%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU344+1 : 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 : n019.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 05:11:32 PM UTC 2026
% Result : Theorem 1.29s 1.72s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 13 unt; 0 def)
% Number of atoms : 107 ( 17 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 110 ( 41 ~; 36 |; 15 &)
% ( 4 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 53 ( 4 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t2_lattice3,conjecture,
! [X1,X2] :
( element(X2,the_carrier(boole_lattice(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_lattice(X1)))
=> ( below(boole_lattice(X1),X2,X3)
<=> subset(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_lattice3) ).
fof(d3_lattices,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below(X1,X2,X3)
<=> join(X1,X2,X3) = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattices) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(dt_k1_lattice3,axiom,
! [X1] :
( strict_latt_str(boole_lattice(X1))
& latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice3) ).
fof(fc1_lattice3,axiom,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice3) ).
fof(t1_lattice3,axiom,
! [X1,X2] :
( element(X2,the_carrier(boole_lattice(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_lattice(X1)))
=> ( join(boole_lattice(X1),X2,X3) = set_union2(X2,X3)
& meet(boole_lattice(X1),X2,X3) = set_intersection2(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_lattice3) ).
fof(t12_xboole_1,axiom,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(t7_xboole_1,axiom,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2] :
( element(X2,the_carrier(boole_lattice(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_lattice(X1)))
=> ( below(boole_lattice(X1),X2,X3)
<=> subset(X2,X3) ) ) ),
inference(assume_negation,[status(cth)],[t2_lattice3]) ).
fof(c_0_9,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below(X1,X2,X3)
<=> join(X1,X2,X3) = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[d3_lattices]) ).
fof(c_0_10,plain,
! [X189] :
( ( meet_semilatt_str(X189)
| ~ latt_str(X189) )
& ( join_semilatt_str(X189)
| ~ latt_str(X189) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(c_0_11,plain,
! [X174] :
( strict_latt_str(boole_lattice(X174))
& latt_str(boole_lattice(X174)) ),
inference(variable_rename,[status(thm)],[dt_k1_lattice3]) ).
fof(c_0_12,plain,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_lattice3]) ).
fof(c_0_13,negated_conjecture,
( element(esk17_0,the_carrier(boole_lattice(esk16_0)))
& element(esk18_0,the_carrier(boole_lattice(esk16_0)))
& ( ~ below(boole_lattice(esk16_0),esk17_0,esk18_0)
| ~ subset(esk17_0,esk18_0) )
& ( below(boole_lattice(esk16_0),esk17_0,esk18_0)
| subset(esk17_0,esk18_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_14,plain,
! [X166,X167,X168] :
( ( ~ below(X166,X167,X168)
| join(X166,X167,X168) = X168
| ~ element(X168,the_carrier(X166))
| ~ element(X167,the_carrier(X166))
| empty_carrier(X166)
| ~ join_semilatt_str(X166) )
& ( join(X166,X167,X168) != X168
| below(X166,X167,X168)
| ~ element(X168,the_carrier(X166))
| ~ element(X167,the_carrier(X166))
| empty_carrier(X166)
| ~ join_semilatt_str(X166) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
cnf(c_0_15,plain,
( join_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X207] :
( ~ empty_carrier(boole_lattice(X207))
& strict_latt_str(boole_lattice(X207)) ),
inference(variable_rename,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
( ~ below(boole_lattice(esk16_0),esk17_0,esk18_0)
| ~ subset(esk17_0,esk18_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( below(X1,X2,X3)
| empty_carrier(X1)
| join(X1,X2,X3) != X3
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
join_semilatt_str(boole_lattice(X1)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
element(esk18_0,the_carrier(boole_lattice(esk16_0))),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,negated_conjecture,
element(esk17_0,the_carrier(boole_lattice(esk16_0))),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,plain,
~ empty_carrier(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_24,plain,
! [X254,X255,X256] :
( ( join(boole_lattice(X254),X255,X256) = set_union2(X255,X256)
| ~ element(X256,the_carrier(boole_lattice(X254)))
| ~ element(X255,the_carrier(boole_lattice(X254))) )
& ( meet(boole_lattice(X254),X255,X256) = set_intersection2(X255,X256)
| ~ element(X256,the_carrier(boole_lattice(X254)))
| ~ element(X255,the_carrier(boole_lattice(X254))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_lattice3])])])]) ).
fof(c_0_25,plain,
! [X251,X252] :
( ~ subset(X251,X252)
| set_union2(X251,X252) = X252 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
cnf(c_0_26,negated_conjecture,
( join(boole_lattice(esk16_0),esk17_0,esk18_0) != esk18_0
| ~ subset(esk17_0,esk18_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_27,plain,
( join(boole_lattice(X1),X2,X3) = set_union2(X2,X3)
| ~ element(X3,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,plain,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( below(boole_lattice(esk16_0),esk17_0,esk18_0)
| subset(esk17_0,esk18_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_30,negated_conjecture,
~ subset(esk17_0,esk18_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_21]),c_0_22])]),c_0_28]) ).
cnf(c_0_31,plain,
( join(X1,X2,X3) = X3
| empty_carrier(X1)
| ~ below(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_32,negated_conjecture,
below(boole_lattice(esk16_0),esk17_0,esk18_0),
inference(sr,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_33,plain,
! [X276,X277] : subset(X276,set_union2(X276,X277)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
cnf(c_0_34,negated_conjecture,
join(boole_lattice(esk16_0),esk17_0,esk18_0) = esk18_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_20]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_35,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_36,negated_conjecture,
set_union2(esk17_0,esk18_0) = esk18_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_34]),c_0_21]),c_0_22])]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU344+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n019.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 02:58:29 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.29/1.72 % Version : CSE_E---1.7
% 1.29/1.72 % Problem : theBenchmark.p
% 1.29/1.72 % SZS status Theorem for theBenchmark.p
% 1.29/1.72 % SZS output start CNFRefutation
% See solution above
% 1.29/1.72 % Total time : 1.373s
%------------------------------------------------------------------------------