%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : BOO004-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 09:36:05 AM UTC 2026
% Result : Unsatisfiable 0.22s 0.33s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 24 ( 15 unt; 1 def)
% Number of atoms : 40 ( 3 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 34 ( 18 ~; 15 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity2) ).
fof(f7,axiom,
! [X0] : product(multiplicative_identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_identity1) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2)
| ~ sum(X0,X5,X6)
| product(X2,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity5) ).
fof(f18,axiom,
! [X0] : sum(X0,inverse(X0),multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_inverse2) ).
fof(f19,axiom,
! [X0] : product(inverse(X0),X0,additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse1) ).
fof(f22,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplication_is_well_defined) ).
fof(f23,negated_conjecture,
~ sum(x,x,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_both_equalities) ).
fof(f47,plain,
! [X0,X1] :
( ~ product(multiplicative_identity,X0,X1)
| X0 = X1 ),
inference(resolution,[],[f22,f7]) ).
fof(f97,plain,
! [X2,X3,X0,X1,X4] :
( ~ sum(X0,inverse(X1),X3)
| ~ sum(X0,X1,X2)
| ~ sum(X0,additive_identity,X4)
| product(X3,X2,X4) ),
inference(resolution,[],[f13,f19]) ).
fof(f331,definition,
( spl0_1
<=> ! [X0] : sum(X0,X0,X0) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f332,plain,
( ! [X0] : sum(X0,X0,X0)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f438,plain,
! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X2)
| ~ sum(X0,X0,X1)
| product(multiplicative_identity,X1,X2) ),
inference(resolution,[],[f97,f18]) ).
fof(f1330,plain,
! [X0,X1] :
( ~ sum(X0,X0,X1)
| product(multiplicative_identity,X1,X0) ),
inference(resolution,[],[f438,f6]) ).
fof(f1427,plain,
! [X0] : product(multiplicative_identity,add(X0,X0),X0),
inference(resolution,[],[f1330,f1]) ).
fof(f1436,plain,
! [X0] : add(X0,X0) = X0,
inference(resolution,[],[f1427,f47]) ).
fof(f1485,plain,
! [X0] : sum(X0,X0,X0),
inference(superposition,[],[f1,f1436]) ).
fof(f1489,plain,
spl0_1,
inference(avatar_split_clause,[],[f1485,f331]) ).
fof(f1539,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f332,f23]) ).
fof(f1540,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f1539]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f1489]) ).
cnf(s4,plain,
~ spl0_1,
inference(sat_conversion,[],[f1540]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s2,s4]) ).
fof(f1544,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : BOO004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 % Computer : n018.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Mon Sep 28 21:05:25 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.25 Running first-order model finding
% 0.10/0.26 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.33 % (3783494)Will run a generic schedule for satisfiability detection.
% 0.22/0.33 % (3783502)dis+10_1_sil=32000:sp=arity:random_seed=2654341981:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.33 % (3783500)% WARNING: option uhcvi not known.
% 0.22/0.33 % (3783501)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1576724824:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.33 % (3783499)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3485258859_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.33 % (3783503)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1284529101:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.33 % (3783500)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=813019989:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.33 % (3783504)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2121668891:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.33 % (3783505)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=80697514:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.33 % TRYING [1]
% 0.22/0.33 % TRYING [2]
% 0.22/0.33 % TRYING [3]
% 0.22/0.33 % TRYING [4]
% 0.22/0.33 % (3783502) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3783494-3783502"...
% 0.22/0.33 % (3783502)...printing done.
% 0.22/0.33 % (3783502)Refutation found. Thanks to Tanya!
% 0.22/0.33 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.33 % (3783502)------------------------------
% 0.22/0.33 % (3783502)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (3783502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (3783502)CaDiCaL version: 2.1.3
% 0.22/0.33 % (3783502)Termination reason: Refutation
% 0.22/0.33 % (3783502)Time elapsed: 0.021 s
% 0.22/0.33 % (3783502)Peak memory usage: 12 MB
% 0.22/0.33 % (3783502)Instructions burned: 62 (million)
% 0.22/0.33 % (3783494)Success in time 0.062 s
% 0.22/0.33 % Vampire exiting
%------------------------------------------------------------------------------