%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU101+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n011.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 05:10:37 PM UTC 2026
% Result : Theorem 1.30s 1.73s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 8 unt; 0 def)
% Number of atoms : 125 ( 3 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 136 ( 50 ~; 57 |; 19 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t10_finsub_1,conjecture,
! [X1] :
( preboolean(X1)
<=> ! [X2,X3] :
( ( in(X2,X1)
& in(X3,X1) )
=> ( in(set_union2(X2,X3),X1)
& in(set_difference(X2,X3),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_finsub_1) ).
fof(d1_finsub_1,axiom,
! [X1] :
( cup_closed(X1)
<=> ! [X2,X3] :
( ( in(X2,X1)
& in(X3,X1) )
=> in(set_union2(X2,X3),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_finsub_1) ).
fof(cc1_finsub_1,axiom,
! [X1] :
( preboolean(X1)
=> ( cup_closed(X1)
& diff_closed(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finsub_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(d3_finsub_1,axiom,
! [X1] :
( diff_closed(X1)
<=> ! [X2,X3] :
( ( in(X2,X1)
& in(X3,X1) )
=> in(set_difference(X2,X3),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_finsub_1) ).
fof(cc2_finsub_1,axiom,
! [X1] :
( ( cup_closed(X1)
& diff_closed(X1) )
=> preboolean(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finsub_1) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( preboolean(X1)
<=> ! [X2,X3] :
( ( in(X2,X1)
& in(X3,X1) )
=> ( in(set_union2(X2,X3),X1)
& in(set_difference(X2,X3),X1) ) ) ),
inference(assume_negation,[status(cth)],[t10_finsub_1]) ).
fof(c_0_7,negated_conjecture,
! [X124,X125] :
( ( in(esk16_0,esk15_0)
| ~ preboolean(esk15_0) )
& ( in(esk17_0,esk15_0)
| ~ preboolean(esk15_0) )
& ( ~ in(set_union2(esk16_0,esk17_0),esk15_0)
| ~ in(set_difference(esk16_0,esk17_0),esk15_0)
| ~ preboolean(esk15_0) )
& ( in(set_union2(X124,X125),esk15_0)
| ~ in(X124,esk15_0)
| ~ in(X125,esk15_0)
| preboolean(esk15_0) )
& ( in(set_difference(X124,X125),esk15_0)
| ~ in(X124,esk15_0)
| ~ in(X125,esk15_0)
| preboolean(esk15_0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
fof(c_0_8,plain,
! [X81,X82,X83,X84] :
( ( ~ cup_closed(X81)
| ~ in(X82,X81)
| ~ in(X83,X81)
| in(set_union2(X82,X83),X81) )
& ( in(esk1_1(X84),X84)
| cup_closed(X84) )
& ( in(esk2_1(X84),X84)
| cup_closed(X84) )
& ( ~ in(set_union2(esk1_1(X84),esk2_1(X84)),X84)
| cup_closed(X84) ) ),
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_finsub_1])])])])])]) ).
fof(c_0_9,plain,
! [X75] :
( ( cup_closed(X75)
| ~ preboolean(X75) )
& ( diff_closed(X75)
| ~ preboolean(X75) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_finsub_1])])]) ).
cnf(c_0_10,negated_conjecture,
( in(set_union2(X1,X2),esk15_0)
| preboolean(esk15_0)
| ~ in(X1,esk15_0)
| ~ in(X2,esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( in(esk1_1(X1),X1)
| cup_closed(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( cup_closed(X1)
| ~ preboolean(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X79,X80] : set_union2(X79,X80) = set_union2(X80,X79),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_14,plain,
! [X87,X88,X89,X90] :
( ( ~ diff_closed(X87)
| ~ in(X88,X87)
| ~ in(X89,X87)
| in(set_difference(X88,X89),X87) )
& ( in(esk3_1(X90),X90)
| diff_closed(X90) )
& ( in(esk4_1(X90),X90)
| diff_closed(X90) )
& ( ~ in(set_difference(esk3_1(X90),esk4_1(X90)),X90)
| diff_closed(X90) ) ),
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_finsub_1])])])])])]) ).
cnf(c_0_15,negated_conjecture,
( cup_closed(esk15_0)
| in(set_union2(X1,esk1_1(esk15_0)),esk15_0)
| ~ in(X1,esk15_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_16,plain,
( in(esk2_1(X1),X1)
| cup_closed(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
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,
( ~ in(set_union2(esk16_0,esk17_0),esk15_0)
| ~ in(set_difference(esk16_0,esk17_0),esk15_0)
| ~ preboolean(esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,plain,
( in(set_difference(X2,X3),X1)
| ~ diff_closed(X1)
| ~ in(X2,X1)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
( in(esk16_0,esk15_0)
| ~ preboolean(esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_21,negated_conjecture,
( in(esk17_0,esk15_0)
| ~ preboolean(esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,plain,
( diff_closed(X1)
| ~ preboolean(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_23,plain,
( cup_closed(X1)
| ~ in(set_union2(esk1_1(X1),esk2_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_24,negated_conjecture,
( cup_closed(esk15_0)
| in(set_union2(esk1_1(esk15_0),esk2_1(esk15_0)),esk15_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_25,negated_conjecture,
( ~ preboolean(esk15_0)
| ~ in(set_union2(esk16_0,esk17_0),esk15_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21]),c_0_22]) ).
cnf(c_0_26,plain,
( in(set_union2(X2,X3),X1)
| ~ cup_closed(X1)
| ~ in(X2,X1)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,negated_conjecture,
cup_closed(esk15_0),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_28,plain,
! [X78] :
( ~ cup_closed(X78)
| ~ diff_closed(X78)
| preboolean(X78) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_finsub_1])]) ).
cnf(c_0_29,negated_conjecture,
~ preboolean(esk15_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]),c_0_20]),c_0_21]) ).
cnf(c_0_30,plain,
( preboolean(X1)
| ~ cup_closed(X1)
| ~ diff_closed(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( in(set_difference(X1,X2),esk15_0)
| preboolean(esk15_0)
| ~ in(X1,esk15_0)
| ~ in(X2,esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_32,plain,
( in(esk4_1(X1),X1)
| diff_closed(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_33,negated_conjecture,
~ diff_closed(esk15_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_27])]) ).
cnf(c_0_34,plain,
( diff_closed(X1)
| ~ in(set_difference(esk3_1(X1),esk4_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_35,negated_conjecture,
( in(set_difference(X1,esk4_1(esk15_0)),esk15_0)
| ~ in(X1,esk15_0) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_29]),c_0_33]) ).
cnf(c_0_36,negated_conjecture,
~ in(esk3_1(esk15_0),esk15_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_33]) ).
cnf(c_0_37,plain,
( in(esk3_1(X1),X1)
| diff_closed(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU101+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.16/0.33 % Computer : n011.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 02:42:17 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.30/1.73 % Version : CSE_E---1.7
% 1.30/1.73 % Problem : theBenchmark.p
% 1.30/1.73 % SZS status Theorem for theBenchmark.p
% 1.30/1.73 % SZS output start CNFRefutation
% See solution above
% 1.30/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------