%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM453+1 : 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 : n002.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 12:15:15 PM UTC 2026
% Result : Theorem 3.71s 1.45s
% Output : Refutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 9 unt; 0 def)
% Number of atoms : 121 ( 55 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 129 ( 56 ~; 57 |; 11 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
fof(f4,axiom,
! [X0] :
( aInteger0(X0)
=> aInteger0(smndt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( aInteger0(X0)
& aInteger0(X1)
& aInteger0(X2) )
=> sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(f8,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(f9,axiom,
! [X0] :
( aInteger0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(f10,axiom,
! [X0] :
( aInteger0(X0)
=> ( sdtpldt0(X0,smndt0(X0)) = sz00
& sz00 = sdtpldt0(smndt0(X0),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
fof(f46,axiom,
( aInteger0(xp)
& xp != sz00
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2171) ).
fof(f48,conjecture,
( sdtpldt0(sz10,xp) != sz10
& sdtpldt0(sz10,smndt0(xp)) != sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f49,negated_conjecture,
~ ( sdtpldt0(sz10,xp) != sz10
& sdtpldt0(sz10,smndt0(xp)) != sz10 ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f55,plain,
( sz10 = sdtpldt0(sz10,xp)
| sz10 = sdtpldt0(sz10,smndt0(xp)) ),
inference(ennf_transformation,[],[f49]) ).
fof(f71,plain,
! [X0] :
( ( sdtpldt0(X0,smndt0(X0)) = sz00
& sz00 = sdtpldt0(smndt0(X0),X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f72,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f75,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f76,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f77,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f79,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(flattening,[],[f78]) ).
fof(f134,plain,
sz00 != xp,
inference(cnf_transformation,[],[f46]) ).
fof(f135,plain,
aInteger0(xp),
inference(cnf_transformation,[],[f46]) ).
fof(f138,plain,
( sz10 = sdtpldt0(sz10,smndt0(xp))
| sz10 = sdtpldt0(sz10,xp) ),
inference(cnf_transformation,[],[f55]) ).
fof(f177,plain,
aInteger0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f185,plain,
! [X0] :
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f186,plain,
! [X0] :
( sz00 = sdtpldt0(X0,smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f187,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f191,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f192,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f193,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(cnf_transformation,[],[f79]) ).
fof(f608,plain,
! [X0] :
( sdtpldt0(sz10,sdtpldt0(smndt0(xp),X0)) = sdtpldt0(sz10,X0)
| ~ aInteger0(sz10)
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(X0)
| sz10 = sdtpldt0(sz10,xp) ),
inference(superposition,[],[f193,f138]) ).
fof(f643,plain,
! [X0] :
( sdtpldt0(sz10,sdtpldt0(smndt0(xp),X0)) = sdtpldt0(sz10,X0)
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(X0)
| sz10 = sdtpldt0(sz10,xp) ),
inference(forward_subsumption_resolution,[],[f608,f177]) ).
fof(f650,plain,
( sdtpldt0(sz10,xp) = sdtpldt0(sz10,sz00)
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(xp)
| sz10 = sdtpldt0(sz10,xp)
| ~ aInteger0(xp) ),
inference(superposition,[],[f643,f185]) ).
fof(f661,plain,
( sdtpldt0(sz10,xp) = sdtpldt0(sz10,sz00)
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(xp)
| sz10 = sdtpldt0(sz10,xp) ),
inference(duplicate_literal_removal,[],[f650]) ).
fof(f665,plain,
( sdtpldt0(sz10,xp) = sdtpldt0(sz10,sz00)
| ~ aInteger0(xp)
| sz10 = sdtpldt0(sz10,xp) ),
inference(forward_subsumption_resolution,[],[f661,f187]) ).
fof(f667,plain,
( sdtpldt0(sz10,xp) = sdtpldt0(sz10,sz00)
| sz10 = sdtpldt0(sz10,xp) ),
inference(forward_subsumption_resolution,[],[f665,f135]) ).
fof(f669,plain,
( sz10 = sdtpldt0(sz10,xp)
| ~ aInteger0(sz10)
| sz10 = sdtpldt0(sz10,xp) ),
inference(superposition,[],[f191,f667]) ).
fof(f672,plain,
( sz10 = sdtpldt0(sz10,xp)
| ~ aInteger0(sz10) ),
inference(duplicate_literal_removal,[],[f669]) ).
fof(f676,plain,
sz10 = sdtpldt0(sz10,xp),
inference(forward_subsumption_resolution,[],[f672,f177]) ).
fof(f743,plain,
( sz10 = sdtpldt0(xp,sz10)
| ~ aInteger0(sz10)
| ~ aInteger0(xp) ),
inference(superposition,[],[f192,f676]) ).
fof(f745,plain,
( sz10 = sdtpldt0(xp,sz10)
| ~ aInteger0(xp) ),
inference(forward_subsumption_resolution,[],[f743,f177]) ).
fof(f750,plain,
sz10 = sdtpldt0(xp,sz10),
inference(forward_subsumption_resolution,[],[f745,f135]) ).
fof(f782,plain,
! [X0] :
( sdtpldt0(sz10,X0) = sdtpldt0(xp,sdtpldt0(sz10,X0))
| ~ aInteger0(xp)
| ~ aInteger0(sz10)
| ~ aInteger0(X0) ),
inference(superposition,[],[f193,f750]) ).
fof(f784,plain,
! [X0] :
( sdtpldt0(sz10,X0) = sdtpldt0(xp,sdtpldt0(sz10,X0))
| ~ aInteger0(sz10)
| ~ aInteger0(X0) ),
inference(forward_subsumption_resolution,[],[f782,f135]) ).
