%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : BOO012-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 09:36:08 AM UTC 2026
% Result : Unsatisfiable 0.76s 0.50s
% Output : Refutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 39 ( 22 unt; 1 def)
% Number of atoms : 65 ( 16 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 56 ( 30 ~; 25 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 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 : 62 ( 0 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_multiplication) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| product(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',commutativity_of_multiplication) ).
fof(f5,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_identity2) ).
fof(f8,axiom,
! [X0] : product(X0,multiplicative_identity,X0),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_identity2) ).
fof(f9,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X0,X5,X6)
| ~ product(X0,X3,X4)
| ~ sum(X1,X3,X5)
| ~ product(X0,X1,X2)
| sum(X2,X4,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity1) ).
fof(f18,axiom,
! [X0] : sum(X0,inverse(X0),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_inverse2) ).
fof(f19,axiom,
! [X0] : product(inverse(X0),X0,additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse1) ).
fof(f20,axiom,
! [X0] : product(X0,inverse(X0),additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse2) ).
fof(f21,axiom,
! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',addition_is_well_defined) ).
fof(f22,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplication_is_well_defined) ).
fof(f23,negated_conjecture,
inverse(inverse(x)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_is_an_involution) ).
fof(f24,plain,
x != inverse(inverse(x)),
inference(reorient_equations,[],[f23]) ).
fof(f57,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(resolution,[],[f4,f2]) ).
fof(f121,plain,
! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| X0 = X1 ),
inference(resolution,[],[f21,f5]) ).
fof(f122,plain,
! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| X0 = X1 ),
inference(resolution,[],[f21,f6]) ).
fof(f359,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| multiply(X0,X1) = X2 ),
inference(resolution,[],[f22,f2]) ).
fof(f382,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(X0,X3,X4)
| ~ sum(X3,X1,multiplicative_identity)
| ~ product(X0,X1,X2)
| sum(X4,X2,X0) ),
inference(resolution,[],[f9,f8]) ).
fof(f543,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(resolution,[],[f359,f57]) ).
fof(f628,plain,
! [X2,X3,X0,X1] :
( ~ product(X2,X1,X3)
| ~ sum(X0,X1,multiplicative_identity)
| sum(multiply(X2,X0),X3,X2) ),
inference(resolution,[],[f382,f2]) ).
fof(f631,plain,
! [X2,X0,X1] :
( ~ sum(inverse(X0),X1,multiplicative_identity)
| ~ product(X0,X1,X2)
| sum(additive_identity,X2,X0) ),
inference(resolution,[],[f382,f20]) ).
fof(f4275,plain,
! [X0,X1] :
( ~ product(X0,inverse(inverse(X0)),X1)
| sum(additive_identity,X1,X0) ),
inference(resolution,[],[f631,f18]) ).
fof(f4409,plain,
! [X0] : sum(additive_identity,multiply(X0,inverse(inverse(X0))),X0),
inference(resolution,[],[f4275,f2]) ).
fof(f4430,plain,
! [X0] : multiply(X0,inverse(inverse(X0))) = X0,
inference(resolution,[],[f4409,f121]) ).
fof(f4719,definition,
( spl0_68
<=> ! [X0] : inverse(inverse(X0)) = X0 ),
introduced(definition,[new_symbols(definition,[spl0_68])],[avatar_definition]) ).
fof(f4720,plain,
( ! [X0] : inverse(inverse(X0)) = X0
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f4719]) ).
fof(f4742,plain,
( x != x
| ~ spl0_68 ),
inference(superposition,[],[f24,f4720]) ).
fof(f4780,plain,
( $false
| ~ spl0_68 ),
inference(trivial_inequality_removal,[],[f4742]) ).
fof(f4781,plain,
~ spl0_68,
inference(avatar_contradiction_clause,[],[f4780]) ).
fof(f6801,plain,
! [X0,X1] :
( sum(multiply(inverse(X1),X0),additive_identity,inverse(X1))
| ~ sum(X0,X1,multiplicative_identity) ),
inference(resolution,[],[f628,f19]) ).
fof(f9395,plain,
! [X0,X1] :
( ~ sum(X0,X1,multiplicative_identity)
| inverse(X1) = multiply(inverse(X1),X0) ),
inference(resolution,[],[f6801,f122]) ).
fof(f9517,plain,
! [X0] : inverse(inverse(X0)) = multiply(inverse(inverse(X0)),X0),
inference(resolution,[],[f9395,f18]) ).
fof(f9601,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,inverse(inverse(X0))),
inference(forward_demodulation,[],[f9517,f543]) ).
fof(f9631,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f9601,f4430]) ).
fof(f9658,plain,
spl0_68,
inference(avatar_split_clause,[],[f9631,f4719]) ).
cnf(s2031,plain,
~ spl0_68,
inference(sat_conversion,[],[f4781]) ).
cnf(s3535,plain,
spl0_68,
inference(sat_conversion,[],[f9658]) ).
cnf(s3536,plain,
$false,
inference(rat,[],[s2031,s3535]) ).
fof(f9659,plain,
$false,
inference(avatar_sat_refutation,[],[s3536]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO012-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n026.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 21:06:42 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.25 Running first-order model finding
% 0.08/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.76/0.50 % (74879)Will run a generic schedule for satisfiability detection.
