%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM848+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 : n018.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 12:17:15 PM UTC 2026
% Result : Theorem 3.53s 1.44s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 11 unt; 0 def)
% Number of atoms : 13 ( 12 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 10 ( 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(286, 441, 4)') ).
fof(f2,negated_conjecture,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f10,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(f12,axiom,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f18,plain,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(flattening,[],[f2]) ).
fof(f21,plain,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
! [X0,X1] : vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0),
inference(cnf_transformation,[],[f10]) ).
fof(f31,plain,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
inference(cnf_transformation,[],[f12]) ).
fof(f42,plain,
vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) != vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),
inference(superposition,[],[f21,f31]) ).
fof(f71,plain,
! [X0,X1] : vmul(X0,vsucc(X1)) = vplus(X0,vmul(X0,X1)),
inference(forward_demodulation,[],[f30,f31]) ).
fof(f79,plain,
vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(superposition,[],[f42,f71]) ).
fof(f82,plain,
$false,
inference(trivial_inequality_removal,[],[f79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM848+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n018.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 21:32:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 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
% 3.53/1.44 % (2746540)Detected formulas, will run a generic FOF schedule.
% 3.53/1.44 % (2746551)dis-21_1_sil=8000:lcm=predicate:random_seed=2810408006: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)
% 3.53/1.44 % (2746551)Refutation not found, incomplete strategy
% 3.53/1.44 % (2746551)------------------------------
% 3.53/1.44 % (2746551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.44 % (2746551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.44 % (2746551)CaDiCaL version: 2.1.3
% 3.53/1.44 % (2746551)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.44 % (2746551)Time elapsed: 0.001 s
% 3.53/1.44 % (2746551)Peak memory usage: 88 MB
% 3.53/1.44 % (2746551)Instructions burned: 1 (million)
% 3.53/1.44 % (2746550)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=518601474:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.53/1.44 % (2746549)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2880223969:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.53/1.44 % (2746547)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=3946389271:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.53/1.44 % (2746548)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2779931132:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.53/1.44 % (2746545)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=2502246604:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.53/1.44 % (2746546)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=2344248417:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.53/1.44 % (2746548)Refutation not found, incomplete strategy
% 3.53/1.44 % (2746548)------------------------------
% 3.53/1.44 % (2746548)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.44 % (2746548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.44 % (2746548)CaDiCaL version: 2.1.3
% 3.53/1.44 % (2746548)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.44 % (2746548)Time elapsed: 0.001 s
% 3.53/1.44 % (2746548)Peak memory usage: 88 MB
% 3.53/1.44 % (2746548)Instructions burned: 1 (million)
% 3.53/1.44 % (2746550)First to succeed.
% 3.53/1.44 % (2746550)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2746540"
% 3.53/1.44 % (2746549)Instruction limit reached!
% 3.53/1.44 % (2746549)------------------------------
% 3.53/1.44 % (2746549)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.44 % (2746549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.44 % (2746549)CaDiCaL version: 2.1.3
% 3.53/1.44 % (2746549)Termination reason: Instruction limit
% 3.53/1.44 % (2746549)Termination phase: Saturation
% 3.53/1.44 % (2746549)Time elapsed: 0.059 s
% 3.53/1.44 % (2746549)Peak memory usage: 88 MB
% 3.53/1.44 % (2746549)Instructions burned: 121 (million)
% 3.53/1.44 % (2746551)------------------------------
% 3.53/1.44 % (2746551)------------------------------
% 3.53/1.44 % (2746559)lrs+10_1_sil=8000:sp=occurrence:random_seed=1395714558:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.53/1.44 % (2746559)Also succeeded, but the first one will report.
% 3.53/1.44 % (2746560)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2056182757:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.53/1.44 % (2746548)------------------------------
% 3.53/1.44 % (2746548)------------------------------
% 3.53/1.44 % (2746550)Refutation found. Thanks to Tanya!
% 3.53/1.44 % SZS status Theorem for theBenchmark
% 3.53/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.44 % (2746550)------------------------------
% 3.53/1.44 % (2746550)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.44 % (2746550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.44 % (2746550)CaDiCaL version: 2.1.3
% 3.53/1.44 % (2746550)Termination reason: Refutation
% 3.53/1.44 % (2746550)Time elapsed: 0.003 s
% 3.53/1.44 % (2746550)Peak memory usage: 89 MB
% 3.53/1.44 % (2746550)Instructions burned: 3 (million)
% 3.53/1.44 % (2746550)------------------------------
% 3.53/1.44 % (2746550)------------------------------
% 3.53/1.44 % (2746540)Success in time 0.412 s
% 3.53/1.44 % Vampire exiting
%------------------------------------------------------------------------------