%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM423+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 : n012.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 12:15:07 PM UTC 2026
% Result : Theorem 2.01s 0.89s
% Output : Refutation 2.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 11 unt; 0 def)
% Number of atoms : 178 ( 50 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 220 ( 86 ~; 91 |; 33 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 66 ( 61 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).
fof(f6,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> aInteger0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
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(f15,axiom,
! [X0] :
( aInteger0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(f18,axiom,
! [X0] :
( aInteger0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).
fof(f19,axiom,
! [X0,X1,X2] :
( ( aInteger0(X0)
& aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).
fof(f20,axiom,
( aInteger0(xa)
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__671) ).
fof(f21,conjecture,
sdteqdtlpzmzozddtrp0(xa,xa,xq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f22,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(flattening,[],[f22]) ).
fof(f27,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(ennf_transformation,[],[f19]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(flattening,[],[f28]) ).
fof(f34,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f35,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0] :
( ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) ) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f37,plain,
! [X0] :
( ( sdtpldt0(X0,smndt0(X0)) = sz00
& sz00 = sdtpldt0(smndt0(X0),X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
& ( aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(nnf_transformation,[],[f29]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ! [X2] :
( ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(nnf_transformation,[],[f36]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ! [X2] :
( ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ! [X2] :
( ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aInteger0(X1)
& X1 != sz00
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = X0 ) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(rectify,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ! [X2] :
( ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aInteger0(X1)
& X1 != sz00
& aInteger0(sK0(X0,X1))
& sdtasdt0(X1,sK0(X0,X1)) = X0 )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f51]) ).
fof(f53,plain,
sz00 != xq,
inference(cnf_transformation,[],[f20]) ).
fof(f54,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f20]) ).
fof(f55,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f20]) ).
fof(f56,plain,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(cnf_transformation,[],[f23]) ).
fof(f59,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f60,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(cnf_transformation,[],[f48]) ).
fof(f65,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f70,plain,
! [X2,X0,X1] :
( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f72,plain,
! [X0] :
( sz00 = sdtpldt0(X0,smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f81,plain,
! [X2,X1] :
( aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(X2)
| ~ aInteger0(sdtasdt0(X1,X2)) ),
inference(equality_resolution,[],[f70]) ).
fof(f163,plain,
! [X2,X1] :
( aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(X2) ),
inference(forward_subsumption_resolution,[],[f81,f65]) ).
fof(f166,plain,
! [X0] :
( aDivisorOf0(X0,sz00)
| ~ aInteger0(X0)
| sz00 = X0
| ~ aInteger0(sz00)
| ~ aInteger0(X0) ),
inference(superposition,[],[f163,f59]) ).
fof(f172,plain,
! [X0] :
( aDivisorOf0(X0,sz00)
| ~ aInteger0(X0)
| sz00 = X0
| ~ aInteger0(sz00) ),
inference(duplicate_literal_removal,[],[f166]) ).
fof(f173,plain,
! [X0] :
( aDivisorOf0(X0,sz00)
| ~ aInteger0(X0)
| sz00 = X0 ),
inference(forward_subsumption_resolution,[],[f172,f60]) ).
fof(f356,plain,
! [X0,X1] :
( ~ aDivisorOf0(X0,sz00)
| sdteqdtlpzmzozddtrp0(X1,X1,X0)
| ~ aInteger0(X1)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| sz00 = X0
| ~ aInteger0(X1) ),
inference(superposition,[],[f62,f72]) ).
fof(f364,plain,
! [X0,X1] :
( ~ aDivisorOf0(X0,sz00)
| sdteqdtlpzmzozddtrp0(X1,X1,X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| sz00 = X0 ),
inference(duplicate_literal_removal,[],[f356]) ).
fof(f371,plain,
! [X0,X1] :
( sdteqdtlpzmzozddtrp0(X1,X1,X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| sz00 = X0 ),
inference(forward_subsumption_resolution,[],[f364,f173]) ).
fof(f378,plain,
( ~ aInteger0(xa)
| ~ aInteger0(xq)
| sz00 = xq ),
inference(resolution,[],[f371,f56]) ).
fof(f379,plain,
( ~ aInteger0(xq)
| sz00 = xq ),
inference(forward_subsumption_resolution,[],[f378,f55]) ).
fof(f380,plain,
sz00 = xq,
inference(forward_subsumption_resolution,[],[f379,f54]) ).
fof(f381,plain,
$false,
inference(forward_subsumption_resolution,[],[f380,f53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM423+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sun Sep 27 19:51:22 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 2.01/0.88 % (2694811)Detected formulas, will run a generic FOF schedule.
% 2.01/0.88 % (2694822)dis-21_1_sil=8000:lcm=predicate:random_seed=1136109042: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)
% 2.01/0.88 % (2694818)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=723948778:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.01/0.88 % (2694819)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4063214537:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.01/0.88 % (2694820)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=212805925:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.01/0.88 % (2694821)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3487390852:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.01/0.88 % (2694816)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=198348285:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.01/0.89 % (2694817)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=1449124082:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.01/0.89 % (2694819)Refutation not found, incomplete strategy
% 2.01/0.89 % (2694819)------------------------------
% 2.01/0.89 % (2694819)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.01/0.89 % (2694819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/0.89 % (2694819)CaDiCaL version: 2.1.3
% 2.01/0.89 % (2694819)Termination reason: Refutation not found, incomplete strategy
% 2.01/0.89 % (2694819)Time elapsed: 0.001 s
% 2.01/0.89 % (2694819)Peak memory usage: 88 MB
% 2.01/0.89 % (2694822)Refutation not found, incomplete strategy
% 2.01/0.89 % (2694822)------------------------------
% 2.01/0.89 % (2694822)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.01/0.89 % (2694822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/0.89 % (2694822)CaDiCaL version: 2.1.3
% 2.01/0.89 % (2694822)Termination reason: Refutation not found, incomplete strategy
% 2.01/0.89 % (2694822)Time elapsed: 0.002 s
% 2.01/0.89 % (2694822)Peak memory usage: 88 MB
% 2.01/0.89 % (2694822)Instructions burned: 3 (million)
% 2.01/0.89 % (2694820)First to succeed.
% 2.01/0.89 % (2694820)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2694811"
% 2.01/0.89 % (2694821)Also succeeded, but the first one will report.
% 2.01/0.89 % (2694822)------------------------------
% 2.01/0.89 % (2694822)------------------------------
% 2.01/0.89 % (2694819)------------------------------
% 2.01/0.89 % (2694819)------------------------------
% 2.01/0.89 % (2694820)Refutation found. Thanks to Tanya!
% 2.01/0.89 % SZS status Theorem for theBenchmark
% 2.01/0.89 % SZS output start Proof for theBenchmark
% See solution above
% 2.01/0.89 % (2694820)------------------------------
% 2.01/0.89 % (2694820)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.01/0.89 % (2694820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/0.89 % (2694820)CaDiCaL version: 2.1.3
% 2.01/0.89 % (2694820)Termination reason: Refutation
% 2.01/0.89 % (2694820)Time elapsed: 0.004 s
% 2.01/0.89 % (2694820)Peak memory usage: 88 MB
% 2.01/0.89 % (2694820)Instructions burned: 10 (million)
% 2.01/0.89 % (2694820)------------------------------
% 2.01/0.89 % (2694820)------------------------------
% 2.01/0.89 % (2694811)Success in time 0.259 s
% 2.01/0.89 % Vampire exiting
%------------------------------------------------------------------------------