%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM458+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:15:16 PM UTC 2026
% Result : Theorem 3.40s 1.38s
% Output : Refutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 10 unt; 0 def)
% Number of atoms : 76 ( 15 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 91 ( 39 ~; 35 |; 12 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 26 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(f20,axiom,
aNaturalNumber0(xm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__718) ).
fof(f21,conjecture,
sdtlseqdt0(xm,xm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f22,negated_conjecture,
~ sdtlseqdt0(xm,xm),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f24,plain,
~ sdtlseqdt0(xm,xm),
inference(flattening,[],[f22]) ).
fof(f33,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f50,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f51,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f50]) ).
fof(f54,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f51]) ).
fof(f55,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X0,X3) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(rectify,[],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK0(X0,X1))
& sdtpldt0(X0,sK0(X0,X1)) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f55]) ).
fof(f59,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f67,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f85,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f89,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f20]) ).
fof(f90,plain,
~ sdtlseqdt0(xm,xm),
inference(cnf_transformation,[],[f24]) ).
fof(f91,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f85]) ).
fof(f104,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f91,f67]) ).
fof(f105,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| sdtlseqdt0(X0,X0) ),
inference(duplicate_literal_removal,[],[f104]) ).
fof(f106,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f105,f59]) ).
fof(f108,plain,
~ aNaturalNumber0(xm),
inference(resolution,[],[f106,f90]) ).
fof(f113,plain,
$false,
inference(forward_subsumption_resolution,[],[f108,f89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM458+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n010.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 20:00:47 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.40/1.38 % (1270418)Detected formulas, will run a generic FOF schedule.
% 3.40/1.38 % (1270429)dis-21_1_sil=8000:lcm=predicate:random_seed=1608817900: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)
% 3.40/1.38 % (1270429)Instruction limit reached!
% 3.40/1.38 % (1270429)------------------------------
% 3.40/1.38 % (1270429)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.38 % (1270429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.38 % (1270429)CaDiCaL version: 2.1.3
% 3.40/1.38 % (1270429)Termination reason: Instruction limit
% 3.40/1.38 % (1270429)Termination phase: Saturation
% 3.40/1.38 % (1270429)Time elapsed: 0.042 s
% 3.40/1.38 % (1270429)Peak memory usage: 90 MB
% 3.40/1.38 % (1270429)Instructions burned: 130 (million)
% 3.40/1.38 % (1270425)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=461439781:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.40/1.38 % (1270427)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2032200611:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.40/1.38 % (1270426)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3766257966:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.40/1.38 % (1270424)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=3720876107:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.40/1.38 % (1270423)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=2313785891:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.40/1.38 % (1270428)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3231601149:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.40/1.38 % (1270426)Refutation not found, incomplete strategy
% 3.40/1.38 % (1270426)------------------------------
% 3.40/1.38 % (1270426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.38 % (1270426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.38 % (1270426)CaDiCaL version: 2.1.3
% 3.40/1.38 % (1270426)Termination reason: Refutation not found, incomplete strategy
% 3.40/1.38 % (1270426)Time elapsed: 0.001 s
% 3.40/1.38 % (1270426)Peak memory usage: 88 MB
% 3.40/1.38 % (1270428)First to succeed.
% 3.40/1.38 % (1270428)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1270418"
% 3.40/1.38 % (1270427)Instruction limit reached!
% 3.40/1.38 % (1270427)------------------------------
% 3.40/1.38 % (1270427)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.38 % (1270427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.38 % (1270427)CaDiCaL version: 2.1.3
% 3.40/1.38 % (1270427)Termination reason: Instruction limit
% 3.40/1.38 % (1270427)Termination phase: Saturation
% 3.40/1.38 % (1270427)Time elapsed: 0.064 s
% 3.40/1.38 % (1270427)Peak memory usage: 88 MB
% 3.40/1.38 % (1270427)Instructions burned: 119 (million)
% 3.40/1.38 % (1270437)lrs+10_1_sil=8000:sp=occurrence:random_seed=3026484092:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.40/1.38 % (1270437)Instruction limit reached!
% 3.40/1.38 % (1270437)------------------------------
% 3.40/1.38 % (1270437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.38 % (1270437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.38 % (1270437)CaDiCaL version: 2.1.3
% 3.40/1.38 % (1270437)Termination reason: Instruction limit
% 3.40/1.38 % (1270437)Termination phase: Saturation
% 3.40/1.38 % (1270437)Time elapsed: 0.083 s
% 3.40/1.38 % (1270437)Peak memory usage: 92 MB
% 3.40/1.38 % (1270437)Instructions burned: 286 (million)
% 3.40/1.38 % (1270438)lrs+10_1_sil=32000:urr=on:br=off:random_seed=847950309:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.40/1.38 % (1270438)Refutation not found, incomplete strategy
% 3.40/1.38 % (1270438)------------------------------
% 3.40/1.38 % (1270438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.38 % (1270438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.38 % (1270438)CaDiCaL version: 2.1.3
% 3.40/1.38 % (1270438)Termination reason: Refutation not found, incomplete strategy
% 3.40/1.38 % (1270438)Time elapsed: 0.002 s
% 3.40/1.38 % (1270438)Peak memory usage: 88 MB
% 3.40/1.38 % (1270438)Instructions burned: 1 (million)
% 3.40/1.38 % (1270426)------------------------------
% 3.40/1.38 % (1270426)------------------------------
% 3.40/1.38 % (1270428)Refutation found. Thanks to Tanya!
% 3.40/1.38 % SZS status Theorem for theBenchmark
% 3.40/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.40/1.38 % (1270428)------------------------------
% 3.40/1.38 % (1270428)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.38 % (1270428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.38 % (1270428)CaDiCaL version: 2.1.3
% 3.40/1.38 % (1270428)Termination reason: Refutation
% 3.40/1.38 % (1270428)Time elapsed: 0.005 s
% 3.40/1.38 % (1270428)Peak memory usage: 89 MB
% 3.40/1.38 % (1270428)Instructions burned: 3 (million)
% 3.40/1.38 % (1270428)------------------------------
% 3.40/1.38 % (1270428)------------------------------
% 3.40/1.38 % (1270418)Success in time 0.413 s
% 3.40/1.38 % Vampire exiting
%------------------------------------------------------------------------------