%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG002-1 : 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 : n012.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 09:20:02 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.24s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 47 ( 14 unt; 3 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 82 ( 36 ~; 43 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 26 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(X0,multiplicative_identity,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f2,axiom,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_abelian) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| product(X0,additive_inverse(X1),additive_inverse(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_to_inverse) ).
fof(f6,axiom,
! [X0] :
( product(X0,multiplicative_inverse(X0),multiplicative_identity)
| product(X0,X0,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_and_identity) ).
fof(f7,axiom,
! [X0] :
( ~ greater_than_0(additive_inverse(X0))
| ~ greater_than_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_greater_than_0) ).
fof(f8,axiom,
! [X0] :
( ~ greater_than_0(X0)
| ~ product(X0,X0,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',greater_than_0_square) ).
fof(f9,axiom,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| product(X1,X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_product) ).
fof(f10,axiom,
! [X0] :
( greater_than_0(additive_inverse(X0))
| product(X0,X0,additive_identity)
| greater_than_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_and_inverse) ).
fof(f11,axiom,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X0,additive_identity)
| product(X2,X2,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',square_to_0) ).
fof(f12,axiom,
! [X2,X0,X1] :
( ~ greater_than_0(X0)
| ~ product(X0,X1,X2)
| ~ greater_than_0(X1)
| greater_than_0(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_and_greater_than_0) ).
fof(f13,axiom,
greater_than_0(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_greater_than_0) ).
fof(f14,negated_conjecture,
~ greater_than_0(multiplicative_inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_inverse_greater_than_0) ).
fof(f15,plain,
~ product(a,a,additive_identity),
inference(resolution,[],[f8,f13]) ).
fof(f18,plain,
! [X0] :
( product(multiplicative_inverse(X0),X0,multiplicative_identity)
| product(X0,X0,additive_identity) ),
inference(resolution,[],[f6,f9]) ).
fof(f30,plain,
! [X0] : product(X0,additive_inverse(multiplicative_identity),additive_inverse(X0)),
inference(resolution,[],[f5,f1]) ).
fof(f34,plain,
! [X0] :
( product(X0,additive_inverse(multiplicative_inverse(X0)),additive_inverse(multiplicative_identity))
| product(X0,X0,additive_identity) ),
inference(resolution,[],[f5,f6]) ).
fof(f39,plain,
! [X0,X1] :
( ~ greater_than_0(X0)
| ~ product(a,X0,X1)
| greater_than_0(X1) ),
inference(resolution,[],[f12,f13]) ).
fof(f69,plain,
! [X0,X1] :
( ~ product(a,additive_inverse(X0),X1)
| greater_than_0(X1)
| product(X0,X0,additive_identity)
| greater_than_0(X0) ),
inference(resolution,[],[f39,f10]) ).
fof(f70,plain,
! [X0] :
( product(X0,X0,additive_identity)
| ~ product(multiplicative_inverse(X0),multiplicative_inverse(X0),additive_identity)
| product(multiplicative_identity,multiplicative_identity,additive_identity) ),
inference(resolution,[],[f18,f11]) ).
fof(f74,plain,
! [X0] :
( ~ product(multiplicative_inverse(X0),multiplicative_inverse(X0),additive_identity)
| product(X0,X0,additive_identity) ),
inference(forward_subsumption_resolution,[],[f70,f2]) ).
fof(f146,plain,
( greater_than_0(additive_inverse(a))
| product(multiplicative_identity,multiplicative_identity,additive_identity)
| greater_than_0(multiplicative_identity) ),
inference(resolution,[],[f69,f30]) ).
fof(f149,plain,
( greater_than_0(additive_inverse(multiplicative_identity))
| product(multiplicative_inverse(a),multiplicative_inverse(a),additive_identity)
| greater_than_0(multiplicative_inverse(a))
| product(a,a,additive_identity) ),
inference(resolution,[],[f69,f34]) ).
fof(f150,plain,
( greater_than_0(additive_inverse(multiplicative_identity))
| greater_than_0(multiplicative_inverse(a))
| product(a,a,additive_identity) ),
inference(forward_subsumption_resolution,[],[f149,f74]) ).
fof(f153,plain,
( greater_than_0(additive_inverse(a))
| greater_than_0(multiplicative_identity) ),
inference(forward_subsumption_resolution,[],[f146,f2]) ).
