%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT385+4 : TPTP v9.2.1. Released v4.0.0.
% 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 : n004.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 04:38:26 PM UTC 2026
% Result : Theorem 1.30s 1.73s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 6 unt; 0 def)
% Number of atoms : 277 ( 8 equ)
% Maximal formula atoms : 48 ( 13 avg)
% Number of connectives : 343 ( 87 ~; 102 |; 116 &)
% ( 1 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 10 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-3 aty)
% Number of variables : 64 ( 1 sgn 51 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1] :
( ( aElementOf0(X1,xU)
& ( ( aElementOf0(X1,xU)
& ! [X2] :
( aElementOf0(X2,xP)
=> sdtlseqdt0(X1,X2) ) )
| aLowerBoundOfIn0(X1,xP,xU) )
& ! [X2] :
( ( aElementOf0(X2,xU)
& ! [X3] :
( aElementOf0(X3,xP)
=> sdtlseqdt0(X2,X3) )
& aLowerBoundOfIn0(X2,xP,xU) )
=> sdtlseqdt0(X2,X1) ) )
| aInfimumOfIn0(X1,xP,xU) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__1123,hypothesis,
( aSet0(xU)
& ! [X1] :
( ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xU) ) )
| aSubsetOf0(X1,xU) )
=> ? [X2] :
( aElementOf0(X2,xU)
& aElementOf0(X2,xU)
& ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) )
& aLowerBoundOfIn0(X2,X1,xU)
& ! [X3] :
( ( ( aElementOf0(X3,xU)
& ! [X4] :
( aElementOf0(X4,X1)
=> sdtlseqdt0(X3,X4) ) )
| aLowerBoundOfIn0(X3,X1,xU) )
=> sdtlseqdt0(X3,X2) )
& aInfimumOfIn0(X2,X1,xU)
& ? [X3] :
( aElementOf0(X3,xU)
& aElementOf0(X3,xU)
& ! [X4] :
( aElementOf0(X4,X1)
=> sdtlseqdt0(X4,X3) )
& aUpperBoundOfIn0(X3,X1,xU)
& ! [X4] :
( ( ( aElementOf0(X4,xU)
& ! [X5] :
( aElementOf0(X5,X1)
=> sdtlseqdt0(X5,X4) ) )
| aUpperBoundOfIn0(X4,X1,xU) )
=> sdtlseqdt0(X3,X4) )
& aSupremumOfIn0(X3,X1,xU) ) ) )
& aCompleteLattice0(xU)
& aFunction0(xf)
& ! [X1,X2] :
( ( aElementOf0(X1,szDzozmdt0(xf))
& aElementOf0(X2,szDzozmdt0(xf)) )
=> ( sdtlseqdt0(X1,X2)
=> sdtlseqdt0(sdtlpdtrp0(xf,X1),sdtlpdtrp0(xf,X2)) ) )
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1123) ).
fof(m__1244,hypothesis,
( aSet0(xP)
& ! [X1] :
( ( aElementOf0(X1,xP)
=> ( aElementOf0(X1,xU)
& sdtlseqdt0(sdtlpdtrp0(xf,X1),X1)
& ! [X2] :
( aElementOf0(X2,xT)
=> sdtlseqdt0(X2,X1) )
& aUpperBoundOfIn0(X1,xT,xU) ) )
& ( ( aElementOf0(X1,xU)
& sdtlseqdt0(sdtlpdtrp0(xf,X1),X1)
& ( ! [X2] :
( aElementOf0(X2,xT)
=> sdtlseqdt0(X2,X1) )
| aUpperBoundOfIn0(X1,xT,xU) ) )
=> aElementOf0(X1,xP) ) )
& xP = cS1241(xU,xf,xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1244) ).
fof(c_0_3,plain,
! [X1] :
( epred1_1(X1)
<=> ? [X2] :
( aElementOf0(X2,xU)
& ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) )
& aLowerBoundOfIn0(X2,X1,xU)
& ! [X3] :
( ( ( aElementOf0(X3,xU)
& ! [X4] :
( aElementOf0(X4,X1)
=> sdtlseqdt0(X3,X4) ) )
| aLowerBoundOfIn0(X3,X1,xU) )
=> sdtlseqdt0(X3,X2) )
& aInfimumOfIn0(X2,X1,xU)
& ? [X3] :
( aElementOf0(X3,xU)
& ! [X4] :
( aElementOf0(X4,X1)
=> sdtlseqdt0(X4,X3) )
& aUpperBoundOfIn0(X3,X1,xU)
& ! [X4] :
( ( ( aElementOf0(X4,xU)
& ! [X5] :
( aElementOf0(X5,X1)
=> sdtlseqdt0(X5,X4) ) )
| aUpperBoundOfIn0(X4,X1,xU) )
=> sdtlseqdt0(X3,X4) )
& aSupremumOfIn0(X3,X1,xU) ) ) ),
introduced(definition) ).
