%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM427+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 : n003.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 12:15:08 PM UTC 2026
% Result : Theorem 3.48s 1.46s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 16 unt; 0 def)
% Number of atoms : 162 ( 40 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 199 ( 82 ~; 77 |; 31 &)
% ( 5 <=>; 4 =>; 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 54 ( 49 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( aInteger0(X0)
=> aInteger0(smndt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(f6,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> aInteger0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
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(f21,axiom,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__704) ).
fof(f23,axiom,
( aInteger0(xn)
& sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__747) ).
fof(f24,axiom,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__767) ).
fof(f25,conjecture,
sdteqdtlpzmzozddtrp0(xb,xa,xq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f26,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f28,plain,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(flattening,[],[f26]) ).
fof(f29,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f32,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f33,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f32]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) ) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f52,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(f53,plain,
! [X0,X1,X2] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(flattening,[],[f52]) ).
fof(f56,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,[],[f51]) ).
fof(f57,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,[],[f56]) ).
fof(f58,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,[],[f57]) ).
fof(f59,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))],[f58]) ).
fof(f60,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,[],[f53]) ).
fof(f63,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f65,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f87,plain,
! [X2,X0,X1] :
( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f89,plain,
! [X2,X0,X1] :
( sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(cnf_transformation,[],[f60]) ).
fof(f91,plain,
sz00 != xq,
inference(cnf_transformation,[],[f21]) ).
fof(f92,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f21]) ).
fof(f93,plain,
aInteger0(xb),
inference(cnf_transformation,[],[f21]) ).
fof(f94,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f21]) ).
fof(f97,plain,
aInteger0(xn),
inference(cnf_transformation,[],[f23]) ).
fof(f98,plain,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(cnf_transformation,[],[f24]) ).
fof(f99,plain,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(cnf_transformation,[],[f28]) ).
fof(f100,plain,
! [X2,X1] :
( aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(X2)
| ~ aInteger0(sdtasdt0(X1,X2)) ),
inference(equality_resolution,[],[f87]) ).
fof(f110,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(xb)
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| sz00 = xq ),
inference(resolution,[],[f89,f99]) ).
fof(f113,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| sz00 = xq ),
inference(forward_subsumption_resolution,[],[f110,f93]) ).
fof(f114,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(xq)
| sz00 = xq ),
inference(forward_subsumption_resolution,[],[f113,f94]) ).
fof(f115,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sz00 = xq ),
inference(forward_subsumption_resolution,[],[f114,f92]) ).
fof(f116,plain,
~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))),
inference(forward_subsumption_resolution,[],[f115,f91]) ).
fof(f117,plain,
~ aDivisorOf0(xq,sdtasdt0(xq,smndt0(xn))),
inference(forward_demodulation,[],[f116,f98]) ).
fof(f310,plain,
! [X2,X1] :
( aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(X2) ),
inference(forward_subsumption_resolution,[],[f100,f65]) ).
fof(f315,plain,
( ~ aInteger0(xq)
| sz00 = xq
| ~ aInteger0(smndt0(xn)) ),
inference(resolution,[],[f310,f117]) ).
fof(f333,plain,
( sz00 = xq
| ~ aInteger0(smndt0(xn)) ),
inference(forward_subsumption_resolution,[],[f315,f92]) ).
fof(f347,plain,
~ aInteger0(smndt0(xn)),
inference(forward_subsumption_resolution,[],[f333,f91]) ).
fof(f348,plain,
~ aInteger0(xn),
inference(resolution,[],[f347,f63]) ).
fof(f350,plain,
$false,
inference(forward_subsumption_resolution,[],[f348,f97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM427+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n003.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 19:53:26 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 3.48/1.46 % (883537)Detected formulas, will run a generic FOF schedule.
