%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN069+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 : n017.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 05:36:02 PM UTC 2026
% Result : Theorem 1.24s 1.71s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 5 unt; 0 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 102 ( 37 ~; 38 |; 23 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 34 ( 7 sgn 13 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel45_1,axiom,
! [X1] :
( ( big_f(X1)
& ! [X2] :
( ( big_g(X2)
& big_h(X1,X2) )
=> big_j(X1,X2) ) )
=> ! [X3] :
( big_g(X3)
& big_h(X1,X3)
& big_k(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel45_1) ).
fof(pel45_3,axiom,
? [X1] :
( big_f(X1)
& ! [X2] :
( big_h(X1,X2)
=> big_l(X2) )
& ! [X3] :
( ( big_g(X3)
& big_h(X1,X3) )
=> big_j(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel45_3) ).
fof(pel45_2,axiom,
~ ? [X2] :
( big_l(X2)
& big_k(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel45_2) ).
fof(pel45,conjecture,
? [X1] :
( big_f(X1)
& ~ ? [X2] :
( big_g(X2)
& big_h(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel45) ).
fof(c_0_4,plain,
! [X13,X15,X16,X17] :
( ( big_g(X15)
| big_g(esk1_1(X13))
| ~ big_f(X13) )
& ( big_h(X13,X16)
| big_g(esk1_1(X13))
| ~ big_f(X13) )
& ( big_k(X17)
| big_g(esk1_1(X13))
| ~ big_f(X13) )
& ( big_g(X15)
| big_h(X13,esk1_1(X13))
| ~ big_f(X13) )
& ( big_h(X13,X16)
| big_h(X13,esk1_1(X13))
| ~ big_f(X13) )
& ( big_k(X17)
| big_h(X13,esk1_1(X13))
| ~ big_f(X13) )
& ( big_g(X15)
| ~ big_j(X13,esk1_1(X13))
| ~ big_f(X13) )
& ( big_h(X13,X16)
| ~ big_j(X13,esk1_1(X13))
| ~ big_f(X13) )
& ( big_k(X17)
| ~ big_j(X13,esk1_1(X13))
| ~ big_f(X13) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[pel45_1])])])])])]) ).
fof(c_0_5,plain,
! [X20,X21] :
( big_f(esk2_0)
& ( ~ big_h(esk2_0,X20)
| big_l(X20) )
& ( ~ big_g(X21)
| ~ big_h(esk2_0,X21)
| big_j(esk2_0,X21) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pel45_3])])])]) ).
cnf(c_0_6,plain,
( big_g(X1)
| big_g(esk1_1(X2))
| ~ big_f(X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
big_f(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( big_g(esk1_1(esk2_0))
| big_g(X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
fof(c_0_9,plain,
! [X18] :
( ~ big_l(X18)
| ~ big_k(X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pel45_2])]) ).
cnf(c_0_10,plain,
( big_k(X1)
| ~ big_j(X2,esk1_1(X2))
| ~ big_f(X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,plain,
( big_j(esk2_0,X1)
| ~ big_g(X1)
| ~ big_h(esk2_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,plain,
big_g(esk1_1(esk2_0)),
inference(ef,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( ~ big_l(X1)
| ~ big_k(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( big_l(X1)
| ~ big_h(esk2_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,plain,
( big_k(X1)
| big_h(X2,esk1_1(X2))
| ~ big_f(X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_16,plain,
( big_k(X1)
| ~ big_h(esk2_0,esk1_1(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_7]),c_0_12])]) ).
fof(c_0_17,negated_conjecture,
~ ? [X1] :
( big_f(X1)
& ~ ? [X2] :
( big_g(X2)
& big_h(X1,X2) ) ),
inference(assume_negation,[status(cth)],[pel45]) ).
cnf(c_0_18,plain,
( ~ big_k(X1)
| ~ big_h(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
big_k(X1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_7]),c_0_16]) ).
fof(c_0_20,negated_conjecture,
! [X22] :
( ( big_g(esk3_1(X22))
| ~ big_f(X22) )
& ( big_h(X22,esk3_1(X22))
| ~ big_f(X22) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
cnf(c_0_21,plain,
~ big_h(esk2_0,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]) ).
cnf(c_0_22,negated_conjecture,
( big_h(X1,esk3_1(X1))
| ~ big_f(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_7])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN069+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
% 0.14/0.33 % Computer : n017.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 08:09:27 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.24/1.71 % Version : CSE_E---1.7
% 1.24/1.71 % Problem : theBenchmark.p
% 1.24/1.71 % SZS status Theorem for theBenchmark.p
% 1.24/1.71 % SZS output start CNFRefutation
% See solution above
% 1.24/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------