%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM845+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 12:25:53 PM UTC 2026
% Result : Theorem 0.17s 0.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 38 unt; 0 def)
% Number of atoms : 68 ( 67 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 8 |; 4 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 47 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( vmul(vsucc(vd411),X0) = vplus(vmul(vd411,X0),X0)
=> vmul(vsucc(vd411),vsucc(X0)) = vplus(vmul(vd411,vsucc(X0)),vsucc(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(ind(267), imp(267))') ).
fof(f2,negated_conjecture,
~ ! [X0] :
( vmul(vsucc(vd411),X0) = vplus(vmul(vd411,X0),X0)
=> vmul(vsucc(vd411),vsucc(X0)) = vplus(vmul(vd411,vsucc(X0)),vsucc(X0)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f7,axiom,
! [X0] :
( vmul(vsucc(vd411),X0) = vplus(vmul(vd411,X0),X0)
=> vplus(vmul(vd411,X0),vplus(X0,vsucc(vd411))) = vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 4)') ).
fof(f15,axiom,
! [X0,X1] :
( vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0)
& vmul(X0,v1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
fof(f50,axiom,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f52,axiom,
! [X0] : vplus(v1,X0) = vsucc(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
fof(f53,axiom,
! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof(f54,axiom,
! [X0,X1] :
( vplus(X0,vsucc(X1)) = vsucc(vplus(X0,X1))
& vplus(X0,v1) = vsucc(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
fof(f60,plain,
? [X0] :
( vmul(vsucc(vd411),vsucc(X0)) != vplus(vmul(vd411,vsucc(X0)),vsucc(X0))
& vmul(vsucc(vd411),X0) = vplus(vmul(vd411,X0),X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f65,plain,
! [X0] :
( vplus(vmul(vd411,X0),vplus(X0,vsucc(vd411))) = vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f98,plain,
( vmul(vsucc(vd411),vsucc(sK0)) != vplus(vmul(vd411,vsucc(sK0)),vsucc(sK0))
& vmul(vsucc(vd411),sK0) = vplus(vmul(vd411,sK0),sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f60]) ).
fof(f110,plain,
vmul(vsucc(vd411),sK0) = vplus(vmul(vd411,sK0),sK0),
inference(cnf_transformation,[],[f98]) ).
fof(f111,plain,
vmul(vsucc(vd411),vsucc(sK0)) != vplus(vmul(vd411,vsucc(sK0)),vsucc(sK0)),
inference(cnf_transformation,[],[f98]) ).
fof(f116,plain,
! [X0] :
( vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0)) = vplus(vmul(vd411,X0),vplus(X0,vsucc(vd411)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f125,plain,
! [X0,X1] : vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0),
inference(cnf_transformation,[],[f15]) ).
fof(f168,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f50]) ).
fof(f170,plain,
! [X0] : vsucc(X0) = vplus(v1,X0),
inference(cnf_transformation,[],[f52]) ).
fof(f171,plain,
! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f53]) ).
fof(f172,plain,
! [X0] : vsucc(X0) = vplus(X0,v1),
inference(cnf_transformation,[],[f54]) ).
fof(f173,plain,
! [X0,X1] : vsucc(vplus(X0,X1)) = vplus(X0,vsucc(X1)),
inference(cnf_transformation,[],[f54]) ).
fof(f179,plain,
vmul(vplus(v1,vd411),vplus(v1,sK0)) != vplus(vmul(vd411,vplus(v1,sK0)),vplus(v1,sK0)),
inference(definition_unfolding,[],[f111,f170,f170,f170,f170]) ).
fof(f180,plain,
vplus(vmul(vd411,sK0),sK0) = vmul(vplus(v1,vd411),sK0),
inference(definition_unfolding,[],[f110,f170]) ).
fof(f185,plain,
! [X0] :
( vplus(vmul(vd411,X0),vplus(vplus(v1,vd411),X0)) = vplus(vmul(vd411,X0),vplus(X0,vplus(v1,vd411)))
| vplus(vmul(vd411,X0),X0) != vmul(vplus(v1,vd411),X0) ),
inference(definition_unfolding,[],[f116,f170,f170,f170]) ).
fof(f192,plain,
! [X0,X1] : vplus(vmul(X0,X1),X0) = vmul(X0,vplus(v1,X1)),
inference(definition_unfolding,[],[f125,f170]) ).
fof(f194,plain,
! [X0,X1] : vplus(v1,vplus(X0,X1)) = vplus(X0,vplus(v1,X1)),
inference(definition_unfolding,[],[f173,f170,f170]) ).
