%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN063+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 : n007.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 05:35:58 PM UTC 2026
% Result : Theorem 0.27s 1.62s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 57 ( 3 unt; 0 def)
% Number of atoms : 303 ( 0 equ)
% Maximal formula atoms : 114 ( 5 avg)
% Number of connectives : 394 ( 148 ~; 206 |; 34 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 14 ( 8 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel33,conjecture,
( ! [X1] :
( ( big_p(a)
& ( big_p(X1)
=> big_p(b) ) )
=> big_p(c) )
<=> ! [X2] :
( ( ~ big_p(a)
| big_p(X2)
| big_p(c) )
& ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel33) ).
fof(i_0_1,negated_conjecture,
~ ( ! [X1] :
( ( big_p(a)
& ( big_p(X1)
=> big_p(b) ) )
=> big_p(c) )
<=> ! [X2] :
( ( ~ big_p(a)
| big_p(X2)
| big_p(c) )
& ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[pel33])]) ).
fof(i_0_2,negated_conjecture,
! [X7,X8] :
( ( big_p(a)
| big_p(a)
| big_p(a) )
& ( big_p(b)
| big_p(a)
| big_p(a) )
& ( ~ big_p(c)
| big_p(a)
| big_p(a) )
& ( big_p(a)
| ~ big_p(esk2_0)
| big_p(a) )
& ( big_p(b)
| ~ big_p(esk2_0)
| big_p(a) )
& ( ~ big_p(c)
| ~ big_p(esk2_0)
| big_p(a) )
& ( big_p(a)
| ~ big_p(c)
| big_p(a) )
& ( big_p(b)
| ~ big_p(c)
| big_p(a) )
& ( ~ big_p(c)
| ~ big_p(c)
| big_p(a) )
& ( big_p(a)
| big_p(a)
| ~ big_p(esk1_0)
| big_p(b) )
& ( big_p(b)
| big_p(a)
| ~ big_p(esk1_0)
| big_p(b) )
& ( ~ big_p(c)
| big_p(a)
| ~ big_p(esk1_0)
| big_p(b) )
& ( big_p(a)
| ~ big_p(esk2_0)
| ~ big_p(esk1_0)
| big_p(b) )
& ( big_p(b)
| ~ big_p(esk2_0)
| ~ big_p(esk1_0)
| big_p(b) )
& ( ~ big_p(c)
| ~ big_p(esk2_0)
| ~ big_p(esk1_0)
| big_p(b) )
& ( big_p(a)
| ~ big_p(c)
| ~ big_p(esk1_0)
| big_p(b) )
& ( big_p(b)
| ~ big_p(c)
| ~ big_p(esk1_0)
| big_p(b) )
& ( ~ big_p(c)
| ~ big_p(c)
| ~ big_p(esk1_0)
| big_p(b) )
& ( big_p(a)
| big_p(a)
| ~ big_p(c) )
& ( big_p(b)
| big_p(a)
| ~ big_p(c) )
& ( ~ big_p(c)
| big_p(a)
| ~ big_p(c) )
& ( big_p(a)
| ~ big_p(esk2_0)
| ~ big_p(c) )
& ( big_p(b)
| ~ big_p(esk2_0)
| ~ big_p(c) )
& ( ~ big_p(c)
| ~ big_p(esk2_0)
| ~ big_p(c) )
& ( big_p(a)
| ~ big_p(c)
| ~ big_p(c) )
& ( big_p(b)
| ~ big_p(c)
| ~ big_p(c) )
& ( ~ big_p(c)
| ~ big_p(c)
| ~ big_p(c) )
& ( ~ big_p(a)
| big_p(X8)
| big_p(c)
| big_p(X7)
| ~ big_p(a)
| big_p(c) )
& ( ~ big_p(a)
| ~ big_p(b)
| big_p(c)
| big_p(X7)
| ~ big_p(a)
| big_p(c) )
& ( ~ big_p(a)
| big_p(X8)
| big_p(c)
| ~ big_p(b)
| ~ big_p(a)
| big_p(c) )
& ( ~ big_p(a)
| ~ big_p(b)
| big_p(c)
| ~ big_p(b)
| ~ big_p(a)
| big_p(c) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[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_p(c)
| big_p(X1)
| big_p(c)
| ~ big_p(a)
| ~ big_p(b)
| ~ big_p(a) ),
inference(split_conjunct,[status(thm)],[i_0_2]) ).
