%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU106+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n020.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 05:10:38 PM UTC 2026
% Result : Theorem 1.19s 1.88s
% Output : CNFRefutation 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 15 unt; 0 def)
% Number of atoms : 100 ( 12 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 106 ( 44 ~; 40 |; 11 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 59 ( 1 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t10_finsub_1,axiom,
! [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/sandbox/benchmark/theBenchmark.p',t10_finsub_1) ).
fof(t100_xboole_1,axiom,
! [X1,X2] : set_difference(X1,X2) = symmetric_difference(X1,set_intersection2(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_xboole_1) ).
fof(t95_xboole_1,axiom,
! [X1,X2] : set_intersection2(X1,X2) = symmetric_difference(symmetric_difference(X1,X2),set_union2(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_xboole_1) ).
fof(commutativity_k5_xboole_0,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = symmetric_difference(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).
fof(t17_finsub_1,conjecture,
! [X1] :
( ~ empty(X1)
=> ( ! [X2] :
( element(X2,X1)
=> ! [X3] :
( element(X3,X1)
=> ( in(symmetric_difference(X2,X3),X1)
& in(set_union2(X2,X3),X1) ) ) )
=> preboolean(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_finsub_1) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(c_0_7,plain,
! [X139,X140,X141,X142] :
( ( in(set_union2(X140,X141),X139)
| ~ in(X140,X139)
| ~ in(X141,X139)
| ~ preboolean(X139) )
& ( in(set_difference(X140,X141),X139)
| ~ in(X140,X139)
| ~ in(X141,X139)
| ~ preboolean(X139) )
& ( in(esk11_1(X142),X142)
| preboolean(X142) )
& ( in(esk12_1(X142),X142)
| preboolean(X142) )
& ( ~ in(set_union2(esk11_1(X142),esk12_1(X142)),X142)
| ~ in(set_difference(esk11_1(X142),esk12_1(X142)),X142)
| preboolean(X142) ) ),
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)],[t10_finsub_1])])])])])]) ).
fof(c_0_8,plain,
! [X137,X138] : set_difference(X137,X138) = symmetric_difference(X137,set_intersection2(X137,X138)),
inference(variable_rename,[status(thm)],[t100_xboole_1]) ).
fof(c_0_9,plain,
! [X170,X171] : set_intersection2(X170,X171) = symmetric_difference(symmetric_difference(X170,X171),set_union2(X170,X171)),
inference(variable_rename,[status(thm)],[t95_xboole_1]) ).
cnf(c_0_10,plain,
( preboolean(X1)
| ~ in(set_union2(esk11_1(X1),esk12_1(X1)),X1)
| ~ in(set_difference(esk11_1(X1),esk12_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
set_difference(X1,X2) = symmetric_difference(X1,set_intersection2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
set_intersection2(X1,X2) = symmetric_difference(symmetric_difference(X1,X2),set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X99,X100] : symmetric_difference(X99,X100) = symmetric_difference(X100,X99),
inference(variable_rename,[status(thm)],[commutativity_k5_xboole_0]) ).
fof(c_0_14,negated_conjecture,
~ ! [X1] :
( ~ empty(X1)
=> ( ! [X2] :
( element(X2,X1)
=> ! [X3] :
( element(X3,X1)
=> ( in(symmetric_difference(X2,X3),X1)
& in(set_union2(X2,X3),X1) ) ) )
=> preboolean(X1) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t17_finsub_1])]) ).
cnf(c_0_15,plain,
( preboolean(X1)
| ~ in(set_union2(esk11_1(X1),esk12_1(X1)),X1)
| ~ in(symmetric_difference(esk11_1(X1),symmetric_difference(symmetric_difference(esk11_1(X1),esk12_1(X1)),set_union2(esk11_1(X1),esk12_1(X1)))),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_16,plain,
symmetric_difference(X1,X2) = symmetric_difference(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,negated_conjecture,
! [X146,X147] :
( ~ empty(esk13_0)
& ( in(symmetric_difference(X146,X147),esk13_0)
| ~ element(X147,esk13_0)
| ~ element(X146,esk13_0) )
& ( in(set_union2(X146,X147),esk13_0)
| ~ element(X147,esk13_0)
| ~ element(X146,esk13_0) )
& ~ preboolean(esk13_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_14])])])])]) ).
