TSTP Solution File: NUN060+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUN060+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 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 Apr 30 14:40:18 EDT 2024
% Result : Theorem 0.13s 0.36s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of formulae : 51 ( 10 unt; 0 def)
% Number of atoms : 196 ( 29 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 217 ( 72 ~; 49 |; 83 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 178 ( 111 !; 67 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f296,plain,
$false,
inference(unit_resulting_resolution,[],[f93,f249,f290,f126]) ).
fof(f126,plain,
! [X4,X5] :
( ~ r2(X5,X4)
| ~ sP26(X5)
| sP27(X4) ),
inference(cnf_transformation,[],[f126_D]) ).
fof(f126_D,plain,
! [X4] :
( ! [X5] :
( ~ r2(X5,X4)
| ~ sP26(X5) )
<=> ~ sP27(X4) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP27])]) ).
fof(f290,plain,
! [X0] : ~ sP27(X0),
inference(unit_resulting_resolution,[],[f167,f98,f128]) ).
fof(f128,plain,
! [X3,X4] :
( ~ r2(X4,X3)
| ~ sP27(X4)
| sP28(X3) ),
inference(cnf_transformation,[],[f128_D]) ).
fof(f128_D,plain,
! [X3] :
( ! [X4] :
( ~ r2(X4,X3)
| ~ sP27(X4) )
<=> ~ sP28(X3) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP28])]) ).
fof(f98,plain,
! [X0,X1] : r2(X1,sK21(X0,X1)),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( r3(X0,X1,sK19(X0,X1))
& r2(sK19(X0,X1),sK18(X0,X1))
& sK18(X0,X1) = sK20(X0,X1)
& r3(X0,sK21(X0,X1),sK20(X0,X1))
& r2(X1,sK21(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21])],[f22,f61,f60,f59,f58]) ).
fof(f58,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,X2) )
& ? [X4] :
( X2 = X4
& ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) ) ) )
=> ( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,sK18(X0,X1)) )
& ? [X4] :
( sK18(X0,X1) = X4
& ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X0,X1] :
( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,sK18(X0,X1)) )
=> ( r3(X0,X1,sK19(X0,X1))
& r2(sK19(X0,X1),sK18(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
! [X0,X1] :
( ? [X4] :
( sK18(X0,X1) = X4
& ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) ) )
=> ( sK18(X0,X1) = sK20(X0,X1)
& ? [X5] :
( r3(X0,X5,sK20(X0,X1))
& r2(X1,X5) ) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
! [X0,X1] :
( ? [X5] :
( r3(X0,X5,sK20(X0,X1))
& r2(X1,X5) )
=> ( r3(X0,sK21(X0,X1),sK20(X0,X1))
& r2(X1,sK21(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1] :
? [X2] :
( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,X2) )
& ? [X4] :
( X2 = X4
& ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) ) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X13,X14] :
? [X15] :
( ? [X18] :
( r3(X13,X14,X18)
& r2(X18,X15) )
& ? [X16] :
( X15 = X16
& ? [X17] :
( r3(X13,X17,X16)
& r2(X14,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).
fof(f167,plain,
! [X0] : ~ sP28(X0),
inference(unit_resulting_resolution,[],[f102,f129]) ).
fof(f129,plain,
! [X2,X3,X1] :
( ~ r3(X1,X3,X2)
| ~ sP28(X3) ),
inference(general_splitting,[],[f127,f128_D]) ).
fof(f127,plain,
! [X2,X3,X1,X4] :
( ~ r2(X4,X3)
| ~ r3(X1,X3,X2)
| ~ sP27(X4) ),
inference(general_splitting,[],[f125,f126_D]) ).
fof(f125,plain,
! [X2,X3,X1,X4,X5] :
( ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r3(X1,X3,X2)
| ~ sP26(X5) ),
inference(general_splitting,[],[f123,f124_D]) ).
fof(f124,plain,
! [X6,X5] :
( ~ r2(X6,X5)
| ~ sP25(X6)
| sP26(X5) ),
inference(cnf_transformation,[],[f124_D]) ).
fof(f124_D,plain,
! [X5] :
( ! [X6] :
( ~ r2(X6,X5)
| ~ sP25(X6) )
<=> ~ sP26(X5) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP26])]) ).
fof(f123,plain,
! [X2,X3,X1,X6,X4,X5] :
( ~ r2(X6,X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r3(X1,X3,X2)
| ~ sP25(X6) ),
inference(general_splitting,[],[f115,f122_D]) ).
fof(f122,plain,
! [X6,X7] :
( ~ r2(X7,X6)
| ~ r1(X7)
| sP25(X6) ),
inference(cnf_transformation,[],[f122_D]) ).
fof(f122_D,plain,
! [X6] :
( ! [X7] :
( ~ r2(X7,X6)
| ~ r1(X7) )
<=> ~ sP25(X6) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP25])]) ).
fof(f115,plain,
! [X2,X3,X1,X6,X7,X4,X5] :
( ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r3(X1,X3,X2) ),
inference(equality_resolution,[],[f75]) ).
fof(f75,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r3(X1,X3,X2)
| X0 != X2 ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ r2(X7,X6)
| ~ r1(X7) )
| ~ r2(X6,X5) )
| ~ r2(X5,X4) )
| ~ r2(X4,X3) )
| ~ r3(X1,X3,X2) )
| X0 != X2 ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,plain,
~ ? [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( r2(X7,X6)
& r1(X7) )
& r2(X6,X5) )
& r2(X5,X4) )
& r2(X4,X3) )
& r3(X1,X3,X2) )
& X0 = X2 ),
inference(rectify,[],[f13]) ).
