%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM612+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:41:12 PM UTC 2026
% Result : Theorem 0.07s 0.42s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 20
% Syntax : Number of formulae : 77 ( 13 unt; 10 def)
% Number of atoms : 246 ( 31 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 261 ( 92 ~; 87 |; 55 &)
% ( 15 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 10 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 56 ( 54 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0] :
( ( isFinite0(W0)
& aSet0(W0) )
=> ! [W1] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [W0] :
( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( ( aElementOf0(W1,W0)
& isFinite0(W0) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f80,hypothesis,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f99,hypothesis,
( aElementOf0(xQ,slbdtsldtrb0(xO,xK))
& sbrdtbr0(xQ) = xK
& aSubsetOf0(xQ,xO)
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSet0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f103,hypothesis,
( xp = szmzizndt0(xQ)
& ! [W0] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(xp,W0) )
& aElementOf0(xp,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f104,hypothesis,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [W0] :
( aElementOf0(W0,xP)
<=> ( W0 != szmzizndt0(xQ)
& aElementOf0(W0,xQ)
& aElement0(W0) ) )
& ! [W0] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) )
& aSet0(xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f107,hypothesis,
( aSubsetOf0(xP,xQ)
& ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xQ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f109,conjecture,
( aElementOf0(sbrdtbr0(xP),szNzAzT0)
& szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f110,negated_conjecture,
~ ( aElementOf0(sbrdtbr0(xP),szNzAzT0)
& szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) ),
inference(negated_conjecture,[status(cth)],[f109]) ).
fof(f135,plain,
! [W0] :
( ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) ) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f136,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f135]) ).
fof(f137,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f136]) ).
fof(f138,plain,
! [W0] :
( ( ! [W1] :
( ( ~ aElementOf0(sK1_skl(W1,W0),W0)
& aElementOf0(sK1_skl(W1,W0),W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f137]) ).
fof(f139,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f143,plain,
! [W0] :
( ! [W1] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) )
| ~ isFinite0(W0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f144,plain,
! [X0,X1] :
( isFinite0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f190,plain,
! [W0] :
( ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f191,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f227,plain,
! [W0] :
( ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f228,plain,
! [W0] :
( ( ( ~ isFinite0(W0)
| aElementOf0(sbrdtbr0(W0),szNzAzT0) )
& ( isFinite0(W0)
| ~ aElementOf0(sbrdtbr0(W0),szNzAzT0) ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f227]) ).
fof(f229,plain,
! [X0] :
( isFinite0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f228]) ).
fof(f230,plain,
! [X0] :
( ~ isFinite0(X0)
| aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f228]) ).
fof(f237,plain,
! [W0] :
( ! [W1] :
( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0)
| ~ aElementOf0(W1,W0)
| ~ isFinite0(W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f238,plain,
! [X0,X1] :
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0)
| ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f237]) ).
fof(f405,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f406,plain,
szszuzczcdt0(xk) = xK,
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f598,plain,
( aElementOf0(xQ,slbdtsldtrb0(xO,xK))
& sbrdtbr0(xQ) = xK
& aSubsetOf0(xQ,xO)
& ! [W0] :
( aElementOf0(W0,xO)
| ~ aElementOf0(W0,xQ) )
& aSet0(xQ) ),
inference(pre_NNF_transformation,[status(thm)],[f99]) ).
fof(f599,plain,
aSet0(xQ),
inference(cnf_transformation,[status(thm)],[f598]) ).
fof(f602,plain,
sbrdtbr0(xQ) = xK,
inference(cnf_transformation,[status(thm)],[f598]) ).
fof(f618,plain,
( xp = szmzizndt0(xQ)
& ! [W0] :
( sdtlseqdt0(xp,W0)
| ~ aElementOf0(W0,xQ) )
& aElementOf0(xp,xQ) ),
inference(pre_NNF_transformation,[status(thm)],[f103]) ).
fof(f619,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[status(thm)],[f618]) ).
fof(f621,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[status(thm)],[f618]) ).
fof(f622,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [W0] :
( aElementOf0(W0,xP)
<=> ( W0 != szmzizndt0(xQ)
& aElementOf0(W0,xQ)
& aElement0(W0) ) )
& ! [W0] :
( sdtlseqdt0(szmzizndt0(xQ),W0)
| ~ aElementOf0(W0,xQ) )
& aSet0(xP) ),
inference(pre_NNF_transformation,[status(thm)],[f104]) ).
fof(f623,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [W0] :
( ( W0 = szmzizndt0(xQ)
| ~ aElementOf0(W0,xQ)
| ~ aElement0(W0)
| aElementOf0(W0,xP) )
& ( ( W0 != szmzizndt0(xQ)
& aElementOf0(W0,xQ)
& aElement0(W0) )
| ~ aElementOf0(W0,xP) ) )
& ! [W0] :
( sdtlseqdt0(szmzizndt0(xQ),W0)
| ~ aElementOf0(W0,xQ) )
& aSet0(xP) ),
inference(NNF_transformation,[status(thm)],[f622]) ).
