%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN070+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 05:36:03 PM UTC 2026
% Result : Theorem 0.28s 1.62s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 15 unt; 0 def)
% Number of atoms : 120 ( 0 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 139 ( 59 ~; 51 |; 19 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 58 ( 18 sgn 16 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel46_3,axiom,
! [X1,X2] :
( ( big_f(X1)
& big_f(X2)
& big_h(X1,X2) )
=> ~ big_j(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel46_3) ).
fof(pel46_2,axiom,
( ? [X1] :
( big_f(X1)
& ~ big_g(X1) )
=> ? [X3] :
( big_f(X3)
& ~ big_g(X3)
& ! [X2] :
( ( big_f(X2)
& ~ big_g(X2) )
=> big_j(X3,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel46_2) ).
fof(pel46,conjecture,
! [X1] :
( big_f(X1)
=> big_g(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel46) ).
fof(pel46_1,axiom,
! [X1,X2] :
( ( big_f(X1)
& ( ( big_f(X2)
& big_h(X2,X1) )
=> big_g(X2) ) )
=> big_g(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel46_1) ).
fof(i_0_4,plain,
! [X1,X2] :
( ( big_f(X1)
& big_f(X2)
& big_h(X1,X2) )
=> ~ big_j(X2,X1) ),
inference(fof_simplification,[status(thm)],[pel46_3]) ).
fof(i_0_5,plain,
( ? [X1] :
( big_f(X1)
& ~ big_g(X1) )
=> ? [X3] :
( big_f(X3)
& ~ big_g(X3)
& ! [X2] :
( ( big_f(X2)
& ~ big_g(X2) )
=> big_j(X3,X2) ) ) ),
inference(fof_simplification,[status(thm)],[pel46_2]) ).
fof(i_0_6,negated_conjecture,
~ ! [X1] :
( big_f(X1)
=> big_g(X1) ),
inference(assume_negation,[status(cth)],[pel46]) ).
fof(i_0_7,plain,
! [X17,X18] :
( ~ big_f(X17)
| ~ big_f(X18)
| ~ big_h(X17,X18)
| ~ big_j(X18,X17) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_4])]) ).
fof(i_0_8,plain,
! [X14,X16] :
( ( big_f(esk1_0)
| ~ big_f(X14)
| big_g(X14) )
& ( ~ big_g(esk1_0)
| ~ big_f(X14)
| big_g(X14) )
& ( ~ big_f(X16)
| big_g(X16)
| big_j(esk1_0,X16)
| ~ big_f(X14)
| big_g(X14) ) ),
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_5])])])])]) ).
fof(i_0_9,plain,
! [X12,X13] :
( ( big_f(X13)
| ~ big_f(X12)
| big_g(X12) )
& ( big_h(X13,X12)
| ~ big_f(X12)
| big_g(X12) )
& ( ~ big_g(X13)
| ~ big_f(X12)
| big_g(X12) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pel46_1])])]) ).
fof(i_0_10,negated_conjecture,
( big_f(esk2_0)
& ~ big_g(esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6])])]) ).
cnf(i_0_11,plain,
( ~ big_f(X1)
| ~ big_f(X2)
| ~ big_h(X1,X2)
| ~ big_j(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7]),
[final] ).
cnf(i_0_12,plain,
( big_g(X1)
| big_j(esk1_0,X1)
| big_g(X2)
| ~ big_f(X1)
| ~ big_f(X2) ),
inference(split_conjunct,[status(thm)],[i_0_8]),
[final] ).
cnf(i_0_13,plain,
( big_h(X1,X2)
| big_g(X2)
| ~ big_f(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_14,plain,
( big_g(X2)
| ~ big_g(X1)
| ~ big_f(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_15,plain,
( big_g(X1)
| ~ big_g(esk1_0)
| ~ big_f(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8]),
[final] ).
cnf(i_0_16,plain,
( big_f(X1)
| big_g(X2)
| ~ big_f(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_17,plain,
( big_f(esk1_0)
| big_g(X1)
| ~ big_f(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8]),
[final] ).
cnf(i_0_18,negated_conjecture,
~ big_g(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_19,negated_conjecture,
big_f(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_20,plain,
big_h(X1,esk2_0),
inference(scs_inference,[],[i_0_18,i_0_19,i_0_13]) ).
cnf(i_0_21,plain,
( big_g(X1)
| ~ big_f(X1)
| big_h(X2,X1) ),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_22,plain,
~ big_g(X1),
inference(scs_inference,[],[i_0_18,i_0_19,i_0_13,i_0_14]) ).
cnf(i_0_23,plain,
( ~ big_f(X1)
| big_g(X1)
| ~ big_g(X2) ),
inference(rename_variables,[],[i_0_14]) ).
cnf(i_0_24,plain,
big_f(X1),
inference(scs_inference,[],[i_0_18,i_0_19,i_0_13,i_0_14,i_0_16]) ).
cnf(i_0_25,plain,
( ~ big_f(X1)
| big_f(X2)
| big_g(X1) ),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_26,plain,
~ big_j(esk2_0,esk2_0),
inference(scs_inference,[],[i_0_18,i_0_19,i_0_13,i_0_14,i_0_16,i_0_11]) ).
cnf(i_0_27,plain,
( ~ big_h(X1,X2)
| ~ big_j(X2,X1)
| ~ big_f(X1)
| ~ big_f(X2) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_28,plain,
big_h(X1,X2),
inference(scs_inference,[],[i_0_22,i_0_24,i_0_13]) ).
cnf(i_0_29,plain,
~ big_g(X1),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_30,plain,
( big_g(X1)
| ~ big_f(X1)
| big_h(X2,X1) ),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_31,plain,
~ big_j(esk2_0,esk2_0),
inference(scs_inference,[],[i_0_20,i_0_22,i_0_24,i_0_13,i_0_11]) ).
cnf(i_0_32,plain,
big_h(X1,esk2_0),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_33,plain,
big_f(X1),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_34,plain,
big_f(X1),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_35,plain,
( ~ big_h(X1,X2)
| ~ big_j(X2,X1)
| ~ big_f(X1)
| ~ big_f(X2) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_36,plain,
~ big_j(X1,X1),
inference(scs_inference,[],[i_0_28,i_0_24,i_0_11]) ).
cnf(i_0_37,plain,
big_h(X1,X2),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_38,plain,
( ~ big_h(X1,X2)
| ~ big_j(X2,X1)
| ~ big_f(X1)
| ~ big_f(X2) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_39,plain,
$false,
inference(scs_inference,[],[i_0_22,i_0_28,i_0_24,i_0_11,i_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN070+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 : n007.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 08:09:54 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.28/1.62 % Version : CSE_E---1.7
% 0.28/1.62 % Problem : theBenchmark.p
% 0.28/1.62 % SZS status Theorem for theBenchmark.p
% 0.28/1.62 % SZS output start CNFRefutation
% See solution above
% 0.28/1.65 % Total time : 1.275s
%------------------------------------------------------------------------------