fof(f785,plain,
! [X0] :
( sdtpldt0(sz10,X0) = sdtpldt0(xp,sdtpldt0(sz10,X0))
| ~ aInteger0(X0) ),
inference(forward_subsumption_resolution,[],[f784,f177]) ).
fof(f988,plain,
( sz00 = sdtpldt0(xp,sz00)
| ~ aInteger0(smndt0(sz10))
| ~ aInteger0(sz10) ),
inference(superposition,[],[f785,f186]) ).
fof(f998,plain,
( sz00 = sdtpldt0(xp,sz00)
| ~ aInteger0(sz10) ),
inference(forward_subsumption_resolution,[],[f988,f187]) ).
fof(f999,plain,
sz00 = sdtpldt0(xp,sz00),
inference(forward_subsumption_resolution,[],[f998,f177]) ).
fof(f1001,plain,
( sz00 = xp
| ~ aInteger0(xp) ),
inference(superposition,[],[f191,f999]) ).
fof(f1005,plain,
~ aInteger0(xp),
inference(forward_subsumption_resolution,[],[f1001,f134]) ).
fof(f1008,plain,
$false,
inference(forward_subsumption_resolution,[],[f1005,f135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM453+1 : 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 : n002.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 20:02:37 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 3.71/1.45 % (3843834)Detected formulas, will run a generic FOF schedule.
% 3.71/1.45 % (3843842)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3263070203:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.71/1.45 % (3843842)Instruction limit reached!
% 3.71/1.45 % (3843842)------------------------------
% 3.71/1.45 % (3843842)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.45 % (3843842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.45 % (3843842)CaDiCaL version: 2.1.3
% 3.71/1.45 % (3843842)Termination reason: Instruction limit
% 3.71/1.45 % (3843842)Termination phase: Saturation
% 3.71/1.45 % (3843842)Time elapsed: 0.038 s
% 3.71/1.45 % (3843842)Peak memory usage: 90 MB
% 3.71/1.45 % (3843842)Instructions burned: 110 (million)
% 3.71/1.45 % (3843841)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=3316231877:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.71/1.45 % (3843844)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4213030157:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.71/1.45 % (3843840)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=3165169259:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.71/1.45 % (3843839)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=636579632:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.71/1.45 % (3843845)dis-21_1_sil=8000:lcm=predicate:random_seed=417315265: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)
% 3.71/1.45 % (3843843)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3428133038:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.71/1.45 % (3843843)First to succeed.
% 3.71/1.45 % (3843843)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3843834"
% 3.71/1.45 % (3843845)Instruction limit reached!
% 3.71/1.45 % (3843845)------------------------------
% 3.71/1.45 % (3843845)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.45 % (3843845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.45 % (3843845)CaDiCaL version: 2.1.3
% 3.71/1.45 % (3843845)Termination reason: Instruction limit
% 3.71/1.45 % (3843845)Termination phase: Saturation
% 3.71/1.45 % (3843845)Time elapsed: 0.080 s
% 3.71/1.45 % (3843845)Peak memory usage: 89 MB
% 3.71/1.45 % (3843845)Instructions burned: 130 (million)
% 3.71/1.45 % (3843844)Instruction limit reached!
% 3.71/1.45 % (3843844)------------------------------
% 3.71/1.45 % (3843844)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.45 % (3843844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.45 % (3843844)CaDiCaL version: 2.1.3
% 3.71/1.45 % (3843844)Termination reason: Instruction limit
% 3.71/1.45 % (3843844)Termination phase: Saturation
% 3.71/1.45 % (3843844)Time elapsed: 0.092 s
% 3.71/1.45 % (3843844)Peak memory usage: 90 MB
% 3.71/1.45 % (3843844)Instructions burned: 140 (million)
% 3.71/1.45 % (3843853)lrs+10_1_sil=8000:sp=occurrence:random_seed=1504027089:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.71/1.45 % (3843853)Instruction limit reached!
% 3.71/1.45 % (3843853)------------------------------
% 3.71/1.45 % (3843853)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.45 % (3843853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.45 % (3843853)CaDiCaL version: 2.1.3
% 3.71/1.45 % (3843853)Termination reason: Instruction limit
% 3.71/1.45 % (3843853)Termination phase: Saturation
% 3.71/1.45 % (3843853)Time elapsed: 0.090 s
% 3.71/1.45 % (3843853)Peak memory usage: 92 MB
% 3.71/1.45 % (3843853)Instructions burned: 286 (million)
% 3.71/1.45 % (3843854)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2845975716:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.71/1.45 % (3843855)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1789236192:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.71/1.45 % (3843843)Refutation found. Thanks to Tanya!
% 3.71/1.45 % SZS status Theorem for theBenchmark
% 3.71/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.71/1.45 % (3843843)------------------------------
% 3.71/1.45 % (3843843)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.45 % (3843843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.45 % (3843843)CaDiCaL version: 2.1.3
% 3.71/1.45 % (3843843)Termination reason: Refutation
% 3.71/1.45 % (3843843)Time elapsed: 0.020 s
% 3.71/1.45 % (3843843)Peak memory usage: 88 MB
% 3.71/1.45 % (3843843)Instructions burned: 29 (million)
% 3.71/1.45 % (3843843)------------------------------
% 3.71/1.45 % (3843843)------------------------------
% 3.71/1.45 % (3843834)Success in time 0.452 s
% 3.71/1.45 % Vampire exiting
%------------------------------------------------------------------------------