%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN059+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 : n012.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 05:35:57 PM UTC 2026
% Result : Theorem 1.11s 1.62s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 3
% Syntax : Number of formulae : 69 ( 16 unt; 0 def)
% Number of atoms : 252 ( 0 equ)
% Maximal formula atoms : 60 ( 3 avg)
% Number of connectives : 284 ( 101 ~; 154 |; 21 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 49 ( 18 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel29,conjecture,
( ( ! [X1] :
( big_f(X1)
=> big_h(X1) )
& ! [X3] :
( big_g(X3)
=> big_j(X3) ) )
<=> ! [X4,X2] :
( ( big_f(X4)
& big_g(X2) )
=> ( big_h(X4)
& big_j(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel29) ).
fof(pel29_2,axiom,
? [X2] : big_g(X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel29_2) ).
fof(pel29_1,axiom,
? [X1] : big_f(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel29_1) ).
fof(c_0_3,negated_conjecture,
~ ( ( ! [X1] :
( big_f(X1)
=> big_h(X1) )
& ! [X3] :
( big_g(X3)
=> big_j(X3) ) )
<=> ! [X4,X2] :
( ( big_f(X4)
& big_g(X2) )
=> ( big_h(X4)
& big_j(X2) ) ) ),
inference(assume_negation,[status(cth)],[pel29]) ).
fof(c_0_4,negated_conjecture,
! [X17,X18,X19,X20] :
( ( big_f(esk5_0)
| big_g(esk4_0)
| big_f(esk3_0) )
& ( big_g(esk6_0)
| big_g(esk4_0)
| big_f(esk3_0) )
& ( ~ big_h(esk5_0)
| ~ big_j(esk6_0)
| big_g(esk4_0)
| big_f(esk3_0) )
& ( big_f(esk5_0)
| ~ big_j(esk4_0)
| big_f(esk3_0) )
& ( big_g(esk6_0)
| ~ big_j(esk4_0)
| big_f(esk3_0) )
& ( ~ big_h(esk5_0)
| ~ big_j(esk6_0)
| ~ big_j(esk4_0)
| big_f(esk3_0) )
& ( big_f(esk5_0)
| big_g(esk4_0)
| ~ big_h(esk3_0) )
& ( big_g(esk6_0)
| big_g(esk4_0)
| ~ big_h(esk3_0) )
& ( ~ big_h(esk5_0)
| ~ big_j(esk6_0)
| big_g(esk4_0)
| ~ big_h(esk3_0) )
& ( big_f(esk5_0)
| ~ big_j(esk4_0)
| ~ big_h(esk3_0) )
& ( big_g(esk6_0)
| ~ big_j(esk4_0)
| ~ big_h(esk3_0) )
& ( ~ big_h(esk5_0)
| ~ big_j(esk6_0)
| ~ big_j(esk4_0)
| ~ big_h(esk3_0) )
& ( big_h(X19)
| ~ big_f(X19)
| ~ big_g(X20)
| ~ big_f(X17)
| big_h(X17) )
& ( big_j(X20)
| ~ big_f(X19)
| ~ big_g(X20)
| ~ big_f(X17)
| big_h(X17) )
& ( big_h(X19)
| ~ big_f(X19)
| ~ big_g(X20)
| ~ big_g(X18)
| big_j(X18) )
& ( big_j(X20)
| ~ big_f(X19)
| ~ big_g(X20)
| ~ big_g(X18)
| big_j(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])])])])]) ).
cnf(c_0_5,negated_conjecture,
( big_j(X1)
| big_j(X3)
| ~ big_f(X2)
| ~ big_g(X1)
| ~ big_g(X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_6,negated_conjecture,
( big_f(esk5_0)
| big_g(esk4_0)
| big_f(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
( big_f(esk5_0)
| big_f(esk3_0)
| ~ big_j(esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
( big_g(esk6_0)
| big_g(esk4_0)
| big_f(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_9,plain,
big_g(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[pel29_2])]) ).
cnf(c_0_10,negated_conjecture,
( big_j(X1)
| big_f(esk5_0)
| big_f(esk3_0)
| ~ big_g(X1)
| ~ big_f(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7]) ).
