%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO029-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 09:35:56 AM UTC 2026
% Result : Unsatisfiable 5.84s 1.94s
% Output : Refutation 5.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 60 ( 60 unt; 6 def)
% Number of atoms : 60 ( 59 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 55 ( 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : add(X0,multiply(X1,multiply(X0,X2))) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
fof(f2,axiom,
! [X2,X0,X1] : add(add(multiply(X0,X1),multiply(X1,X2)),X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,add(X0,X2))) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2) ).
fof(f6,negated_conjecture,
! [X0,X1] : add(multiply(X0,X1),multiply(X0,inverse(X1))) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b2) ).
fof(f7,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
fof(f8,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
fof(f11,negated_conjecture,
add(b,inverse(b)) != add(a,inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equal_inverse) ).
fof(f17,definition,
! [X0,X1] : sF2(X0,X1) = multiply(X0,inverse(X1)),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f18,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = sF2(X0,X1),
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
! [X0,X1] : sF3(X0,X1) = add(multiply(X0,X1),sF2(X0,X1)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f20,plain,
! [X0,X1] : add(multiply(X0,X1),sF2(X0,X1)) = sF3(X0,X1),
inference(reorient_equations,[],[f19]) ).
fof(f21,plain,
! [X0,X1] : sF3(X0,X1) = X0,
inference(definition_folding,[],[f6,f20,f18]) ).
fof(f22,definition,
sF4 = inverse(b),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f23,plain,
inverse(b) = sF4,
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
sF5 = add(b,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f25,plain,
add(b,sF4) = sF5,
inference(reorient_equations,[],[f24]) ).
fof(f26,definition,
sF6 = inverse(a),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f27,plain,
inverse(a) = sF6,
inference(reorient_equations,[],[f26]) ).
fof(f28,definition,
sF7 = add(a,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f29,plain,
add(a,sF6) = sF7,
inference(reorient_equations,[],[f28]) ).
fof(f30,plain,
sF5 != sF7,
inference(definition_folding,[],[f11,f29,f27,f25,f23]) ).
fof(f31,plain,
! [X0,X1] : add(multiply(X0,X1),sF2(X0,X1)) = X0,
inference(forward_demodulation,[],[f21,f20]) ).
fof(f33,plain,
! [X0,X1] : add(multiply(X0,X1),multiply(X0,inverse(X1))) = X0,
inference(forward_demodulation,[],[f31,f18]) ).
fof(f36,plain,
! [X0,X1] : add(multiply(X0,X1),multiply(X1,inverse(X0))) = X1,
inference(superposition,[],[f33,f8]) ).
fof(f40,plain,
! [X0] : add(multiply(X0,a),multiply(X0,sF6)) = X0,
inference(superposition,[],[f33,f27]) ).
fof(f46,plain,
! [X0] : add(X0,X0) = X0,
inference(superposition,[],[f2,f33]) ).
fof(f66,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = X0,
inference(superposition,[],[f4,f46]) ).
fof(f67,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = X0,
inference(superposition,[],[f4,f46]) ).
fof(f81,plain,
sF4 = multiply(sF4,sF5),
inference(superposition,[],[f66,f25]) ).
fof(f82,plain,
sF6 = multiply(sF6,sF7),
inference(superposition,[],[f66,f29]) ).
fof(f84,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = X0,
inference(superposition,[],[f1,f66]) ).
fof(f137,plain,
b = multiply(b,sF5),
inference(superposition,[],[f67,f25]) ).
fof(f138,plain,
a = multiply(a,sF7),
inference(superposition,[],[f67,f29]) ).
fof(f177,plain,
sF5 = add(sF5,b),
inference(superposition,[],[f84,f137]) ).
fof(f178,plain,
sF7 = add(sF7,a),
inference(superposition,[],[f84,f138]) ).
fof(f179,plain,
sF5 = add(sF5,sF4),
inference(superposition,[],[f84,f81]) ).
fof(f180,plain,
sF7 = add(sF7,sF6),
inference(superposition,[],[f84,f82]) ).
fof(f194,plain,
sF7 = add(sF6,sF7),
inference(forward_demodulation,[],[f180,f7]) ).
fof(f195,plain,
sF5 = add(sF4,sF5),
inference(forward_demodulation,[],[f179,f7]) ).
fof(f196,plain,
sF7 = add(a,sF7),
inference(forward_demodulation,[],[f178,f7]) ).
fof(f197,plain,
sF5 = add(b,sF5),
inference(forward_demodulation,[],[f177,f7]) ).
fof(f204,plain,
! [X0] : sF6 = multiply(sF6,add(X0,sF7)),
inference(superposition,[],[f4,f194]) ).
fof(f252,plain,
! [X0] : sF4 = multiply(sF4,add(X0,sF5)),
inference(superposition,[],[f4,f195]) ).
fof(f263,plain,
! [X0] : a = multiply(a,add(X0,sF7)),
inference(superposition,[],[f4,f196]) ).
fof(f274,plain,
! [X0] : b = multiply(b,add(X0,sF5)),
inference(superposition,[],[f4,f197]) ).
fof(f315,plain,
! [X0] : sF6 = multiply(sF6,add(sF7,X0)),
inference(superposition,[],[f204,f7]) ).
fof(f413,plain,
! [X0] : a = multiply(a,add(sF7,X0)),
inference(superposition,[],[f263,f7]) ).
