%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU132+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 : n024.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 05:10:43 PM UTC 2026
% Result : Theorem 2.10s 1.89s
% Output : CNFRefutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 4 unt; 0 def)
% Number of atoms : 86 ( 11 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 94 ( 35 ~; 41 |; 10 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 73 ( 4 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t33_xboole_1,conjecture,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
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(c_0_3,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_4,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
inference(assume_negation,[status(cth)],[t33_xboole_1]) ).
fof(c_0_5,plain,
! [X36,X37,X38,X39,X40,X41,X42,X43] :
( ( in(X39,X36)
| ~ in(X39,X38)
| X38 != set_difference(X36,X37) )
& ( ~ in(X39,X37)
| ~ in(X39,X38)
| X38 != set_difference(X36,X37) )
& ( ~ in(X40,X36)
| in(X40,X37)
| in(X40,X38)
| X38 != set_difference(X36,X37) )
& ( ~ in(esk2_3(X41,X42,X43),X43)
| ~ in(esk2_3(X41,X42,X43),X41)
| in(esk2_3(X41,X42,X43),X42)
| X43 = set_difference(X41,X42) )
& ( in(esk2_3(X41,X42,X43),X41)
| in(esk2_3(X41,X42,X43),X43)
| X43 = set_difference(X41,X42) )
& ( ~ in(esk2_3(X41,X42,X43),X42)
| in(esk2_3(X41,X42,X43),X43)
| X43 = set_difference(X41,X42) ) ),
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_3])])])])])]) ).
fof(c_0_6,plain,
! [X30,X31,X32,X33,X34] :
( ( ~ subset(X30,X31)
| ~ in(X32,X30)
| in(X32,X31) )
& ( in(esk1_2(X33,X34),X33)
| subset(X33,X34) )
& ( ~ in(esk1_2(X33,X34),X34)
| subset(X33,X34) ) ),
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(esk5_0,esk6_0)
& ~ subset(set_difference(esk5_0,esk7_0),set_difference(esk6_0,esk7_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_8,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[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(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,plain,
( in(X1,set_difference(X2,X3))
| in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( in(X1,esk6_0)
| ~ in(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,negated_conjecture,
( in(X1,set_difference(esk6_0,X2))
| in(X1,X2)
| ~ in(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
( subset(set_difference(X1,X2),X3)
| in(esk1_2(set_difference(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( ~ in(X1,set_difference(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_21,negated_conjecture,
( subset(set_difference(esk5_0,X1),X2)
| in(esk1_2(set_difference(esk5_0,X1),X2),set_difference(esk6_0,X3))
| in(esk1_2(set_difference(esk5_0,X1),X2),X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( subset(set_difference(X1,X2),X3)
| ~ in(esk1_2(set_difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_23,negated_conjecture,
( subset(set_difference(esk5_0,X1),set_difference(esk6_0,X2))
| in(esk1_2(set_difference(esk5_0,X1),set_difference(esk6_0,X2)),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
~ subset(set_difference(esk5_0,esk7_0),set_difference(esk6_0,esk7_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_25,negated_conjecture,
subset(set_difference(esk5_0,X1),set_difference(esk6_0,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU132+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.25 % DateTime : Mon May 4 21:44:41 EDT 2026
% 0.06/0.25 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 2.10/1.89 % Version : CSE_E---1.7
% 2.10/1.89 % Problem : theBenchmark.p
% 2.10/1.89 % SZS status Theorem for theBenchmark.p
% 2.10/1.89 % SZS output start CNFRefutation
% See solution above
% 2.20/1.90 % Total time : 1.361s
%------------------------------------------------------------------------------