% 3.48/1.46 % (883546)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1545983569:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.48/1.46 % (883548)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=980063323:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.48/1.46 % (883547)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=282444683:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.48/1.46 % (883545)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=2607497699:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.48/1.46 % (883544)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=2416044145:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.48/1.46 % (883543)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=146445458:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.48/1.46 % (883549)dis-21_1_sil=8000:lcm=predicate:random_seed=3839283815: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)
% 3.48/1.46 % (883546)Instruction limit reached!
% 3.48/1.46 % (883546)------------------------------
% 3.48/1.46 % (883546)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.46 % (883546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.46 % (883546)CaDiCaL version: 2.1.3
% 3.48/1.46 % (883546)Termination reason: Instruction limit
% 3.48/1.46 % (883546)Termination phase: Saturation
% 3.48/1.46 % (883546)Time elapsed: 0.037 s
% 3.48/1.46 % (883546)Peak memory usage: 90 MB
% 3.48/1.46 % (883546)Instructions burned: 112 (million)
% 3.48/1.46 % (883549)Refutation not found, incomplete strategy
% 3.48/1.46 % (883549)------------------------------
% 3.48/1.46 % (883549)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.46 % (883549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.46 % (883549)CaDiCaL version: 2.1.3
% 3.48/1.46 % (883549)Termination reason: Refutation not found, incomplete strategy
% 3.48/1.46 % (883549)Time elapsed: 0.004 s
% 3.48/1.46 % (883549)Peak memory usage: 88 MB
% 3.48/1.46 % (883549)Instructions burned: 4 (million)
% 3.48/1.46 % (883548)First to succeed.
% 3.48/1.46 % (883548)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-883537"
% 3.48/1.46 % (883547)Instruction limit reached!
% 3.48/1.46 % (883547)------------------------------
% 3.48/1.46 % (883547)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.46 % (883547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.46 % (883547)CaDiCaL version: 2.1.3
% 3.48/1.46 % (883547)Termination reason: Instruction limit
% 3.48/1.46 % (883547)Termination phase: Saturation
% 3.48/1.46 % (883547)Time elapsed: 0.067 s
% 3.48/1.46 % (883547)Peak memory usage: 88 MB
% 3.48/1.46 % (883547)Instructions burned: 120 (million)
% 3.48/1.46 % (883557)lrs+10_1_sil=8000:sp=occurrence:random_seed=2071564583:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.48/1.46 % (883557)Also succeeded, but the first one will report.
% 3.48/1.46 % (883558)lrs+10_1_sil=32000:urr=on:br=off:random_seed=603117824:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.48/1.46 % (883558)Refutation not found, incomplete strategy
% 3.48/1.46 % (883558)------------------------------
% 3.48/1.46 % (883558)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.46 % (883558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.46 % (883558)CaDiCaL version: 2.1.3
% 3.48/1.46 % (883558)Termination reason: Refutation not found, incomplete strategy
% 3.48/1.46 % (883558)Time elapsed: 0.002 s
% 3.48/1.46 % (883558)Peak memory usage: 88 MB
% 3.48/1.46 % (883558)Instructions burned: 2 (million)
% 3.48/1.46 % (883549)------------------------------
% 3.48/1.46 % (883549)------------------------------
% 3.48/1.46 % (883548)Refutation found. Thanks to Tanya!
% 3.48/1.46 % SZS status Theorem for theBenchmark
% 3.48/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.46 % (883548)------------------------------
% 3.48/1.46 % (883548)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.46 % (883548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.46 % (883548)CaDiCaL version: 2.1.3
% 3.48/1.46 % (883548)Termination reason: Refutation
% 3.48/1.46 % (883548)Time elapsed: 0.009 s
% 3.48/1.46 % (883548)Peak memory usage: 89 MB
% 3.48/1.46 % (883548)Instructions burned: 10 (million)
% 3.48/1.46 % (883548)------------------------------
% 3.48/1.46 % (883548)------------------------------
% 3.48/1.46 % (883537)Success in time 0.41 s
% 3.48/1.46 % Vampire exiting
%------------------------------------------------------------------------------