%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET628+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : 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 05:08:10 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 8 unt; 0 def)
% Number of atoms : 88 ( 16 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 91 ( 38 ~; 36 |; 9 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 56 ( 3 sgn 32 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(empty_defn,axiom,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_defn) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(prove_th110,conjecture,
! [X1] :
( intersect(X1,X1)
<=> not_equal(X1,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th110) ).
fof(not_equal_defn,axiom,
! [X1,X2] :
( not_equal(X1,X2)
<=> X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_equal_defn) ).
fof(c_0_6,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_7,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[empty_defn]) ).
fof(c_0_8,plain,
! [X24] : ~ member(X24,empty_set),
inference(variable_rename,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X25,X26,X27,X28,X29,X30] :
( ( ~ member(X27,X25)
| member(X27,X26)
| X25 != X26 )
& ( ~ member(X28,X26)
| member(X28,X25)
| X25 != X26 )
& ( ~ member(esk2_2(X29,X30),X29)
| ~ member(esk2_2(X29,X30),X30)
| X29 = X30 )
& ( member(esk2_2(X29,X30),X29)
| member(esk2_2(X29,X30),X30)
| X29 = X30 ) ),
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_10,plain,
! [X18,X19,X21,X22,X23] :
( ( member(esk1_2(X18,X19),X18)
| ~ intersect(X18,X19) )
& ( member(esk1_2(X18,X19),X19)
| ~ intersect(X18,X19) )
& ( ~ member(X23,X21)
| ~ member(X23,X22)
| intersect(X21,X22) ) ),
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_11,plain,
! [X36,X37,X38] :
( ( ~ empty(X36)
| ~ member(X37,X36) )
& ( member(esk3_1(X38),X38)
| empty(X38) ) ),
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_12,negated_conjecture,
~ ! [X1] :
( intersect(X1,X1)
<=> not_equal(X1,empty_set) ),
inference(assume_negation,[status(cth)],[prove_th110]) ).
cnf(c_0_13,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( member(esk2_2(X1,X2),X1)
| member(esk2_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( intersect(X2,X3)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( member(esk3_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,negated_conjecture,
( ( ~ intersect(esk4_0,esk4_0)
| ~ not_equal(esk4_0,empty_set) )
& ( intersect(esk4_0,esk4_0)
| not_equal(esk4_0,empty_set) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_18,plain,
! [X32,X33] :
( ( ~ not_equal(X32,X33)
| X32 != X33 )
& ( X32 = X33
| not_equal(X32,X33) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[not_equal_defn])]) ).
cnf(c_0_19,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,plain,
( empty_set = X1
| member(esk2_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,plain,
( empty(X1)
| intersect(X2,X1)
| ~ member(esk3_1(X1),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( ~ intersect(esk4_0,esk4_0)
| ~ not_equal(esk4_0,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( X1 = X2
| not_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( empty_set = X1
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( empty(X1)
| intersect(X1,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_16]) ).
cnf(c_0_26,negated_conjecture,
( esk4_0 = empty_set
| ~ intersect(esk4_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
( empty_set = X1
| intersect(X1,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
( ~ not_equal(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,plain,
( member(esk1_2(X1,X2),X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_30,negated_conjecture,
( intersect(esk4_0,esk4_0)
| not_equal(esk4_0,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_31,negated_conjecture,
esk4_0 = empty_set,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
~ not_equal(X1,X1),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_33,plain,
~ intersect(empty_set,X1),
inference(spm,[status(thm)],[c_0_13,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_31]),c_0_31]),c_0_32]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET628+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.13 % 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
% 0.15/0.34 % Computer : n020.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 02:30:05 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------