%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO005-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 09:35:48 AM UTC 2026
% Result : Unsatisfiable 2.51s 1.12s
% Output : Refutation 2.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 52 ( 52 unt; 1 def)
% Number of atoms : 52 ( 46 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 80 ( 80 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f4,axiom,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
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(f10,axiom,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse1) ).
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(f16,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_id2) ).
fof(f17,negated_conjecture,
add(a,multiplicative_identity) != multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_plus_1_is_a) ).
fof(f18,plain,
multiplicative_identity != add(a,multiplicative_identity),
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
~ sP0(add(a,multiplicative_identity)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f20,plain,
sP0(multiplicative_identity),
inference(inequality_splitting,[],[f18,f19]) ).
fof(f21,plain,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = multiply(add(multiply(X0,X1),X0),add(multiply(X0,X1),X2)),
inference(backward_demodulation,[],[f6,f4]) ).
fof(f22,plain,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = multiply(add(multiply(X0,X2),X1),add(multiply(X0,X2),X2)),
inference(backward_demodulation,[],[f5,f4]) ).
fof(f23,plain,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = multiply(add(multiply(X0,X2),X1),multiply(add(X0,X2),add(X2,X2))),
inference(forward_demodulation,[],[f22,f3]) ).
fof(f24,plain,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = multiply(add(multiply(X0,X1),X0),multiply(add(X0,X2),add(X1,X2))),
inference(forward_demodulation,[],[f21,f3]) ).
fof(f25,plain,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = multiply(multiply(add(X0,X1),add(X2,X1)),multiply(add(X0,X2),add(X2,X2))),
inference(forward_demodulation,[],[f23,f3]) ).
fof(f26,plain,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = multiply(multiply(add(X0,X0),add(X1,X0)),multiply(add(X0,X2),add(X1,X2))),
inference(forward_demodulation,[],[f24,f3]) ).
fof(f28,plain,
multiplicative_identity = inverse(additive_identity),
inference(superposition,[],[f16,f7]) ).
fof(f30,plain,
! [X0] : add(inverse(X0),X0) = inverse(additive_identity),
inference(backward_demodulation,[],[f9,f28]) ).
fof(f31,plain,
! [X0] : multiply(X0,inverse(additive_identity)) = X0,
inference(backward_demodulation,[],[f13,f28]) ).
fof(f32,plain,
! [X0] : multiply(inverse(additive_identity),X0) = X0,
inference(backward_demodulation,[],[f14,f28]) ).
fof(f33,plain,
~ sP0(add(a,inverse(additive_identity))),
inference(backward_demodulation,[],[f19,f28]) ).
fof(f34,plain,
sP0(inverse(additive_identity)),
inference(backward_demodulation,[],[f20,f28]) ).
fof(f69,plain,
! [X0,X1] : multiply(add(X0,X1),add(inverse(X0),X1)) = add(additive_identity,X1),
inference(superposition,[],[f3,f10]) ).
fof(f73,plain,
! [X0,X1] : add(additive_identity,X1) = multiply(add(inverse(X0),X1),add(X0,X1)),
inference(superposition,[],[f3,f12]) ).
fof(f85,plain,
! [X0,X1] : multiply(add(inverse(X0),X1),add(X0,X1)) = X1,
inference(forward_demodulation,[],[f73,f16]) ).
fof(f86,plain,
! [X0,X1] : multiply(add(X0,X1),add(inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f69,f16]) ).
fof(f116,plain,
! [X0] : multiply(inverse(additive_identity),add(X0,X0)) = X0,
inference(superposition,[],[f85,f30]) ).
fof(f143,plain,
! [X0] : add(X0,X0) = X0,
inference(forward_demodulation,[],[f116,f32]) ).
fof(f144,plain,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = multiply(multiply(X0,add(X1,X0)),multiply(add(X0,X2),add(X1,X2))),
inference(backward_demodulation,[],[f26,f143]) ).
fof(f145,plain,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = multiply(multiply(add(X0,X1),add(X2,X1)),multiply(add(X0,X2),X2)),
inference(backward_demodulation,[],[f25,f143]) ).
