TSTP Solution File: SEU406+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU406+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n018.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 : Sun May 5 09:39:07 EDT 2024
% Result : Theorem 0.14s 0.35s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 17 unt; 0 def)
% Number of atoms : 169 ( 9 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 215 ( 89 ~; 62 |; 56 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 84 ( 73 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2482,plain,
$false,
inference(subsumption_resolution,[],[f2479,f2430]) ).
fof(f2430,plain,
~ r2_hidden(sK2,k4_xboole_0(sK4,sK5)),
inference(unit_resulting_resolution,[],[f1904,f58]) ).
fof(f58,plain,
( ~ r2_hidden(sK3,k4_xboole_0(sK4,sK5))
| ~ r2_hidden(sK2,k4_xboole_0(sK4,sK5)) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
( ( ~ r2_hidden(sK3,k4_xboole_0(sK4,sK5))
| ~ r2_hidden(sK2,sK5) )
& ( ~ r2_hidden(sK3,sK5)
| ~ r2_hidden(sK2,k4_xboole_0(sK4,sK5)) )
& ( ~ r2_hidden(sK3,sK5)
| ~ r2_hidden(sK2,sK5) )
& ( ~ r2_hidden(sK3,k4_xboole_0(sK4,sK5))
| ~ r2_hidden(sK2,k4_xboole_0(sK4,sK5)) )
& r2_hidden(sK3,k2_xboole_0(sK4,sK5))
& r2_hidden(sK2,k2_xboole_0(sK4,sK5)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f27,f40]) ).
fof(f40,plain,
( ? [X0,X1,X2,X3] :
( ( ~ r2_hidden(X1,k4_xboole_0(X2,X3))
| ~ r2_hidden(X0,X3) )
& ( ~ r2_hidden(X1,X3)
| ~ r2_hidden(X0,k4_xboole_0(X2,X3)) )
& ( ~ r2_hidden(X1,X3)
| ~ r2_hidden(X0,X3) )
& ( ~ r2_hidden(X1,k4_xboole_0(X2,X3))
| ~ r2_hidden(X0,k4_xboole_0(X2,X3)) )
& r2_hidden(X1,k2_xboole_0(X2,X3))
& r2_hidden(X0,k2_xboole_0(X2,X3)) )
=> ( ( ~ r2_hidden(sK3,k4_xboole_0(sK4,sK5))
| ~ r2_hidden(sK2,sK5) )
& ( ~ r2_hidden(sK3,sK5)
| ~ r2_hidden(sK2,k4_xboole_0(sK4,sK5)) )
& ( ~ r2_hidden(sK3,sK5)
| ~ r2_hidden(sK2,sK5) )
& ( ~ r2_hidden(sK3,k4_xboole_0(sK4,sK5))
| ~ r2_hidden(sK2,k4_xboole_0(sK4,sK5)) )
& r2_hidden(sK3,k2_xboole_0(sK4,sK5))
& r2_hidden(sK2,k2_xboole_0(sK4,sK5)) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
? [X0,X1,X2,X3] :
( ( ~ r2_hidden(X1,k4_xboole_0(X2,X3))
| ~ r2_hidden(X0,X3) )
& ( ~ r2_hidden(X1,X3)
| ~ r2_hidden(X0,k4_xboole_0(X2,X3)) )
& ( ~ r2_hidden(X1,X3)
| ~ r2_hidden(X0,X3) )
& ( ~ r2_hidden(X1,k4_xboole_0(X2,X3))
| ~ r2_hidden(X0,k4_xboole_0(X2,X3)) )
& r2_hidden(X1,k2_xboole_0(X2,X3))
& r2_hidden(X0,k2_xboole_0(X2,X3)) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2,X3] :
~ ( ~ ( r2_hidden(X1,k4_xboole_0(X2,X3))
& r2_hidden(X0,X3) )
& ~ ( r2_hidden(X1,X3)
& r2_hidden(X0,k4_xboole_0(X2,X3)) )
& ~ ( r2_hidden(X1,X3)
& r2_hidden(X0,X3) )
& ~ ( r2_hidden(X1,k4_xboole_0(X2,X3))
& r2_hidden(X0,k4_xboole_0(X2,X3)) )
& r2_hidden(X1,k2_xboole_0(X2,X3))
& r2_hidden(X0,k2_xboole_0(X2,X3)) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X0,X1,X2,X3] :
~ ( ~ ( r2_hidden(X1,k4_xboole_0(X2,X3))
& r2_hidden(X0,X3) )
& ~ ( r2_hidden(X1,X3)
& r2_hidden(X0,k4_xboole_0(X2,X3)) )
& ~ ( r2_hidden(X1,X3)
& r2_hidden(X0,X3) )
& ~ ( r2_hidden(X1,k4_xboole_0(X2,X3))
& r2_hidden(X0,k4_xboole_0(X2,X3)) )
& r2_hidden(X1,k2_xboole_0(X2,X3))
& r2_hidden(X0,k2_xboole_0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_latsum_1) ).
