%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU112+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 : n004.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 05:10:38 PM UTC 2026
% Result : Theorem 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 13 unt; 0 def)
% Number of atoms : 30 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 7 |; 1 &)
% ( 0 <=>; 2 =>; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 2 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t25_finsub_1,conjecture,
! [X1,X2] : subset(set_union2(finite_subsets(X1),finite_subsets(X2)),finite_subsets(set_union2(X1,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_finsub_1) ).
fof(t8_xboole_1,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(t7_xboole_1,axiom,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t23_finsub_1,axiom,
! [X1,X2] :
( subset(X1,X2)
=> subset(finite_subsets(X1),finite_subsets(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finsub_1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] : subset(set_union2(finite_subsets(X1),finite_subsets(X2)),finite_subsets(set_union2(X1,X2))),
inference(assume_negation,[status(cth)],[t25_finsub_1]) ).
fof(c_0_6,negated_conjecture,
~ subset(set_union2(finite_subsets(esk11_0),finite_subsets(esk12_0)),finite_subsets(set_union2(esk11_0,esk12_0))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_7,plain,
! [X135,X136,X137] :
( ~ subset(X135,X136)
| ~ subset(X137,X136)
| subset(set_union2(X135,X137),X136) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])]) ).
fof(c_0_8,plain,
! [X131,X132] : subset(X131,set_union2(X131,X132)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(c_0_9,plain,
! [X81,X82] : set_union2(X81,X82) = set_union2(X82,X81),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_10,negated_conjecture,
~ subset(set_union2(finite_subsets(esk11_0),finite_subsets(esk12_0)),finite_subsets(set_union2(esk11_0,esk12_0))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( subset(set_union2(X1,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X114,X115] :
( ~ subset(X114,X115)
| subset(finite_subsets(X114),finite_subsets(X115)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_finsub_1])]) ).
cnf(c_0_13,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( ~ subset(finite_subsets(esk12_0),finite_subsets(set_union2(esk11_0,esk12_0)))
| ~ subset(finite_subsets(esk11_0),finite_subsets(set_union2(esk11_0,esk12_0))) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
( subset(finite_subsets(X1),finite_subsets(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
~ subset(finite_subsets(esk11_0),finite_subsets(set_union2(esk11_0,esk12_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_16]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU112+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
% 0.14/0.32 % Computer : n004.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:44:17 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Theorem for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------