fof(f195,plain,
! [X0] : vplus(v1,X0) = vplus(X0,v1),
inference(definition_unfolding,[],[f172,f170]) ).
fof(f201,plain,
! [X0,X1] : vmul(X0,vplus(v1,X1)) = vplus(X0,vmul(X0,X1)),
inference(forward_demodulation,[],[f192,f168]) ).
fof(f203,plain,
! [X0] :
( vplus(vmul(vd411,X0),vplus(vplus(vd411,v1),X0)) = vplus(vmul(vd411,X0),vplus(X0,vplus(vd411,v1)))
| vplus(vmul(vd411,X0),X0) != vmul(vplus(v1,vd411),X0) ),
inference(forward_demodulation,[],[f185,f195]) ).
fof(f205,plain,
vplus(vmul(vd411,sK0),sK0) = vmul(vplus(vd411,v1),sK0),
inference(forward_demodulation,[],[f180,f195]) ).
fof(f206,plain,
vmul(vplus(v1,vd411),vplus(v1,sK0)) != vplus(v1,vplus(vmul(vd411,vplus(v1,sK0)),sK0)),
inference(forward_demodulation,[],[f179,f194]) ).
fof(f208,plain,
! [X0] :
( vplus(vmul(vd411,X0),vplus(vd411,vplus(v1,X0))) = vplus(vmul(vd411,X0),vplus(X0,vplus(vd411,v1)))
| vplus(vmul(vd411,X0),X0) != vmul(vplus(v1,vd411),X0) ),
inference(forward_demodulation,[],[f203,f171]) ).
fof(f210,plain,
vmul(vplus(vd411,v1),sK0) = vplus(sK0,vmul(vd411,sK0)),
inference(forward_demodulation,[],[f205,f168]) ).
fof(f211,plain,
vmul(vplus(v1,vd411),vplus(v1,sK0)) != vplus(v1,vplus(sK0,vmul(vd411,vplus(v1,sK0)))),
inference(forward_demodulation,[],[f206,f168]) ).
fof(f212,plain,
! [X0] :
( vplus(vmul(vd411,X0),X0) != vmul(vplus(vd411,v1),X0)
| vplus(vmul(vd411,X0),vplus(vd411,vplus(v1,X0))) = vplus(vmul(vd411,X0),vplus(X0,vplus(vd411,v1))) ),
inference(forward_demodulation,[],[f208,f195]) ).
fof(f214,plain,
vmul(vplus(v1,vd411),vplus(v1,sK0)) != vplus(v1,vplus(sK0,vplus(vd411,vmul(vd411,sK0)))),
inference(forward_demodulation,[],[f211,f201]) ).
fof(f215,plain,
! [X0] :
( vmul(vplus(vd411,v1),X0) != vplus(X0,vmul(vd411,X0))
| vplus(vmul(vd411,X0),vplus(vd411,vplus(v1,X0))) = vplus(vmul(vd411,X0),vplus(X0,vplus(vd411,v1))) ),
inference(forward_demodulation,[],[f212,f168]) ).
fof(f217,plain,
vplus(v1,vplus(sK0,vplus(vd411,vmul(vd411,sK0)))) != vmul(vplus(vd411,v1),vplus(v1,sK0)),
inference(forward_demodulation,[],[f214,f195]) ).
fof(f598,plain,
! [X2,X0,X1] : vplus(X0,vplus(X1,X2)) = vplus(X2,vplus(X0,X1)),
inference(superposition,[],[f168,f171]) ).
fof(f638,plain,
! [X2,X0,X1] : vplus(v1,vplus(X2,vplus(X0,X1))) = vplus(X2,vplus(X0,vplus(v1,X1))),
inference(superposition,[],[f194,f194]) ).
fof(f790,plain,
! [X2,X0,X1] : vplus(X0,vplus(X1,vmul(vplus(X0,X1),X2))) = vmul(vplus(X0,X1),vplus(v1,X2)),
inference(superposition,[],[f171,f201]) ).
fof(f946,plain,
( vmul(vplus(vd411,v1),sK0) != vmul(vplus(vd411,v1),sK0)
| vplus(vmul(vd411,sK0),vplus(vd411,vplus(v1,sK0))) = vplus(vmul(vd411,sK0),vplus(sK0,vplus(vd411,v1))) ),
inference(superposition,[],[f215,f210]) ).
fof(f947,plain,
vplus(vmul(vd411,sK0),vplus(vd411,vplus(v1,sK0))) = vplus(vmul(vd411,sK0),vplus(sK0,vplus(vd411,v1))),
inference(trivial_inequality_removal,[],[f946]) ).
