%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO010-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 09:35:51 AM UTC 2026
% Result : Unsatisfiable 2.77s 1.09s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 36 ( 36 unt; 4 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 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 : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 38 ( 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
fof(f3,axiom,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
fof(f6,negated_conjecture,
! [X0] : multiply(X0,multiplicative_identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_id1) ).
fof(f7,axiom,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f8,plain,
! [X0] : multiplicative_identity = add(X0,inverse(X0)),
inference(reorient_equations,[],[f7]) ).
fof(f11,negated_conjecture,
add(a,multiply(a,b)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_plus_ab_is_a) ).
fof(f12,plain,
a != add(a,multiply(a,b)),
inference(reorient_equations,[],[f11]) ).
fof(f16,definition,
! [X0] : sF1(X0) = multiply(X0,multiplicative_identity),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f17,plain,
! [X0] : multiply(X0,multiplicative_identity) = sF1(X0),
inference(reorient_equations,[],[f16]) ).
fof(f18,plain,
! [X0] : sF1(X0) = X0,
inference(definition_folding,[],[f6,f17]) ).
fof(f19,definition,
! [X0] : sF2(X0) = add(X0,inverse(X0)),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f20,plain,
! [X0] : add(X0,inverse(X0)) = sF2(X0),
inference(reorient_equations,[],[f19]) ).
fof(f21,plain,
! [X0] : multiplicative_identity = sF2(X0),
inference(definition_folding,[],[f8,f20]) ).
fof(f25,definition,
sF4 = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f26,plain,
multiply(a,b) = sF4,
inference(reorient_equations,[],[f25]) ).
fof(f27,definition,
sF5 = add(a,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f28,plain,
add(a,sF4) = sF5,
inference(reorient_equations,[],[f27]) ).
fof(f29,plain,
a != sF5,
inference(definition_folding,[],[f12,f28,f26]) ).
fof(f31,plain,
! [X0] : multiplicative_identity = add(X0,inverse(X0)),
inference(forward_demodulation,[],[f21,f20]) ).
fof(f32,plain,
! [X0] : multiply(X0,multiplicative_identity) = X0,
inference(forward_demodulation,[],[f18,f17]) ).
fof(f34,plain,
! [X0] : multiply(multiplicative_identity,X0) = X0,
inference(superposition,[],[f32,f2]) ).
fof(f73,plain,
! [X0,X1] : multiply(multiplicative_identity,add(X0,X1)) = add(X0,multiply(inverse(X0),X1)),
inference(superposition,[],[f3,f31]) ).
fof(f75,plain,
! [X0,X1] : add(multiply(multiplicative_identity,X0),multiply(multiplicative_identity,X1)) = add(X0,multiply(inverse(X0),X1)),
inference(forward_demodulation,[],[f73,f4]) ).
fof(f78,plain,
! [X0,X1] : add(multiply(multiplicative_identity,X0),X1) = add(X0,multiply(inverse(X0),X1)),
inference(forward_demodulation,[],[f75,f34]) ).
fof(f80,plain,
! [X0,X1] : add(X0,X1) = add(X0,multiply(inverse(X0),X1)),
inference(forward_demodulation,[],[f78,f34]) ).
fof(f196,plain,
! [X0] : add(X0,inverse(X0)) = add(X0,multiplicative_identity),
inference(superposition,[],[f80,f32]) ).
fof(f211,plain,
! [X0] : multiplicative_identity = add(X0,multiplicative_identity),
inference(forward_demodulation,[],[f196,f31]) ).
fof(f224,plain,
! [X0,X1] : multiply(X0,multiplicative_identity) = add(multiply(X0,X1),multiply(X0,multiplicative_identity)),
inference(superposition,[],[f4,f211]) ).
fof(f231,plain,
! [X0,X1] : add(multiply(X0,X1),X0) = X0,
inference(forward_demodulation,[],[f224,f32]) ).
fof(f232,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = X0,
inference(forward_demodulation,[],[f231,f1]) ).
fof(f314,plain,
a = add(a,sF4),
inference(superposition,[],[f232,f26]) ).
fof(f324,plain,
a = sF5,
inference(forward_demodulation,[],[f314,f28]) ).
fof(f330,plain,
a != a,
inference(superposition,[],[f29,f324]) ).
fof(f331,plain,
$false,
inference(trivial_inequality_removal,[],[f330]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO010-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n013.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 21:03:06 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 2.77/1.09 % (1576501)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.77/1.09 % (1576613)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=453135360:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.77/1.09 % (1576613)First to succeed.
% 2.77/1.09 % (1576613)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1576501"
% 2.77/1.09 % (1576606)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=3611766006:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.77/1.09 % (1576609)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2069609808:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.77/1.09 % (1576607)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=517044124:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.77/1.09 % (1576605)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=1707168091:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.77/1.09 % (1576609)Also succeeded, but the first one will report.
% 2.77/1.09 % (1576615)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=460226988:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.77/1.09 % (1576614)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=324766287:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.77/1.09 % (1576615)Also succeeded, but the first one will report.
% 2.77/1.09 % (1576614)Also succeeded, but the first one will report.
% 2.77/1.09 % (1576613)Refutation found. Thanks to Tanya!
% 2.77/1.09 % SZS status Unsatisfiable for theBenchmark
% 2.77/1.09 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/1.10 % (1576613)------------------------------
% 2.77/1.10 % (1576613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.10 % (1576613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.10 % (1576613)CaDiCaL version: 2.1.3
% 2.77/1.10 % (1576613)Termination reason: Refutation
% 2.77/1.10 % (1576613)Time elapsed: 0.005 s
% 2.77/1.10 % (1576613)Peak memory usage: 88 MB
% 2.77/1.10 % (1576613)Instructions burned: 11 (million)
% 2.77/1.10 % (1576613)------------------------------
% 2.77/1.10 % (1576613)------------------------------
% 2.77/1.10 % (1576501)Success in time 0.322 s
% 2.77/1.10 % Vampire exiting
%------------------------------------------------------------------------------