%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM851+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 : n019.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 12:17:16 PM UTC 2026
% Result : Theorem 3.41s 1.12s
% Output : Refutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 17 unt; 0 def)
% Number of atoms : 17 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 13 ( 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
vmul(vplus(vd471,vd473),vd469) = vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct2(conseq(302)), 475, 1)') ).
fof(f2,negated_conjecture,
vmul(vplus(vd471,vd473),vd469) != vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f4,axiom,
vd470 = vplus(vd471,vd473),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq(302)), 474, 0)') ).
fof(f7,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(f8,axiom,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof(f29,plain,
vmul(vplus(vd471,vd473),vd469) != vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
inference(flattening,[],[f2]) ).
fof(f42,plain,
vmul(vplus(vd471,vd473),vd469) != vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
inference(cnf_transformation,[],[f29]) ).
fof(f44,plain,
vplus(vd471,vd473) = vd470,
inference(cnf_transformation,[],[f4]) ).
fof(f47,plain,
! [X2,X0,X1] : vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f48,plain,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f86,plain,
vmul(vplus(vd471,vd473),vd469) != vplus(vmul(vd471,vd469),vmul(vd469,vd473)),
inference(superposition,[],[f42,f48]) ).
fof(f88,plain,
vplus(vmul(vd471,vd469),vmul(vd469,vd473)) != vmul(vd469,vplus(vd471,vd473)),
inference(forward_demodulation,[],[f86,f48]) ).
fof(f90,plain,
vplus(vmul(vd471,vd469),vmul(vd469,vd473)) != vmul(vd469,vd470),
inference(forward_demodulation,[],[f88,f44]) ).
fof(f302,plain,
! [X2,X0,X1] : vmul(X1,vplus(X0,X2)) = vplus(vmul(X0,X1),vmul(X1,X2)),
inference(superposition,[],[f47,f48]) ).
fof(f2741,plain,
vmul(vd469,vplus(vd471,vd473)) != vmul(vd469,vd470),
inference(superposition,[],[f90,f302]) ).
fof(f2785,plain,
vmul(vd469,vd470) != vmul(vd469,vd470),
inference(forward_demodulation,[],[f2741,f44]) ).
fof(f2786,plain,
$false,
inference(trivial_inequality_removal,[],[f2785]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM851+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n019.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 27 21:31:04 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.38 Running first-order theorem proving
% 0.14/0.38 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
% 3.41/1.12 % (3423951)Detected formulas, will run a generic FOF schedule.
% 3.41/1.12 % (3423961)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1777569744:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.41/1.12 % (3423959)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2082105943:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.41/1.12 % (3423956)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=498573661:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.41/1.12 % (3423962)dis-21_1_sil=8000:lcm=predicate:random_seed=251585936: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)
% 3.41/1.12 % (3423960)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1267876324:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.41/1.12 % (3423957)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=2739463285:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.41/1.12 % (3423958)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=4181029073:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.41/1.12 % (3423959)Refutation not found, incomplete strategy
% 3.41/1.12 % (3423959)------------------------------
% 3.41/1.12 % (3423959)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.12 % (3423959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.12 % (3423959)CaDiCaL version: 2.1.3
% 3.41/1.12 % (3423959)Termination reason: Refutation not found, incomplete strategy
% 3.41/1.12 % (3423959)Time elapsed: 0.002 s
% 3.41/1.12 % (3423959)Peak memory usage: 88 MB
% 3.41/1.12 % (3423959)Instructions burned: 1 (million)
% 3.41/1.12 % (3423962)Refutation not found, incomplete strategy
% 3.41/1.12 % (3423962)------------------------------
% 3.41/1.12 % (3423962)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.12 % (3423962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.12 % (3423962)CaDiCaL version: 2.1.3
% 3.41/1.12 % (3423962)Termination reason: Refutation not found, incomplete strategy
% 3.41/1.12 % (3423962)Time elapsed: 0.003 s
% 3.41/1.12 % (3423962)Peak memory usage: 88 MB
% 3.41/1.12 % (3423962)Instructions burned: 3 (million)
% 3.41/1.12 % (3423961)First to succeed.
% 3.41/1.12 % (3423961)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3423951"
% 3.41/1.12 % (3423960)Instruction limit reached!
% 3.41/1.12 % (3423960)------------------------------
% 3.41/1.12 % (3423960)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.12 % (3423960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.12 % (3423960)CaDiCaL version: 2.1.3
% 3.41/1.12 % (3423960)Termination reason: Instruction limit
% 3.41/1.12 % (3423960)Termination phase: Saturation
% 3.41/1.12 % (3423960)Time elapsed: 0.068 s
% 3.41/1.12 % (3423960)Peak memory usage: 89 MB
% 3.41/1.12 % (3423960)Instructions burned: 119 (million)
% 3.41/1.12 % (3423970)lrs+10_1_sil=8000:sp=occurrence:random_seed=2156581718:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.41/1.12 % (3423962)------------------------------
% 3.41/1.12 % (3423962)------------------------------
% 3.41/1.12 % (3423959)------------------------------
% 3.41/1.12 % (3423959)------------------------------
% 3.41/1.12 % (3423961)Refutation found. Thanks to Tanya!
% 3.41/1.12 % SZS status Theorem for theBenchmark
% 3.41/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 3.41/1.12 % (3423961)------------------------------
% 3.41/1.12 % (3423961)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.12 % (3423961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.12 % (3423961)CaDiCaL version: 2.1.3
% 3.41/1.12 % (3423961)Termination reason: Refutation
% 3.41/1.12 % (3423961)Time elapsed: 0.058 s
% 3.41/1.12 % (3423961)Peak memory usage: 89 MB
% 3.41/1.12 % (3423961)Instructions burned: 98 (million)
% 3.41/1.12 % (3423961)------------------------------
% 3.41/1.12 % (3423961)------------------------------
% 3.41/1.12 % (3423951)Success in time 0.451 s
% 3.41/1.12 % Vampire exiting
%------------------------------------------------------------------------------