cnf(i_0_4,negated_conjecture,
( big_p(X1)
| big_p(c)
| big_p(c)
| ~ big_p(a)
| ~ big_p(b)
| ~ big_p(a) ),
inference(split_conjunct,[status(thm)],[i_0_2]) ).
cnf(i_0_5,negated_conjecture,
( big_p(X1)
| big_p(c)
| big_p(X2)
| big_p(c)
| ~ big_p(a)
| ~ big_p(a) ),
inference(split_conjunct,[status(thm)],[i_0_2]) ).
cnf(i_0_6,negated_conjecture,
( big_p(c)
| big_p(c)
| ~ big_p(a)
| ~ big_p(b)
| ~ big_p(b)
| ~ big_p(a) ),
inference(split_conjunct,[status(thm)],[i_0_2]) ).
cnf(i_0_7,negated_conjecture,
( big_p(b)
| big_p(b)
| ~ big_p(esk2_0)
| ~ big_p(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]) ).
cnf(i_0_8,negated_conjecture,
( big_p(b)
| big_p(b)
| ~ big_p(c)
| ~ big_p(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]) ).
cnf(i_0_9,negated_conjecture,
( big_p(b)
| ~ big_p(c)
| ~ big_p(c)
| ~ big_p(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]) ).
cnf(i_0_10,negated_conjecture,
( big_p(a)
| big_p(a)
| big_p(b)
| ~ big_p(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]) ).
cnf(i_0_11,negated_conjecture,
( big_p(b)
| big_p(a)
| big_p(b)
| ~ big_p(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]) ).
cnf(i_0_12,negated_conjecture,
( ~ big_p(c)
| ~ big_p(esk2_0)
| ~ big_p(c) ),
inference(split_conjunct,[status(thm)],[i_0_2]) ).
cnf(i_0_13,negated_conjecture,
( big_p(b)
| ~ big_p(c)
| ~ big_p(c) ),
inference(split_conjunct,[status(thm)],[i_0_2]) ).
cnf(i_0_14,negated_conjecture,
( big_p(a)
| big_p(a)
| ~ big_p(esk2_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]) ).
cnf(i_0_15,negated_conjecture,
( big_p(a)
| big_p(a)
| ~ big_p(c) ),
inference(split_conjunct,[status(thm)],[i_0_2]) ).
cnf(i_0_16,negated_conjecture,
( big_p(a)
| big_p(a)
| ~ big_p(c) ),
inference(split_conjunct,[status(thm)],[i_0_2]) ).
cnf(i_0_17,negated_conjecture,
( big_p(a)
| ~ big_p(c)
| ~ big_p(c) ),
inference(split_conjunct,[status(thm)],[i_0_2]) ).
cnf(i_0_18,negated_conjecture,
( big_p(a)
| big_p(a)
| ~ big_p(c) ),
inference(split_conjunct,[status(thm)],[i_0_2]) ).
cnf(i_0_19,negated_conjecture,
( big_p(a)
| ~ big_p(c)
| ~ big_p(c) ),
inference(split_conjunct,[status(thm)],[i_0_2]) ).
cnf(i_0_20,negated_conjecture,
( big_p(a)
| ~ big_p(c)
| ~ big_p(c) ),
inference(split_conjunct,[status(thm)],[i_0_2]) ).
cnf(i_0_21,negated_conjecture,
( big_p(b)
| big_p(a)
| big_p(a) ),
inference(split_conjunct,[status(thm)],[i_0_2]) ).
cnf(i_0_22,negated_conjecture,
( ~ big_p(c)
| ~ big_p(c)
| ~ big_p(c) ),
inference(split_conjunct,[status(thm)],[i_0_2]) ).
cnf(i_0_23,negated_conjecture,
( big_p(a)
| big_p(a)
| big_p(a) ),
inference(split_conjunct,[status(thm)],[i_0_2]) ).
