%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU125+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 : n017.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 1.48s 1.78s
% Output : CNFRefutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 13 unt; 0 def)
% Number of atoms : 95 ( 16 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 90 ( 31 ~; 42 |; 11 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 74 ( 4 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t8_xboole_1,conjecture,
! [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(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(t1_boole,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
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_5,negated_conjecture,
~ ! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
inference(assume_negation,[status(cth)],[t8_xboole_1]) ).
fof(c_0_6,plain,
! [X39,X40,X41,X42,X43,X44,X45,X46] :
( ( ~ in(X42,X41)
| in(X42,X39)
| in(X42,X40)
| X41 != set_union2(X39,X40) )
& ( ~ in(X43,X39)
| in(X43,X41)
| X41 != set_union2(X39,X40) )
& ( ~ in(X43,X40)
| in(X43,X41)
| X41 != set_union2(X39,X40) )
& ( ~ in(esk1_3(X44,X45,X46),X44)
| ~ in(esk1_3(X44,X45,X46),X46)
| X46 = set_union2(X44,X45) )
& ( ~ in(esk1_3(X44,X45,X46),X45)
| ~ in(esk1_3(X44,X45,X46),X46)
| X46 = set_union2(X44,X45) )
& ( in(esk1_3(X44,X45,X46),X46)
| in(esk1_3(X44,X45,X46),X44)
| in(esk1_3(X44,X45,X46),X45)
| X46 = set_union2(X44,X45) ) ),
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])])])])])]) ).
fof(c_0_7,plain,
! [X48,X49,X50,X51,X52] :
( ( ~ subset(X48,X49)
| ~ in(X50,X48)
| in(X50,X49) )
& ( in(esk2_2(X51,X52),X51)
| subset(X51,X52) )
& ( ~ in(esk2_2(X51,X52),X52)
| subset(X51,X52) ) ),
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_8,negated_conjecture,
( subset(esk5_0,esk6_0)
& subset(esk7_0,esk6_0)
& ~ subset(set_union2(esk5_0,esk7_0),esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_9,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
subset(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| ~ in(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( in(X1,esk6_0)
| ~ in(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( in(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,plain,
( subset(X1,set_union2(X2,X3))
| ~ in(esk2_2(X1,set_union2(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( subset(esk5_0,X1)
| in(esk2_2(esk5_0,X1),esk6_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
subset(esk5_0,set_union2(X1,esk6_0)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_19,plain,
! [X62] : set_union2(X62,empty_set) = X62,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(c_0_20,plain,
! [X37,X38] : set_union2(X37,X38) = set_union2(X38,X37),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_21,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
( in(X1,set_union2(X2,esk6_0))
| ~ in(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_18]) ).
cnf(c_0_23,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
subset(esk7_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X3,X2)) ),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_27,negated_conjecture,
( subset(X1,set_union2(X2,esk6_0))
| ~ in(esk2_2(X1,set_union2(X2,esk6_0)),esk5_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_22]) ).
cnf(c_0_28,plain,
set_union2(empty_set,X1) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( in(X1,esk6_0)
| ~ in(X1,esk7_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_25]) ).
cnf(c_0_30,plain,
( subset(set_union2(X1,X2),X3)
| in(esk2_2(set_union2(X1,X2),X3),X2)
| in(esk2_2(set_union2(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_31,negated_conjecture,
( subset(X1,esk6_0)
| ~ in(esk2_2(X1,esk6_0),esk5_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( subset(set_union2(esk7_0,X1),X2)
| in(esk2_2(set_union2(esk7_0,X1),X2),esk6_0)
| in(esk2_2(set_union2(esk7_0,X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
~ subset(set_union2(esk5_0,esk7_0),esk6_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_34,negated_conjecture,
in(esk2_2(set_union2(esk5_0,esk7_0),esk6_0),esk6_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_24]),c_0_24]),c_0_33]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_34]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU125+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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 : n017.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 02:42:57 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.48/1.78 % Version : CSE_E---1.7
% 1.48/1.78 % Problem : theBenchmark.p
% 1.48/1.78 % SZS status Theorem for theBenchmark.p
% 1.48/1.78 % SZS output start CNFRefutation
% See solution above
% 1.48/1.78 % Total time : 1.371s
%------------------------------------------------------------------------------