%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM849+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:25:54 PM UTC 2026
% Result : Theorem 0.09s 0.47s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 17 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 0 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 23 ( 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( vmul(vmul(vd448,vd449),X0) = vmul(vd448,vmul(vd449,X0))
=> vmul(vmul(vd448,vd449),vsucc(X0)) = vmul(vd448,vmul(vd449,vsucc(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(ind(296), imp(296))') ).
fof(f2,negated_conjecture,
~ ! [X0] :
( vmul(vmul(vd448,vd449),X0) = vmul(vd448,vmul(vd449,X0))
=> vmul(vmul(vd448,vd449),vsucc(X0)) = vmul(vd448,vmul(vd449,vsucc(X0))) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f9,axiom,
! [X0,X1,X2] : vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
fof(f13,axiom,
! [X0,X1] :
( vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0)
& vmul(X0,v1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
fof(f48,axiom,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f50,axiom,
! [X0] : vplus(v1,X0) = vsucc(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
fof(f58,plain,
? [X0] :
( vmul(vmul(vd448,vd449),vsucc(X0)) != vmul(vd448,vmul(vd449,vsucc(X0)))
& vmul(vmul(vd448,vd449),X0) = vmul(vd448,vmul(vd449,X0)) ),
inference(ennf_transformation,[],[f2]) ).
fof(f92,plain,
( vmul(vmul(vd448,vd449),vsucc(sK0)) != vmul(vd448,vmul(vd449,vsucc(sK0)))
& vmul(vmul(vd448,vd449),sK0) = vmul(vd448,vmul(vd449,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f58]) ).
fof(f104,plain,
vmul(vmul(vd448,vd449),sK0) = vmul(vd448,vmul(vd449,sK0)),
inference(cnf_transformation,[],[f92]) ).
fof(f105,plain,
vmul(vmul(vd448,vd449),vsucc(sK0)) != vmul(vd448,vmul(vd449,vsucc(sK0))),
inference(cnf_transformation,[],[f92]) ).
fof(f112,plain,
! [X2,X0,X1] : vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f117,plain,
! [X0,X1] : vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f160,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f48]) ).
fof(f162,plain,
! [X0] : vsucc(X0) = vplus(v1,X0),
inference(cnf_transformation,[],[f50]) ).
fof(f171,plain,
vmul(vmul(vd448,vd449),vplus(v1,sK0)) != vmul(vd448,vmul(vd449,vplus(v1,sK0))),
inference(definition_unfolding,[],[f105,f162,f162]) ).
fof(f175,plain,
! [X0,X1] : vplus(vmul(X0,X1),X0) = vmul(X0,vplus(v1,X1)),
inference(definition_unfolding,[],[f117,f162]) ).
fof(f184,plain,
! [X0,X1] : vmul(X0,vplus(v1,X1)) = vplus(X0,vmul(X0,X1)),
inference(forward_demodulation,[],[f175,f160]) ).
fof(f799,plain,
vmul(vd448,vmul(vd449,vplus(v1,sK0))) != vplus(vmul(vd448,vd449),vmul(vmul(vd448,vd449),sK0)),
inference(superposition,[],[f171,f184]) ).
fof(f846,plain,
vmul(vd448,vmul(vd449,vplus(v1,sK0))) != vplus(vmul(vd448,vd449),vmul(vd448,vmul(vd449,sK0))),
inference(forward_demodulation,[],[f799,f104]) ).
fof(f850,plain,
vmul(vd448,vmul(vd449,vplus(v1,sK0))) != vmul(vd448,vplus(vd449,vmul(vd449,sK0))),
inference(forward_demodulation,[],[f846,f112]) ).
fof(f852,plain,
vmul(vd448,vplus(vd449,vmul(vd449,sK0))) != vmul(vd448,vplus(vd449,vmul(vd449,sK0))),
inference(forward_demodulation,[],[f850,f184]) ).
fof(f853,plain,
$false,
inference(trivial_inequality_removal,[],[f852]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM849+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 21:30:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.47 % (571373)Will run a generic schedule for satisfiability detection.
% 0.09/0.47 % (571378)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3956005983_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.47 % TRYING [1]
% 0.09/0.47 % TRYING [2]
% 0.09/0.47 % TRYING [3]
% 0.09/0.47 % (571383)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1418220314:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.47 % (571384)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1846802968:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.47 % (571380)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1584235981:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.47 % (571381)dis+10_1_sil=32000:sp=arity:random_seed=2004899110:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.47 % (571382)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1531036075:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.47 % TRYING [4]
% 0.09/0.47 % (571379)% WARNING: option uhcvi not known.
% 0.09/0.47 % (571379)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1867625191:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.47 % (571383) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-571373-571383"...
% 0.09/0.47 % TRYING [5]
% 0.09/0.47 % (571383)...printing done.
% 0.09/0.47 % (571383)Refutation found. Thanks to Tanya!
% 0.09/0.47 % SZS status Theorem for theBenchmark
% 0.09/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.47 % (571383)------------------------------
% 0.09/0.47 % (571383)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.47 % (571383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.47 % (571383)CaDiCaL version: 2.1.3
% 0.09/0.47 % (571383)Termination reason: Refutation
% 0.09/0.47 % (571383)Time elapsed: 0.019 s
% 0.09/0.47 % (571383)Peak memory usage: 12 MB
% 0.09/0.47 % (571383)Instructions burned: 28 (million)
% 0.09/0.47 % (571373)Success in time 0.059 s
% 0.09/0.47 % Vampire exiting
%------------------------------------------------------------------------------