%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM435+3 : 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 12:15:10 PM UTC 2026
% Result : Theorem 3.98s 1.51s
% Output : Refutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 10 unt; 0 def)
% Number of atoms : 65 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 77 ( 37 ~; 29 |; 9 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0,X1,X2] :
( ( aInteger0(X0)
& aInteger0(X1)
& aInteger0(X2) )
=> sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(f12,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f23,axiom,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xp)
& xp != sz00
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__979) ).
fof(f25,axiom,
( aInteger0(xm)
& sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1032) ).
fof(f26,conjecture,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f27,negated_conjecture,
sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,plain,
sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(flattening,[],[f27]) ).
fof(f53,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f54,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(ennf_transformation,[],[f11]) ).
fof(f56,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(flattening,[],[f55]) ).
fof(f66,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f23]) ).
fof(f68,plain,
aInteger0(xp),
inference(cnf_transformation,[],[f23]) ).
fof(f76,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(sdtasdt0(xp,xq),xm),
inference(cnf_transformation,[],[f25]) ).
fof(f77,plain,
aInteger0(xm),
inference(cnf_transformation,[],[f25]) ).
fof(f78,plain,
sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f28]) ).
fof(f103,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f104,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(cnf_transformation,[],[f56]) ).
fof(f341,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X1,sdtasdt0(X0,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(superposition,[],[f104,f103]) ).
fof(f375,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X1,sdtasdt0(X0,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aInteger0(X2) ),
inference(duplicate_literal_removal,[],[f341]) ).
fof(f3718,plain,
( sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm))
| ~ aInteger0(xq)
| ~ aInteger0(xp)
| ~ aInteger0(xm) ),
inference(superposition,[],[f76,f375]) ).
fof(f3815,plain,
( ~ aInteger0(xq)
| ~ aInteger0(xp)
| ~ aInteger0(xm) ),
inference(forward_subsumption_resolution,[],[f3718,f78]) ).
fof(f3864,plain,
( ~ aInteger0(xp)
| ~ aInteger0(xm) ),
inference(forward_subsumption_resolution,[],[f3815,f66]) ).
fof(f3885,plain,
~ aInteger0(xm),
inference(forward_subsumption_resolution,[],[f3864,f68]) ).
fof(f3891,plain,
$false,
inference(forward_subsumption_resolution,[],[f3885,f77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM435+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 19:53:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.98/1.51 % (515063)Detected formulas, will run a generic FOF schedule.
% 3.98/1.51 % (515068)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=1571909455:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.98/1.51 % (515072)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4082383353:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.98/1.51 % (515069)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=841251911:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.98/1.51 % (515074)dis-21_1_sil=8000:lcm=predicate:random_seed=1500693670: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)
% 3.98/1.51 % (515073)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1653813399:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.98/1.51 % (515071)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4035523777:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.98/1.51 % (515070)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=1395272832:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.98/1.51 % (515074)Refutation not found, incomplete strategy
% 3.98/1.51 % (515074)------------------------------
% 3.98/1.51 % (515074)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.51 % (515074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.51 % (515074)CaDiCaL version: 2.1.3
% 3.98/1.51 % (515074)Termination reason: Refutation not found, incomplete strategy
% 3.98/1.51 % (515074)Time elapsed: 0.007 s
% 3.98/1.51 % (515074)Peak memory usage: 88 MB
% 3.98/1.51 % (515074)Instructions burned: 8 (million)
% 3.98/1.51 % (515072)First to succeed.
% 3.98/1.51 % (515072)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-515063"
% 3.98/1.51 % (515071)Instruction limit reached!
% 3.98/1.51 % (515071)------------------------------
% 3.98/1.51 % (515071)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.51 % (515071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.51 % (515071)CaDiCaL version: 2.1.3
% 3.98/1.51 % (515071)Termination reason: Instruction limit
% 3.98/1.51 % (515071)Termination phase: Saturation
% 3.98/1.51 % (515071)Time elapsed: 0.067 s
% 3.98/1.51 % (515071)Peak memory usage: 89 MB
% 3.98/1.51 % (515071)Instructions burned: 110 (million)
% 3.98/1.51 % (515073)Instruction limit reached!
% 3.98/1.51 % (515073)------------------------------
% 3.98/1.51 % (515073)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.51 % (515073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.51 % (515073)CaDiCaL version: 2.1.3
% 3.98/1.51 % (515073)Termination reason: Instruction limit
% 3.98/1.51 % (515073)Termination phase: Saturation
% 3.98/1.51 % (515073)Time elapsed: 0.085 s
% 3.98/1.51 % (515073)Peak memory usage: 90 MB
% 3.98/1.51 % (515073)Instructions burned: 140 (million)
% 3.98/1.51 % (515082)lrs+10_1_sil=8000:sp=occurrence:random_seed=1308300304:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.98/1.51 % (515083)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1151205712:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.98/1.51 % (515074)------------------------------
% 3.98/1.51 % (515074)------------------------------
% 3.98/1.51 % (515072)Refutation found. Thanks to Tanya!
% 3.98/1.51 % SZS status Theorem for theBenchmark
% 3.98/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 3.98/1.51 % (515072)------------------------------
% 3.98/1.51 % (515072)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.51 % (515072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.51 % (515072)CaDiCaL version: 2.1.3
% 3.98/1.51 % (515072)Termination reason: Refutation
% 3.98/1.51 % (515072)Time elapsed: 0.057 s
% 3.98/1.51 % (515072)Peak memory usage: 89 MB
% 3.98/1.51 % (515072)Instructions burned: 99 (million)
% 3.98/1.51 % (515072)------------------------------
% 3.98/1.51 % (515072)------------------------------
% 3.98/1.51 % (515063)Success in time 0.47 s
% 3.98/1.51 % Vampire exiting
%------------------------------------------------------------------------------