TSTP Solution File: NUN054+2 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : NUN054+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -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 : Wed Aug 31 18:08:00 EDT 2022
% Result : Theorem 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 72 ( 26 unt; 0 def)
% Number of atoms : 233 ( 60 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 250 ( 89 ~; 60 |; 90 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 187 ( 129 !; 58 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f842,plain,
$false,
inference(subsumption_resolution,[],[f841,f104]) ).
fof(f104,plain,
r1(sK4),
inference(equality_resolution,[],[f68]) ).
fof(f68,plain,
! [X1] :
( r1(X1)
| sK4 != X1 ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X1] :
( ( r1(X1)
& sK4 = X1 )
| ( ~ r1(X1)
& sK4 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f1,f32]) ).
fof(f32,plain,
( ? [X0] :
! [X1] :
( ( r1(X1)
& X0 = X1 )
| ( ~ r1(X1)
& X0 != X1 ) )
=> ! [X1] :
( ( r1(X1)
& sK4 = X1 )
| ( ~ r1(X1)
& sK4 != X1 ) ) ),
introduced(choice_axiom,[]) ).
fof(f1,axiom,
? [X0] :
! [X1] :
( ( r1(X1)
& X0 = X1 )
| ( ~ r1(X1)
& X0 != X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f841,plain,
~ r1(sK4),
inference(resolution,[],[f838,f203]) ).
fof(f203,plain,
! [X0] : r3(X0,sK19(sK4),sK19(X0)),
inference(superposition,[],[f151,f188]) ).
fof(f188,plain,
! [X2] : sK11(X2,sK4) = sK19(X2),
inference(resolution,[],[f185,f95]) ).
fof(f95,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| sK19(X0) = X2 ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X2] :
( ( sK19(X0) != X2
& ~ r2(X0,X2) )
| ( sK19(X0) = X2
& r2(X0,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f21,f56]) ).
fof(f56,plain,
! [X0] :
( ? [X1] :
! [X2] :
( ( X1 != X2
& ~ r2(X0,X2) )
| ( X1 = X2
& r2(X0,X2) ) )
=> ! [X2] :
( ( sK19(X0) != X2
& ~ r2(X0,X2) )
| ( sK19(X0) = X2
& r2(X0,X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0] :
? [X1] :
! [X2] :
( ( X1 != X2
& ~ r2(X0,X2) )
| ( X1 = X2
& r2(X0,X2) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2] :
? [X3] :
! [X4] :
( ( X3 = X4
& r2(X2,X4) )
| ( X3 != X4
& ~ r2(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f185,plain,
! [X0] : r2(X0,sK11(X0,sK4)),
inference(superposition,[],[f82,f179]) ).
fof(f179,plain,
! [X0] : sK14(X0,sK4) = X0,
inference(superposition,[],[f171,f170]) ).
fof(f170,plain,
! [X0] : sK18(sK4,X0) = X0,
inference(resolution,[],[f90,f124]) ).
fof(f124,plain,
! [X0] : r3(X0,sK4,X0),
inference(backward_demodulation,[],[f118,f120]) ).
fof(f120,plain,
! [X0] : sK7(X0) = sK4,
inference(resolution,[],[f67,f74]) ).
fof(f74,plain,
! [X0] : r1(sK7(X0)),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0] :
( sK6(X0) = X0
& r3(X0,sK7(X0),sK6(X0))
& r1(sK7(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f18,f37,f36]) ).
fof(f36,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r3(X0,X2,X1)
& r1(X2) ) )
=> ( sK6(X0) = X0
& ? [X2] :
( r3(X0,X2,sK6(X0))
& r1(X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
! [X0] :
( ? [X2] :
( r3(X0,X2,sK6(X0))
& r1(X2) )
=> ( r3(X0,sK7(X0),sK6(X0))
& r1(sK7(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0] :
? [X1] :
( X0 = X1
& ? [X2] :
( r3(X0,X2,X1)
& r1(X2) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X29] :
? [X30] :
( X29 = X30
& ? [X31] :
( r3(X29,X31,X30)
& r1(X31) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).
