%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM846+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 : n016.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 3.67s 1.48s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 24 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 8 ( 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(286, 441, 2)') ).
fof(f2,negated_conjecture,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,axiom,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd436,vd437),vmul(vd436,vd439)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(285, 440, 0)') ).
fof(f9,axiom,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof(f47,axiom,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f57,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(flattening,[],[f2]) ).
fof(f67,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(cnf_transformation,[],[f57]) ).
fof(f71,plain,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd436,vd437),vmul(vd436,vd439)),
inference(cnf_transformation,[],[f5]) ).
fof(f75,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f47]) ).
fof(f88,plain,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f149,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vplus(vmul(vd436,vd437),vmul(vd439,vd436)),vd436),
inference(superposition,[],[f67,f88]) ).
fof(f152,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd439,vd436))),
inference(forward_demodulation,[],[f149,f75]) ).
fof(f160,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vd436,vplus(vmul(vd439,vd436),vmul(vd436,vd437))),
inference(forward_demodulation,[],[f152,f75]) ).
fof(f166,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vd436,vplus(vmul(vd439,vd436),vmul(vd437,vd436))),
inference(forward_demodulation,[],[f160,f88]) ).
fof(f172,plain,
vplus(vd436,vmul(vd436,vplus(vd437,vd439))) != vplus(vd436,vplus(vmul(vd439,vd436),vmul(vd437,vd436))),
inference(forward_demodulation,[],[f166,f75]) ).
fof(f176,plain,
vplus(vd436,vmul(vd436,vplus(vd439,vd437))) != vplus(vd436,vplus(vmul(vd439,vd436),vmul(vd437,vd436))),
inference(forward_demodulation,[],[f172,f75]) ).
fof(f383,plain,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd436,vd439),vmul(vd436,vd437)),
inference(forward_demodulation,[],[f71,f75]) ).
fof(f384,plain,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd436,vd439),vmul(vd437,vd436)),
inference(forward_demodulation,[],[f383,f88]) ).
fof(f385,plain,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd437,vd436),vmul(vd436,vd439)),
inference(forward_demodulation,[],[f384,f75]) ).
fof(f386,plain,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd437,vd436),vmul(vd439,vd436)),
inference(forward_demodulation,[],[f385,f88]) ).
fof(f387,plain,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd439,vd436),vmul(vd437,vd436)),
inference(forward_demodulation,[],[f386,f75]) ).
fof(f388,plain,
vmul(vd436,vplus(vd439,vd437)) = vplus(vmul(vd439,vd436),vmul(vd437,vd436)),
inference(forward_demodulation,[],[f387,f75]) ).
fof(f389,plain,
vplus(vd436,vmul(vd436,vplus(vd439,vd437))) != vplus(vd436,vmul(vd436,vplus(vd439,vd437))),
inference(superposition,[],[f176,f388]) ).
fof(f400,plain,
$false,
inference(trivial_inequality_removal,[],[f389]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM846+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n016.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sun Sep 27 21:35:17 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 3.67/1.48 % (3010226)Detected formulas, will run a generic FOF schedule.
% 3.67/1.48 % (3010233)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=10259154:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.67/1.48 % (3010234)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=855133024:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.67/1.48 % (3010235)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3020348108:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.67/1.48 % (3010231)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=1897310623:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.67/1.48 % (3010232)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=2679716561:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.67/1.48 % (3010237)dis-21_1_sil=8000:lcm=predicate:random_seed=1053010362: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)
% 3.67/1.48 % (3010236)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2399179072:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.67/1.48 % (3010234)Refutation not found, incomplete strategy
% 3.67/1.48 % (3010234)------------------------------
% 3.67/1.48 % (3010234)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.48 % (3010234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.48 % (3010234)CaDiCaL version: 2.1.3
% 3.67/1.48 % (3010234)Termination reason: Refutation not found, incomplete strategy
% 3.67/1.48 % (3010234)Time elapsed: 0.002 s
% 3.67/1.48 % (3010234)Peak memory usage: 88 MB
% 3.67/1.48 % (3010234)Instructions burned: 1 (million)
% 3.67/1.48 % (3010235)First to succeed.
% 3.67/1.48 % (3010235)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3010226"
% 3.67/1.48 % (3010236)Also succeeded, but the first one will report.
% 3.67/1.48 % (3010237)Instruction limit reached!
% 3.67/1.48 % (3010237)------------------------------
% 3.67/1.48 % (3010237)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.48 % (3010237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.48 % (3010237)CaDiCaL version: 2.1.3
% 3.67/1.48 % (3010237)Termination reason: Instruction limit
% 3.67/1.48 % (3010237)Termination phase: Saturation
% 3.67/1.48 % (3010237)Time elapsed: 0.082 s
% 3.67/1.48 % (3010237)Peak memory usage: 89 MB
% 3.67/1.48 % (3010237)Instructions burned: 130 (million)
% 3.67/1.48 % (3010234)------------------------------
% 3.67/1.48 % (3010234)------------------------------
% 3.67/1.48 % (3010245)lrs+10_1_sil=8000:sp=occurrence:random_seed=2644840451:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.67/1.48 % (3010245)Also succeeded, but the first one will report.
% 3.67/1.48 % (3010235)Refutation found. Thanks to Tanya!
% 3.67/1.48 % SZS status Theorem for theBenchmark
% 3.67/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.49 % (3010235)------------------------------
% 3.67/1.49 % (3010235)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.49 % (3010235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.49 % (3010235)CaDiCaL version: 2.1.3
% 3.67/1.49 % (3010235)Termination reason: Refutation
% 3.67/1.49 % (3010235)Time elapsed: 0.009 s
% 3.67/1.49 % (3010235)Peak memory usage: 88 MB
% 3.67/1.49 % (3010235)Instructions burned: 13 (million)
% 3.67/1.49 % (3010235)------------------------------
% 3.67/1.49 % (3010235)------------------------------
% 3.67/1.49 % (3010226)Success in time 0.438 s
% 3.67/1.49 % Vampire exiting
%------------------------------------------------------------------------------