fof(c_0_4,negated_conjecture,
~ ? [X1] :
( ( aElementOf0(X1,xU)
& ( ( aElementOf0(X1,xU)
& ! [X2] :
( aElementOf0(X2,xP)
=> sdtlseqdt0(X1,X2) ) )
| aLowerBoundOfIn0(X1,xP,xU) )
& ! [X2] :
( ( aElementOf0(X2,xU)
& ! [X3] :
( aElementOf0(X3,xP)
=> sdtlseqdt0(X2,X3) )
& aLowerBoundOfIn0(X2,xP,xU) )
=> sdtlseqdt0(X2,X1) ) )
| aInfimumOfIn0(X1,xP,xU) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_5,plain,
! [X1] :
( epred1_1(X1)
=> ? [X2] :
( aElementOf0(X2,xU)
& ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) )
& aLowerBoundOfIn0(X2,X1,xU)
& ! [X3] :
( ( ( aElementOf0(X3,xU)
& ! [X4] :
( aElementOf0(X4,X1)
=> sdtlseqdt0(X3,X4) ) )
| aLowerBoundOfIn0(X3,X1,xU) )
=> sdtlseqdt0(X3,X2) )
& aInfimumOfIn0(X2,X1,xU)
& ? [X3] :
( aElementOf0(X3,xU)
& ! [X4] :
( aElementOf0(X4,X1)
=> sdtlseqdt0(X4,X3) )
& aUpperBoundOfIn0(X3,X1,xU)
& ! [X4] :
( ( ( aElementOf0(X4,xU)
& ! [X5] :
( aElementOf0(X5,X1)
=> sdtlseqdt0(X5,X4) ) )
| aUpperBoundOfIn0(X4,X1,xU) )
=> sdtlseqdt0(X3,X4) )
& aSupremumOfIn0(X3,X1,xU) ) ) ),
inference(split_equiv,[status(thm)],[c_0_3]) ).
fof(c_0_6,hypothesis,
( aSet0(xU)
& ! [X1] :
( ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xU) ) )
| aSubsetOf0(X1,xU) )
=> epred1_1(X1) )
& aCompleteLattice0(xU)
& aFunction0(xf)
& ! [X1,X2] :
( ( aElementOf0(X1,szDzozmdt0(xf))
& aElementOf0(X2,szDzozmdt0(xf)) )
=> ( sdtlseqdt0(X1,X2)
=> sdtlseqdt0(sdtlpdtrp0(xf,X1),sdtlpdtrp0(xf,X2)) ) )
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[m__1123]),c_0_3]) ).
fof(c_0_7,negated_conjecture,
! [X163,X166,X167] :
( ( aElementOf0(esk15_1(X163),xU)
| aElementOf0(esk14_1(X163),xP)
| ~ aElementOf0(X163,xU)
| ~ aElementOf0(X163,xU) )
& ( ~ aElementOf0(X166,xP)
| sdtlseqdt0(esk15_1(X163),X166)
| aElementOf0(esk14_1(X163),xP)
| ~ aElementOf0(X163,xU)
| ~ aElementOf0(X163,xU) )
& ( aLowerBoundOfIn0(esk15_1(X163),xP,xU)
| aElementOf0(esk14_1(X163),xP)
| ~ aElementOf0(X163,xU)
| ~ aElementOf0(X163,xU) )
& ( ~ sdtlseqdt0(esk15_1(X163),X163)
| aElementOf0(esk14_1(X163),xP)
| ~ aElementOf0(X163,xU)
| ~ aElementOf0(X163,xU) )
& ( aElementOf0(esk15_1(X163),xU)
| ~ sdtlseqdt0(X163,esk14_1(X163))
| ~ aElementOf0(X163,xU)
| ~ aElementOf0(X163,xU) )
& ( ~ aElementOf0(X166,xP)
| sdtlseqdt0(esk15_1(X163),X166)
| ~ sdtlseqdt0(X163,esk14_1(X163))
| ~ aElementOf0(X163,xU)
| ~ aElementOf0(X163,xU) )
& ( aLowerBoundOfIn0(esk15_1(X163),xP,xU)
| ~ sdtlseqdt0(X163,esk14_1(X163))
| ~ aElementOf0(X163,xU)
| ~ aElementOf0(X163,xU) )
& ( ~ sdtlseqdt0(esk15_1(X163),X163)
| ~ sdtlseqdt0(X163,esk14_1(X163))
| ~ aElementOf0(X163,xU)
| ~ aElementOf0(X163,xU) )
& ( aElementOf0(esk15_1(X163),xU)
| ~ aLowerBoundOfIn0(X163,xP,xU)
| ~ aElementOf0(X163,xU) )
& ( ~ aElementOf0(X166,xP)
| sdtlseqdt0(esk15_1(X163),X166)
| ~ aLowerBoundOfIn0(X163,xP,xU)
| ~ aElementOf0(X163,xU) )
& ( aLowerBoundOfIn0(esk15_1(X163),xP,xU)
| ~ aLowerBoundOfIn0(X163,xP,xU)
| ~ aElementOf0(X163,xU) )
& ( ~ sdtlseqdt0(esk15_1(X163),X163)
| ~ aLowerBoundOfIn0(X163,xP,xU)
| ~ aElementOf0(X163,xU) )
& ~ aInfimumOfIn0(X167,xP,xU) ),
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)],[c_0_4])])])])])]) ).
