%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : HEN007-1 : 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 : n009.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 10:19:16 AM UTC 2026
% Result : Unsatisfiable 0.94s 0.70s
% Output : Refutation 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of formulae : 62 ( 31 unt; 2 def)
% Number of atoms : 109 ( 17 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 94 ( 47 ~; 45 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 4 ( 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 : 69 ( 0 sgn 69 !; 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(f3,axiom,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| less_equal(X2,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
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(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xLEy) ).
fof(f11,axiom,
quotient(z,y,zQy),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zQy) ).
fof(f12,axiom,
quotient(z,x,zQx),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zQx) ).
fof(f13,negated_conjecture,
~ less_equal(zQy,zQx),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_zQyLEzQx) ).
fof(f44,plain,
less_equal(zQx,z),
inference(resolution,[],[f3,f12]) ).
fof(f45,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[],[f3,f8]) ).
fof(f58,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f219,plain,
! [X0] : zero = divide(zero,X0),
inference(resolution,[],[f58,f45]) ).
fof(f300,plain,
! [X0] : quotient(zero,X0,zero),
inference(superposition,[],[f8,f219]) ).
fof(f326,plain,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| divide(X0,X1) = X2 ),
inference(resolution,[],[f9,f8]) ).
fof(f457,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| zero = divide(X0,X1) ),
inference(resolution,[],[f326,f1]) ).
fof(f547,plain,
zero = divide(x,y),
inference(resolution,[],[f457,f10]) ).
fof(f549,plain,
zero = divide(zQx,z),
inference(resolution,[],[f457,f44]) ).
fof(f563,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(f568,plain,
quotient(x,y,zero),
inference(superposition,[],[f8,f547]) ).
fof(f584,plain,
quotient(zQx,z,zero),
inference(superposition,[],[f8,f549]) ).
fof(f761,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ quotient(X3,X1,X5)
| ~ quotient(X0,X3,X4)
| ~ quotient(X0,X1,X2)
| less_equal(divide(X2,X5),divide(X4,X1)) ),
inference(resolution,[],[f563,f8]) ).
fof(f764,plain,
! [X2,X3,X0,X1,X4] :
( ~ quotient(X3,X1,X4)
| ~ quotient(X0,X3,zero)
| ~ quotient(X0,X1,X2)
| less_equal(divide(X2,X4),zero) ),
inference(resolution,[],[f563,f300]) ).
fof(f844,plain,
! [X0,X1] :
( ~ quotient(X0,z,zero)
| ~ quotient(X0,y,X1)
| less_equal(divide(X1,zQy),zero) ),
inference(resolution,[],[f764,f11]) ).
fof(f1109,plain,
! [X0] :
( less_equal(divide(X0,zQy),zero)
| ~ quotient(zQx,y,X0) ),
inference(resolution,[],[f844,f584]) ).
fof(f1802,plain,
! [X2,X3,X0,X1] :
( ~ quotient(X0,zero,X1)
| ~ quotient(X0,X2,X3)
| less_equal(divide(X3,zero),divide(X1,X2)) ),
inference(resolution,[],[f761,f300]) ).
fof(f1808,plain,
! [X2,X0,X1] :
( ~ quotient(X0,y,X2)
| ~ quotient(X0,x,X1)
| less_equal(divide(X2,zero),divide(X1,y)) ),
inference(resolution,[],[f761,f568]) ).
fof(f4048,plain,
! [X0] :
( less_equal(divide(zQy,zero),divide(X0,y))
| ~ quotient(z,x,X0) ),
inference(resolution,[],[f1808,f11]) ).
fof(f4318,plain,
! [X0] :
( ~ quotient(zQx,y,X0)
| zero = divide(X0,zQy) ),
inference(resolution,[],[f1109,f58]) ).
fof(f5803,plain,
zero = divide(divide(zQx,y),zQy),
inference(resolution,[],[f4318,f8]) ).
fof(f6673,plain,
quotient(divide(zQx,y),zQy,zero),
inference(superposition,[],[f8,f5803]) ).
fof(f6680,plain,
less_equal(divide(zQx,y),zQy),
inference(resolution,[],[f6673,f2]) ).
fof(f6692,plain,
( ~ less_equal(zQy,divide(zQx,y))
| zQy = divide(zQx,y) ),
inference(resolution,[],[f6680,f6]) ).
fof(f7168,plain,
! [X0] :
( ~ quotient(z,x,X0)
| zero = divide(divide(zQy,zero),divide(X0,y)) ),
inference(resolution,[],[f4048,f457]) ).
fof(f8169,plain,
! [X2,X0,X1] :
( less_equal(divide(X2,zero),divide(divide(X0,zero),X1))
| ~ quotient(X0,X1,X2) ),
inference(resolution,[],[f1802,f8]) ).
fof(f9080,definition,
( spl0_154
<=> zQy = divide(zQx,y) ),
introduced(definition,[new_symbols(definition,[spl0_154])],[avatar_definition]) ).
fof(f9082,plain,
( zQy = divide(zQx,y)
| ~ spl0_154 ),
inference(avatar_component_clause,[],[f9080]) ).
fof(f9084,definition,
( spl0_155
<=> less_equal(zQy,divide(zQx,y)) ),
introduced(definition,[new_symbols(definition,[spl0_155])],[avatar_definition]) ).
fof(f9086,plain,
( ~ less_equal(zQy,divide(zQx,y))
| spl0_155 ),
inference(avatar_component_clause,[],[f9084]) ).
fof(f9087,plain,
( spl0_154
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f6692,f9084,f9080]) ).