fof(f1904,plain,
r2_hidden(sK3,k4_xboole_0(sK4,sK5)),
inference(unit_resulting_resolution,[],[f1489,f1894,f82]) ).
fof(f82,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| r2_hidden(X1,X2)
| r2_hidden(X1,X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ~ r2_hidden(X1,X0)
& ~ r2_hidden(X1,X2) ) )
& ( r2_hidden(X1,X0)
| r2_hidden(X1,X2)
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f49]) ).
fof(f49,plain,
! [X1,X3,X0] :
( ( sP0(X1,X3,X0)
| ( ~ r2_hidden(X3,X1)
& ~ r2_hidden(X3,X0) ) )
& ( r2_hidden(X3,X1)
| r2_hidden(X3,X0)
| ~ sP0(X1,X3,X0) ) ),
inference(flattening,[],[f48]) ).
fof(f48,plain,
! [X1,X3,X0] :
( ( sP0(X1,X3,X0)
| ( ~ r2_hidden(X3,X1)
& ~ r2_hidden(X3,X0) ) )
& ( r2_hidden(X3,X1)
| r2_hidden(X3,X0)
| ~ sP0(X1,X3,X0) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X1,X3,X0] :
( sP0(X1,X3,X0)
<=> ( r2_hidden(X3,X1)
| r2_hidden(X3,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f1894,plain,
~ r2_hidden(sK3,sK5),
inference(subsumption_resolution,[],[f1889,f59]) ).
fof(f59,plain,
( ~ r2_hidden(sK3,sK5)
| ~ r2_hidden(sK2,sK5) ),
inference(cnf_transformation,[],[f41]) ).
fof(f1889,plain,
( r2_hidden(sK2,sK5)
| ~ r2_hidden(sK3,sK5) ),
inference(resolution,[],[f1616,f60]) ).
fof(f60,plain,
( ~ r2_hidden(sK2,k4_xboole_0(sK4,sK5))
| ~ r2_hidden(sK3,sK5) ),
inference(cnf_transformation,[],[f41]) ).
fof(f1616,plain,
( r2_hidden(sK2,k4_xboole_0(sK4,sK5))
| r2_hidden(sK2,sK5) ),
inference(resolution,[],[f1488,f82]) ).
fof(f1488,plain,
sP0(k4_xboole_0(sK4,sK5),sK2,sK5),
inference(unit_resulting_resolution,[],[f56,f487,f78]) ).
fof(f78,plain,
! [X2,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ r2_hidden(X4,X2)
| sP0(X1,X4,X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ( ( ~ sP0(X1,sK7(X0,X1,X2),X0)
| ~ r2_hidden(sK7(X0,X1,X2),X2) )
& ( sP0(X1,sK7(X0,X1,X2),X0)
| r2_hidden(sK7(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( r2_hidden(X4,X2)
| ~ sP0(X1,X4,X0) )
& ( sP0(X1,X4,X0)
| ~ r2_hidden(X4,X2) ) )
| ~ sP1(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f45,f46]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ sP0(X1,X3,X0)
| ~ r2_hidden(X3,X2) )
& ( sP0(X1,X3,X0)
| r2_hidden(X3,X2) ) )
=> ( ( ~ sP0(X1,sK7(X0,X1,X2),X0)
| ~ r2_hidden(sK7(X0,X1,X2),X2) )
& ( sP0(X1,sK7(X0,X1,X2),X0)
| r2_hidden(sK7(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ? [X3] :
( ( ~ sP0(X1,X3,X0)
| ~ r2_hidden(X3,X2) )
& ( sP0(X1,X3,X0)
| r2_hidden(X3,X2) ) ) )
& ( ! [X4] :
( ( r2_hidden(X4,X2)
| ~ sP0(X1,X4,X0) )
& ( sP0(X1,X4,X0)
| ~ r2_hidden(X4,X2) ) )
| ~ sP1(X0,X1,X2) ) ),
inference(rectify,[],[f44]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ? [X3] :
( ( ~ sP0(X1,X3,X0)
| ~ r2_hidden(X3,X2) )
& ( sP0(X1,X3,X0)
| r2_hidden(X3,X2) ) ) )
& ( ! [X3] :
( ( r2_hidden(X3,X2)
| ~ sP0(X1,X3,X0) )
& ( sP0(X1,X3,X0)
| ~ r2_hidden(X3,X2) ) )
| ~ sP1(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1,X2] :
( sP1(X0,X1,X2)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> sP0(X1,X3,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f487,plain,
! [X0,X1] : sP1(X0,k4_xboole_0(X1,X0),k2_xboole_0(X1,X0)),
inference(superposition,[],[f459,f69]) ).