fof(f67,plain,
! [X1] :
( ~ r1(X1)
| sK4 = X1 ),
inference(cnf_transformation,[],[f33]) ).
fof(f118,plain,
! [X0] : r3(X0,sK7(X0),X0),
inference(forward_demodulation,[],[f75,f76]) ).
fof(f76,plain,
! [X0] : sK6(X0) = X0,
inference(cnf_transformation,[],[f38]) ).
fof(f75,plain,
! [X0] : r3(X0,sK7(X0),sK6(X0)),
inference(cnf_transformation,[],[f38]) ).
fof(f90,plain,
! [X3,X0,X1] :
( ~ r3(X1,X0,X3)
| sK18(X0,X1) = X3 ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1,X3] :
( ( r3(X1,X0,X3)
& sK18(X0,X1) = X3 )
| ( sK18(X0,X1) != X3
& ~ r3(X1,X0,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f17,f54]) ).
fof(f54,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( r3(X1,X0,X3)
& X2 = X3 )
| ( X2 != X3
& ~ r3(X1,X0,X3) ) )
=> ! [X3] :
( ( r3(X1,X0,X3)
& sK18(X0,X1) = X3 )
| ( sK18(X0,X1) != X3
& ~ r3(X1,X0,X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X0,X1] :
? [X2] :
! [X3] :
( ( r3(X1,X0,X3)
& X2 = X3 )
| ( X2 != X3
& ~ r3(X1,X0,X3) ) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X6,X5] :
? [X7] :
! [X8] :
( ( ~ r3(X5,X6,X8)
& X7 != X8 )
| ( X7 = X8
& r3(X5,X6,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f171,plain,
! [X2,X1] : sK18(X1,X2) = sK14(X2,X1),
inference(resolution,[],[f90,f81]) ).
fof(f81,plain,
! [X0,X1] : r3(X0,X1,sK14(X0,X1)),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1] :
( sK12(X0,X1) = sK11(X0,X1)
& r3(X0,sK13(X0,X1),sK12(X0,X1))
& r2(X1,sK13(X0,X1))
& r2(sK14(X0,X1),sK11(X0,X1))
& r3(X0,X1,sK14(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14])],[f44,f48,f47,f46,f45]) ).
fof(f45,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( X2 = X3
& ? [X4] :
( r3(X0,X4,X3)
& r2(X1,X4) ) )
& ? [X5] :
( r2(X5,X2)
& r3(X0,X1,X5) ) )
=> ( ? [X3] :
( sK11(X0,X1) = X3
& ? [X4] :
( r3(X0,X4,X3)
& r2(X1,X4) ) )
& ? [X5] :
( r2(X5,sK11(X0,X1))
& r3(X0,X1,X5) ) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
! [X0,X1] :
( ? [X3] :
( sK11(X0,X1) = X3
& ? [X4] :
( r3(X0,X4,X3)
& r2(X1,X4) ) )
=> ( sK12(X0,X1) = sK11(X0,X1)
& ? [X4] :
( r3(X0,X4,sK12(X0,X1))
& r2(X1,X4) ) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
! [X0,X1] :
( ? [X4] :
( r3(X0,X4,sK12(X0,X1))
& r2(X1,X4) )
=> ( r3(X0,sK13(X0,X1),sK12(X0,X1))
& r2(X1,sK13(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
! [X0,X1] :
( ? [X5] :
( r2(X5,sK11(X0,X1))
& r3(X0,X1,X5) )
=> ( r2(sK14(X0,X1),sK11(X0,X1))
& r3(X0,X1,sK14(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
! [X0,X1] :
? [X2] :
( ? [X3] :
( X2 = X3
& ? [X4] :
( r3(X0,X4,X3)
& r2(X1,X4) ) )
& ? [X5] :
( r2(X5,X2)
& r3(X0,X1,X5) ) ),
inference(rectify,[],[f15]) ).
