%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN056+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 : n029.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 05:35:56 PM UTC 2026
% Result : Theorem 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 6 unt; 0 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 88 ( 36 ~; 36 |; 7 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 28 ( 5 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel26,conjecture,
( ! [X1] :
( big_p(X1)
=> big_r(X1) )
<=> ! [X2] :
( big_q(X2)
=> big_s(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel26) ).
fof(pel26_1,axiom,
( ? [X1] : big_p(X1)
<=> ? [X2] : big_q(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel26_1) ).
fof(pel26_2,axiom,
! [X1,X2] :
( ( big_p(X1)
& big_q(X2) )
=> ( big_r(X1)
<=> big_s(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel26_2) ).
fof(c_0_3,negated_conjecture,
~ ( ! [X1] :
( big_p(X1)
=> big_r(X1) )
<=> ! [X2] :
( big_q(X2)
=> big_s(X2) ) ),
inference(assume_negation,[status(cth)],[pel26]) ).
fof(c_0_4,plain,
! [X9,X11] :
( ( ~ big_p(X9)
| big_q(esk1_0) )
& ( ~ big_q(X11)
| big_p(esk2_0) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pel26_1])])])]) ).
fof(c_0_5,negated_conjecture,
! [X17,X18] :
( ( big_q(esk4_0)
| big_p(esk3_0) )
& ( ~ big_s(esk4_0)
| big_p(esk3_0) )
& ( big_q(esk4_0)
| ~ big_r(esk3_0) )
& ( ~ big_s(esk4_0)
| ~ big_r(esk3_0) )
& ( ~ big_p(X17)
| big_r(X17)
| ~ big_q(X18)
| big_s(X18) ) ),
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_3])])])])]) ).
fof(c_0_6,plain,
! [X13,X14] :
( ( ~ big_r(X13)
| big_s(X14)
| ~ big_p(X13)
| ~ big_q(X14) )
& ( ~ big_s(X14)
| big_r(X13)
| ~ big_p(X13)
| ~ big_q(X14) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pel26_2])])]) ).
cnf(c_0_7,plain,
( big_p(esk2_0)
| ~ big_q(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
( big_q(esk4_0)
| big_p(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( big_r(X2)
| ~ big_s(X1)
| ~ big_p(X2)
| ~ big_q(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( big_r(X1)
| big_s(X2)
| ~ big_p(X1)
| ~ big_q(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
( big_q(esk1_0)
| ~ big_p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_12,negated_conjecture,
( big_p(esk3_0)
| big_p(esk2_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_13,plain,
( big_r(X1)
| ~ big_q(X2)
| ~ big_p(X1) ),
inference(csr,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
big_q(esk1_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_11]) ).
cnf(c_0_15,plain,
( big_s(X2)
| ~ big_r(X1)
| ~ big_p(X1)
| ~ big_q(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,negated_conjecture,
( big_q(esk4_0)
| ~ big_r(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,negated_conjecture,
( big_r(X1)
| ~ big_p(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( ~ big_s(esk4_0)
| ~ big_r(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_19,negated_conjecture,
( big_p(esk3_0)
| ~ big_s(esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_20,plain,
( big_s(X1)
| ~ big_q(X1)
| ~ big_p(X2) ),
inference(csr,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_21,negated_conjecture,
big_q(esk4_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_8]) ).
cnf(c_0_22,negated_conjecture,
~ big_s(esk4_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_17]),c_0_19]) ).
cnf(c_0_23,negated_conjecture,
big_p(esk2_0),
inference(spm,[status(thm)],[c_0_7,c_0_14]) ).
cnf(c_0_24,negated_conjecture,
~ big_p(X1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_23,c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN056+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
% 0.15/0.33 % Computer : n029.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 08:08:14 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Theorem for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.373s
%------------------------------------------------------------------------------