fof(f152,plain,
! [X0,X1] : multiply(X0,add(inverse(X0),X1)) = multiply(multiply(X0,inverse(additive_identity)),multiply(add(X0,X1),add(inverse(X0),X1))),
inference(superposition,[],[f144,f30]) ).
fof(f197,plain,
! [X0,X1] : multiply(X0,add(inverse(X0),X1)) = multiply(multiply(X0,inverse(additive_identity)),X1),
inference(forward_demodulation,[],[f152,f86]) ).
fof(f208,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,add(inverse(X0),X1)),
inference(forward_demodulation,[],[f197,f31]) ).
fof(f253,plain,
! [X0,X1] : multiply(add(X1,additive_identity),X0) = multiply(multiply(add(X1,additive_identity),X0),multiply(add(X1,X0),X0)),
inference(superposition,[],[f145,f15]) ).
fof(f291,plain,
! [X0,X1] : multiply(X1,X0) = multiply(multiply(X1,X0),multiply(add(X1,X0),X0)),
inference(forward_demodulation,[],[f253,f15]) ).
fof(f356,plain,
! [X0] : additive_identity = multiply(X0,add(inverse(X0),additive_identity)),
inference(superposition,[],[f86,f15]) ).
fof(f379,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(forward_demodulation,[],[f356,f208]) ).
fof(f433,plain,
! [X0,X1] : add(additive_identity,X1) = multiply(add(X0,X1),add(additive_identity,X1)),
inference(superposition,[],[f3,f379]) ).
fof(f439,plain,
! [X0,X1] : multiply(add(X0,X1),X1) = X1,
inference(forward_demodulation,[],[f433,f16]) ).
fof(f448,plain,
! [X0,X1] : multiply(X1,X0) = multiply(multiply(X1,X0),X0),
inference(backward_demodulation,[],[f291,f439]) ).
fof(f510,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = X0,
inference(superposition,[],[f448,f85]) ).
fof(f584,plain,
! [X0] : inverse(additive_identity) = add(X0,inverse(additive_identity)),
inference(superposition,[],[f32,f510]) ).
fof(f587,plain,
~ sP0(inverse(additive_identity)),
inference(backward_demodulation,[],[f33,f584]) ).
fof(f592,plain,
$false,
inference(forward_subsumption_resolution,[],[f587,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO005-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n006.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 21:03:11 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 2.51/1.12 % (198269)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.51/1.12 % (198300)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=752572985:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.51/1.12 % (198300)First to succeed.
% 2.51/1.12 % (198300)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-198269"
% 2.51/1.12 % (198302)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1069794221:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.51/1.12 % (198301)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1662999314:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.51/1.12 % (198303)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2130404314:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.51/1.12 % (198299)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3575200292:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.51/1.12 % (198298)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=965795196:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.51/1.12 % (198297)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=2566587510:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.51/1.12 % (198303)Also succeeded, but the first one will report.
% 2.51/1.12 % (198301)Also succeeded, but the first one will report.
% 2.51/1.12 % (198302)Also succeeded, but the first one will report.
% 2.51/1.12 % (198300)Refutation found. Thanks to Tanya!
% 2.51/1.12 % SZS status Unsatisfiable for theBenchmark
% 2.51/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 2.51/1.13 % (198300)------------------------------
% 2.51/1.13 % (198300)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.51/1.13 % (198300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/1.13 % (198300)CaDiCaL version: 2.1.3
% 2.51/1.13 % (198300)Termination reason: Refutation
% 2.51/1.13 % (198300)Time elapsed: 0.011 s
% 2.51/1.13 % (198300)Peak memory usage: 88 MB
% 2.51/1.13 % (198300)Instructions burned: 32 (million)
% 2.51/1.13 % (198300)------------------------------
% 2.51/1.13 % (198300)------------------------------
% 2.51/1.13 % (198269)Success in time 0.268 s
% 2.51/1.13 % Vampire exiting
%------------------------------------------------------------------------------