%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET591+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 : n012.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 05:08:03 PM UTC 2026
% Result : Theorem 1.13s 1.62s
% Output : CNFRefutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 10 unt; 0 def)
% Number of atoms : 81 ( 10 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 85 ( 37 ~; 28 |; 11 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 59 ( 7 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_defn,axiom,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_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(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(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(prove_th50,conjecture,
! [X1,X2] :
( subset(X1,difference(X2,X1))
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th50) ).
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] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[empty_defn]) ).
fof(c_0_7,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_8,plain,
! [X18,X19,X20,X21,X22] :
( ( ~ subset(X18,X19)
| ~ member(X20,X18)
| member(X20,X19) )
& ( member(esk1_2(X21,X22),X21)
| subset(X21,X22) )
& ( ~ member(esk1_2(X21,X22),X22)
| subset(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)],[subset_defn])])])])])]) ).
fof(c_0_9,plain,
! [X31,X32,X33] :
( ( ~ empty(X31)
| ~ member(X32,X31) )
& ( member(esk2_1(X33),X33)
| empty(X33) ) ),
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_6])])])])]) ).
fof(c_0_10,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_11,plain,
! [X24,X25,X26] :
( ( member(X26,X24)
| ~ member(X26,difference(X24,X25)) )
& ( ~ member(X26,X25)
| ~ member(X26,difference(X24,X25)) )
& ( ~ member(X26,X24)
| member(X26,X25)
| member(X26,difference(X24,X25)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_12,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( member(esk2_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,difference(X2,X1))
=> X1 = empty_set ),
inference(assume_negation,[status(cth)],[prove_th50]) ).
fof(c_0_15,plain,
! [X27] : ~ member(X27,empty_set),
inference(variable_rename,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( empty(X1)
| member(esk2_1(X1),X2)
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_18,negated_conjecture,
( subset(esk3_0,difference(esk4_0,esk3_0))
& esk3_0 != empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_19,plain,
! [X28,X29] :
( ( subset(X28,X29)
| X28 != X29 )
& ( subset(X29,X28)
| X28 != X29 )
& ( ~ subset(X28,X29)
| ~ subset(X29,X28)
| X28 = X29 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_20,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_22,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_23,plain,
( empty(X1)
| ~ member(esk2_1(X1),X2)
| ~ subset(X1,difference(X3,X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,negated_conjecture,
subset(esk3_0,difference(esk4_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
( subset(X1,X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_28,negated_conjecture,
empty(esk3_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_13]) ).
cnf(c_0_29,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
subset(esk3_0,X1),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
esk3_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SET591+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.07 % 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
% 0.08/0.25 % Computer : n012.cluster.edu
% 0.08/0.25 % Model : x86_64 x86_64
% 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.25 % Memory : 8042.1875MB
% 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.25 % CPULimit : 300
% 0.08/0.25 % WCLimit : 300
% 0.08/0.25 % DateTime : Tue May 5 02:28:16 EDT 2026
% 0.08/0.25 % CPUTime :
% 0.08/0.25 % start to proof: theBenchmark
% 1.13/1.62 % Version : CSE_E---1.7
% 1.13/1.62 % Problem : theBenchmark.p
% 1.13/1.62 % SZS status Theorem for theBenchmark.p
% 1.13/1.62 % SZS output start CNFRefutation
% See solution above
% 1.13/1.62 % Total time : 1.362s
%------------------------------------------------------------------------------