fof(f948,plain,
vplus(vmul(vd411,sK0),vplus(vd411,vplus(v1,sK0))) = vplus(vplus(vd411,v1),vplus(vmul(vd411,sK0),sK0)),
inference(forward_demodulation,[],[f947,f598]) ).
fof(f952,plain,
vplus(vmul(vd411,sK0),vplus(vd411,vplus(v1,sK0))) = vplus(sK0,vplus(vplus(vd411,v1),vmul(vd411,sK0))),
inference(forward_demodulation,[],[f948,f598]) ).
fof(f955,plain,
vplus(vmul(vd411,sK0),vplus(vd411,vplus(v1,sK0))) = vplus(sK0,vplus(vd411,vplus(v1,vmul(vd411,sK0)))),
inference(forward_demodulation,[],[f952,f171]) ).
fof(f957,plain,
vplus(v1,vplus(sK0,vplus(vd411,vmul(vd411,sK0)))) = vplus(vmul(vd411,sK0),vplus(vd411,vplus(v1,sK0))),
inference(forward_demodulation,[],[f955,f638]) ).
fof(f959,plain,
vplus(v1,vplus(sK0,vplus(vd411,vmul(vd411,sK0)))) = vplus(v1,vplus(vmul(vd411,sK0),vplus(vd411,sK0))),
inference(forward_demodulation,[],[f957,f638]) ).
fof(f961,plain,
vplus(v1,vplus(sK0,vplus(vd411,vmul(vd411,sK0)))) = vplus(v1,vplus(sK0,vplus(vmul(vd411,sK0),vd411))),
inference(forward_demodulation,[],[f959,f598]) ).
fof(f963,plain,
vplus(v1,vplus(sK0,vplus(vd411,vmul(vd411,sK0)))) = vplus(v1,vplus(vd411,vplus(sK0,vmul(vd411,sK0)))),
inference(forward_demodulation,[],[f961,f598]) ).
fof(f965,plain,
vplus(v1,vplus(sK0,vplus(vd411,vmul(vd411,sK0)))) = vplus(vd411,vplus(v1,vplus(sK0,vmul(vd411,sK0)))),
inference(forward_demodulation,[],[f963,f194]) ).
fof(f967,plain,
vplus(v1,vplus(sK0,vplus(vd411,vmul(vd411,sK0)))) = vplus(vd411,vplus(v1,vmul(vplus(vd411,v1),sK0))),
inference(forward_demodulation,[],[f965,f210]) ).
fof(f969,plain,
vplus(v1,vplus(sK0,vplus(vd411,vmul(vd411,sK0)))) = vmul(vplus(vd411,v1),vplus(v1,sK0)),
inference(forward_demodulation,[],[f967,f790]) ).
fof(f970,plain,
$false,
inference(forward_subsumption_resolution,[],[f969,f217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM845+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n010.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 21:30:47 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.50 % (1327480)Will run a generic schedule for satisfiability detection.
% 0.17/0.50 % (1327485)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1682960576_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.50 % (1327486)% WARNING: option uhcvi not known.
% 0.17/0.50 % TRYING [1]
% 0.17/0.50 % TRYING [2]
% 0.17/0.50 % (1327486)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=43212143:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.50 % (1327487)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2501182488:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.50 % TRYING [3]
% 0.17/0.50 % (1327488)dis+10_1_sil=32000:sp=arity:random_seed=3047020103:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.50 % (1327489)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=949352230:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.50 % (1327491)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=252649743:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.50 % (1327490)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=601327080:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.50 % TRYING [4]
% 0.17/0.50 % TRYING [5]
% 0.17/0.50 % (1327490) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1327480-1327490"...
% 0.17/0.50 % (1327490)...printing done.
% 0.17/0.50 % (1327490)Refutation found. Thanks to Tanya!
% 0.17/0.50 % SZS status Theorem for theBenchmark
% 0.17/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.50 % (1327490)------------------------------
% 0.17/0.50 % (1327490)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.50 % (1327490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.50 % (1327490)CaDiCaL version: 2.1.3
% 0.17/0.50 % (1327490)Termination reason: Refutation
% 0.17/0.50 % (1327490)Time elapsed: 0.028 s
% 0.17/0.50 % (1327490)Peak memory usage: 12 MB
% 0.17/0.50 % (1327490)Instructions burned: 42 (million)
% 0.17/0.50 % (1327480)Success in time 0.069 s
% 0.17/0.50 % Vampire exiting
%------------------------------------------------------------------------------