%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU114+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 : n029.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 1.61s 1.80s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 10 unt; 0 def)
% Number of atoms : 119 ( 17 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 128 ( 48 ~; 55 |; 13 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 66 ( 1 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
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(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(cc2_finset_1,axiom,
! [X1] :
( finite(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> finite(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
fof(t27_finsub_1,conjecture,
! [X1] :
( finite(X1)
=> finite_subsets(X1) = powerset(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finsub_1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(t26_finsub_1,axiom,
! [X1] : subset(finite_subsets(X1),powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finsub_1) ).
fof(c_0_9,plain,
! [X81,X82,X83,X84] :
( ( subset(X83,X81)
| ~ in(X83,X82)
| X82 != finite_subsets(X81)
| ~ preboolean(X82) )
& ( finite(X83)
| ~ in(X83,X82)
| X82 != finite_subsets(X81)
| ~ preboolean(X82) )
& ( ~ subset(X84,X81)
| ~ finite(X84)
| in(X84,X82)
| X82 != finite_subsets(X81)
| ~ preboolean(X82) )
& ( ~ in(esk2_2(X81,X82),X82)
| ~ subset(esk2_2(X81,X82),X81)
| ~ finite(esk2_2(X81,X82))
| X82 = finite_subsets(X81)
| ~ preboolean(X82) )
& ( subset(esk2_2(X81,X82),X81)
| in(esk2_2(X81,X82),X82)
| X82 = finite_subsets(X81)
| ~ preboolean(X82) )
& ( finite(esk2_2(X81,X82))
| in(esk2_2(X81,X82),X82)
| X82 = finite_subsets(X81)
| ~ preboolean(X82) ) ),
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_10,plain,
! [X86] : preboolean(finite_subsets(X86)),
inference(variable_rename,[status(thm)],[dt_k5_finsub_1]) ).
fof(c_0_11,plain,
! [X109,X110] :
( ~ in(X109,X110)
| element(X109,X110) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(c_0_12,plain,
! [X75,X76,X77,X78,X79] :
( ( ~ subset(X75,X76)
| ~ in(X77,X75)
| in(X77,X76) )
& ( in(esk1_2(X78,X79),X78)
| subset(X78,X79) )
& ( ~ in(esk1_2(X78,X79),X79)
| subset(X78,X79) ) ),
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_13,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| ~ finite(X1)
| X3 != finite_subsets(X2)
| ~ preboolean(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
preboolean(finite_subsets(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X115,X116] :
( ( ~ element(X115,powerset(X116))
| subset(X115,X116) )
& ( ~ subset(X115,X116)
| element(X115,powerset(X116)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
cnf(c_0_16,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,plain,
! [X68,X69] :
( ~ finite(X68)
| ~ element(X69,powerset(X68))
| finite(X69) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_finset_1])])]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1] :
( finite(X1)
=> finite_subsets(X1) = powerset(X1) ),
inference(assume_negation,[status(cth)],[t27_finsub_1]) ).
cnf(c_0_20,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,plain,
( in(X1,finite_subsets(X2))
| ~ subset(X1,X2)
| ~ finite(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_13]),c_0_14])]) ).
cnf(c_0_22,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( subset(X1,X2)
| element(esk1_2(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
( finite(X2)
| ~ finite(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_25,negated_conjecture,
( finite(esk13_0)
& 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_26,plain,
( subset(X1,finite_subsets(X2))
| ~ subset(esk1_2(X1,finite_subsets(X2)),X2)
| ~ finite(esk1_2(X1,finite_subsets(X2))) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
( subset(esk1_2(powerset(X1),X2),X1)
| subset(powerset(X1),X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( subset(powerset(X1),X2)
| finite(esk1_2(powerset(X1),X2))
| ~ finite(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
finite(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_30,plain,
! [X73,X74] :
( ( subset(X73,X74)
| X73 != X74 )
& ( subset(X74,X73)
| X73 != X74 )
& ( ~ subset(X73,X74)
| ~ subset(X74,X73)
| X73 = X74 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(c_0_31,plain,
( subset(powerset(X1),finite_subsets(X1))
| ~ finite(esk1_2(powerset(X1),finite_subsets(X1))) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,negated_conjecture,
( subset(powerset(esk13_0),X1)
| finite(esk1_2(powerset(esk13_0),X1)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_33,plain,
! [X111] : subset(finite_subsets(X111),powerset(X111)),
inference(variable_rename,[status(thm)],[t26_finsub_1]) ).
cnf(c_0_34,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,negated_conjecture,
subset(powerset(esk13_0),finite_subsets(esk13_0)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
subset(finite_subsets(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,negated_conjecture,
finite_subsets(esk13_0) != powerset(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU114+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 : n029.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 02:44:29 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.61/1.80 % Version : CSE_E---1.7
% 1.61/1.80 % Problem : theBenchmark.p
% 1.61/1.80 % SZS status Theorem for theBenchmark.p
% 1.61/1.80 % SZS output start CNFRefutation
% See solution above
% 1.61/1.80 % Total time : 1.368s
%------------------------------------------------------------------------------