%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET162+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 : n022.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 05:07:29 PM UTC 2026
% Result : Theorem 1.33s 1.91s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 18 unt; 0 def)
% Number of atoms : 67 ( 15 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 59 ( 24 ~; 24 |; 7 &)
% ( 3 <=>; 1 =>; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 57 ( 4 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(prove_union_empty_set,conjecture,
! [X1] : union(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_union_empty_set) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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,
! [X22,X23,X24] :
( ( ~ member(X24,union(X22,X23))
| member(X24,X22)
| member(X24,X23) )
& ( ~ member(X24,X22)
| member(X24,union(X22,X23)) )
& ( ~ member(X24,X23)
| member(X24,union(X22,X23)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).
fof(c_0_8,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_9,plain,
! [X25] : ~ member(X25,empty_set),
inference(variable_rename,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,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_10,c_0_11]) ).
cnf(c_0_16,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_17,plain,
! [X28,X29] : union(X28,X29) = union(X29,X28),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
fof(c_0_18,negated_conjecture,
~ ! [X1] : union(X1,empty_set) = X1,
inference(assume_negation,[status(cth)],[prove_union_empty_set]) ).
fof(c_0_19,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_20,plain,
( subset(union(X1,empty_set),X2)
| member(esk1_2(union(X1,empty_set),X2),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_16,c_0_11]) ).
cnf(c_0_22,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,negated_conjecture,
union(esk4_0,empty_set) != esk4_0,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
cnf(c_0_24,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
subset(union(X1,empty_set),X1),
inference(spm,[status(thm)],[c_0_12,c_0_20]) ).
cnf(c_0_26,plain,
subset(X1,union(X1,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
union(esk4_0,empty_set) != esk4_0,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
union(X1,empty_set) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_29,negated_conjecture,
union(empty_set,esk4_0) != esk4_0,
inference(rw,[status(thm)],[c_0_27,c_0_22]) ).
cnf(c_0_30,plain,
union(empty_set,X1) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.21 % Problem : SET162+3 : TPTP v9.2.1. Released v2.2.0.
% 0.03/0.21 % 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
% 0.12/0.45 % Computer : n022.cluster.edu
% 0.12/0.45 % Model : x86_64 x86_64
% 0.12/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.45 % Memory : 8042.1875MB
% 0.12/0.45 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.45 % CPULimit : 300
% 0.12/0.45 % WCLimit : 300
% 0.12/0.45 % DateTime : Tue May 5 02:13:36 EDT 2026
% 0.12/0.45 % CPUTime :
% 0.12/0.46 % start to proof: theBenchmark
% 1.33/1.91 % Version : CSE_E---1.7
% 1.33/1.91 % Problem : theBenchmark.p
% 1.33/1.91 % SZS status Theorem for theBenchmark.p
% 1.33/1.91 % SZS output start CNFRefutation
% See solution above
% 1.33/1.91 % Total time : 1.375s
%------------------------------------------------------------------------------