%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU113+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n007.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 05:10:39 PM UTC 2026
% Result : Theorem 1.29s 1.72s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 10 unt; 0 def)
% Number of atoms : 96 ( 8 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 104 ( 38 ~; 41 |; 18 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 52 ( 2 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc1_finsub_1,axiom,
! [X1] :
( ~ empty(powerset(X1))
& cup_closed(powerset(X1))
& diff_closed(powerset(X1))
& preboolean(powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finsub_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(d5_finsub_1,axiom,
! [X1,X2] :
( preboolean(X2)
=> ( X2 = finite_subsets(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( subset(X3,X1)
& finite(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_finsub_1) ).
fof(dt_k5_finsub_1,axiom,
! [X1] : preboolean(finite_subsets(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(t26_finsub_1,conjecture,
! [X1] : subset(finite_subsets(X1),powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finsub_1) ).
fof(c_0_7,plain,
! [X1] :
( ~ empty(powerset(X1))
& cup_closed(powerset(X1))
& diff_closed(powerset(X1))
& preboolean(powerset(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_finsub_1]) ).
fof(c_0_8,plain,
! [X103,X104] :
( ~ element(X103,X104)
| empty(X104)
| in(X103,X104) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_9,plain,
! [X105,X106] :
( ( ~ element(X105,powerset(X106))
| subset(X105,X106) )
& ( ~ subset(X105,X106)
| element(X105,powerset(X106)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_10,plain,
! [X82] :
( ~ empty(powerset(X82))
& cup_closed(powerset(X82))
& diff_closed(powerset(X82))
& preboolean(powerset(X82)) ),
inference(variable_rename,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X74,X75,X76,X77] :
( ( subset(X76,X74)
| ~ in(X76,X75)
| X75 != finite_subsets(X74)
| ~ preboolean(X75) )
& ( finite(X76)
| ~ in(X76,X75)
| X75 != finite_subsets(X74)
| ~ preboolean(X75) )
& ( ~ subset(X77,X74)
| ~ finite(X77)
| in(X77,X75)
| X75 != finite_subsets(X74)
| ~ preboolean(X75) )
& ( ~ in(esk2_2(X74,X75),X75)
| ~ subset(esk2_2(X74,X75),X74)
| ~ finite(esk2_2(X74,X75))
| X75 = finite_subsets(X74)
| ~ preboolean(X75) )
& ( subset(esk2_2(X74,X75),X74)
| in(esk2_2(X74,X75),X75)
| X75 = finite_subsets(X74)
| ~ preboolean(X75) )
& ( finite(esk2_2(X74,X75))
| in(esk2_2(X74,X75),X75)
| X75 = finite_subsets(X74)
| ~ preboolean(X75) ) ),
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)],[d5_finsub_1])])])])])]) ).
fof(c_0_12,plain,
! [X79] : preboolean(finite_subsets(X79)),
inference(variable_rename,[status(thm)],[dt_k5_finsub_1]) ).
fof(c_0_13,plain,
! [X68,X69,X70,X71,X72] :
( ( ~ subset(X68,X69)
| ~ in(X70,X68)
| in(X70,X69) )
& ( in(esk1_2(X71,X72),X71)
| subset(X71,X72) )
& ( ~ in(esk1_2(X71,X72),X72)
| subset(X71,X72) ) ),
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)],[d3_tarski])])])])])]) ).
cnf(c_0_14,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( subset(X1,X2)
| ~ in(X1,X3)
| X3 != finite_subsets(X2)
| ~ preboolean(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
preboolean(finite_subsets(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1] : subset(finite_subsets(X1),powerset(X1)),
inference(assume_negation,[status(cth)],[t26_finsub_1]) ).
cnf(c_0_20,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_22,plain,
( subset(X1,X2)
| ~ in(X1,finite_subsets(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_17]),c_0_18])]) ).
cnf(c_0_23,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_24,negated_conjecture,
~ subset(finite_subsets(esk13_0),powerset(esk13_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_25,plain,
( subset(X1,powerset(X2))
| ~ subset(esk1_2(X1,powerset(X2)),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( subset(esk1_2(finite_subsets(X1),X2),X1)
| subset(finite_subsets(X1),X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
~ subset(finite_subsets(esk13_0),powerset(esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,plain,
subset(finite_subsets(X1),powerset(X1)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU113+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n007.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 02:43:24 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.29/1.72 % Version : CSE_E---1.7
% 1.29/1.72 % Problem : theBenchmark.p
% 1.29/1.72 % SZS status Theorem for theBenchmark.p
% 1.29/1.72 % SZS output start CNFRefutation
% See solution above
% 1.29/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------