%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM474+2 : 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 : n013.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 12:15:21 PM UTC 2026
% Result : Theorem 3.69s 1.45s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 14 unt; 0 def)
% Number of atoms : 54 ( 26 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 53 ( 24 ~; 15 |; 13 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(f34,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
fof(f37,axiom,
( aNaturalNumber0(xp)
& xm = sdtasdt0(xl,xp)
& xp = sdtsldt0(xm,xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1360) ).
fof(f38,axiom,
( aNaturalNumber0(xq)
& sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
& xq = sdtsldt0(sdtpldt0(xm,xn),xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1379) ).
fof(f40,axiom,
( aNaturalNumber0(xr)
& sdtpldt0(xp,xr) = xq
& xr = sdtmndt0(xq,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1422) ).
fof(f41,conjecture,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f42,negated_conjecture,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f44,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
inference(flattening,[],[f42]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f48]) ).
fof(f109,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f34]) ).
fof(f118,plain,
xm = sdtasdt0(xl,xp),
inference(cnf_transformation,[],[f37]) ).
fof(f119,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f37]) ).
fof(f121,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(cnf_transformation,[],[f38]) ).
fof(f127,plain,
xq = sdtpldt0(xp,xr),
inference(cnf_transformation,[],[f40]) ).
fof(f128,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f40]) ).
fof(f129,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
inference(cnf_transformation,[],[f44]) ).
fof(f133,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f49]) ).
fof(f1072,plain,
( sdtpldt0(sdtasdt0(xl,xp),xn) != sdtasdt0(xl,sdtpldt0(xp,xr))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr) ),
inference(superposition,[],[f129,f133]) ).
fof(f1113,plain,
( sdtpldt0(sdtasdt0(xl,xp),xn) != sdtasdt0(xl,sdtpldt0(xp,xr))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr) ),
inference(forward_subsumption_resolution,[],[f1072,f109]) ).
fof(f1150,plain,
( sdtpldt0(sdtasdt0(xl,xp),xn) != sdtasdt0(xl,sdtpldt0(xp,xr))
| ~ aNaturalNumber0(xr) ),
inference(forward_subsumption_resolution,[],[f1113,f119]) ).
fof(f1165,plain,
sdtpldt0(sdtasdt0(xl,xp),xn) != sdtasdt0(xl,sdtpldt0(xp,xr)),
inference(forward_subsumption_resolution,[],[f1150,f128]) ).
fof(f1166,plain,
sdtasdt0(xl,xq) != sdtpldt0(sdtasdt0(xl,xp),xn),
inference(forward_demodulation,[],[f1165,f127]) ).
fof(f1167,plain,
sdtpldt0(xm,xn) != sdtasdt0(xl,xq),
inference(forward_demodulation,[],[f1166,f118]) ).
fof(f1168,plain,
$false,
inference(forward_subsumption_resolution,[],[f1167,f121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM474+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 % Computer : n013.cluster.edu
% 0.12/0.42 % Model : x86_64 x86_64
% 0.12/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.42 % Memory : 8046.5625MB
% 0.12/0.42 % OS : Linux 6.8.0-71-generic
% 0.12/0.42 % CPULimit : 300
% 0.12/0.42 % WCLimit : 300
% 0.12/0.42 % DateTime : Sun Sep 27 20:04:48 UTC 2026
% 0.12/0.43 % CPUTime :
% 0.12/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.46 Running first-order theorem proving
% 0.12/0.46 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
% 3.69/1.45 % (517421)Detected formulas, will run a generic FOF schedule.
% 3.69/1.45 % (517428)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=1282242290:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.69/1.45 % (517427)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=4149563475:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.69/1.45 % (517426)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=1659823731:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.69/1.45 % (517430)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=274149016:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.69/1.45 % (517432)dis-21_1_sil=8000:lcm=predicate:random_seed=1148818629: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)
% 3.69/1.45 % (517431)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=461308754:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.69/1.45 % (517429)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1468808606:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.69/1.45 % (517430)First to succeed.
% 3.69/1.45 % (517430)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-517421"
% 3.69/1.45 % (517429)Instruction limit reached!
% 3.69/1.45 % (517429)------------------------------
% 3.69/1.45 % (517429)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.45 % (517429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.45 % (517429)CaDiCaL version: 2.1.3
% 3.69/1.45 % (517429)Termination reason: Instruction limit
% 3.69/1.45 % (517429)Termination phase: Saturation
% 3.69/1.45 % (517429)Time elapsed: 0.062 s
% 3.69/1.45 % (517429)Peak memory usage: 89 MB
% 3.69/1.45 % (517429)Instructions burned: 110 (million)
% 3.69/1.45 % (517432)Instruction limit reached!
% 3.69/1.45 % (517432)------------------------------
% 3.69/1.45 % (517432)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.45 % (517432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.45 % (517432)CaDiCaL version: 2.1.3
% 3.69/1.45 % (517432)Termination reason: Instruction limit
% 3.69/1.45 % (517432)Termination phase: Saturation
% 3.69/1.45 % (517432)Time elapsed: 0.080 s
% 3.69/1.45 % (517432)Peak memory usage: 90 MB
% 3.69/1.45 % (517432)Instructions burned: 130 (million)
% 3.69/1.45 % (517431)Instruction limit reached!
% 3.69/1.45 % (517431)------------------------------
% 3.69/1.45 % (517431)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.45 % (517431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.45 % (517431)CaDiCaL version: 2.1.3
% 3.69/1.45 % (517431)Termination reason: Instruction limit
% 3.69/1.45 % (517431)Termination phase: Saturation
% 3.69/1.45 % (517431)Time elapsed: 0.086 s
% 3.69/1.45 % (517431)Peak memory usage: 90 MB
% 3.69/1.45 % (517431)Instructions burned: 140 (million)
% 3.69/1.45 % (517440)lrs+10_1_sil=8000:sp=occurrence:random_seed=2230426520:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.69/1.45 % (517442)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2182811395:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.69/1.45 % (517441)lrs+10_1_sil=32000:urr=on:br=off:random_seed=722538161:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.69/1.45 % (517430)Refutation found. Thanks to Tanya!
% 3.69/1.45 % SZS status Theorem for theBenchmark
% 3.69/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.45 % (517430)------------------------------
% 3.69/1.45 % (517430)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.45 % (517430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.45 % (517430)CaDiCaL version: 2.1.3
% 3.69/1.45 % (517430)Termination reason: Refutation
% 3.69/1.45 % (517430)Time elapsed: 0.018 s
% 3.69/1.45 % (517430)Peak memory usage: 88 MB
% 3.69/1.45 % (517430)Instructions burned: 29 (million)
% 3.69/1.45 % (517430)------------------------------
% 3.69/1.45 % (517430)------------------------------
% 3.69/1.45 % (517421)Success in time 0.452 s
% 3.69/1.45 % Vampire exiting
%------------------------------------------------------------------------------