%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM844+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 3.62s 1.42s
% Output : Refutation 3.62s
% 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/sandbox/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(f14,axiom,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f18,axiom,
! [X0,X1] :
( vplus(X0,vsucc(X1)) = vsucc(vplus(X0,X1))
& vplus(X0,v1) = vsucc(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
fof(f22,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
inference(flattening,[],[f2]) ).
fof(f24,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
inference(cnf_transformation,[],[f14]) ).
fof(f40,plain,
! [X0] : vsucc(X0) = vplus(X0,v1),
inference(cnf_transformation,[],[f18]) ).
fof(f43,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vplus(vd411,v1))) != vplus(vmul(vd411,vd413),vplus(vplus(vd411,v1),vd413)),
inference(definition_unfolding,[],[f24,f40,f40]) ).
fof(f60,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vplus(vd411,v1))) != vplus(vmul(vd411,vd413),vplus(vd413,vplus(vd411,v1))),
inference(superposition,[],[f43,f39]) ).
fof(f61,plain,
$false,
inference(trivial_inequality_removal,[],[f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM844+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n010.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 21:30:02 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 3.62/1.42 % (1325374)Detected formulas, will run a generic FOF schedule.
% 3.62/1.42 % (1325433)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=2324919057:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.62/1.42 % (1325434)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=1095041932:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.62/1.42 % (1325437)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4077863665:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.62/1.42 % (1325436)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2812559976:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.62/1.42 % (1325435)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=3419839133:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.62/1.42 % (1325437)First to succeed.
% 3.62/1.42 % (1325436)Refutation not found, incomplete strategy
% 3.62/1.42 % (1325436)------------------------------
% 3.62/1.42 % (1325436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.42 % (1325436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.42 % (1325436)CaDiCaL version: 2.1.3
% 3.62/1.42 % (1325436)Termination reason: Refutation not found, incomplete strategy
% 3.62/1.42 % (1325436)Time elapsed: 0.002 s
% 3.62/1.42 % (1325436)Peak memory usage: 88 MB
% 3.62/1.42 % (1325436)Instructions burned: 1 (million)
% 3.62/1.42 % (1325437)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1325374"
% 3.62/1.42 % (1325438)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1614486354:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.62/1.42 % (1325438)Also succeeded, but the first one will report.
% 3.62/1.42 % (1325439)dis-21_1_sil=8000:lcm=predicate:random_seed=485654401: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)
% 3.62/1.42 % (1325439)Refutation not found, incomplete strategy
% 3.62/1.42 % (1325439)------------------------------
% 3.62/1.42 % (1325439)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.42 % (1325439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.42 % (1325439)CaDiCaL version: 2.1.3
% 3.62/1.42 % (1325439)Termination reason: Refutation not found, incomplete strategy
% 3.62/1.42 % (1325439)Time elapsed: 0.004 s
% 3.62/1.42 % (1325439)Peak memory usage: 88 MB
% 3.62/1.42 % (1325439)Instructions burned: 2 (million)
% 3.62/1.42 % (1325436)------------------------------
% 3.62/1.42 % (1325436)------------------------------
% 3.62/1.42 % (1325437)Refutation found. Thanks to Tanya!
% 3.62/1.42 % SZS status Theorem for theBenchmark
% 3.62/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 3.62/1.42 % (1325437)------------------------------
% 3.62/1.42 % (1325437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.42 % (1325437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.42 % (1325437)CaDiCaL version: 2.1.3
% 3.62/1.42 % (1325437)Termination reason: Refutation
% 3.62/1.42 % (1325437)Time elapsed: 0.002 s
% 3.62/1.42 % (1325437)Peak memory usage: 88 MB
% 3.62/1.42 % (1325437)Instructions burned: 1 (million)
% 3.62/1.42 % (1325437)------------------------------
% 3.62/1.42 % (1325437)------------------------------
% 3.62/1.42 % (1325374)Success in time 0.44 s
% 3.62/1.42 % Vampire exiting
%------------------------------------------------------------------------------