%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU126+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 : n009.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 05:10:41 PM UTC 2026
% Result : Theorem 1.77s 1.86s
% Output : CNFRefutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 8 unt; 0 def)
% Number of atoms : 68 ( 21 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 69 ( 23 ~; 32 |; 8 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 47 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
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(t12_xboole_1,conjecture,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_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(c_0_4,plain,
! [X42,X43,X44,X45,X46,X47,X48,X49] :
( ( ~ in(X45,X44)
| in(X45,X42)
| in(X45,X43)
| X44 != set_union2(X42,X43) )
& ( ~ in(X46,X42)
| in(X46,X44)
| X44 != set_union2(X42,X43) )
& ( ~ in(X46,X43)
| in(X46,X44)
| X44 != set_union2(X42,X43) )
& ( ~ in(esk1_3(X47,X48,X49),X47)
| ~ in(esk1_3(X47,X48,X49),X49)
| X49 = set_union2(X47,X48) )
& ( ~ in(esk1_3(X47,X48,X49),X48)
| ~ in(esk1_3(X47,X48,X49),X49)
| X49 = set_union2(X47,X48) )
& ( in(esk1_3(X47,X48,X49),X49)
| in(esk1_3(X47,X48,X49),X47)
| in(esk1_3(X47,X48,X49),X48)
| X49 = set_union2(X47,X48) ) ),
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)],[d2_xboole_0])])])])])]) ).
cnf(c_0_5,plain,
( in(esk1_3(X1,X2,X3),X3)
| in(esk1_3(X1,X2,X3),X1)
| in(esk1_3(X1,X2,X3),X2)
| X3 = set_union2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_6,plain,
! [X51,X52,X53,X54,X55] :
( ( ~ subset(X51,X52)
| ~ in(X53,X51)
| in(X53,X52) )
& ( in(esk2_2(X54,X55),X54)
| subset(X54,X55) )
& ( ~ in(esk2_2(X54,X55),X55)
| subset(X54,X55) ) ),
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_7,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk1_3(X1,X2,X3),X2)
| ~ in(esk1_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( set_union2(X1,X2) = X2
| in(esk1_3(X1,X2,X2),X1)
| in(esk1_3(X1,X2,X2),X2) ),
inference(ef,[status(thm)],[c_0_5]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
inference(assume_negation,[status(cth)],[t12_xboole_1]) ).
cnf(c_0_10,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( set_union2(X1,X2) = X2
| in(esk1_3(X1,X2,X2),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
fof(c_0_12,negated_conjecture,
( subset(esk5_0,esk6_0)
& set_union2(esk5_0,esk6_0) != esk6_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_13,plain,
! [X38,X39] : set_union2(X38,X39) = set_union2(X39,X38),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_14,plain,
( set_union2(X1,X2) = X2
| in(esk1_3(X1,X2,X2),X3)
| ~ subset(X1,X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
subset(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
set_union2(esk5_0,esk6_0) != esk6_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( set_union2(esk5_0,X1) = X1
| in(esk1_3(esk5_0,X1,X1),esk6_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
set_union2(esk6_0,esk5_0) != esk6_0,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
~ in(esk1_3(esk5_0,esk6_0,esk6_0),esk6_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_18]),c_0_17]),c_0_19]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_18]),c_0_17]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU126+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
% 0.15/0.32 % Computer : n009.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:44:11 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.77/1.86 % Version : CSE_E---1.7
% 1.77/1.86 % Problem : theBenchmark.p
% 1.77/1.86 % SZS status Theorem for theBenchmark.p
% 1.77/1.86 % SZS output start CNFRefutation
% See solution above
% 1.77/1.86 % Total time : 1.373s
%------------------------------------------------------------------------------