fof(f15,plain,
! [X1,X0] :
? [X2] :
( ? [X3] :
( X2 = X3
& ? [X4] :
( r3(X1,X4,X3)
& r2(X0,X4) ) )
& ? [X5] :
( r2(X5,X2)
& r3(X1,X0,X5) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X14,X13] :
? [X15] :
( ? [X16] :
( X15 = X16
& ? [X17] :
( r3(X13,X17,X16)
& r2(X14,X17) ) )
& ? [X18] :
( r3(X13,X14,X18)
& r2(X18,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).
fof(f82,plain,
! [X0,X1] : r2(sK14(X0,X1),sK11(X0,X1)),
inference(cnf_transformation,[],[f49]) ).
fof(f151,plain,
! [X0,X1] : r3(X0,sK19(X1),sK11(X0,X1)),
inference(backward_demodulation,[],[f102,f144]) ).
fof(f144,plain,
! [X3,X4] : sK19(X3) = sK13(X4,X3),
inference(resolution,[],[f95,f83]) ).
fof(f83,plain,
! [X0,X1] : r2(X1,sK13(X0,X1)),
inference(cnf_transformation,[],[f49]) ).
fof(f102,plain,
! [X0,X1] : r3(X0,sK13(X0,X1),sK11(X0,X1)),
inference(definition_unfolding,[],[f84,f85]) ).
fof(f85,plain,
! [X0,X1] : sK12(X0,X1) = sK11(X0,X1),
inference(cnf_transformation,[],[f49]) ).
fof(f84,plain,
! [X0,X1] : r3(X0,sK13(X0,X1),sK12(X0,X1)),
inference(cnf_transformation,[],[f49]) ).
fof(f838,plain,
! [X0] :
( ~ r3(X0,sK19(sK4),sK19(sK4))
| ~ r1(X0) ),
inference(resolution,[],[f208,f131]) ).
fof(f131,plain,
sP20(sK19(sK4)),
inference(resolution,[],[f130,f111]) ).
fof(f111,plain,
! [X0] : r2(X0,sK19(X0)),
inference(equality_resolution,[],[f96]) ).
fof(f96,plain,
! [X2,X0] :
( sK19(X0) != X2
| r2(X0,X2) ),
inference(cnf_transformation,[],[f57]) ).
fof(f130,plain,
! [X0] :
( ~ r2(sK4,X0)
| sP20(X0) ),
inference(resolution,[],[f114,f104]) ).
fof(f114,plain,
! [X2,X1] :
( ~ r1(X2)
| sP20(X1)
| ~ r2(X2,X1) ),
inference(cnf_transformation,[],[f114_D]) ).
fof(f114_D,plain,
! [X1] :
( ! [X2] :
( ~ r1(X2)
| ~ r2(X2,X1) )
<=> ~ sP20(X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP20])]) ).
fof(f208,plain,
! [X0,X1] :
( ~ sP20(X1)
| ~ r3(X0,sK19(sK4),X1)
| ~ r1(X0) ),
inference(resolution,[],[f117,f139]) ).
fof(f139,plain,
sP21(sK19(sK4)),
inference(resolution,[],[f134,f111]) ).
fof(f134,plain,
! [X0] :
( ~ r2(sK4,X0)
| sP21(X0) ),
inference(resolution,[],[f116,f104]) ).
fof(f116,plain,
! [X3,X5] :
( ~ r1(X5)
| sP21(X3)
| ~ r2(X5,X3) ),
inference(cnf_transformation,[],[f116_D]) ).
fof(f116_D,plain,
! [X3] :
( ! [X5] :
( ~ r1(X5)
| ~ r2(X5,X3) )
<=> ~ sP21(X3) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP21])]) ).
