%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU145+2 : 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 : 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 05:10:46 PM UTC 2026
% Result : Theorem 1.95s 1.92s
% Output : CNFRefutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 12 unt; 0 def)
% Number of atoms : 108 ( 35 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 118 ( 41 ~; 51 |; 16 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 68 ( 0 sgn 44 !; 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(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
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(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(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(c_0_5,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_6,negated_conjecture,
( subset(esk8_0,esk9_0)
& ~ in(esk10_0,esk8_0)
& ~ subset(esk8_0,set_difference(esk9_0,singleton(esk10_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_7,lemma,
! [X279] : unordered_pair(X279,X279) = singleton(X279),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
cnf(c_0_8,negated_conjecture,
~ subset(esk8_0,set_difference(esk9_0,singleton(esk10_0))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X175,X176,X177,X178,X179] :
( ( ~ subset(X175,X176)
| ~ in(X177,X175)
| in(X177,X176) )
& ( in(esk5_2(X178,X179),X178)
| subset(X178,X179) )
& ( ~ in(esk5_2(X178,X179),X179)
| subset(X178,X179) ) ),
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_11,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]) ).
cnf(c_0_12,negated_conjecture,
~ subset(esk8_0,set_difference(esk9_0,unordered_pair(esk10_0,esk10_0))),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( in(esk5_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X190,X191,X192,X193,X194,X195,X196,X197] :
( ( in(X193,X190)
| ~ in(X193,X192)
| X192 != set_difference(X190,X191) )
& ( ~ in(X193,X191)
| ~ in(X193,X192)
| X192 != set_difference(X190,X191) )
& ( ~ in(X194,X190)
| in(X194,X191)
| in(X194,X192)
| X192 != set_difference(X190,X191) )
& ( ~ in(esk7_3(X195,X196,X197),X197)
| ~ in(esk7_3(X195,X196,X197),X195)
| in(esk7_3(X195,X196,X197),X196)
| X197 = set_difference(X195,X196) )
& ( in(esk7_3(X195,X196,X197),X195)
| in(esk7_3(X195,X196,X197),X197)
| X197 = set_difference(X195,X196) )
& ( ~ in(esk7_3(X195,X196,X197),X196)
| in(esk7_3(X195,X196,X197),X197)
| X197 = set_difference(X195,X196) ) ),
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_11])])])])])]) ).
cnf(c_0_15,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
in(esk5_2(esk8_0,set_difference(esk9_0,unordered_pair(esk10_0,esk10_0))),esk8_0),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( in(esk5_2(esk8_0,set_difference(esk9_0,unordered_pair(esk10_0,esk10_0))),X1)
| ~ subset(esk8_0,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
subset(esk8_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_20,plain,
! [X157,X158,X159,X160,X161,X162,X163,X164] :
( ( ~ in(X160,X159)
| X160 = X157
| X160 = X158
| X159 != unordered_pair(X157,X158) )
& ( X161 != X157
| in(X161,X159)
| X159 != unordered_pair(X157,X158) )
& ( X161 != X158
| in(X161,X159)
| X159 != unordered_pair(X157,X158) )
& ( esk3_3(X162,X163,X164) != X162
| ~ in(esk3_3(X162,X163,X164),X164)
| X164 = unordered_pair(X162,X163) )
& ( esk3_3(X162,X163,X164) != X163
| ~ in(esk3_3(X162,X163,X164),X164)
| X164 = unordered_pair(X162,X163) )
& ( in(esk3_3(X162,X163,X164),X164)
| esk3_3(X162,X163,X164) = X162
| esk3_3(X162,X163,X164) = X163
| X164 = unordered_pair(X162,X163) ) ),
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_tarski])])])])])]) ).
cnf(c_0_21,plain,
( in(X1,set_difference(X2,X3))
| in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
in(esk5_2(esk8_0,set_difference(esk9_0,unordered_pair(esk10_0,esk10_0))),esk9_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
( subset(X1,X2)
| ~ in(esk5_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_25,negated_conjecture,
( in(esk5_2(esk8_0,set_difference(esk9_0,unordered_pair(esk10_0,esk10_0))),set_difference(esk9_0,X1))
| in(esk5_2(esk8_0,set_difference(esk9_0,unordered_pair(esk10_0,esk10_0))),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X3,X2)) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_27,negated_conjecture,
in(esk5_2(esk8_0,set_difference(esk9_0,unordered_pair(esk10_0,esk10_0))),unordered_pair(esk10_0,esk10_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_12]) ).
cnf(c_0_28,negated_conjecture,
esk5_2(esk8_0,set_difference(esk9_0,unordered_pair(esk10_0,esk10_0))) = esk10_0,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
~ in(esk10_0,esk8_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_28]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU145+2 : 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 : n029.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 02:45:29 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.95/1.92 % Version : CSE_E---1.7
% 1.95/1.92 % Problem : theBenchmark.p
% 1.95/1.92 % SZS status Theorem for theBenchmark.p
% 1.95/1.92 % SZS output start CNFRefutation
% See solution above
% 1.95/1.92 % Total time : 1.369s
%------------------------------------------------------------------------------