fof(f69,plain,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f459,plain,
! [X0,X1] : sP1(X0,k4_xboole_0(X1,X0),k2_xboole_0(X0,X1)),
inference(superposition,[],[f89,f70]) ).
fof(f70,plain,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X0,k4_xboole_0(X1,X0)),
inference(cnf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X0,k4_xboole_0(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f89,plain,
! [X0,X1] : sP1(X0,X1,k2_xboole_0(X0,X1)),
inference(equality_resolution,[],[f85]) ).
fof(f85,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| k2_xboole_0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( k2_xboole_0(X0,X1) = X2
| ~ sP1(X0,X1,X2) )
& ( sP1(X0,X1,X2)
| k2_xboole_0(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1,X2] :
( k2_xboole_0(X0,X1) = X2
<=> sP1(X0,X1,X2) ),
inference(definition_folding,[],[f5,f38,f37]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( k2_xboole_0(X0,X1) = X2
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ( r2_hidden(X3,X1)
| r2_hidden(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f56,plain,
r2_hidden(sK2,k2_xboole_0(sK4,sK5)),
inference(cnf_transformation,[],[f41]) ).
fof(f1489,plain,
sP0(k4_xboole_0(sK4,sK5),sK3,sK5),
inference(unit_resulting_resolution,[],[f57,f487,f78]) ).
fof(f57,plain,
r2_hidden(sK3,k2_xboole_0(sK4,sK5)),
inference(cnf_transformation,[],[f41]) ).
fof(f2479,plain,
r2_hidden(sK2,k4_xboole_0(sK4,sK5)),
inference(unit_resulting_resolution,[],[f1488,f2431,f82]) ).
fof(f2431,plain,
~ r2_hidden(sK2,sK5),
inference(unit_resulting_resolution,[],[f1904,f61]) ).
fof(f61,plain,
( ~ r2_hidden(sK3,k4_xboole_0(sK4,sK5))
| ~ r2_hidden(sK2,sK5) ),
inference(cnf_transformation,[],[f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU406+1 : TPTP v8.1.2. Released v3.4.0.
% 0.09/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.30 % Computer : n018.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri May 3 11:36:16 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.10/0.30 % (4703)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.31 % (4706)WARNING: value z3 for option sas not known
% 0.14/0.32 % (4706)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.32 % (4709)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.32 % (4708)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.32 % (4704)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.32 % (4705)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.32 % (4710)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.32 % (4707)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.32 TRYING [1]
% 0.14/0.32 TRYING [2]
% 0.14/0.32 TRYING [3]
% 0.14/0.32 TRYING [1]
% 0.14/0.32 TRYING [2]
% 0.14/0.32 TRYING [4]
% 0.14/0.33 TRYING [3]
% 0.14/0.34 TRYING [5]
% 0.14/0.35 % (4710)First to succeed.
% 0.14/0.35 % (4710)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4703"
% 0.14/0.35 % (4710)Refutation found. Thanks to Tanya!
% 0.14/0.35 % SZS status Theorem for theBenchmark
% 0.14/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.36 % (4710)------------------------------
% 0.14/0.36 % (4710)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.36 % (4710)Termination reason: Refutation
% 0.14/0.36
% 0.14/0.36 % (4710)Memory used [KB]: 1265
% 0.14/0.36 % (4710)Time elapsed: 0.038 s
% 0.14/0.36 % (4710)Instructions burned: 74 (million)
% 0.14/0.36 % (4703)Success in time 0.053 s
%------------------------------------------------------------------------------