%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM848+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 12:17:15 PM UTC 2026
% Result : Theorem 3.01s 1.06s
% Output : Refutation 3.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 20 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 9 ~; 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 : 19 ( 19 !; 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/sandbox2/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(f11,axiom,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof(f12,axiom,
! [X0,X1] : vmul(vsucc(X0),X1) = vplus(vmul(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).
fof(f49,axiom,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f53,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(f59,plain,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(flattening,[],[f2]) ).
fof(f69,plain,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(cnf_transformation,[],[f59]) ).
fof(f73,plain,
! [X0,X1] : vmul(vsucc(X0),X1) = vplus(vmul(X0,X1),X1),
inference(cnf_transformation,[],[f12]) ).
fof(f74,plain,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f81,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f49]) ).
fof(f95,plain,
! [X0] : vsucc(X0) = vplus(X0,v1),
inference(cnf_transformation,[],[f53]) ).
fof(f101,plain,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vplus(vd439,v1))),
inference(definition_unfolding,[],[f69,f95]) ).
fof(f104,plain,
! [X0,X1] : vplus(vmul(X0,X1),X1) = vmul(vplus(X0,v1),X1),
inference(definition_unfolding,[],[f73,f95]) ).
fof(f140,plain,
vplus(vmul(vd436,vd437),vmul(vd436,vplus(vd439,v1))) != vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),
inference(superposition,[],[f101,f81]) ).
fof(f145,plain,
vplus(vmul(vd436,vd437),vmul(vd436,vplus(vd439,v1))) != vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd439,vd436))),
inference(forward_demodulation,[],[f140,f74]) ).
fof(f147,plain,
vplus(vmul(vd437,vd436),vmul(vd436,vplus(vd439,v1))) != vplus(vmul(vd437,vd436),vplus(vd436,vmul(vd439,vd436))),
inference(forward_demodulation,[],[f145,f74]) ).
fof(f207,plain,
! [X0,X1] : vmul(vplus(X0,v1),X1) = vplus(X1,vmul(X0,X1)),
inference(forward_demodulation,[],[f104,f81]) ).
fof(f267,plain,
vplus(vmul(vd437,vd436),vmul(vd436,vplus(vd439,v1))) != vplus(vmul(vd437,vd436),vmul(vplus(vd439,v1),vd436)),
inference(superposition,[],[f147,f207]) ).
fof(f272,plain,
vplus(vmul(vd437,vd436),vmul(vd436,vplus(vd439,v1))) != vplus(vmul(vd437,vd436),vmul(vd436,vplus(vd439,v1))),
inference(forward_demodulation,[],[f267,f74]) ).
fof(f273,plain,
$false,
inference(trivial_inequality_removal,[],[f272]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM848+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.35 % Computer : n016.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sun Sep 27 21:35:03 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 3.01/1.06 % (3009809)Detected formulas, will run a generic FOF schedule.
% 3.01/1.06 % (3009819)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2325905651:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.01/1.06 % (3009818)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=87863007:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.01/1.06 % (3009814)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=2560636666:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.01/1.06 % (3009817)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3042203472:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.01/1.06 % (3009820)dis-21_1_sil=8000:lcm=predicate:random_seed=4078673207: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)
% 3.01/1.06 % (3009815)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=251584631:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.01/1.06 % (3009816)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=2918984569:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.01/1.06 % (3009817)Refutation not found, incomplete strategy
% 3.01/1.06 % (3009817)------------------------------
% 3.01/1.06 % (3009817)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.01/1.06 % (3009817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/1.06 % (3009817)CaDiCaL version: 2.1.3
% 3.01/1.06 % (3009817)Termination reason: Refutation not found, incomplete strategy
% 3.01/1.06 % (3009817)Time elapsed: 0.002 s
% 3.01/1.06 % (3009817)Peak memory usage: 88 MB
% 3.01/1.06 % (3009817)Instructions burned: 1 (million)
% 3.01/1.06 % (3009818)First to succeed.
% 3.01/1.06 % (3009818)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3009809"
% 3.01/1.06 % (3009819)Also succeeded, but the first one will report.
% 3.01/1.06 % (3009820)Instruction limit reached!
% 3.01/1.06 % (3009820)------------------------------
% 3.01/1.06 % (3009820)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.01/1.06 % (3009820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/1.06 % (3009820)CaDiCaL version: 2.1.3
% 3.01/1.06 % (3009820)Termination reason: Instruction limit
% 3.01/1.06 % (3009820)Termination phase: Saturation
% 3.01/1.06 % (3009820)Time elapsed: 0.079 s
% 3.01/1.06 % (3009820)Peak memory usage: 89 MB
% 3.01/1.06 % (3009820)Instructions burned: 130 (million)
% 3.01/1.06 % (3009828)lrs+10_1_sil=8000:sp=occurrence:random_seed=351594858:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.01/1.06 % (3009828)Also succeeded, but the first one will report.
% 3.01/1.06 % (3009817)------------------------------
% 3.01/1.06 % (3009817)------------------------------
% 3.01/1.06 % (3009818)Refutation found. Thanks to Tanya!
% 3.01/1.06 % SZS status Theorem for theBenchmark
% 3.01/1.06 % SZS output start Proof for theBenchmark
% See solution above
% 3.01/1.06 % (3009818)------------------------------
% 3.01/1.06 % (3009818)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.01/1.06 % (3009818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/1.06 % (3009818)CaDiCaL version: 2.1.3
% 3.01/1.06 % (3009818)Termination reason: Refutation
% 3.01/1.06 % (3009818)Time elapsed: 0.006 s
% 3.01/1.06 % (3009818)Peak memory usage: 88 MB
% 3.01/1.06 % (3009818)Instructions burned: 8 (million)
% 3.01/1.06 % (3009818)------------------------------
% 3.01/1.06 % (3009818)------------------------------
% 3.01/1.06 % (3009809)Success in time 0.392 s
% 3.01/1.06 % Vampire exiting
%------------------------------------------------------------------------------