fof(f568,plain,
! [X0] : add(multiply(a,X0),multiply(X0,sF6)) = X0,
inference(superposition,[],[f40,f8]) ).
fof(f1030,plain,
! [X0] : add(sF7,X0) = add(a,multiply(add(sF7,X0),sF6)),
inference(superposition,[],[f568,f413]) ).
fof(f1066,plain,
! [X0] : add(sF7,X0) = add(a,multiply(sF6,add(sF7,X0))),
inference(forward_demodulation,[],[f1030,f8]) ).
fof(f1071,plain,
! [X0] : add(a,sF6) = add(sF7,X0),
inference(forward_demodulation,[],[f1066,f315]) ).
fof(f1075,plain,
! [X0] : sF7 = add(sF7,X0),
inference(forward_demodulation,[],[f1071,f29]) ).
fof(f1150,plain,
! [X0] : add(X0,sF5) = add(b,multiply(add(X0,sF5),inverse(b))),
inference(superposition,[],[f36,f274]) ).
fof(f1205,plain,
! [X0] : add(X0,sF5) = add(b,multiply(add(X0,sF5),sF4)),
inference(forward_demodulation,[],[f1150,f23]) ).
fof(f1213,plain,
! [X0] : add(X0,sF5) = add(b,multiply(sF4,add(X0,sF5))),
inference(forward_demodulation,[],[f1205,f8]) ).
fof(f1220,plain,
! [X0] : add(b,sF4) = add(X0,sF5),
inference(forward_demodulation,[],[f1213,f252]) ).
fof(f1225,plain,
! [X0] : sF5 = add(X0,sF5),
inference(forward_demodulation,[],[f1220,f25]) ).
fof(f1229,plain,
sF5 = sF7,
inference(superposition,[],[f1225,f1075]) ).
fof(f1256,plain,
sF5 != sF5,
inference(superposition,[],[f30,f1229]) ).
fof(f1268,plain,
$false,
inference(trivial_inequality_removal,[],[f1256]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : BOO029-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.27 % Computer : n002.cluster.edu
% 0.11/0.27 % Model : x86_64 x86_64
% 0.11/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.27 % Memory : 8046.5625MB
% 0.11/0.27 % OS : Linux 6.8.0-71-generic
% 0.11/0.27 % CPULimit : 300
% 0.11/0.27 % WCLimit : 300
% 0.11/0.27 % DateTime : Mon Sep 28 21:07:37 UTC 2026
% 0.11/0.27 % CPUTime :
% 0.11/0.28 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.33 Running first-order theorem proving
% 0.27/0.33 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
% 5.84/1.94 % (765030)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.84/1.94 % (765050)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3743082077:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 5.84/1.94 % (765051)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=196750150:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 5.84/1.94 % (765049)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3293735901:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 5.84/1.94 % (765052)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2848823943:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 5.84/1.94 % (765053)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1208776100:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 5.84/1.94 % (765047)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=1339666569:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 5.84/1.94 % (765048)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=4151702360:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 5.84/1.94 % (765050)Instruction limit reached!
% 5.84/1.94 % (765050)------------------------------
% 5.84/1.94 % (765050)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.84/1.94 % (765050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.84/1.94 % (765050)CaDiCaL version: 2.1.3
% 5.84/1.94 % (765050)Termination reason: Instruction limit
% 5.84/1.94 % (765050)Termination phase: Saturation
% 5.84/1.94 % (765050)Time elapsed: 0.072 s
% 5.84/1.94 % (765050)Peak memory usage: 89 MB
% 5.84/1.94 % (765050)Instructions burned: 137 (million)
% 5.84/1.94 % (765051)First to succeed.
% 5.84/1.94 % (765051)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-765030"
% 5.84/1.94 % (765061)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=6875971:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 5.84/1.94 % (765052)Instruction limit reached!
% 5.84/1.94 % (765052)------------------------------
% 5.84/1.94 % (765052)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.84/1.94 % (765052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.84/1.94 % (765052)CaDiCaL version: 2.1.3
% 5.84/1.94 % (765052)Termination reason: Instruction limit
% 5.84/1.94 % (765052)Termination phase: Saturation
% 5.84/1.94 % (765052)Time elapsed: 0.264 s
% 5.84/1.94 % (765052)Peak memory usage: 90 MB
% 5.84/1.94 % (765052)Instructions burned: 258 (million)
% 5.84/1.94 % (765051)Refutation found. Thanks to Tanya!
% 5.84/1.94 % SZS status Unsatisfiable for theBenchmark
% 5.84/1.94 % SZS output start Proof for theBenchmark
% See solution above
% 5.84/1.94 % (765051)------------------------------
% 5.84/1.94 % (765051)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.84/1.94 % (765051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.84/1.94 % (765051)CaDiCaL version: 2.1.3
% 5.84/1.94 % (765051)Termination reason: Refutation
% 5.84/1.94 % (765051)Time elapsed: 0.042 s
% 5.84/1.94 % (765051)Peak memory usage: 88 MB
% 5.84/1.94 % (765051)Instructions burned: 38 (million)
% 5.84/1.94 % (765051)------------------------------
% 5.84/1.94 % (765051)------------------------------
% 5.84/1.94 % (765030)Success in time 0.675 s
% 5.84/1.94 % Vampire exiting
%------------------------------------------------------------------------------