fof(f624,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [W0] :
( W0 = szmzizndt0(xQ)
| ~ aElementOf0(W0,xQ)
| ~ aElement0(W0)
| aElementOf0(W0,xP) )
& ! [W0] :
( ( W0 != szmzizndt0(xQ)
& aElementOf0(W0,xQ)
& aElement0(W0) )
| ~ aElementOf0(W0,xP) )
& ! [W0] :
( sdtlseqdt0(szmzizndt0(xQ),W0)
| ~ aElementOf0(W0,xQ) )
& aSet0(xP) ),
inference(miniscoping,[status(thm)],[f623]) ).
fof(f631,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(cnf_transformation,[status(thm)],[f624]) ).
fof(f636,plain,
( aSubsetOf0(xP,xQ)
& ! [W0] :
( aElementOf0(W0,xQ)
| ~ aElementOf0(W0,xP) ) ),
inference(pre_NNF_transformation,[status(thm)],[f107]) ).
fof(f638,plain,
aSubsetOf0(xP,xQ),
inference(cnf_transformation,[status(thm)],[f636]) ).
fof(f642,plain,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ) ),
inference(pre_NNF_transformation,[status(thm)],[f110]) ).
fof(f643,plain,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ) ),
inference(cnf_transformation,[status(thm)],[f642]) ).
fof(f826,definition,
( sQ0_spl
<=> szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f829,definition,
( sQ1_spl
<=> aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f831,plain,
( sQ1_spl
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(component_clause,[status(thm)],[f829]) ).
fof(f832,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f643,f826,f829]) ).
fof(f916,plain,
( aSet0(xP)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[f139,f638]) ).
fof(f917,definition,
( sQ14_spl
<=> aSet0(xQ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f919,plain,
( sQ14_spl
| ~ aSet0(xQ) ),
inference(component_clause,[status(thm)],[f917]) ).
fof(f920,definition,
( sQ15_spl
<=> aSet0(xP) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f923,plain,
( sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f916,f917,f920]) ).
fof(f924,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f919,f599]) ).
fof(f925,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f924]) ).
fof(f965,plain,
( isFinite0(xP)
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[f144,f638]) ).
fof(f969,definition,
( sQ23_spl
<=> isFinite0(xP) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f973,definition,
( sQ24_spl
<=> isFinite0(xQ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f976,plain,
( sQ23_spl
| ~ sQ24_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f965,f917,f973,f969]) ).
fof(f1936,plain,
( sQ1_spl
| ~ isFinite0(xP)
| ~ aSet0(xP) ),
inference(resolution,[status(thm)],[f831,f230]) ).
fof(f1937,plain,
( sQ1_spl
| ~ sQ23_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1936,f920,f969,f829]) ).
fof(f1969,plain,
( aElementOf0(xK,szNzAzT0)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(paramodulation,[status(thm)],[f406,f191]) ).
fof(f1979,definition,
( sQ130_spl
<=> aElementOf0(xk,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f1981,plain,
( sQ130_spl
| ~ aElementOf0(xk,szNzAzT0) ),
inference(component_clause,[status(thm)],[f1979]) ).
fof(f1990,definition,
( sQ133_spl
<=> aElementOf0(xK,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f1993,plain,
( sQ133_spl
| ~ sQ130_spl ),
inference(split_clause,[status(thm)],[f1969,f1979,f1990]) ).
fof(f2027,plain,
( sQ130_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1981,f405]) ).
fof(f2028,plain,
sQ130_spl,
inference(contradiction_clause,[status(thm)],[f2027]) ).
fof(f2314,plain,
( isFinite0(xQ)
| ~ aElementOf0(xK,szNzAzT0)
| ~ aSet0(xQ) ),
inference(paramodulation,[status(thm)],[f602,f229]) ).
fof(f2326,plain,
( sQ24_spl
| ~ sQ133_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f2314,f917,f1990,f973]) ).
fof(f2911,plain,
xP = sdtmndt0(xQ,xp),
inference(backward_demodulation,[status(thm)],[f621,f631]) ).
fof(f3170,plain,
( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
| ~ aElementOf0(xp,xQ)
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(paramodulation,[status(thm)],[f2911,f238]) ).
fof(f3176,definition,
( sQ300_spl
<=> aElementOf0(xp,xQ) ),
introduced(definition,[new_symbols(definition,[sQ300_spl])],[split_symbol_definition]) ).
fof(f3178,plain,
( sQ300_spl
| ~ aElementOf0(xp,xQ) ),
inference(component_clause,[status(thm)],[f3176]) ).
fof(f3179,plain,
( sQ0_spl
| ~ sQ300_spl
| ~ sQ24_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f3170,f917,f973,f3176,f826]) ).
fof(f3187,plain,
( sQ300_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3178,f619]) ).
fof(f3188,plain,
sQ300_spl,
inference(contradiction_clause,[status(thm)],[f3187]) ).
fof(f3189,plain,
$false,
inference(sat_refutation,[status(thm)],[f832,f923,f925,f976,f1937,f1993,f2028,f2326,f3179,f3188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM612+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 21 02:44:06 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 % Drodi V4.1.1
% 0.07/0.42 % Refutation found
% 0.07/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.44 % Elapsed time: 0.141075 seconds
% 0.07/0.44 % CPU time: 0.843925 seconds
% 0.07/0.44 % Total memory used: 140.169 MB
% 0.07/0.44 % Net memory used: 138.680 MB
%------------------------------------------------------------------------------