%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM460+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 : Tue Sep 29 12:15:17 PM UTC 2026
% Result : Theorem 0.18s 1.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 8 unt; 1 def)
% Number of atoms : 129 ( 31 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 144 ( 49 ~; 39 |; 51 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 33 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(f22,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__773) ).
fof(f23,conjecture,
( ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,X0) = xn )
& sdtlseqdt0(xm,xn)
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xn,X0) = xl )
& sdtlseqdt0(xn,xl) )
=> ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,X0) = xl )
| sdtlseqdt0(xm,xl) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f24,negated_conjecture,
~ ( ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,X0) = xn )
& sdtlseqdt0(xm,xn)
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xn,X0) = xl )
& sdtlseqdt0(xn,xl) )
=> ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,X0) = xl )
| sdtlseqdt0(xm,xl) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f25,plain,
~ ( ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,X0) = xn )
& sdtlseqdt0(xm,xn)
& ? [X1] :
( aNaturalNumber0(X1)
& xl = sdtpldt0(xn,X1) )
& sdtlseqdt0(xn,xl) )
=> ( ? [X2] :
( aNaturalNumber0(X2)
& xl = sdtpldt0(xm,X2) )
| sdtlseqdt0(xm,xl) ) ),
inference(rectify,[],[f24]) ).
fof(f27,plain,
( ! [X2] :
( ~ aNaturalNumber0(X2)
| xl != sdtpldt0(xm,X2) )
& ~ sdtlseqdt0(xm,xl)
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,X0) = xn )
& sdtlseqdt0(xm,xn)
& ? [X1] :
( aNaturalNumber0(X1)
& xl = sdtpldt0(xn,X1) )
& sdtlseqdt0(xn,xl) ),
inference(ennf_transformation,[],[f25]) ).
fof(f28,plain,
( ! [X2] :
( ~ aNaturalNumber0(X2)
| xl != sdtpldt0(xm,X2) )
& ~ sdtlseqdt0(xm,xl)
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,X0) = xn )
& sdtlseqdt0(xm,xn)
& ? [X1] :
( aNaturalNumber0(X1)
& xl = sdtpldt0(xn,X1) )
& sdtlseqdt0(xn,xl) ),
inference(flattening,[],[f27]) ).
fof(f36,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f37,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f36]) ).
fof(f40,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f41,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xl != sdtpldt0(xm,X0) )
& ~ sdtlseqdt0(xm,xl)
& ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtpldt0(xm,X1) )
& sdtlseqdt0(xm,xn)
& ? [X2] :
( aNaturalNumber0(X2)
& xl = sdtpldt0(xn,X2) )
& sdtlseqdt0(xn,xl) ),
inference(rectify,[],[f28]) ).
fof(f43,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xl != sdtpldt0(xm,X0) )
& ~ sdtlseqdt0(xm,xl)
& aNaturalNumber0(sK0)
& xn = sdtpldt0(xm,sK0)
& sdtlseqdt0(xm,xn)
& aNaturalNumber0(sK1)
& xl = sdtpldt0(xn,sK1)
& sdtlseqdt0(xn,xl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0),skolemize(X2,sK1)],[f42]) ).
fof(f49,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f22]) ).
fof(f51,plain,
xl = sdtpldt0(xn,sK1),
inference(cnf_transformation,[],[f43]) ).
fof(f52,plain,
aNaturalNumber0(sK1),
inference(cnf_transformation,[],[f43]) ).
fof(f54,plain,
xn = sdtpldt0(xm,sK0),
inference(cnf_transformation,[],[f43]) ).
fof(f55,plain,
aNaturalNumber0(sK0),
inference(cnf_transformation,[],[f43]) ).
fof(f57,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| xl != sdtpldt0(xm,X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f65,plain,
! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f67,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f68,definition,
~ sP3(xl),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f69,plain,
! [X0] :
( sP3(sdtpldt0(xm,X0))
| ~ aNaturalNumber0(X0) ),
inference(inequality_splitting,[],[f57,f68]) ).
fof(f116,plain,
! [X0] :
( sdtpldt0(xn,X0) = sdtpldt0(xm,sdtpldt0(sK0,X0))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sK0)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f65,f54]) ).
fof(f119,plain,
! [X0] :
( sdtpldt0(xn,X0) = sdtpldt0(xm,sdtpldt0(sK0,X0))
| ~ aNaturalNumber0(sK0)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f116,f49]) ).
