%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET199+4 : 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 05:07:34 PM UTC 2026
% Result : Theorem 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 50 ( 6 unt; 0 def)
% Number of atoms : 130 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 143 ( 63 ~; 64 |; 10 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 2 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thI46,conjecture,
! [X1,X3,X5] :
( ( subset(X1,X3)
& subset(X1,X5) )
<=> subset(X1,intersection(X3,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI46) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(power_set,axiom,
! [X3,X1] :
( member(X3,power_set(X1))
<=> subset(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',power_set) ).
fof(intersection,axiom,
! [X3,X1,X2] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',intersection) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X3,X5] :
( ( subset(X1,X3)
& subset(X1,X5) )
<=> subset(X1,intersection(X3,X5)) ),
inference(assume_negation,[status(cth)],[thI46]) ).
fof(c_0_5,negated_conjecture,
( ( ~ subset(esk4_0,esk5_0)
| ~ subset(esk4_0,esk6_0)
| ~ subset(esk4_0,intersection(esk5_0,esk6_0)) )
& ( subset(esk4_0,esk5_0)
| subset(esk4_0,intersection(esk5_0,esk6_0)) )
& ( subset(esk4_0,esk6_0)
| subset(esk4_0,intersection(esk5_0,esk6_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_6,plain,
! [X37,X38,X39,X40,X41] :
( ( ~ subset(X37,X38)
| ~ member(X39,X37)
| member(X39,X38) )
& ( member(esk1_2(X40,X41),X40)
| subset(X40,X41) )
& ( ~ member(esk1_2(X40,X41),X41)
| subset(X40,X41) ) ),
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])])])])])]) ).
fof(c_0_7,plain,
! [X45,X46] :
( ( ~ member(X45,power_set(X46))
| subset(X45,X46) )
& ( ~ subset(X45,X46)
| member(X45,power_set(X46)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[power_set])]) ).
cnf(c_0_8,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ subset(esk4_0,esk6_0)
| ~ subset(esk4_0,intersection(esk5_0,esk6_0)) ),
inference(split_conjunct,[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,power_set(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( subset(esk4_0,esk6_0)
| subset(esk4_0,intersection(esk5_0,esk6_0)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
( subset(esk4_0,esk5_0)
| subset(esk4_0,intersection(esk5_0,esk6_0)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
( ~ member(esk1_2(esk4_0,intersection(esk5_0,esk6_0)),intersection(esk5_0,esk6_0))
| ~ subset(esk4_0,esk5_0)
| ~ subset(esk4_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( member(esk4_0,power_set(intersection(esk5_0,esk6_0)))
| subset(esk4_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,negated_conjecture,
( member(esk4_0,power_set(intersection(esk5_0,esk6_0)))
| subset(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_12]) ).
fof(c_0_17,plain,
! [X47,X48,X49] :
( ( member(X47,X48)
| ~ member(X47,intersection(X48,X49)) )
& ( member(X47,X49)
| ~ member(X47,intersection(X48,X49)) )
& ( ~ member(X47,X48)
| ~ member(X47,X49)
| member(X47,intersection(X48,X49)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection])])]) ).
cnf(c_0_18,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
( member(esk1_2(esk4_0,intersection(esk5_0,esk6_0)),esk4_0)
| ~ subset(esk4_0,esk5_0)
| ~ subset(esk4_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_13]) ).
cnf(c_0_20,plain,
( subset(X1,X2)
| ~ member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_21,negated_conjecture,
( member(esk4_0,power_set(intersection(esk5_0,esk6_0)))
| ~ member(esk1_2(esk4_0,intersection(esk5_0,esk6_0)),intersection(esk5_0,esk6_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_22,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( member(esk4_0,power_set(intersection(esk5_0,esk6_0)))
| member(X1,esk6_0)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_24,negated_conjecture,
( member(esk1_2(esk4_0,intersection(esk5_0,esk6_0)),esk4_0)
| member(esk4_0,power_set(intersection(esk5_0,esk6_0))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_15]),c_0_16]) ).