fof(c_0_11,plain,
big_f(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[pel29_1])]) ).
cnf(c_0_12,negated_conjecture,
( big_j(esk6_0)
| big_j(X1)
| big_g(esk4_0)
| big_f(esk3_0)
| ~ big_g(X1)
| ~ big_f(X2) ),
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( big_h(X1)
| big_h(X3)
| ~ big_f(X1)
| ~ big_g(X2)
| ~ big_f(X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_14,plain,
big_g(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( big_f(esk3_0)
| big_f(esk5_0)
| ~ big_f(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_6]),c_0_7]) ).
cnf(c_0_16,plain,
big_f(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
( big_j(esk6_0)
| big_g(esk4_0)
| big_f(esk3_0)
| ~ big_f(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_8]) ).
cnf(c_0_18,negated_conjecture,
( big_h(X1)
| big_h(X2)
| ~ big_f(X2)
| ~ big_f(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( big_f(esk5_0)
| big_f(esk3_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( big_g(esk4_0)
| big_f(esk3_0)
| ~ big_h(esk5_0)
| ~ big_j(esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_21,negated_conjecture,
( big_j(esk6_0)
| big_g(esk4_0)
| big_f(esk3_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( big_h(esk5_0)
| big_h(X1)
| big_f(esk3_0)
| ~ big_f(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( big_g(esk4_0)
| big_f(esk3_0)
| ~ big_h(esk5_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
( big_h(esk5_0)
| big_f(esk3_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_25,negated_conjecture,
( big_g(esk4_0)
| big_f(esk3_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,negated_conjecture,
( big_j(esk4_0)
| big_j(X1)
| big_f(esk3_0)
| ~ big_g(X1)
| ~ big_f(X2) ),
inference(spm,[status(thm)],[c_0_5,c_0_25]) ).
cnf(c_0_27,negated_conjecture,
( big_j(esk4_0)
| big_f(esk3_0)
| ~ big_f(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( big_g(esk6_0)
| big_f(esk3_0)
| ~ big_j(esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_29,negated_conjecture,
( big_j(esk4_0)
| big_f(esk3_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_19]) ).
cnf(c_0_30,negated_conjecture,
( big_g(esk6_0)
| big_f(esk3_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
( big_j(esk6_0)
| big_j(X1)
| big_f(esk3_0)
| ~ big_g(X1)
| ~ big_f(X2) ),
inference(spm,[status(thm)],[c_0_5,c_0_30]) ).
cnf(c_0_32,negated_conjecture,
( big_f(esk3_0)
| ~ big_h(esk5_0)
| ~ big_j(esk6_0)
| ~ big_j(esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_33,negated_conjecture,
( big_j(esk6_0)
| big_f(esk3_0)
| ~ big_f(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( big_f(esk3_0)
| ~ big_j(esk4_0)
| ~ big_j(esk6_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_24]) ).
cnf(c_0_35,negated_conjecture,
( big_j(esk6_0)
| big_f(esk3_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_19]) ).
cnf(c_0_36,negated_conjecture,
big_f(esk3_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_29]) ).
cnf(c_0_37,negated_conjecture,
( big_h(esk3_0)
| big_h(X1)
| ~ big_f(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_36]) ).
cnf(c_0_38,negated_conjecture,
( big_f(esk5_0)
| big_g(esk4_0)
| ~ big_h(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_39,negated_conjecture,
big_h(esk3_0),
inference(spm,[status(thm)],[c_0_37,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( big_f(esk5_0)
| ~ big_j(esk4_0)
| ~ big_h(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_41,negated_conjecture,
( big_g(esk4_0)
| big_f(esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).
cnf(c_0_42,negated_conjecture,
( big_f(esk5_0)
| ~ big_j(esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_39])]) ).
cnf(c_0_43,negated_conjecture,
( big_j(X1)
| big_f(esk5_0)
| ~ big_g(X1)
| ~ big_f(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_41]),c_0_42]) ).
