%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU328+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n008.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 05:11:30 PM UTC 2026
% Result : Theorem 1.67s 1.81s
% Output : CNFRefutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 13 unt; 0 def)
% Number of atoms : 58 ( 28 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 22 ~; 16 |; 3 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 42 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t48_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_setfam_1) ).
fof(d4_subset_1,axiom,
! [X1] : cast_to_subset(X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
fof(dt_k2_subset_1,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(t12_tops_2,conjecture,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,meet_of_subsets(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_tops_2) ).
fof(redefinition_k6_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(dt_k6_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(meet_of_subsets(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
fof(d5_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
fof(c_0_7,plain,
! [X181,X182] :
( ~ element(X182,powerset(powerset(X181)))
| X182 = empty_set
| union_of_subsets(X181,complements_of_subsets(X181,X182)) = subset_difference(X181,cast_to_subset(X181),meet_of_subsets(X181,X182)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t48_setfam_1])]) ).
fof(c_0_8,plain,
! [X127] : cast_to_subset(X127) = X127,
inference(variable_rename,[status(thm)],[d4_subset_1]) ).
fof(c_0_9,plain,
! [X130] : element(cast_to_subset(X130),powerset(X130)),
inference(variable_rename,[status(thm)],[dt_k2_subset_1]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,meet_of_subsets(X1,X2)) ) ),
inference(assume_negation,[status(cth)],[t12_tops_2]) ).
fof(c_0_11,plain,
! [X168,X169,X170] :
( ~ element(X169,powerset(X168))
| ~ element(X170,powerset(X168))
| subset_difference(X168,X169,X170) = set_difference(X169,X170) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1])]) ).
cnf(c_0_12,plain,
( X1 = empty_set
| union_of_subsets(X2,complements_of_subsets(X2,X1)) = subset_difference(X2,cast_to_subset(X2),meet_of_subsets(X2,X1))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
cast_to_subset(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
element(cast_to_subset(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,plain,
! [X135,X136] :
( ~ element(X136,powerset(powerset(X135)))
| element(meet_of_subsets(X135,X136),powerset(X135)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_setfam_1])]) ).
fof(c_0_16,negated_conjecture,
( element(esk6_0,powerset(powerset(esk5_0)))
& esk6_0 != empty_set
& union_of_subsets(esk5_0,complements_of_subsets(esk5_0,esk6_0)) != subset_complement(esk5_0,meet_of_subsets(esk5_0,esk6_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_17,plain,
( subset_difference(X2,X1,X3) = set_difference(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( X1 = empty_set
| union_of_subsets(X2,complements_of_subsets(X2,X1)) = subset_difference(X2,X2,meet_of_subsets(X2,X1))
| ~ element(X1,powerset(powerset(X2))) ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
element(X1,powerset(X1)),
inference(rw,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_20,plain,
( element(meet_of_subsets(X2,X1),powerset(X2))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
union_of_subsets(esk5_0,complements_of_subsets(esk5_0,esk6_0)) != subset_complement(esk5_0,meet_of_subsets(esk5_0,esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( union_of_subsets(X1,complements_of_subsets(X1,X2)) = set_difference(X1,meet_of_subsets(X1,X2))
| X2 = empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_23,negated_conjecture,
element(esk6_0,powerset(powerset(esk5_0))),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
esk6_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_25,plain,
! [X128,X129] :
( ~ element(X129,powerset(X128))
| subset_complement(X128,X129) = set_difference(X128,X129) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])]) ).
cnf(c_0_26,negated_conjecture,
subset_complement(esk5_0,meet_of_subsets(esk5_0,esk6_0)) != set_difference(esk5_0,meet_of_subsets(esk5_0,esk6_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]),c_0_24]) ).
cnf(c_0_27,plain,
( subset_complement(X2,X1) = set_difference(X2,X1)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_28,negated_conjecture,
~ element(meet_of_subsets(esk5_0,esk6_0),powerset(esk5_0)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_20]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU328+1 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.16/0.32 % Computer : n008.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 02:57:43 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.67/1.81 % Version : CSE_E---1.7
% 1.67/1.81 % Problem : theBenchmark.p
% 1.67/1.81 % SZS status Theorem for theBenchmark.p
% 1.67/1.81 % SZS output start CNFRefutation
% See solution above
% 1.67/1.81 % Total time : 1.372s
%------------------------------------------------------------------------------