cnf(c_0_25,negated_conjecture,
( member(esk4_0,power_set(intersection(esk5_0,esk6_0)))
| member(X1,esk5_0)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_26,negated_conjecture,
( ~ member(esk4_0,power_set(intersection(esk5_0,esk6_0)))
| ~ subset(esk4_0,esk5_0)
| ~ subset(esk4_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_20]) ).
cnf(c_0_27,negated_conjecture,
( member(esk4_0,power_set(intersection(esk5_0,esk6_0)))
| ~ member(esk1_2(esk4_0,intersection(esk5_0,esk6_0)),esk6_0)
| ~ member(esk1_2(esk4_0,intersection(esk5_0,esk6_0)),esk5_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( member(esk1_2(esk4_0,intersection(esk5_0,esk6_0)),esk6_0)
| member(esk4_0,power_set(intersection(esk5_0,esk6_0))) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( member(esk1_2(esk4_0,intersection(esk5_0,esk6_0)),esk5_0)
| member(esk4_0,power_set(intersection(esk5_0,esk6_0))) ),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( ~ member(esk4_0,power_set(intersection(esk5_0,esk6_0)))
| ~ member(esk1_2(esk4_0,esk6_0),esk6_0)
| ~ subset(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_9]) ).
cnf(c_0_31,plain,
( member(X1,X2)
| ~ member(X3,power_set(X2))
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_32,negated_conjecture,
member(esk4_0,power_set(intersection(esk5_0,esk6_0))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_33,negated_conjecture,
( member(esk1_2(esk4_0,esk6_0),esk4_0)
| ~ member(esk4_0,power_set(intersection(esk5_0,esk6_0)))
| ~ subset(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_13]) ).
cnf(c_0_34,negated_conjecture,
( ~ member(esk4_0,power_set(intersection(esk5_0,esk6_0)))
| ~ member(esk1_2(esk4_0,esk6_0),esk6_0)
| ~ member(esk1_2(esk4_0,esk5_0),esk5_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_9]) ).
cnf(c_0_35,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_36,negated_conjecture,
( member(X1,intersection(esk5_0,esk6_0))
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( member(esk1_2(esk4_0,esk6_0),esk4_0)
| ~ member(esk4_0,power_set(intersection(esk5_0,esk6_0)))
| ~ member(esk1_2(esk4_0,esk5_0),esk5_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_9]) ).
cnf(c_0_38,negated_conjecture,
( ~ member(esk1_2(esk4_0,esk6_0),esk6_0)
| ~ member(esk1_2(esk4_0,esk5_0),esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_32])]) ).
cnf(c_0_39,negated_conjecture,
( member(X1,esk6_0)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( member(esk1_2(esk4_0,esk6_0),esk4_0)
| ~ member(esk1_2(esk4_0,esk5_0),esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_32])]) ).
cnf(c_0_41,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_42,negated_conjecture,
~ member(esk1_2(esk4_0,esk5_0),esk5_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_43,negated_conjecture,
( member(X1,esk5_0)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_41,c_0_36]) ).
cnf(c_0_44,negated_conjecture,
( member(esk1_2(esk4_0,esk5_0),esk4_0)
| ~ member(esk4_0,power_set(intersection(esk5_0,esk6_0)))
| ~ member(esk1_2(esk4_0,esk6_0),esk6_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_13]) ).
cnf(c_0_45,negated_conjecture,
~ member(esk1_2(esk4_0,esk5_0),esk4_0),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,negated_conjecture,
~ member(esk1_2(esk4_0,esk6_0),esk6_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_32])]),c_0_45]) ).
cnf(c_0_47,negated_conjecture,
( member(esk1_2(esk4_0,esk6_0),esk4_0)
| ~ subset(esk4_0,esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_32])]) ).
cnf(c_0_48,negated_conjecture,
~ member(esk1_2(esk4_0,esk6_0),esk4_0),
inference(spm,[status(thm)],[c_0_46,c_0_39]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_13]),c_0_48]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET199+4 : 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
% 0.16/0.33 % Computer : n020.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 02:15:35 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Theorem for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.367s
%------------------------------------------------------------------------------