%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO009-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 09:35:50 AM UTC 2026
% Result : Unsatisfiable 3.64s 1.18s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 32 ( 32 unt; 0 def)
% Number of atoms : 32 ( 31 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 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 : 47 ( 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_multiply) ).
fof(f3,axiom,
! [X2,X0,X1] : add(multiply(X0,X1),X2) = multiply(add(X0,X2),add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
fof(f5,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity3) ).
fof(f6,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity4) ).
fof(f7,axiom,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f8,axiom,
! [X0] : add(inverse(X0),X0) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse2) ).
fof(f9,plain,
! [X0] : multiplicative_identity = add(inverse(X0),X0),
inference(reorient_equations,[],[f8]) ).
fof(f11,axiom,
! [X0] : multiply(inverse(X0),X0) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse2) ).
fof(f12,plain,
! [X0] : additive_identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f11]) ).
fof(f13,axiom,
! [X0] : multiply(X0,multiplicative_identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_id1) ).
fof(f14,axiom,
! [X0] : multiply(multiplicative_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_id2) ).
fof(f15,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_id1) ).
fof(f17,negated_conjecture,
multiply(a,add(a,b)) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_operation) ).
fof(f18,plain,
a != multiply(a,add(a,b)),
inference(reorient_equations,[],[f17]) ).
fof(f70,plain,
! [X0,X1] : add(multiply(X0,inverse(X1)),X1) = multiply(add(X0,X1),multiplicative_identity),
inference(superposition,[],[f3,f9]) ).
fof(f75,plain,
! [X0,X1] : add(X0,X1) = add(multiply(X0,inverse(X1)),X1),
inference(forward_demodulation,[],[f70,f13]) ).
fof(f82,plain,
! [X0,X1] : add(X0,X1) = add(X1,multiply(X0,inverse(X1))),
inference(forward_demodulation,[],[f75,f1]) ).
fof(f92,plain,
! [X0] : add(X0,inverse(X0)) = add(multiplicative_identity,X0),
inference(superposition,[],[f82,f14]) ).
fof(f100,plain,
! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
inference(forward_demodulation,[],[f92,f7]) ).
fof(f189,plain,
! [X0,X1] : add(multiply(X0,X1),additive_identity) = multiply(add(X0,inverse(X1)),X1),
inference(superposition,[],[f5,f12]) ).
fof(f202,plain,
! [X0,X1] : add(multiply(X0,X1),additive_identity) = multiply(X1,add(X0,inverse(X1))),
inference(forward_demodulation,[],[f189,f2]) ).
fof(f210,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,add(X0,inverse(X1))),
inference(forward_demodulation,[],[f202,f15]) ).
fof(f257,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(multiplicative_identity,X1)),
inference(superposition,[],[f6,f13]) ).
fof(f302,plain,
! [X0,X1] : multiply(X0,multiplicative_identity) = add(X0,multiply(X0,X1)),
inference(forward_demodulation,[],[f257,f100]) ).
fof(f307,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = X0,
inference(forward_demodulation,[],[f302,f13]) ).
fof(f430,plain,
! [X0] : multiply(X0,multiplicative_identity) = multiply(X0,X0),
inference(superposition,[],[f210,f7]) ).
fof(f460,plain,
! [X0] : multiply(X0,X0) = X0,
inference(forward_demodulation,[],[f430,f13]) ).
fof(f472,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = add(X0,multiply(X0,X1)),
inference(superposition,[],[f6,f460]) ).
fof(f481,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = X0,
inference(forward_demodulation,[],[f472,f307]) ).
fof(f622,plain,
a != a,
inference(superposition,[],[f18,f481]) ).
fof(f623,plain,
$false,
inference(trivial_inequality_removal,[],[f622]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO009-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n011.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 21:03:46 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running first-order theorem proving
% 0.07/0.20 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
% 3.64/1.18 % (3785042)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.64/1.18 % (3785051)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4026905845:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.64/1.18 % (3785050)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1750948880:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.64/1.18 % (3785053)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2747899618:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.64/1.18 % (3785048)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3150524701:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.64/1.18 % (3785049)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3250337941:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.64/1.18 % (3785047)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=3804062761:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.64/1.18 % (3785052)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1377376697:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.64/1.18 % (3785053)First to succeed.
% 3.64/1.18 % (3785053)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3785042"
% 3.64/1.18 % (3785050)Also succeeded, but the first one will report.
% 3.64/1.18 % (3785051)Instruction limit reached!
% 3.64/1.18 % (3785051)------------------------------
% 3.64/1.18 % (3785051)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.18 % (3785051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.18 % (3785051)CaDiCaL version: 2.1.3
% 3.64/1.18 % (3785051)Termination reason: Instruction limit
% 3.64/1.18 % (3785051)Termination phase: Saturation
% 3.64/1.18 % (3785051)Time elapsed: 0.057 s
% 3.64/1.18 % (3785051)Peak memory usage: 89 MB
% 3.64/1.18 % (3785051)Instructions burned: 183 (million)
% 3.64/1.18 % (3785052)Also succeeded, but the first one will report.
% 3.64/1.18 % (3785061)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3638977726:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 3.64/1.18 % (3785053)Refutation found. Thanks to Tanya!
% 3.64/1.18 % SZS status Unsatisfiable for theBenchmark
% 3.64/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 3.64/1.18 % (3785053)------------------------------
% 3.64/1.18 % (3785053)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.18 % (3785053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.18 % (3785053)CaDiCaL version: 2.1.3
% 3.64/1.18 % (3785053)Termination reason: Refutation
% 3.64/1.18 % (3785053)Time elapsed: 0.013 s
% 3.64/1.18 % (3785053)Peak memory usage: 88 MB
% 3.64/1.18 % (3785053)Instructions burned: 20 (million)
% 3.64/1.18 % (3785053)------------------------------
% 3.64/1.18 % (3785053)------------------------------
% 3.64/1.18 % (3785042)Success in time 0.441 s
% 3.64/1.18 % Vampire exiting
%------------------------------------------------------------------------------