fof(f117,plain,
! [X3,X1,X4] :
( ~ sP21(X3)
| ~ r1(X4)
| ~ sP20(X1)
| ~ r3(X4,X3,X1) ),
inference(general_splitting,[],[f115,f116_D]) ).
fof(f115,plain,
! [X3,X1,X4,X5] :
( ~ r3(X4,X3,X1)
| ~ r1(X4)
| ~ r1(X5)
| ~ r2(X5,X3)
| ~ sP20(X1) ),
inference(general_splitting,[],[f113,f114_D]) ).
fof(f113,plain,
! [X2,X3,X1,X4,X5] :
( ~ r2(X2,X1)
| ~ r1(X2)
| ~ r3(X4,X3,X1)
| ~ r1(X4)
| ~ r1(X5)
| ~ r2(X5,X3) ),
inference(equality_resolution,[],[f99]) ).
fof(f99,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r2(X2,X1)
| ~ r1(X2)
| X0 != X1
| ~ r3(X4,X3,X0)
| ~ r1(X4)
| ~ r1(X5)
| ~ r2(X5,X3) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ~ r2(X2,X1)
| ~ r1(X2) )
| X0 != X1 )
| ! [X3] :
( ! [X4] :
( ~ r3(X4,X3,X0)
| ~ r1(X4) )
| ! [X5] :
( ~ r1(X5)
| ~ r2(X5,X3) ) ) ),
inference(rectify,[],[f25]) ).
fof(f25,plain,
! [X0] :
( ! [X4] :
( ! [X5] :
( ~ r2(X5,X4)
| ~ r1(X5) )
| X0 != X4 )
| ! [X1] :
( ! [X3] :
( ~ r3(X3,X1,X0)
| ~ r1(X3) )
| ! [X2] :
( ~ r1(X2)
| ~ r2(X2,X1) ) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,plain,
~ ? [X0] :
( ? [X1] :
( ? [X2] :
( r1(X2)
& r2(X2,X1) )
& ? [X3] :
( r1(X3)
& r3(X3,X1,X0) ) )
& ? [X4] :
( X0 = X4
& ? [X5] :
( r1(X5)
& r2(X5,X4) ) ) ),
inference(rectify,[],[f13]) ).
fof(f13,negated_conjecture,
~ ? [X38] :
( ? [X21] :
( ? [X16] :
( r1(X16)
& r2(X16,X21) )
& ? [X15] :
( r3(X15,X21,X38)
& r1(X15) ) )
& ? [X22] :
( X22 = X38
& ? [X24] :
( r2(X24,X22)
& r1(X24) ) ) ),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
? [X38] :
( ? [X21] :
( ? [X16] :
( r1(X16)
& r2(X16,X21) )
& ? [X15] :
( r3(X15,X21,X38)
& r1(X15) ) )
& ? [X22] :
( X22 = X38
& ? [X24] :
( r2(X24,X22)
& r1(X24) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zeroplusoneeqone) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : NUN054+2 : TPTP v8.1.0. Released v7.3.0.
% 0.06/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 30 09:45:10 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.49 % (15201)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.20/0.49 % (15193)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.52 % (15193)First to succeed.
% 0.20/0.52 % (15195)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.52 % (15201)Also succeeded, but the first one will report.
% 0.20/0.53 % (15193)Refutation found. Thanks to Tanya!
% 0.20/0.53 % SZS status Theorem for theBenchmark
% 0.20/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53 % (15193)------------------------------
% 0.20/0.53 % (15193)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (15193)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (15193)Termination reason: Refutation
% 0.20/0.53
% 0.20/0.53 % (15193)Memory used [KB]: 5884
% 0.20/0.53 % (15193)Time elapsed: 0.099 s
% 0.20/0.53 % (15193)Instructions burned: 29 (million)
% 0.20/0.53 % (15193)------------------------------
% 0.20/0.53 % (15193)------------------------------
% 0.20/0.53 % (15171)Success in time 0.172 s
%------------------------------------------------------------------------------