%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM844+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 12:17:14 PM UTC 2026
% Result : Theorem 2.55s 1.42s
% Output : Refutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 10 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 5 ~; 0 |; 1 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 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 : 7 ( 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(266, 415, 3)') ).
fof(f2,negated_conjecture,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f46,axiom,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f50,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(f56,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
inference(flattening,[],[f2]) ).
fof(f66,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
inference(cnf_transformation,[],[f56]) ).
fof(f82,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f46]) ).
fof(f92,plain,
! [X0] : vsucc(X0) = vplus(X0,v1),
inference(cnf_transformation,[],[f50]) ).
fof(f95,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vplus(vd411,v1))) != vplus(vmul(vd411,vd413),vplus(vplus(vd411,v1),vd413)),
inference(definition_unfolding,[],[f66,f92,f92]) ).
fof(f122,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vplus(vd411,v1))) != vplus(vmul(vd411,vd413),vplus(vd413,vplus(vd411,v1))),
inference(superposition,[],[f95,f82]) ).
fof(f123,plain,
$false,
inference(trivial_inequality_removal,[],[f122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM844+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n010.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 21:30:02 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 2.55/1.42 % (1325428)Detected formulas, will run a generic FOF schedule.
% 2.55/1.42 % (1325453)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=143005938:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.55/1.42 % (1325453)First to succeed.
% 2.55/1.42 % (1325453)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1325428"
% 2.55/1.42 % (1325450)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=2615953392:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.55/1.42 % (1325449)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=3078033694:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.55/1.42 % (1325451)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=3121745807:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.55/1.42 % (1325452)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1525065660:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.55/1.42 % (1325455)dis-21_1_sil=8000:lcm=predicate:random_seed=1423572889: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)
% 2.55/1.42 % (1325454)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4134239376:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.55/1.42 % (1325452)Refutation not found, incomplete strategy
% 2.55/1.42 % (1325452)------------------------------
% 2.55/1.42 % (1325452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.42 % (1325452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.42 % (1325452)CaDiCaL version: 2.1.3
% 2.55/1.42 % (1325452)Termination reason: Refutation not found, incomplete strategy
% 2.55/1.42 % (1325452)Time elapsed: 0.002 s
% 2.55/1.42 % (1325452)Peak memory usage: 88 MB
% 2.55/1.42 % (1325452)Instructions burned: 1 (million)
% 2.55/1.42 % (1325454)Also succeeded, but the first one will report.
% 2.55/1.42 % (1325455)Instruction limit reached!
% 2.55/1.42 % (1325455)------------------------------
% 2.55/1.42 % (1325455)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.42 % (1325455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.42 % (1325455)CaDiCaL version: 2.1.3
% 2.55/1.42 % (1325455)Termination reason: Instruction limit
% 2.55/1.42 % (1325455)Termination phase: Saturation
% 2.55/1.42 % (1325455)Time elapsed: 0.083 s
% 2.55/1.42 % (1325455)Peak memory usage: 89 MB
% 2.55/1.42 % (1325455)Instructions burned: 130 (million)
% 2.55/1.42 % (1325453)Refutation found. Thanks to Tanya!
% 2.55/1.42 % SZS status Theorem for theBenchmark
% 2.55/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 2.55/1.42 % (1325453)------------------------------
% 2.55/1.42 % (1325453)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.42 % (1325453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.42 % (1325453)CaDiCaL version: 2.1.3
% 2.55/1.42 % (1325453)Termination reason: Refutation
% 2.55/1.42 % (1325453)Time elapsed: 0.001 s
% 2.55/1.42 % (1325453)Peak memory usage: 88 MB
% 2.55/1.42 % (1325453)Instructions burned: 2 (million)
% 2.55/1.42 % (1325453)------------------------------
% 2.55/1.42 % (1325453)------------------------------
% 2.55/1.42 % (1325428)Success in time 0.249 s
% 2.55/1.42 % Vampire exiting
%------------------------------------------------------------------------------