%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : HEN008-1 : 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 : n016.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 10:19:17 AM UTC 2026
% Result : Unsatisfiable 0.21s 0.55s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 38 ( 13 unt; 2 def)
% Number of atoms : 80 ( 7 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 89 ( 47 ~; 40 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).
fof(f2,axiom,
! [X0,X1] :
( ~ quotient(X0,X1,zero)
| less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).
fof(f4,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ quotient(X5,X4,X6)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X3,X5)
| ~ quotient(X0,X1,X2)
| ~ quotient(X2,X3,X7)
| less_equal(X6,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
fof(f5,axiom,
! [X0] : less_equal(zero,X0),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
fof(f6,axiom,
! [X0,X1] :
( ~ less_equal(X1,X0)
| ~ less_equal(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
fof(f8,axiom,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',closure) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',well_defined) ).
fof(f10,axiom,
less_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aLEb) ).
fof(f11,axiom,
quotient(a,c,aQc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aQc) ).
fof(f12,axiom,
quotient(b,c,bQc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bQc) ).
fof(f13,negated_conjecture,
~ less_equal(aQc,bQc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_aQcLEbQc) ).
fof(f20,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f53,plain,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| divide(X0,X1) = X2 ),
inference(resolution,[],[f9,f8]) ).
fof(f57,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ quotient(X5,X1,X6)
| ~ quotient(X3,X1,X4)
| ~ quotient(X3,X0,X5)
| ~ quotient(X0,X1,X2)
| less_equal(divide(X4,X2),X6) ),
inference(resolution,[],[f4,f8]) ).
fof(f90,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| zero = divide(X0,X1) ),
inference(resolution,[],[f53,f1]) ).
fof(f156,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ quotient(X3,X1,X5)
| ~ quotient(X0,X3,X4)
| ~ quotient(X0,X1,X2)
| less_equal(divide(X2,X5),zero)
| ~ less_equal(X4,X1) ),
inference(resolution,[],[f57,f1]) ).
fof(f204,plain,
zero = divide(a,b),
inference(resolution,[],[f90,f10]) ).
fof(f312,plain,
! [X2,X0,X1] :
( ~ quotient(X0,c,X2)
| ~ quotient(X0,b,X1)
| less_equal(divide(X2,bQc),zero)
| ~ less_equal(X1,c) ),
inference(resolution,[],[f156,f12]) ).
fof(f882,plain,
! [X0] :
( ~ quotient(a,b,X0)
| less_equal(divide(aQc,bQc),zero)
| ~ less_equal(X0,c) ),
inference(resolution,[],[f312,f11]) ).
fof(f890,definition,
( spl0_44
<=> less_equal(divide(aQc,bQc),zero) ),
introduced(definition,[new_symbols(definition,[spl0_44])],[avatar_definition]) ).
fof(f892,plain,
( less_equal(divide(aQc,bQc),zero)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f890]) ).
fof(f894,definition,
( spl0_45
<=> ! [X0] :
( ~ quotient(a,b,X0)
| ~ less_equal(X0,c) ) ),
introduced(definition,[new_symbols(definition,[spl0_45])],[avatar_definition]) ).
fof(f895,plain,
( ! [X0] :
( ~ quotient(a,b,X0)
| ~ less_equal(X0,c) )
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f894]) ).
fof(f896,plain,
( spl0_44
| spl0_45 ),
inference(avatar_split_clause,[],[f882,f894,f890]) ).
fof(f910,plain,
( zero = divide(aQc,bQc)
| ~ spl0_44 ),
inference(resolution,[],[f892,f20]) ).
fof(f1068,plain,
( quotient(aQc,bQc,zero)
| ~ spl0_44 ),
inference(superposition,[],[f8,f910]) ).
fof(f1070,plain,
( less_equal(aQc,bQc)
| ~ spl0_44 ),
inference(resolution,[],[f1068,f2]) ).
fof(f1089,plain,
( $false
| ~ spl0_44 ),
inference(forward_subsumption_resolution,[],[f1070,f13]) ).
fof(f1090,plain,
~ spl0_44,
inference(avatar_contradiction_clause,[],[f1089]) ).
fof(f1101,plain,
( ~ less_equal(divide(a,b),c)
| ~ spl0_45 ),
inference(resolution,[],[f895,f8]) ).
fof(f1104,plain,
( ~ less_equal(zero,c)
| ~ spl0_45 ),
inference(forward_demodulation,[],[f1101,f204]) ).
fof(f1109,plain,
( $false
| ~ spl0_45 ),
inference(forward_subsumption_resolution,[],[f1104,f5]) ).
fof(f1110,plain,
~ spl0_45,
inference(avatar_contradiction_clause,[],[f1109]) ).
cnf(s41,plain,
( spl0_44
| spl0_45 ),
inference(sat_conversion,[],[f896]) ).
cnf(s47,plain,
~ spl0_44,
inference(sat_conversion,[],[f1090]) ).
cnf(s50,plain,
~ spl0_45,
inference(sat_conversion,[],[f1110]) ).
cnf(s51,plain,
$false,
inference(rat,[],[s41,s50,s47]) ).
fof(f1111,plain,
$false,
inference(avatar_sat_refutation,[],[s51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 10:55:47 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.16/0.44 Running first-order model finding
% 0.16/0.44 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
% 0.21/0.55 % (2446860)Will run a generic schedule for satisfiability detection.
% 0.21/0.55 % (2446865)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2113863557_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.55 % TRYING [1]
% 0.21/0.55 % TRYING [2]
% 0.21/0.55 % TRYING [3]
% 0.21/0.55 % TRYING [4]
% 0.21/0.55 % (2446866)% WARNING: option uhcvi not known.
% 0.21/0.55 % TRYING [5]
% 0.21/0.55 % (2446868)dis+10_1_sil=32000:sp=arity:random_seed=2868536387:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.55 % (2446867)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=594006179:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.55 % (2446869)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3589598329:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.55 % (2446866)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2575806853:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.55 % TRYING [6]
% 0.21/0.55 % (2446871)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4265398869:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.55 % (2446870)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=162793068:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.55 % (2446868) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2446860-2446868"...
% 0.21/0.55 % (2446868)...printing done.
% 0.21/0.55 % (2446868)Refutation found. Thanks to Tanya!
% 0.21/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.55 % (2446868)------------------------------
% 0.21/0.55 % (2446868)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.55 % (2446868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.55 % (2446868)CaDiCaL version: 2.1.3
% 0.21/0.55 % (2446868)Termination reason: Refutation
% 0.21/0.55 % (2446868)Time elapsed: 0.041 s
% 0.21/0.55 % (2446868)Peak memory usage: 12 MB
% 0.21/0.55 % (2446868)Instructions burned: 34 (million)
% 0.21/0.55 % (2446860)Success in time 0.096 s
% 0.21/0.55 % Vampire exiting
%------------------------------------------------------------------------------