%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET577+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 : n019.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 05:08:01 PM UTC 2026
% Result : Theorem 1.67s 1.87s
% Output : CNFRefutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 15 unt; 0 def)
% Number of atoms : 117 ( 13 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 104 ( 36 ~; 50 |; 10 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 90 ( 10 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th18,conjecture,
! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X2)
| member(X4,X3) ) )
=> X1 = union(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th18) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X2)
| member(X4,X3) ) )
=> X1 = union(X2,X3) ),
inference(assume_negation,[status(cth)],[prove_th18]) ).
fof(c_0_6,plain,
! [X30,X31,X32,X33,X34] :
( ( ~ subset(X30,X31)
| ~ member(X32,X30)
| member(X32,X31) )
& ( member(esk1_2(X33,X34),X33)
| subset(X33,X34) )
& ( ~ member(esk1_2(X33,X34),X34)
| subset(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)],[subset_defn])])])])])]) ).
fof(c_0_7,plain,
! [X23,X24,X25] :
( ( ~ member(X25,union(X23,X24))
| member(X25,X23)
| member(X25,X24) )
& ( ~ member(X25,X23)
| member(X25,union(X23,X24)) )
& ( ~ member(X25,X24)
| member(X25,union(X23,X24)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).
fof(c_0_8,negated_conjecture,
! [X47] :
( ( ~ member(X47,esk3_0)
| member(X47,esk4_0)
| member(X47,esk5_0) )
& ( ~ member(X47,esk4_0)
| member(X47,esk3_0) )
& ( ~ member(X47,esk5_0)
| member(X47,esk3_0) )
& esk3_0 != union(esk4_0,esk5_0) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])]) ).
cnf(c_0_9,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( subset(esk5_0,X1)
| member(esk1_2(esk5_0,X1),esk3_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_16,plain,
! [X28,X29] : union(X28,X29) = union(X29,X28),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_17,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,negated_conjecture,
( subset(esk4_0,X1)
| member(esk1_2(esk4_0,X1),esk3_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_19,negated_conjecture,
subset(esk5_0,union(X1,esk3_0)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( subset(union(X1,X2),X3)
| member(esk1_2(union(X1,X2),X3),X1)
| member(esk1_2(union(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_12]) ).
cnf(c_0_22,negated_conjecture,
subset(esk4_0,union(X1,esk3_0)),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_23,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,negated_conjecture,
subset(esk5_0,union(esk3_0,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_25,plain,
! [X26,X27] :
( ( subset(X26,X27)
| X26 != X27 )
& ( subset(X27,X26)
| X26 != X27 )
& ( ~ subset(X26,X27)
| ~ subset(X27,X26)
| X26 = X27 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_26,plain,
( subset(union(X1,X1),X2)
| member(esk1_2(union(X1,X1),X2),X1) ),
inference(ef,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_28,negated_conjecture,
( member(X1,esk4_0)
| member(X1,esk5_0)
| ~ member(X1,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_29,negated_conjecture,
subset(esk4_0,union(esk3_0,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_30,negated_conjecture,
( member(X1,union(esk3_0,X2))
| ~ member(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
subset(union(X1,X1),X1),
inference(spm,[status(thm)],[c_0_9,c_0_26]) ).
cnf(c_0_33,plain,
subset(X1,union(X1,X2)),
inference(spm,[status(thm)],[c_0_27,c_0_20]) ).
cnf(c_0_34,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_35,negated_conjecture,
( subset(esk3_0,X1)
| member(esk1_2(esk3_0,X1),esk5_0)
| member(esk1_2(esk3_0,X1),esk4_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_12]) ).
cnf(c_0_36,negated_conjecture,
( member(X1,union(esk3_0,X2))
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_37,negated_conjecture,
( subset(X1,union(esk3_0,X2))
| ~ member(esk1_2(X1,union(esk3_0,X2)),esk5_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_30]) ).
cnf(c_0_38,plain,
union(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_39,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( subset(esk3_0,union(X1,esk5_0))
| member(esk1_2(esk3_0,union(X1,esk5_0)),esk4_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
( subset(X1,union(esk3_0,X2))
| ~ member(esk1_2(X1,union(esk3_0,X2)),esk4_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_36]) ).
cnf(c_0_42,negated_conjecture,
( subset(X1,esk3_0)
| ~ member(esk1_2(X1,esk3_0),esk5_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,negated_conjecture,
subset(esk3_0,union(esk4_0,esk5_0)),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
esk3_0 != union(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_45,negated_conjecture,
( subset(X1,esk3_0)
| ~ member(esk1_2(X1,esk3_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_41,c_0_38]) ).
cnf(c_0_46,negated_conjecture,
( subset(union(X1,esk5_0),esk3_0)
| member(esk1_2(union(X1,esk5_0),esk3_0),X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_21]) ).
cnf(c_0_47,negated_conjecture,
~ subset(union(esk4_0,esk5_0),esk3_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_43]),c_0_44]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET577+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : n019.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 02:27:59 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.67/1.87 % Version : CSE_E---1.7
% 1.67/1.87 % Problem : theBenchmark.p
% 1.67/1.87 % SZS status Theorem for theBenchmark.p
% 1.67/1.87 % SZS output start CNFRefutation
% See solution above
% 1.67/1.87 % Total time : 1.369s
%------------------------------------------------------------------------------