%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO004-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 2.27s 0.79s
% Output : Refutation 2.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 39 unt; 1 def)
% Number of atoms : 45 ( 35 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 2 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
fof(f3,axiom,
! [X2,X0,X1] : add(multiply(X0,X1),X2) = multiply(add(X0,X2),add(X1,X2)),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',distributivity3) ).
fof(f8,axiom,
! [X0] : add(inverse(X0),X0) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse2) ).
fof(f9,plain,
! [X0] : multiplicative_identity = add(inverse(X0),X0),
inference(reorient_equations,[],[f8]) ).
fof(f13,axiom,
! [X0] : multiply(X0,multiplicative_identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_id1) ).
fof(f14,axiom,
! [X0] : multiply(multiplicative_identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_id2) ).
fof(f17,negated_conjecture,
add(a,a) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_plus_a_is_a) ).
fof(f18,plain,
a != add(a,a),
inference(reorient_equations,[],[f17]) ).
fof(f20,definition,
( spl0_1
<=> a = add(a,a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f22,plain,
( a != add(a,a)
| spl0_1 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f23,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f18,f20]) ).
fof(f25,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(f26,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,[],[f25,f3]) ).
fof(f28,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,[],[f26,f3]) ).
fof(f71,plain,
! [X0,X1] : add(X0,X1) = multiply(add(X0,X1),add(multiplicative_identity,X1)),
inference(superposition,[],[f3,f13]) ).
fof(f90,plain,
! [X0] : multiplicative_identity = multiply(multiplicative_identity,add(multiplicative_identity,X0)),
inference(superposition,[],[f71,f9]) ).
fof(f100,plain,
! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
inference(forward_demodulation,[],[f90,f14]) ).
fof(f111,plain,
! [X0] : multiplicative_identity = add(X0,multiplicative_identity),
inference(superposition,[],[f1,f100]) ).
fof(f349,plain,
! [X0,X1] : multiply(multiplicative_identity,X1) = multiply(multiply(multiplicative_identity,add(X1,X0)),multiply(add(inverse(X0),X1),add(X1,X1))),
inference(superposition,[],[f28,f9]) ).
fof(f355,plain,
! [X0,X1] : multiply(add(X0,multiplicative_identity),X1) = multiply(multiply(add(X0,multiplicative_identity),multiplicative_identity),multiply(add(X0,X1),add(X1,X1))),
inference(superposition,[],[f28,f111]) ).
fof(f372,plain,
! [X0,X1] : multiply(add(multiplicative_identity,X0),X1) = multiply(multiply(add(multiplicative_identity,X0),add(X1,X0)),multiply(multiplicative_identity,add(X1,X1))),
inference(superposition,[],[f28,f100]) ).
fof(f396,plain,
! [X0,X1] : multiply(add(multiplicative_identity,X0),X1) = multiply(multiply(add(multiplicative_identity,X0),add(X1,X0)),add(X1,X1)),
inference(forward_demodulation,[],[f372,f14]) ).
fof(f407,plain,
! [X0,X1] : multiply(add(X0,multiplicative_identity),X1) = multiply(add(X0,multiplicative_identity),multiply(add(X0,X1),add(X1,X1))),
inference(forward_demodulation,[],[f355,f13]) ).
fof(f411,plain,
! [X0,X1] : multiply(multiplicative_identity,X1) = multiply(add(X1,X0),multiply(add(inverse(X0),X1),add(X1,X1))),
inference(forward_demodulation,[],[f349,f14]) ).
fof(f424,plain,
! [X0,X1] : multiply(multiplicative_identity,X1) = multiply(multiply(multiplicative_identity,add(X1,X0)),add(X1,X1)),
inference(forward_demodulation,[],[f396,f100]) ).
fof(f429,plain,
! [X0,X1] : multiply(multiplicative_identity,X1) = multiply(multiplicative_identity,multiply(add(X0,X1),add(X1,X1))),
inference(forward_demodulation,[],[f407,f111]) ).
fof(f431,plain,
! [X0,X1] : multiply(add(X1,X0),multiply(add(inverse(X0),X1),add(X1,X1))) = X1,
inference(forward_demodulation,[],[f411,f14]) ).
fof(f440,plain,
! [X0,X1] : multiply(multiplicative_identity,X1) = multiply(add(X1,X0),add(X1,X1)),
inference(forward_demodulation,[],[f424,f14]) ).
fof(f445,plain,
! [X0,X1] : multiply(add(X0,X1),add(X1,X1)) = multiply(multiplicative_identity,X1),
inference(forward_demodulation,[],[f429,f14]) ).
fof(f454,plain,
! [X0,X1] : multiply(add(X1,X0),add(X1,X1)) = X1,
inference(forward_demodulation,[],[f440,f14]) ).
fof(f458,plain,
! [X0,X1] : multiply(add(X0,X1),add(X1,X1)) = X1,
inference(forward_demodulation,[],[f445,f14]) ).
fof(f480,plain,
! [X0,X1] : multiply(add(X1,X0),X1) = X1,
inference(backward_demodulation,[],[f431,f458]) ).
fof(f484,plain,
! [X0,X1] : multiply(add(X0,X1),X1) = X1,
inference(superposition,[],[f480,f1]) ).
fof(f770,plain,
! [X0] : add(X0,X0) = X0,
inference(superposition,[],[f484,f454]) ).
fof(f779,plain,
( $false
| spl0_1 ),
inference(backward_subsumption_resolution,[],[f22,f770]) ).
fof(f799,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f779]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f23]) ).
cnf(s7,plain,
spl0_1,
inference(sat_conversion,[],[f799]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s7]) ).
fof(f837,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n007.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Mon Sep 28 21:01:11 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running first-order theorem proving
% 0.10/0.22 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
% 2.27/0.79 % (2819095)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.27/0.79 % (2819105)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=470983177:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.27/0.79 % (2819105)First to succeed.
% 2.27/0.79 % (2819105)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2819095"
% 2.27/0.79 % (2819106)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1395568451:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.27/0.79 % (2819100)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=36483120:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.27/0.79 % (2819103)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2343918187:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.27/0.79 % (2819102)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1096360359:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.27/0.79 % (2819104)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2218785194:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.27/0.79 % (2819101)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=4226034689:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.27/0.79 % (2819106)Also succeeded, but the first one will report.
% 2.27/0.79 % (2819103)Also succeeded, but the first one will report.
% 2.27/0.79 % (2819104)Also succeeded, but the first one will report.
% 2.27/0.79 % (2819105)Refutation found. Thanks to Tanya!
% 2.27/0.79 % SZS status Unsatisfiable for theBenchmark
% 2.27/0.79 % SZS output start Proof for theBenchmark
% See solution above
% 2.27/0.79 % (2819105)------------------------------
% 2.27/0.79 % (2819105)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.27/0.79 % (2819105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.79 % (2819105)CaDiCaL version: 2.1.3
% 2.27/0.79 % (2819105)Termination reason: Refutation
% 2.27/0.79 % (2819105)Time elapsed: 0.015 s
% 2.27/0.79 % (2819105)Peak memory usage: 89 MB
% 2.27/0.79 % (2819105)Instructions burned: 42 (million)
% 2.27/0.79 % (2819105)------------------------------
% 2.27/0.79 % (2819105)------------------------------
% 2.27/0.79 % (2819095)Success in time 0.284 s
% 2.27/0.79 % Vampire exiting
%------------------------------------------------------------------------------