% 0.76/0.50 % (74895)% WARNING: option uhcvi not known.
% 0.76/0.50 % (74895)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3547036159:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.76/0.50 % (74894)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4185053988_2999 on theBenchmark for (2999ds/0Mi)
% 0.76/0.50 % (74896)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=959467764:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.76/0.50 % TRYING [1]
% 0.76/0.50 % TRYING [2]
% 0.76/0.50 % TRYING [3]
% 0.76/0.50 % (74897)dis+10_1_sil=32000:sp=arity:random_seed=1890822280:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.76/0.50 % (74898)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1103957762:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.76/0.50 % TRYING [4]
% 0.76/0.50 % (74900)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1990169509:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.76/0.50 % (74899)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2764953190:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.76/0.50 % TRYING [5]
% 0.76/0.50 % (74898)Instruction limit reached!
% 0.76/0.50 % (74898)------------------------------
% 0.76/0.50 % (74898)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.50 % (74898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.50 % (74898)CaDiCaL version: 2.1.3
% 0.76/0.50 % (74898)Termination reason: Instruction limit
% 0.76/0.50 % (74898)Termination phase: Saturation
% 0.76/0.50 % (74898)Time elapsed: 0.063 s
% 0.76/0.50 % (74898)Peak memory usage: 12 MB
% 0.76/0.50 % (74898)Instructions burned: 118 (million)
% 0.76/0.50 % (74908)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2664663381:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 0.76/0.50 % TRYING [1]
% 0.76/0.50 % TRYING [2]
% 0.76/0.50 % TRYING [3]
% 0.76/0.50 % (74897)Instruction limit reached!
% 0.76/0.50 % (74897)------------------------------
% 0.76/0.50 % (74897)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.50 % (74897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.50 % (74897)CaDiCaL version: 2.1.3
% 0.76/0.50 % (74897)Termination reason: Instruction limit
% 0.76/0.50 % (74897)Termination phase: Saturation
% 0.76/0.50 % (74897)Time elapsed: 0.088 s
% 0.76/0.50 % (74897)Peak memory usage: 11 MB
% 0.76/0.50 % (74897)Instructions burned: 105 (million)
% 0.76/0.50 % TRYING [4]
% 0.76/0.50 % (74900)Instruction limit reached!
% 0.76/0.50 % (74900)------------------------------
% 0.76/0.50 % (74900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.50 % (74900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.50 % (74900)CaDiCaL version: 2.1.3
% 0.76/0.50 % (74900)Termination reason: Instruction limit
% 0.76/0.50 % (74900)Termination phase: Saturation
% 0.76/0.50 % (74900)Time elapsed: 0.094 s
% 0.76/0.50 % (74900)Peak memory usage: 12 MB
% 0.76/0.50 % (74900)Instructions burned: 160 (million)
% 0.76/0.50 % (74910)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=416208010:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 0.76/0.50 % (74911)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=230900480:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.76/0.50 % (74899)Instruction limit reached!
% 0.76/0.50 % (74899)------------------------------
% 0.76/0.50 % (74899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.50 % (74899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.50 % (74899)CaDiCaL version: 2.1.3
% 0.76/0.50 % (74899)Termination reason: Instruction limit
% 0.76/0.50 % (74899)Termination phase: Saturation
% 0.76/0.50 % (74899)Time elapsed: 0.128 s
% 0.76/0.50 % (74899)Peak memory usage: 12 MB
% 0.76/0.50 % (74899)Instructions burned: 134 (million)
% 0.76/0.50 % TRYING [5]
% 0.76/0.50 % (74896) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-74879-74896"...
% 0.76/0.50 % (74896)...printing done.
% 0.76/0.50 % (74896)Refutation found. Thanks to Tanya!
% 0.76/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.76/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.76/0.50 % (74896)------------------------------
% 0.76/0.50 % (74896)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.50 % (74896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.50 % (74896)CaDiCaL version: 2.1.3
% 0.76/0.50 % (74896)Termination reason: Refutation
% 0.76/0.50 % (74896)Time elapsed: 0.183 s
% 0.76/0.50 % (74896)Peak memory usage: 14 MB
% 0.76/0.50 % (74896)Instructions burned: 293 (million)
% 0.76/0.50 % (74879)Success in time 0.234 s
% 0.76/0.50 % Vampire exiting
%------------------------------------------------------------------------------