fof(f154,plain,
( greater_than_0(additive_inverse(multiplicative_identity))
| product(a,a,additive_identity) ),
inference(forward_subsumption_resolution,[],[f150,f14]) ).
fof(f156,definition,
( spl0_5
<=> greater_than_0(multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f158,plain,
( greater_than_0(multiplicative_identity)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f165,definition,
( spl0_7
<=> greater_than_0(additive_inverse(multiplicative_identity)) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f167,plain,
( greater_than_0(additive_inverse(multiplicative_identity))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f174,definition,
( spl0_9
<=> greater_than_0(additive_inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f176,plain,
( greater_than_0(additive_inverse(a))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f177,plain,
( spl0_5
| spl0_9 ),
inference(avatar_split_clause,[],[f153,f174,f156]) ).
fof(f178,plain,
greater_than_0(additive_inverse(multiplicative_identity)),
inference(forward_subsumption_resolution,[],[f154,f15]) ).
fof(f179,plain,
spl0_7,
inference(avatar_split_clause,[],[f178,f165]) ).
fof(f187,plain,
( ~ greater_than_0(multiplicative_identity)
| ~ spl0_7 ),
inference(resolution,[],[f167,f7]) ).
fof(f192,plain,
( $false
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f187,f158]) ).
fof(f193,plain,
( ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f192]) ).
fof(f204,plain,
( ~ greater_than_0(a)
| ~ spl0_9 ),
inference(resolution,[],[f176,f7]) ).
fof(f209,plain,
( $false
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f204,f13]) ).
fof(f210,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[],[f209]) ).
cnf(s6,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f177]) ).
cnf(s7,plain,
spl0_7,
inference(sat_conversion,[],[f179]) ).
cnf(s8,plain,
( ~ spl0_5
| ~ spl0_7 ),
inference(sat_conversion,[],[f193]) ).
cnf(s9,plain,
~ spl0_9,
inference(sat_conversion,[],[f210]) ).
cnf(s10,plain,
~ spl0_5,
inference(rat,[],[s8,s7]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s6,s9,s10]) ).
fof(f211,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.02/0.18 % Computer : n012.cluster.edu
% 0.02/0.18 % Model : x86_64 x86_64
% 0.02/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.18 % Memory : 8046.5625MB
% 0.02/0.18 % OS : Linux 6.8.0-71-generic
% 0.02/0.18 % CPULimit : 300
% 0.02/0.18 % WCLimit : 300
% 0.02/0.18 % DateTime : Mon Sep 28 19:16:19 UTC 2026
% 0.02/0.18 % CPUTime :
% 0.02/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.02/0.20 Running first-order model finding
% 0.02/0.20 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
% 0.09/0.24 % (3656990)Will run a generic schedule for satisfiability detection.
% 0.09/0.24 % (3656996)% WARNING: option uhcvi not known.
% 0.09/0.24 % (3656996)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4013126296:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.24 % (3656995)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=541701784_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.24 % (3656997)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=580389946:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.24 % (3656998)dis+10_1_sil=32000:sp=arity:random_seed=798108744:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.24 % (3657001)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=904843019:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.24 % (3656999)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3653197681:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.24 % (3657000)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3558855528:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.24 % TRYING [1]
% 0.09/0.24 % TRYING [2]
% 0.09/0.24 % TRYING [3]
% 0.09/0.24 % TRYING [4]
% 0.09/0.24 % (3657000) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3656990-3657000"...
% 0.09/0.24 % (3657001) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3656990-3657001"...
% 0.09/0.24 % (3657000)...printing done.
% 0.09/0.24 % (3657001)...printing done.
% 0.09/0.24 % (3657000)Refutation found. Thanks to Tanya!
% 0.09/0.24 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.24 % (3657000)------------------------------
% 0.09/0.24 % (3657000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.24 % (3657000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.24 % (3657000)CaDiCaL version: 2.1.3
% 0.09/0.24 % (3657000)Termination reason: Refutation
% 0.09/0.24 % (3657000)Time elapsed: 0.002 s
% 0.09/0.24 % (3657000)Peak memory usage: 12 MB
% 0.09/0.24 % (3657000)Instructions burned: 5 (million)
% 0.09/0.24 % (3656990)Success in time 0.031 s
% 0.09/0.24 % Vampire exiting
%------------------------------------------------------------------------------