fof(c_0_18,plain,
! [X149,X150] :
( ~ in(X149,X150)
| element(X149,X150) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(c_0_19,plain,
! [X120] : set_union2(X120,X120) = X120,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
cnf(c_0_20,plain,
( preboolean(X1)
| ~ in(symmetric_difference(esk11_1(X1),symmetric_difference(set_union2(esk11_1(X1),esk12_1(X1)),symmetric_difference(esk11_1(X1),esk12_1(X1)))),X1)
| ~ in(set_union2(esk11_1(X1),esk12_1(X1)),X1) ),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( in(symmetric_difference(X1,X2),esk13_0)
| ~ element(X2,esk13_0)
| ~ element(X1,esk13_0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
~ preboolean(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( in(set_union2(X1,X2),esk13_0)
| ~ element(X2,esk13_0)
| ~ element(X1,esk13_0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
( ~ element(symmetric_difference(set_union2(esk11_1(esk13_0),esk12_1(esk13_0)),symmetric_difference(esk11_1(esk13_0),esk12_1(esk13_0))),esk13_0)
| ~ element(esk11_1(esk13_0),esk13_0)
| ~ in(set_union2(esk11_1(esk13_0),esk12_1(esk13_0)),esk13_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_27,negated_conjecture,
( element(symmetric_difference(X1,X2),esk13_0)
| ~ element(X2,esk13_0)
| ~ element(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_28,negated_conjecture,
( in(X1,esk13_0)
| ~ element(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( ~ element(symmetric_difference(esk11_1(esk13_0),esk12_1(esk13_0)),esk13_0)
| ~ element(set_union2(esk11_1(esk13_0),esk12_1(esk13_0)),esk13_0)
| ~ element(esk11_1(esk13_0),esk13_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_30,negated_conjecture,
( element(set_union2(X1,X2),esk13_0)
| ~ element(X2,esk13_0)
| ~ element(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,plain,
( in(esk12_1(X1),X1)
| preboolean(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_32,negated_conjecture,
( ~ element(esk11_1(esk13_0),esk13_0)
| ~ element(esk12_1(esk13_0),esk13_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_27]),c_0_30]) ).
cnf(c_0_33,plain,
( element(esk12_1(X1),X1)
| preboolean(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_31]) ).
cnf(c_0_34,plain,
( in(esk11_1(X1),X1)
| preboolean(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_35,negated_conjecture,
~ element(esk11_1(esk13_0),esk13_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_22]) ).
cnf(c_0_36,plain,
( element(esk11_1(X1),X1)
| preboolean(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.19 % Problem : SEU106+1 : TPTP v9.2.1. Released v3.2.0.
% 0.03/0.19 % 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
% 0.13/0.43 % Computer : n020.cluster.edu
% 0.13/0.43 % Model : x86_64 x86_64
% 0.13/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.43 % Memory : 8042.1875MB
% 0.13/0.43 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.43 % CPULimit : 300
% 0.13/0.43 % WCLimit : 300
% 0.13/0.43 % DateTime : Tue May 5 02:43:50 EDT 2026
% 0.14/0.45 % CPUTime :
% 0.14/0.46 % start to proof: theBenchmark
% 1.19/1.88 % Version : CSE_E---1.7
% 1.19/1.88 % Problem : theBenchmark.p
% 1.19/1.88 % SZS status Theorem for theBenchmark.p
% 1.19/1.88 % SZS output start CNFRefutation
% See solution above
% 1.19/1.88 % Total time : 1.383s
%------------------------------------------------------------------------------