cnf(i_0_24,negated_conjecture,
( big_p(b)
| ~ big_p(c)
| ~ big_p(esk2_0)
| ~ big_p(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_25,negated_conjecture,
( big_p(X1)
| big_p(c)
| ~ big_p(a)
| ~ big_p(b) ),
inference(cn,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_26,negated_conjecture,
( big_p(X1)
| big_p(c)
| ~ big_p(a)
| ~ big_p(b) ),
inference(cn,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_27,negated_conjecture,
( big_p(X2)
| big_p(X1)
| big_p(c)
| ~ big_p(a) ),
inference(cn,[status(thm)],[i_0_5]),
[final] ).
cnf(i_0_28,negated_conjecture,
( big_p(a)
| big_p(b)
| ~ big_p(esk2_0)
| ~ big_p(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_29,negated_conjecture,
( big_p(a)
| big_p(b)
| ~ big_p(c)
| ~ big_p(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_30,negated_conjecture,
( big_p(a)
| big_p(b)
| ~ big_p(c)
| ~ big_p(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_31,negated_conjecture,
( big_p(c)
| ~ big_p(a)
| ~ big_p(b) ),
inference(cn,[status(thm)],[i_0_6]),
[final] ).
cnf(i_0_32,negated_conjecture,
( big_p(b)
| ~ big_p(esk1_0)
| ~ big_p(esk2_0) ),
inference(cn,[status(thm)],[i_0_7]),
[final] ).
cnf(i_0_33,negated_conjecture,
( big_p(b)
| ~ big_p(esk2_0)
| ~ big_p(c) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_34,negated_conjecture,
( big_p(b)
| ~ big_p(c)
| ~ big_p(esk1_0) ),
inference(cn,[status(thm)],[i_0_8]),
[final] ).
cnf(i_0_35,negated_conjecture,
( big_p(b)
| ~ big_p(c)
| ~ big_p(esk1_0) ),
inference(cn,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_36,negated_conjecture,
( big_p(a)
| ~ big_p(c)
| ~ big_p(esk2_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_37,negated_conjecture,
( big_p(a)
| ~ big_p(esk2_0)
| ~ big_p(c) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_38,negated_conjecture,
( big_p(b)
| big_p(a)
| ~ big_p(esk2_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_39,negated_conjecture,
( big_p(a)
| big_p(b)
| ~ big_p(esk1_0) ),
inference(cn,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_40,negated_conjecture,
( big_p(a)
| big_p(b)
| ~ big_p(esk1_0) ),
inference(cn,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_41,negated_conjecture,
( big_p(b)
| big_p(a)
| ~ big_p(c) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_42,negated_conjecture,
( big_p(b)
| big_p(a)
| ~ big_p(c) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_43,negated_conjecture,
( ~ big_p(c)
| ~ big_p(esk2_0) ),
inference(cn,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_44,negated_conjecture,
( big_p(b)
| ~ big_p(c) ),
inference(cn,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_45,negated_conjecture,
( big_p(a)
| ~ big_p(esk2_0) ),
inference(cn,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_46,negated_conjecture,
( big_p(a)
| ~ big_p(c) ),
inference(cn,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_47,negated_conjecture,
( big_p(a)
| ~ big_p(c) ),
inference(cn,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_48,negated_conjecture,
( big_p(a)
| ~ big_p(c) ),
inference(cn,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_49,negated_conjecture,
( big_p(a)
| ~ big_p(c) ),
inference(cn,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_50,negated_conjecture,
( big_p(a)
| ~ big_p(c) ),
inference(cn,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_51,negated_conjecture,
( big_p(a)
| ~ big_p(c) ),
inference(cn,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_52,negated_conjecture,
( big_p(a)
| big_p(b) ),
inference(cn,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_53,negated_conjecture,
~ big_p(c),
inference(cn,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_54,negated_conjecture,
big_p(a),
inference(cn,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_55,plain,
( big_p(c)
| ~ big_p(a) ),
nference(factoring_inference,[],[27]) ).
cnf(i_0_56,plain,
$false,
inference(scs_inference,[],[i_0_53,i_0_54,i_0_55]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN063+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
% 0.14/0.33 % Computer : n007.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 08:09:09 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % 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
% 0.27/1.63 % Total time : 1.271s
%------------------------------------------------------------------------------