%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET629+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 : n020.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 05:08:11 PM UTC 2026
% Result : Theorem 1.28s 1.73s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 8 unt; 0 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 73 ( 32 ~; 23 |; 11 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 60 ( 4 sgn 36 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_intersection_and_difference_disjoint,conjecture,
! [X1,X2] : disjoint(intersection(X1,X2),difference(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_and_difference_disjoint) ).
fof(disjoint_defn,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
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(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_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(c_0_6,negated_conjecture,
~ ! [X1,X2] : disjoint(intersection(X1,X2),difference(X1,X2)),
inference(assume_negation,[status(cth)],[prove_intersection_and_difference_disjoint]) ).
fof(c_0_7,plain,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
inference(fof_simplification,[status(thm)],[disjoint_defn]) ).
fof(c_0_8,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(c_0_9,negated_conjecture,
~ disjoint(intersection(esk3_0,esk4_0),difference(esk3_0,esk4_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,plain,
! [X36,X37] :
( ( ~ disjoint(X36,X37)
| ~ intersect(X36,X37) )
& ( intersect(X36,X37)
| disjoint(X36,X37) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).
fof(c_0_11,plain,
! [X27,X28,X29] :
( ( member(X29,X27)
| ~ member(X29,difference(X27,X28)) )
& ( ~ member(X29,X28)
| ~ member(X29,difference(X27,X28)) )
& ( ~ member(X29,X27)
| member(X29,X28)
| member(X29,difference(X27,X28)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,plain,
! [X30,X31,X33,X34,X35] :
( ( member(esk1_2(X30,X31),X30)
| ~ intersect(X30,X31) )
& ( member(esk1_2(X30,X31),X31)
| ~ intersect(X30,X31) )
& ( ~ member(X35,X33)
| ~ member(X35,X34)
| intersect(X33,X34) ) ),
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(c_0_13,plain,
! [X24,X25,X26] :
( ( member(X26,X24)
| ~ member(X26,intersection(X24,X25)) )
& ( member(X26,X25)
| ~ member(X26,intersection(X24,X25)) )
& ( ~ member(X26,X24)
| ~ member(X26,X25)
| member(X26,intersection(X24,X25)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
fof(c_0_14,plain,
! [X40,X41] :
( ~ intersect(X40,X41)
| intersect(X41,X40) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_of_intersect])]) ).
cnf(c_0_15,negated_conjecture,
~ disjoint(intersection(esk3_0,esk4_0),difference(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( intersect(X1,X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( member(esk1_2(X1,X2),X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( member(esk1_2(X1,X2),X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,plain,
( intersect(X2,X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
intersect(intersection(esk3_0,esk4_0),difference(esk3_0,esk4_0)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_23,plain,
( ~ intersect(difference(X1,X2),X3)
| ~ member(esk1_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,plain,
( member(esk1_2(X1,intersection(X2,X3)),X3)
| ~ intersect(X1,intersection(X2,X3)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
intersect(difference(esk3_0,esk4_0),intersection(esk3_0,esk4_0)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
~ intersect(difference(X1,X2),intersection(X3,X2)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_25,c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET629+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.13 % 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
% 0.16/0.34 % Computer : n020.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 02:30:05 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.28/1.73 % Version : CSE_E---1.7
% 1.28/1.73 % Problem : theBenchmark.p
% 1.28/1.73 % SZS status Theorem for theBenchmark.p
% 1.28/1.73 % SZS output start CNFRefutation
% See solution above
% 1.28/1.73 % Total time : 1.372s
%------------------------------------------------------------------------------