%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU108+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 : 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 05:10:38 PM UTC 2026
% Result : Theorem 20.44s 12.76s
% Output : CNFRefutation 20.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 6 unt; 0 def)
% Number of atoms : 110 ( 6 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 118 ( 48 ~; 51 |; 11 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-3 aty)
% Number of variables : 79 ( 2 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
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(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(dt_k6_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> element(subset_difference(X1,X2,X3),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
fof(redefinition_k6_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(dt_k4_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> element(subset_union2(X1,X2,X3),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_subset_1) ).
fof(redefinition_k4_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_union2(X1,X2,X3) = set_union2(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
fof(t20_finsub_1,conjecture,
! [X1] : preboolean(powerset(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_finsub_1) ).
fof(c_0_9,plain,
! [X161,X162] :
( ~ in(X161,X162)
| ~ empty(X162) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(c_0_10,plain,
! [X138,X139,X140,X141] :
( ( in(set_union2(X139,X140),X138)
| ~ in(X139,X138)
| ~ in(X140,X138)
| ~ preboolean(X138) )
& ( in(set_difference(X139,X140),X138)
| ~ in(X139,X138)
| ~ in(X140,X138)
| ~ preboolean(X138) )
& ( in(esk11_1(X141),X141)
| preboolean(X141) )
& ( in(esk12_1(X141),X141)
| preboolean(X141) )
& ( ~ in(set_union2(esk11_1(X141),esk12_1(X141)),X141)
| ~ in(set_difference(esk11_1(X141),esk12_1(X141)),X141)
| preboolean(X141) ) ),
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_11,plain,
! [X148,X149] :
( ~ element(X148,X149)
| empty(X149)
| in(X148,X149) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_12,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( in(esk11_1(X1),X1)
| preboolean(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,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_10]) ).
cnf(c_0_15,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( preboolean(X1)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_17,plain,
! [X99,X100,X101] :
( ~ element(X100,powerset(X99))
| ~ element(X101,powerset(X99))
| element(subset_difference(X99,X100,X101),powerset(X99)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_subset_1])]) ).
fof(c_0_18,plain,
! [X134,X135,X136] :
( ~ element(X135,powerset(X134))
| ~ element(X136,powerset(X134))
| subset_difference(X134,X135,X136) = set_difference(X135,X136) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1])]) ).
fof(c_0_19,plain,
! [X145,X146] :
( ~ in(X145,X146)
| element(X145,X146) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
cnf(c_0_20,plain,
( preboolean(X1)
| ~ element(set_difference(esk11_1(X1),esk12_1(X1)),X1)
| ~ in(set_union2(esk11_1(X1),esk12_1(X1)),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_21,plain,
( element(subset_difference(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( subset_difference(X2,X1,X3) = set_difference(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
( in(esk12_1(X1),X1)
| preboolean(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_25,plain,
! [X96,X97,X98] :
( ~ element(X97,powerset(X96))
| ~ element(X98,powerset(X96))
| element(subset_union2(X96,X97,X98),powerset(X96)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_subset_1])]) ).
fof(c_0_26,plain,
! [X131,X132,X133] :
( ~ element(X132,powerset(X131))
| ~ element(X133,powerset(X131))
| subset_union2(X131,X132,X133) = set_union2(X132,X133) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_subset_1])]) ).
fof(c_0_27,negated_conjecture,
~ ! [X1] : preboolean(powerset(X1)),
inference(assume_negation,[status(cth)],[t20_finsub_1]) ).
cnf(c_0_28,plain,
( preboolean(X1)
| ~ element(set_difference(esk11_1(X1),esk12_1(X1)),X1)
| ~ element(set_union2(esk11_1(X1),esk12_1(X1)),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_15]),c_0_16]) ).
cnf(c_0_29,plain,
( element(set_difference(X1,X2),powerset(X3))
| ~ element(X2,powerset(X3))
| ~ element(X1,powerset(X3)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,plain,
( element(esk11_1(X1),X1)
| preboolean(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_13]) ).
cnf(c_0_31,plain,
( element(esk12_1(X1),X1)
| preboolean(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_32,plain,
( element(subset_union2(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,plain,
( subset_union2(X2,X1,X3) = set_union2(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_34,negated_conjecture,
~ preboolean(powerset(esk13_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
cnf(c_0_35,plain,
( preboolean(powerset(X1))
| ~ element(set_union2(esk11_1(powerset(X1)),esk12_1(powerset(X1))),powerset(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31]) ).
cnf(c_0_36,plain,
( element(set_union2(X1,X2),powerset(X3))
| ~ element(X2,powerset(X3))
| ~ element(X1,powerset(X3)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
~ preboolean(powerset(esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,plain,
preboolean(powerset(X1)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_30]),c_0_31]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU108+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.09 % 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
% 0.06/0.30 % Computer : n024.cluster.edu
% 0.06/0.30 % Model : x86_64 x86_64
% 0.06/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.30 % Memory : 8042.1875MB
% 0.06/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.30 % CPULimit : 300
% 0.06/0.30 % WCLimit : 300
% 0.06/0.30 % DateTime : Mon May 4 21:43:26 EDT 2026
% 0.06/0.30 % CPUTime :
% 0.06/0.31 % start to proof: theBenchmark
% 20.44/12.76 % Version : CSE_E---1.7
% 20.44/12.76 % Problem : theBenchmark.p
% 20.44/12.76 % SZS status Theorem for theBenchmark.p
% 20.44/12.76 % SZS output start CNFRefutation
% See solution above
% 20.55/12.85 % Total time : 9.368s
%------------------------------------------------------------------------------