cnf(c_0_44,negated_conjecture,
( big_g(esk6_0)
| big_g(esk4_0)
| ~ big_h(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_45,negated_conjecture,
( big_f(esk5_0)
| ~ big_f(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_41]),c_0_42]) ).
cnf(c_0_46,negated_conjecture,
( big_g(esk6_0)
| big_g(esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_39])]) ).
cnf(c_0_47,negated_conjecture,
big_f(esk5_0),
inference(spm,[status(thm)],[c_0_45,c_0_36]) ).
cnf(c_0_48,negated_conjecture,
( big_j(esk6_0)
| big_j(X1)
| big_g(esk4_0)
| ~ big_g(X1)
| ~ big_f(X2) ),
inference(spm,[status(thm)],[c_0_5,c_0_46]) ).
cnf(c_0_49,negated_conjecture,
( big_g(esk4_0)
| ~ big_h(esk5_0)
| ~ big_j(esk6_0)
| ~ big_h(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_50,negated_conjecture,
( big_h(esk5_0)
| big_h(X1)
| ~ big_f(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_47]) ).
cnf(c_0_51,negated_conjecture,
( big_j(esk6_0)
| big_g(esk4_0)
| ~ big_f(X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_46]) ).
cnf(c_0_52,negated_conjecture,
( big_g(esk4_0)
| ~ big_j(esk6_0)
| ~ big_h(esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_39])]) ).
cnf(c_0_53,negated_conjecture,
big_h(esk5_0),
inference(spm,[status(thm)],[c_0_50,c_0_47]) ).
cnf(c_0_54,negated_conjecture,
( big_j(esk6_0)
| big_g(esk4_0) ),
inference(spm,[status(thm)],[c_0_51,c_0_36]) ).
cnf(c_0_55,negated_conjecture,
big_g(esk4_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53])]),c_0_54]) ).
cnf(c_0_56,negated_conjecture,
( big_j(esk4_0)
| big_j(X1)
| ~ big_g(X1)
| ~ big_f(X2) ),
inference(spm,[status(thm)],[c_0_5,c_0_55]) ).
cnf(c_0_57,negated_conjecture,
( ~ big_h(esk5_0)
| ~ big_j(esk6_0)
| ~ big_j(esk4_0)
| ~ big_h(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_58,negated_conjecture,
( big_g(esk6_0)
| ~ big_j(esk4_0)
| ~ big_h(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_59,negated_conjecture,
( big_j(esk4_0)
| ~ big_f(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_55]) ).
cnf(c_0_60,negated_conjecture,
( ~ big_j(esk4_0)
| ~ big_j(esk6_0)
| ~ big_h(esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_39])]) ).
cnf(c_0_61,negated_conjecture,
( big_g(esk6_0)
| ~ big_j(esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_39])]) ).
cnf(c_0_62,negated_conjecture,
big_j(esk4_0),
inference(spm,[status(thm)],[c_0_59,c_0_47]) ).
cnf(c_0_63,negated_conjecture,
( ~ big_j(esk4_0)
| ~ big_j(esk6_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_53])]) ).
cnf(c_0_64,negated_conjecture,
big_g(esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62])]) ).
cnf(c_0_65,negated_conjecture,
~ big_j(esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_62])]) ).
cnf(c_0_66,negated_conjecture,
( big_j(X1)
| ~ big_g(X1)
| ~ big_f(X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_64]),c_0_65]) ).
cnf(c_0_67,negated_conjecture,
~ big_f(X1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_64]),c_0_65]) ).
cnf(c_0_68,plain,
$false,
inference(sr,[status(thm)],[c_0_16,c_0_67]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SYN059+1 : TPTP v9.2.1. Released v2.0.0.
% 0.00/0.07 % 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
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue May 5 08:08:45 EDT 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 1.11/1.62 % Version : CSE_E---1.7
% 1.11/1.62 % Problem : theBenchmark.p
% 1.11/1.62 % SZS status Theorem for theBenchmark.p
% 1.11/1.62 % SZS output start CNFRefutation
% See solution above
% 1.11/1.62 % Total time : 1.361s
%------------------------------------------------------------------------------