%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET627+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : n014.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 05:08:10 PM UTC 2026
% Result : Theorem 0.26s 1.62s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 12 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 63 ( 32 ~; 20 |; 5 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 4 sgn 29 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(disjoint_defn,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
fof(empty_defn,axiom,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(prove_th104,conjecture,
! [X1] : disjoint(X1,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th104) ).
fof(intersect_defn,axiom,
! [X1,X2] :
( intersect(X1,X2)
<=> ? [X3] :
( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
fof(symmetry_of_intersect,axiom,
! [X1,X2] :
( intersect(X1,X2)
=> intersect(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_intersect) ).
fof(i_0_6,plain,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
inference(fof_simplification,[status(thm)],[disjoint_defn]) ).
fof(i_0_7,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[empty_defn]) ).
fof(i_0_8,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(i_0_9,negated_conjecture,
~ ! [X1] : disjoint(X1,empty_set),
inference(assume_negation,[status(cth)],[prove_th104]) ).
fof(i_0_10,plain,
! [X16,X17,X19,X20,X21] :
( ( member(esk1_2(X16,X17),X16)
| ~ intersect(X16,X17) )
& ( member(esk1_2(X16,X17),X17)
| ~ intersect(X16,X17) )
& ( ~ member(X21,X19)
| ~ member(X21,X20)
| intersect(X19,X20) ) ),
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)],[intersect_defn])])])])])]) ).
fof(i_0_11,plain,
! [X22,X23] :
( ( ~ disjoint(X22,X23)
| ~ intersect(X22,X23) )
& ( intersect(X22,X23)
| disjoint(X22,X23) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6])]) ).
fof(i_0_12,plain,
! [X24,X25] :
( ~ intersect(X24,X25)
| intersect(X25,X24) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_of_intersect])]) ).
fof(i_0_13,plain,
! [X26,X27,X28] :
( ( ~ empty(X26)
| ~ member(X27,X26) )
& ( member(esk2_1(X28),X28)
| empty(X28) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_7])])])])]) ).
fof(i_0_14,plain,
! [X15] : ~ member(X15,empty_set),
inference(variable_rename,[status(thm)],[i_0_8]) ).
fof(i_0_15,negated_conjecture,
~ disjoint(esk3_0,empty_set),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_9])])]) ).
cnf(i_0_16,plain,
( member(esk1_2(X1,X2),X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_17,plain,
( member(esk1_2(X1,X2),X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_18,plain,
( intersect(X2,X3)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_19,plain,
( ~ disjoint(X1,X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_20,plain,
( intersect(X2,X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_21,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_22,plain,
( intersect(X1,X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_23,plain,
( member(esk2_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_24,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_25,negated_conjecture,
~ disjoint(esk3_0,empty_set),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_26,plain,
intersect(esk3_0,empty_set),
inference(scs_inference,[],[i_0_25,i_0_22]) ).
cnf(i_0_27,plain,
( disjoint(X1,X2)
| intersect(X1,X2) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_28,plain,
~ intersect(empty_set,X1),
inference(scs_inference,[],[i_0_25,i_0_24,i_0_22,i_0_16]) ).
cnf(i_0_29,plain,
~ member(X1,empty_set),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_30,plain,
( member(esk1_2(X1,X2),X1)
| ~ intersect(X1,X2) ),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_31,plain,
$false,
inference(scs_inference,[],[i_0_25,i_0_24,i_0_29,i_0_22,i_0_16,i_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET627+3 : TPTP v9.2.1. Released v2.2.0.
% 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
% 0.16/0.33 % Computer : n014.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:30:22 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.26/1.62 % Version : CSE_E---1.7
% 0.26/1.62 % Problem : theBenchmark.p
% 0.26/1.62 % SZS status Theorem for theBenchmark.p
% 0.26/1.62 % SZS output start CNFRefutation
% See solution above
% 0.26/1.64 % Total time : 1.271s
%------------------------------------------------------------------------------