fof(c_0_8,plain,
! [X168,X170,X171,X174,X175] :
( ( aElementOf0(esk16_1(X168),xU)
| ~ epred1_1(X168) )
& ( ~ aElementOf0(X170,X168)
| sdtlseqdt0(esk16_1(X168),X170)
| ~ epred1_1(X168) )
& ( aLowerBoundOfIn0(esk16_1(X168),X168,xU)
| ~ epred1_1(X168) )
& ( aElementOf0(esk17_2(X168,X171),X168)
| ~ aElementOf0(X171,xU)
| sdtlseqdt0(X171,esk16_1(X168))
| ~ epred1_1(X168) )
& ( ~ sdtlseqdt0(X171,esk17_2(X168,X171))
| ~ aElementOf0(X171,xU)
| sdtlseqdt0(X171,esk16_1(X168))
| ~ epred1_1(X168) )
& ( ~ aLowerBoundOfIn0(X171,X168,xU)
| sdtlseqdt0(X171,esk16_1(X168))
| ~ epred1_1(X168) )
& ( aInfimumOfIn0(esk16_1(X168),X168,xU)
| ~ epred1_1(X168) )
& ( aElementOf0(esk18_1(X168),xU)
| ~ epred1_1(X168) )
& ( ~ aElementOf0(X174,X168)
| sdtlseqdt0(X174,esk18_1(X168))
| ~ epred1_1(X168) )
& ( aUpperBoundOfIn0(esk18_1(X168),X168,xU)
| ~ epred1_1(X168) )
& ( aElementOf0(esk19_2(X168,X175),X168)
| ~ aElementOf0(X175,xU)
| sdtlseqdt0(esk18_1(X168),X175)
| ~ epred1_1(X168) )
& ( ~ sdtlseqdt0(esk19_2(X168,X175),X175)
| ~ aElementOf0(X175,xU)
| sdtlseqdt0(esk18_1(X168),X175)
| ~ epred1_1(X168) )
& ( ~ aUpperBoundOfIn0(X175,X168,xU)
| sdtlseqdt0(esk18_1(X168),X175)
| ~ epred1_1(X168) )
& ( aSupremumOfIn0(esk18_1(X168),X168,xU)
| ~ epred1_1(X168) ) ),
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)],[c_0_5])])])])])]) ).
fof(c_0_9,hypothesis,
! [X153,X155,X156] :
( aSet0(xU)
& ( aElementOf0(esk12_1(X153),X153)
| ~ aSet0(X153)
| epred1_1(X153) )
& ( ~ aElementOf0(esk12_1(X153),xU)
| ~ aSet0(X153)
| epred1_1(X153) )
& ( ~ aSubsetOf0(X153,xU)
| epred1_1(X153) )
& aCompleteLattice0(xU)
& aFunction0(xf)
& ( ~ aElementOf0(X155,szDzozmdt0(xf))
| ~ aElementOf0(X156,szDzozmdt0(xf))
| ~ sdtlseqdt0(X155,X156)
| sdtlseqdt0(sdtlpdtrp0(xf,X155),sdtlpdtrp0(xf,X156)) )
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ),
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_10,hypothesis,
! [X159,X160,X161] :
( aSet0(xP)
& ( aElementOf0(X159,xU)
| ~ aElementOf0(X159,xP) )
& ( sdtlseqdt0(sdtlpdtrp0(xf,X159),X159)
| ~ aElementOf0(X159,xP) )
& ( ~ aElementOf0(X160,xT)
| sdtlseqdt0(X160,X159)
| ~ aElementOf0(X159,xP) )
& ( aUpperBoundOfIn0(X159,xT,xU)
| ~ aElementOf0(X159,xP) )
& ( aElementOf0(esk13_1(X161),xT)
| ~ aElementOf0(X161,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X161),X161)
| aElementOf0(X161,xP) )
& ( ~ sdtlseqdt0(esk13_1(X161),X161)
| ~ aElementOf0(X161,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X161),X161)
| aElementOf0(X161,xP) )
& ( ~ aUpperBoundOfIn0(X161,xT,xU)
| ~ aElementOf0(X161,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X161),X161)
| aElementOf0(X161,xP) )
& xP = cS1241(xU,xf,xT) ),
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)],[m__1244])])])])])]) ).
cnf(c_0_11,negated_conjecture,
~ aInfimumOfIn0(X1,xP,xU),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( aInfimumOfIn0(esk16_1(X1),X1,xU)
| ~ epred1_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,hypothesis,
( aElementOf0(esk12_1(X1),X1)
| epred1_1(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,hypothesis,
aSet0(xP),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
~ epred1_1(xP),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,hypothesis,
( aElementOf0(X1,xU)
| ~ aElementOf0(X1,xP) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,hypothesis,
aElementOf0(esk12_1(xP),xP),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,hypothesis,
( epred1_1(X1)
| ~ aElementOf0(esk12_1(X1),xU)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,hypothesis,
aElementOf0(esk12_1(xP),xU),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_14])]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT385+4 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n004.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 21:49:17 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % 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 : 1.373s
%------------------------------------------------------------------------------