%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO012-2 : 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 : 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 09:35:52 AM UTC 2026
% Result : Unsatisfiable 0.64s 1.01s
% Output : Refutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of formulae : 54 ( 54 unt; 7 def)
% Number of atoms : 54 ( 53 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 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 41 ( 41 !; 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(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,negated_conjecture,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f10,negated_conjecture,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse1) ).
fof(f13,negated_conjecture,
! [X0] : multiply(X0,multiplicative_identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_id1) ).
fof(f14,negated_conjecture,
! [X0] : multiply(multiplicative_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_id2) ).
fof(f16,negated_conjecture,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_id2) ).
fof(f17,negated_conjecture,
inverse(inverse(x)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_is_an_involution) ).
fof(f18,plain,
x != inverse(inverse(x)),
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
! [X0] : sF0(X0) = add(X0,inverse(X0)),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f20,plain,
! [X0] : add(X0,inverse(X0)) = sF0(X0),
inference(reorient_equations,[],[f19]) ).
fof(f21,plain,
! [X0] : multiplicative_identity = sF0(X0),
inference(definition_folding,[],[f7,f20]) ).
fof(f25,definition,
! [X0] : sF2(X0) = multiply(X0,inverse(X0)),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f26,plain,
! [X0] : multiply(X0,inverse(X0)) = sF2(X0),
inference(reorient_equations,[],[f25]) ).
fof(f27,plain,
! [X0] : additive_identity = sF2(X0),
inference(definition_folding,[],[f10,f26]) ).
fof(f31,definition,
! [X0] : sF4(X0) = multiply(X0,multiplicative_identity),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f32,plain,
! [X0] : multiply(X0,multiplicative_identity) = sF4(X0),
inference(reorient_equations,[],[f31]) ).
fof(f33,plain,
! [X0] : sF4(X0) = X0,
inference(definition_folding,[],[f13,f32]) ).
fof(f34,definition,
! [X0] : sF5(X0) = multiply(multiplicative_identity,X0),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f35,plain,
! [X0] : multiply(multiplicative_identity,X0) = sF5(X0),
inference(reorient_equations,[],[f34]) ).
fof(f36,plain,
! [X0] : sF5(X0) = X0,
inference(definition_folding,[],[f14,f35]) ).
fof(f40,definition,
! [X0] : sF7(X0) = add(additive_identity,X0),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f41,plain,
! [X0] : add(additive_identity,X0) = sF7(X0),
inference(reorient_equations,[],[f40]) ).
fof(f42,plain,
! [X0] : sF7(X0) = X0,
inference(definition_folding,[],[f16,f41]) ).
fof(f43,definition,
sF8 = inverse(x),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f44,plain,
inverse(x) = sF8,
inference(reorient_equations,[],[f43]) ).
fof(f45,definition,
sF9 = inverse(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f46,plain,
inverse(sF8) = sF9,
inference(reorient_equations,[],[f45]) ).
fof(f47,plain,
x != sF9,
inference(definition_folding,[],[f18,f46,f44]) ).
fof(f48,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(forward_demodulation,[],[f42,f41]) ).
fof(f50,plain,
! [X0] : multiply(multiplicative_identity,X0) = X0,
inference(forward_demodulation,[],[f36,f35]) ).
fof(f51,plain,
! [X0] : multiply(X0,multiplicative_identity) = X0,
inference(forward_demodulation,[],[f33,f32]) ).
fof(f53,plain,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
inference(forward_demodulation,[],[f27,f26]) ).
fof(f55,plain,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
inference(forward_demodulation,[],[f21,f20]) ).
fof(f110,plain,
additive_identity = multiply(sF8,sF9),
inference(superposition,[],[f53,f46]) ).
fof(f111,plain,
additive_identity = multiply(x,sF8),
inference(superposition,[],[f53,f44]) ).
fof(f117,plain,
multiplicative_identity = add(sF8,sF9),
inference(superposition,[],[f55,f46]) ).
