%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET636+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 05:08:12 PM UTC 2026
% Result : Theorem 1.35s 1.74s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 8 unt; 0 def)
% Number of atoms : 122 ( 18 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 128 ( 54 ~; 52 |; 12 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 4 sgn 42 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_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(disjoint_defn,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
fof(prove_th118,conjecture,
! [X1,X2] :
( disjoint(X1,X2)
<=> intersection(X1,X2) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th118) ).
fof(c_0_7,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[empty_defn]) ).
fof(c_0_8,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_9,plain,
! [X30,X31,X32] :
( ( member(X32,X30)
| ~ member(X32,intersection(X30,X31)) )
& ( member(X32,X31)
| ~ member(X32,intersection(X30,X31)) )
& ( ~ member(X32,X30)
| ~ member(X32,X31)
| member(X32,intersection(X30,X31)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
fof(c_0_10,plain,
! [X55,X56,X57] :
( ( ~ empty(X55)
| ~ member(X56,X55) )
& ( member(esk3_1(X57),X57)
| empty(X57) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
fof(c_0_11,plain,
! [X39] : ~ member(X39,empty_set),
inference(variable_rename,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X59,X60,X61,X62,X63,X64] :
( ( ~ member(X61,X59)
| member(X61,X60)
| X59 != X60 )
& ( ~ member(X62,X60)
| member(X62,X59)
| X59 != X60 )
& ( ~ member(esk4_2(X63,X64),X63)
| ~ member(esk4_2(X63,X64),X64)
| X63 = X64 )
& ( member(esk4_2(X63,X64),X63)
| member(esk4_2(X63,X64),X64)
| X63 = X64 ) ),
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)],[equal_member_defn])])])])])]) ).
fof(c_0_13,plain,
! [X33,X34,X36,X37,X38] :
( ( member(esk1_2(X33,X34),X33)
| ~ intersect(X33,X34) )
& ( member(esk1_2(X33,X34),X34)
| ~ intersect(X33,X34) )
& ( ~ member(X38,X36)
| ~ member(X38,X37)
| intersect(X36,X37) ) ),
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])])])])])]) ).
cnf(c_0_14,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( member(esk3_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
inference(fof_simplification,[status(thm)],[disjoint_defn]) ).
fof(c_0_17,negated_conjecture,
~ ! [X1,X2] :
( disjoint(X1,X2)
<=> intersection(X1,X2) = empty_set ),
inference(assume_negation,[status(cth)],[prove_th118]) ).
cnf(c_0_18,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( member(esk4_2(X1,X2),X1)
| member(esk4_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( intersect(X2,X3)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( empty(intersection(X1,X2))
| member(esk3_1(intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_23,plain,
! [X40,X41] :
( ( ~ disjoint(X40,X41)
| ~ intersect(X40,X41) )
& ( intersect(X40,X41)
| disjoint(X40,X41) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])]) ).
fof(c_0_24,negated_conjecture,
( ( ~ disjoint(esk5_0,esk6_0)
| intersection(esk5_0,esk6_0) != empty_set )
& ( disjoint(esk5_0,esk6_0)
| intersection(esk5_0,esk6_0) = empty_set ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
cnf(c_0_25,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,plain,
( empty_set = X1
| member(esk4_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,plain,
( empty(intersection(X1,X2))
| intersect(X3,X2)
| ~ member(esk3_1(intersection(X1,X2)),X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
( empty(intersection(X1,X2))
| member(esk3_1(intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_15]) ).
cnf(c_0_29,plain,
( ~ disjoint(X1,X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,negated_conjecture,
( disjoint(esk5_0,esk6_0)
| intersection(esk5_0,esk6_0) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( empty_set = X1
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
( empty(intersection(X1,X2))
| intersect(X1,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_34,negated_conjecture,
( intersection(esk5_0,esk6_0) = empty_set
| ~ intersect(esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( intersection(X1,X2) = empty_set
| intersect(X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
( ~ empty(intersection(X1,X2))
| ~ member(X3,X2)
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
intersection(esk5_0,esk6_0) = empty_set,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
empty(empty_set),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_39,negated_conjecture,
( ~ disjoint(esk5_0,esk6_0)
| intersection(esk5_0,esk6_0) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_40,plain,
( intersect(X1,X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_41,negated_conjecture,
( ~ member(X1,esk6_0)
| ~ member(X1,esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_42,plain,
( member(esk1_2(X1,X2),X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_43,negated_conjecture,
( intersect(esk5_0,esk6_0)
| intersection(esk5_0,esk6_0) != empty_set ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
( ~ intersect(X1,esk6_0)
| ~ member(esk1_2(X1,esk6_0),esk5_0) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,plain,
( member(esk1_2(X1,X2),X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_46,negated_conjecture,
intersect(esk5_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_37])]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET636+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
% 0.14/0.32 % Computer : n020.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:30:50 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.35/1.74 % Version : CSE_E---1.7
% 1.35/1.74 % Problem : theBenchmark.p
% 1.35/1.74 % SZS status Theorem for theBenchmark.p
% 1.35/1.74 % SZS output start CNFRefutation
% See solution above
% 1.35/1.74 % Total time : 1.368s
%------------------------------------------------------------------------------