%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU145+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/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 05:10:46 PM UTC 2026
% Result : Theorem 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 4 unt; 0 def)
% Number of atoms : 98 ( 23 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 107 ( 36 ~; 47 |; 14 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 65 ( 0 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l3_zfmisc_1,conjecture,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
inference(assume_negation,[status(cth)],[l3_zfmisc_1]) ).
fof(c_0_5,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_6,plain,
! [X31,X32,X33,X34,X35] :
( ( ~ subset(X31,X32)
| ~ in(X33,X31)
| in(X33,X32) )
& ( in(esk2_2(X34,X35),X34)
| subset(X34,X35) )
& ( ~ in(esk2_2(X34,X35),X35)
| subset(X34,X35) ) ),
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])])])])])]) ).
fof(c_0_7,negated_conjecture,
( subset(esk4_0,esk5_0)
& ~ in(esk6_0,esk4_0)
& ~ subset(esk4_0,set_difference(esk5_0,singleton(esk6_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_8,plain,
! [X37,X38,X39,X40,X41,X42,X43,X44] :
( ( in(X40,X37)
| ~ in(X40,X39)
| X39 != set_difference(X37,X38) )
& ( ~ in(X40,X38)
| ~ in(X40,X39)
| X39 != set_difference(X37,X38) )
& ( ~ in(X41,X37)
| in(X41,X38)
| in(X41,X39)
| X39 != set_difference(X37,X38) )
& ( ~ in(esk3_3(X42,X43,X44),X44)
| ~ in(esk3_3(X42,X43,X44),X42)
| in(esk3_3(X42,X43,X44),X43)
| X44 = set_difference(X42,X43) )
& ( in(esk3_3(X42,X43,X44),X42)
| in(esk3_3(X42,X43,X44),X44)
| X44 = set_difference(X42,X43) )
& ( ~ in(esk3_3(X42,X43,X44),X43)
| in(esk3_3(X42,X43,X44),X44)
| X44 = set_difference(X42,X43) ) ),
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)],[c_0_5])])])])])]) ).
cnf(c_0_9,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
subset(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( in(X1,esk5_0)
| ~ in(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( in(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_14,plain,
! [X24,X25,X26,X27,X28,X29] :
( ( ~ in(X26,X25)
| X26 = X24
| X25 != singleton(X24) )
& ( X27 != X24
| in(X27,X25)
| X25 != singleton(X24) )
& ( ~ in(esk1_2(X28,X29),X29)
| esk1_2(X28,X29) != X28
| X29 = singleton(X28) )
& ( in(esk1_2(X28,X29),X29)
| esk1_2(X28,X29) = X28
| X29 = singleton(X28) ) ),
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)],[d1_tarski])])])])])]) ).
cnf(c_0_15,plain,
( in(X1,set_difference(X2,X3))
| in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
( subset(esk4_0,X1)
| in(esk2_2(esk4_0,X1),esk5_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( subset(X1,X2)
| ~ in(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
( subset(esk4_0,X1)
| in(esk2_2(esk4_0,X1),set_difference(esk5_0,X2))
| in(esk2_2(esk4_0,X1),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
( subset(esk4_0,set_difference(esk5_0,X1))
| in(esk2_2(esk4_0,set_difference(esk5_0,X1)),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
( esk2_2(esk4_0,set_difference(esk5_0,singleton(X1))) = X1
| subset(esk4_0,set_difference(esk5_0,singleton(X1))) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,negated_conjecture,
~ subset(esk4_0,set_difference(esk5_0,singleton(esk6_0))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,negated_conjecture,
( subset(esk4_0,set_difference(esk5_0,singleton(X1)))
| in(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
~ in(esk6_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU145+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n008.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:45:13 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Theorem for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------