fof(f125,plain,
! [X0,X1] : multiply(multiplicative_identity,X1) = add(multiply(X0,X1),multiply(inverse(X0),X1)),
inference(superposition,[],[f5,f55]) ).
fof(f129,plain,
! [X0,X1] : add(multiply(X0,X1),multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f125,f50]) ).
fof(f151,plain,
! [X0] : multiply(X0,multiplicative_identity) = add(multiply(X0,sF8),multiply(X0,sF9)),
inference(superposition,[],[f6,f117]) ).
fof(f152,plain,
! [X0] : add(multiply(X0,sF8),multiply(X0,sF9)) = X0,
inference(forward_demodulation,[],[f151,f51]) ).
fof(f202,plain,
x = add(additive_identity,multiply(x,sF9)),
inference(superposition,[],[f152,f111]) ).
fof(f221,plain,
x = multiply(x,sF9),
inference(forward_demodulation,[],[f202,f48]) ).
fof(f575,plain,
sF9 = add(x,multiply(inverse(x),sF9)),
inference(superposition,[],[f129,f221]) ).
fof(f610,plain,
sF9 = add(x,multiply(sF9,inverse(x))),
inference(forward_demodulation,[],[f575,f2]) ).
fof(f627,plain,
sF9 = add(x,multiply(sF9,sF8)),
inference(forward_demodulation,[],[f610,f44]) ).
fof(f637,plain,
sF9 = add(x,multiply(sF8,sF9)),
inference(forward_demodulation,[],[f627,f2]) ).
fof(f640,plain,
sF9 = add(x,additive_identity),
inference(forward_demodulation,[],[f637,f110]) ).
fof(f641,plain,
sF9 = add(additive_identity,x),
inference(forward_demodulation,[],[f640,f1]) ).
fof(f642,plain,
x = sF9,
inference(forward_demodulation,[],[f641,f48]) ).
fof(f643,plain,
x != x,
inference(superposition,[],[f47,f642]) ).
fof(f652,plain,
$false,
inference(trivial_inequality_removal,[],[f643]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO012-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n006.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Mon Sep 28 21:03:40 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 Running first-order theorem proving
% 0.11/0.21 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
% 0.64/1.01 % (199948)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.64/1.01 % (200094)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=268723566:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.64/1.01 % (200094)First to succeed.
% 0.64/1.01 % (200094)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-199948"
% 0.64/1.01 % (200093)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4084033092:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.64/1.01 % (200096)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4177427777:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.64/1.01 % (200092)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2204863454:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.64/1.01 % (200095)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1319751157:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.64/1.01 % (200091)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=1285910190:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.64/1.01 % (200090)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=3523892894:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.64/1.01 % (200095)Also succeeded, but the first one will report.
% 0.64/1.01 % (200096)Also succeeded, but the first one will report.
% 0.64/1.01 % (200093)Also succeeded, but the first one will report.
% 0.64/1.01 % (200094)Refutation found. Thanks to Tanya!
% 0.64/1.01 % SZS status Unsatisfiable for theBenchmark
% 0.64/1.01 % SZS output start Proof for theBenchmark
% See solution above
% 0.64/1.01 % (200094)------------------------------
% 0.64/1.01 % (200094)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.64/1.01 % (200094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/1.01 % (200094)CaDiCaL version: 2.1.3
% 0.64/1.01 % (200094)Termination reason: Refutation
% 0.64/1.01 % (200094)Time elapsed: 0.007 s
% 0.64/1.01 % (200094)Peak memory usage: 88 MB
% 0.64/1.01 % (200094)Instructions burned: 19 (million)
% 0.64/1.01 % (200094)------------------------------
% 0.64/1.01 % (200094)------------------------------
% 0.64/1.01 % (199948)Success in time 0.268 s
% 0.64/1.01 % Vampire exiting
%------------------------------------------------------------------------------