~ big_p(f(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_6])]) ).
cnf(c_0_14,negated_conjecture,
( big_p(f(esk2_0))
| big_p(f(esk1_0))
| ~ big_p(esk2_0)
| ~ big_p(esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_15,negated_conjecture,
( big_p(f(esk2_0))
| ~ big_p(esk2_0)
| ~ big_p(f(f(esk1_0))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_16,negated_conjecture,
( big_p(esk1_0)
| ~ big_p(f(f(esk2_0))) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( big_p(f(f(X1)))
| big_p(f(esk2_0))
| ~ big_p(f(X1))
| ~ big_p(esk1_0)
| ~ big_p(esk2_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( big_p(esk2_0)
| big_p(esk1_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_12]) ).
cnf(c_0_19,negated_conjecture,
( big_p(f(esk2_0))
| ~ big_p(esk2_0)
| ~ big_p(esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_17]),c_0_14]) ).
cnf(c_0_20,negated_conjecture,
( big_p(f(esk2_0))
| big_p(esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_12]),c_0_18]) ).
cnf(c_0_21,negated_conjecture,
( big_p(f(f(esk2_0)))
| big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_19]),c_0_12]) ).
cnf(c_0_22,negated_conjecture,
( big_p(f(f(esk2_0)))
| big_p(f(f(X1)))
| ~ big_p(f(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_20]),c_0_21]) ).
cnf(c_0_23,negated_conjecture,
( big_p(f(esk1_0))
| ~ big_p(f(f(esk2_0)))
| ~ big_p(f(f(esk2_0)))
| ~ big_p(esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_24,negated_conjecture,
big_p(esk1_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_20]),c_0_16]) ).
cnf(c_0_25,negated_conjecture,
( big_p(f(esk1_0))
| ~ big_p(esk1_0)
| ~ big_p(f(f(esk2_0))) ),
inference(cn,[status(thm)],[c_0_23]) ).
cnf(c_0_26,negated_conjecture,
( big_p(f(esk2_0))
| ~ big_p(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_24])]) ).
cnf(c_0_27,negated_conjecture,
( big_p(f(esk1_0))
| ~ big_p(f(f(esk2_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_24])]) ).
cnf(c_0_28,negated_conjecture,
big_p(f(f(esk2_0))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_26]),c_0_12]) ).
cnf(c_0_29,negated_conjecture,
big_p(f(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_30,negated_conjecture,
~ big_p(f(f(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_28])]) ).
cnf(c_0_31,negated_conjecture,
( big_p(f(f(X1)))
| ~ big_p(f(X1)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_29]),c_0_30]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN084+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 : n001.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 08:13:19 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % 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
%------------------------------------------------------------------------------