fof(f13,negated_conjecture,
~ ? [X38,X21,X22] :
( ? [X15] :
( ? [X16] :
( ? [X24] :
( ? [X18] :
( ? [X33] :
( r2(X33,X18)
& r1(X33) )
& r2(X18,X24) )
& r2(X24,X16) )
& r2(X16,X15) )
& r3(X21,X15,X22) )
& X22 = X38 ),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
? [X38,X21,X22] :
( ? [X15] :
( ? [X16] :
( ? [X24] :
( ? [X18] :
( ? [X33] :
( r2(X33,X18)
& r1(X33) )
& r2(X18,X24) )
& r2(X24,X16) )
& r2(X16,X15) )
& r3(X21,X15,X22) )
& X22 = X38 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',greq4) ).
fof(f102,plain,
! [X0,X1] : r3(X0,X1,sK19(X0,X1)),
inference(cnf_transformation,[],[f62]) ).
fof(f249,plain,
! [X0,X1] : sP26(sK17(X0,sK17(X1,sK24))),
inference(unit_resulting_resolution,[],[f208,f93,f124]) ).
fof(f208,plain,
! [X0] : sP25(sK17(X0,sK24)),
inference(unit_resulting_resolution,[],[f137,f93,f122]) ).
fof(f137,plain,
r1(sK24),
inference(unit_resulting_resolution,[],[f121,f113]) ).
fof(f113,plain,
! [X1] :
( sP4(X1,sK24)
| r1(X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X1] :
( ( sK24 = X1
& r1(X1) )
| sP4(X1,sK24) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f35,f73]) ).
fof(f73,plain,
( ? [X0] :
! [X1] :
( ( X0 = X1
& r1(X1) )
| sP4(X1,X0) )
=> ! [X1] :
( ( sK24 = X1
& r1(X1) )
| sP4(X1,sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
? [X0] :
! [X1] :
( ( X0 = X1
& r1(X1) )
| sP4(X1,X0) ),
inference(definition_folding,[],[f1,f34]) ).
fof(f34,plain,
! [X1,X0] :
( ( X0 != X1
& ~ r1(X1) )
| ~ sP4(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f1,axiom,
? [X0] :
! [X1] :
( ( X0 = X1
& r1(X1) )
| ( X0 != X1
& ~ r1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f121,plain,
! [X1] : ~ sP4(X1,X1),
inference(equality_resolution,[],[f112]) ).
fof(f112,plain,
! [X0,X1] :
( X0 != X1
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( ( X0 != X1
& ~ r1(X0) )
| ~ sP4(X0,X1) ),
inference(rectify,[],[f71]) ).
fof(f71,plain,
! [X1,X0] :
( ( X0 != X1
& ~ r1(X1) )
| ~ sP4(X1,X0) ),
inference(nnf_transformation,[],[f34]) ).
fof(f93,plain,
! [X0,X1] : r2(X1,sK17(X0,X1)),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( r4(X0,X1,sK15(X0,X1))
& r3(sK15(X0,X1),X0,sK14(X0,X1))
& sK14(X0,X1) = sK16(X0,X1)
& r4(X0,sK17(X0,X1),sK16(X0,X1))
& r2(X1,sK17(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17])],[f21,f56,f55,f54,f53]) ).
fof(f53,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,X2) )
& ? [X4] :
( X2 = X4
& ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) ) ) )
=> ( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,sK14(X0,X1)) )
& ? [X4] :
( sK14(X0,X1) = X4
& ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
! [X0,X1] :
( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,sK14(X0,X1)) )
=> ( r4(X0,X1,sK15(X0,X1))
& r3(sK15(X0,X1),X0,sK14(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f55,plain,
! [X0,X1] :
( ? [X4] :
( sK14(X0,X1) = X4
& ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) ) )
=> ( sK14(X0,X1) = sK16(X0,X1)
& ? [X5] :
( r4(X0,X5,sK16(X0,X1))
& r2(X1,X5) ) ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
! [X0,X1] :
( ? [X5] :
( r4(X0,X5,sK16(X0,X1))
& r2(X1,X5) )
=> ( r4(X0,sK17(X0,X1),sK16(X0,X1))
& r2(X1,sK17(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0,X1] :
? [X2] :
( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,X2) )
& ? [X4] :
( X2 = X4
& ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X19,X20] :
? [X21] :
( ? [X24] :
( r4(X19,X20,X24)
& r3(X24,X19,X21) )
& ? [X22] :
( X21 = X22
& ? [X23] :
( r4(X19,X23,X22)
& r2(X20,X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2a) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : NUN060+2 : TPTP v8.1.2. Released v7.3.0.
% 0.08/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 30 02:27:21 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % (2946)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.35 % (2949)WARNING: value z3 for option sas not known
% 0.13/0.36 % (2949)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)
% 0.13/0.36 % (2951)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)
% 0.13/0.36 % (2950)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36 % (2948)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36 % (2952)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)
% 0.13/0.36 % (2953)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)
% 0.13/0.36 TRYING [1]
% 0.13/0.36 % (2947)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.36 TRYING [2]
% 0.13/0.36 TRYING [3]
% 0.13/0.36 % (2953)First to succeed.
% 0.13/0.36 % (2953)Refutation found. Thanks to Tanya!
% 0.13/0.36 % SZS status Theorem for theBenchmark
% 0.13/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.36 % (2953)------------------------------
% 0.13/0.36 % (2953)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.36 % (2953)Termination reason: Refutation
% 0.13/0.36
% 0.13/0.36 % (2953)Memory used [KB]: 919
% 0.13/0.36 % (2953)Time elapsed: 0.006 s
% 0.13/0.36 % (2953)Instructions burned: 10 (million)
% 0.13/0.36 % (2953)------------------------------
% 0.13/0.36 % (2953)------------------------------
% 0.13/0.36 % (2946)Success in time 0.022 s
%------------------------------------------------------------------------------