fof(f124,plain,
! [X0] :
( sdtpldt0(xn,X0) = sdtpldt0(xm,sdtpldt0(sK0,X0))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f119,f55]) ).
fof(f238,plain,
! [X0] :
( ~ aNaturalNumber0(sdtpldt0(sK0,X0))
| sP3(sdtpldt0(xn,X0))
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f69,f124]) ).
fof(f313,plain,
! [X0] :
( sP3(sdtpldt0(xn,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[],[f238,f67]) ).
fof(f320,plain,
! [X0] :
( sP3(sdtpldt0(xn,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0) ),
inference(duplicate_literal_removal,[],[f313]) ).
fof(f324,plain,
! [X0] :
( sP3(sdtpldt0(xn,X0))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f320,f55]) ).
fof(f326,plain,
( sP3(xl)
| ~ aNaturalNumber0(sK1) ),
inference(superposition,[],[f324,f51]) ).
fof(f336,plain,
~ aNaturalNumber0(sK1),
inference(forward_subsumption_resolution,[],[f326,f68]) ).
fof(f338,plain,
$false,
inference(forward_subsumption_resolution,[],[f336,f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM460+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n020.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 20:01:34 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/1.51 % (3709434)Detected formulas, will run a generic FOF schedule.
% 0.18/1.51 % (3709445)dis-21_1_sil=8000:lcm=predicate:random_seed=3401490357:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.18/1.51 % (3709444)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=275516112:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.18/1.51 % (3709442)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3868908284:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.18/1.51 % (3709443)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3385164121:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.18/1.51 % (3709440)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=656514934:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.18/1.51 % (3709441)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3353259092:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.18/1.51 % (3709439)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2689893658:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.18/1.51 % (3709445)Instruction limit reached!
% 0.18/1.51 % (3709445)------------------------------
% 0.18/1.51 % (3709445)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.51 % (3709445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.51 % (3709445)CaDiCaL version: 2.1.3
% 0.18/1.51 % (3709445)Termination reason: Instruction limit
% 0.18/1.51 % (3709445)Termination phase: Saturation
% 0.18/1.51 % (3709445)Time elapsed: 0.042 s
% 0.18/1.51 % (3709445)Peak memory usage: 89 MB
% 0.18/1.51 % (3709445)Instructions burned: 130 (million)
% 0.18/1.51 % (3709442)First to succeed.
% 0.18/1.51 % (3709442)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3709434"
% 0.18/1.51 % (3709443)Also succeeded, but the first one will report.
% 0.18/1.51 % (3709444)Instruction limit reached!
% 0.18/1.51 % (3709444)------------------------------
% 0.18/1.51 % (3709444)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.51 % (3709444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.51 % (3709444)CaDiCaL version: 2.1.3
% 0.18/1.51 % (3709444)Termination reason: Instruction limit
% 0.18/1.51 % (3709444)Termination phase: Saturation
% 0.18/1.51 % (3709444)Time elapsed: 0.082 s
% 0.18/1.51 % (3709444)Peak memory usage: 90 MB
% 0.18/1.51 % (3709444)Instructions burned: 139 (million)
% 0.18/1.51 % (3709453)lrs+10_1_sil=8000:sp=occurrence:random_seed=2752404238:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.18/1.51 % (3709453)Also succeeded, but the first one will report.
% 0.18/1.51 % (3709454)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3559239260:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 0.18/1.51 % (3709442)Refutation found. Thanks to Tanya!
% 0.18/1.51 % SZS status Theorem for theBenchmark
% 0.18/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.51 % (3709442)------------------------------
% 0.18/1.51 % (3709442)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.51 % (3709442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.51 % (3709442)CaDiCaL version: 2.1.3
% 0.18/1.51 % (3709442)Termination reason: Refutation
% 0.18/1.51 % (3709442)Time elapsed: 0.007 s
% 0.18/1.51 % (3709442)Peak memory usage: 89 MB
% 0.18/1.51 % (3709442)Instructions burned: 9 (million)
% 0.18/1.51 % (3709442)------------------------------
% 0.18/1.51 % (3709442)------------------------------
% 0.18/1.51 % (3709434)Success in time 0.444 s
% 0.18/1.51 % Vampire exiting
%------------------------------------------------------------------------------