fof(f9106,plain,
( less_equal(zQy,zQx)
| ~ spl0_154 ),
inference(superposition,[],[f45,f9082]) ).
fof(f9113,plain,
( $false
| ~ spl0_154 ),
inference(forward_subsumption_resolution,[],[f9106,f13]) ).
fof(f9114,plain,
~ spl0_154,
inference(avatar_contradiction_clause,[],[f9113]) ).
fof(f9137,plain,
zero = divide(divide(zQy,zero),divide(zQx,y)),
inference(resolution,[],[f7168,f12]) ).
fof(f9187,plain,
! [X0] :
( ~ quotient(zQy,divide(zQx,y),X0)
| less_equal(divide(X0,zero),zero) ),
inference(superposition,[],[f8169,f9137]) ).
fof(f9211,plain,
less_equal(divide(divide(zQy,divide(zQx,y)),zero),zero),
inference(resolution,[],[f9187,f8]) ).
fof(f9219,plain,
zero = divide(divide(zQy,divide(zQx,y)),zero),
inference(resolution,[],[f9211,f58]) ).
fof(f9230,plain,
quotient(divide(zQy,divide(zQx,y)),zero,zero),
inference(superposition,[],[f8,f9219]) ).
fof(f9240,plain,
less_equal(divide(zQy,divide(zQx,y)),zero),
inference(resolution,[],[f9230,f2]) ).
fof(f9255,plain,
zero = divide(zQy,divide(zQx,y)),
inference(resolution,[],[f9240,f58]) ).
fof(f9263,plain,
quotient(zQy,divide(zQx,y),zero),
inference(superposition,[],[f8,f9255]) ).
fof(f9271,plain,
less_equal(zQy,divide(zQx,y)),
inference(resolution,[],[f9263,f2]) ).
fof(f9282,plain,
( $false
| spl0_155 ),
inference(forward_subsumption_resolution,[],[f9271,f9086]) ).
fof(f9283,plain,
spl0_155,
inference(avatar_contradiction_clause,[],[f9282]) ).
cnf(s3658,plain,
( spl0_154
| ~ spl0_155 ),
inference(sat_conversion,[],[f9087]) ).
cnf(s3664,plain,
~ spl0_154,
inference(sat_conversion,[],[f9114]) ).
cnf(s3752,plain,
spl0_155,
inference(sat_conversion,[],[f9283]) ).
cnf(s3753,plain,
$false,
inference(rat,[],[s3658,s3752,s3664]) ).
fof(f9284,plain,
$false,
inference(avatar_sat_refutation,[],[s3753]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : HEN007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.41 % Computer : n009.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 27 10:50:51 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.45 Running first-order model finding
% 0.15/0.45 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
% 0.94/0.70 % (1856167)Will run a generic schedule for satisfiability detection.
% 0.94/0.70 % (1856172)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4270219038_2999 on theBenchmark for (2999ds/0Mi)
% 0.94/0.70 % TRYING [1]
% 0.94/0.70 % TRYING [2]
% 0.94/0.70 % TRYING [3]
% 0.94/0.70 % TRYING [4]
% 0.94/0.70 % (1856173)% WARNING: option uhcvi not known.
% 0.94/0.70 % TRYING [5]
% 0.94/0.70 % (1856173)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2017931432:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.94/0.70 % (1856174)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=443045709:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.94/0.70 % (1856175)dis+10_1_sil=32000:sp=arity:random_seed=687617998:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.94/0.70 % (1856176)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=566146974:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.94/0.70 % (1856177)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2967581634:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.94/0.70 % (1856178)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3724785303:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.94/0.70 % TRYING [6]
% 0.94/0.70 % TRYING [7]
% 0.94/0.70 % (1856176)Instruction limit reached!
% 0.94/0.70 % (1856176)------------------------------
% 0.94/0.70 % (1856176)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.70 % (1856176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.70 % (1856176)CaDiCaL version: 2.1.3
% 0.94/0.70 % (1856176)Termination reason: Instruction limit
% 0.94/0.70 % (1856176)Termination phase: Saturation
% 0.94/0.70 % (1856176)Time elapsed: 0.056 s
% 0.94/0.70 % (1856176)Peak memory usage: 11 MB
% 0.94/0.70 % (1856176)Instructions burned: 117 (million)
% 0.94/0.70 % (1856175)Instruction limit reached!
% 0.94/0.70 % (1856175)------------------------------
% 0.94/0.70 % (1856175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.70 % (1856175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.70 % (1856175)CaDiCaL version: 2.1.3
% 0.94/0.70 % (1856175)Termination reason: Instruction limit
% 0.94/0.70 % (1856175)Termination phase: Saturation
% 0.94/0.70 % (1856175)Time elapsed: 0.066 s
% 0.94/0.70 % (1856175)Peak memory usage: 12 MB
% 0.94/0.70 % (1856175)Instructions burned: 104 (million)
% 0.94/0.70 % TRYING [8]
% 0.94/0.70 % (1856191)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3672570932:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.94/0.70 % (1856177)Instruction limit reached!
% 0.94/0.70 % (1856177)------------------------------
% 0.94/0.70 % (1856177)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.70 % (1856177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.70 % (1856177)CaDiCaL version: 2.1.3
% 0.94/0.70 % (1856177)Termination reason: Instruction limit
% 0.94/0.70 % (1856177)Termination phase: Saturation
% 0.94/0.70 % (1856177)Time elapsed: 0.076 s
% 0.94/0.70 % (1856177)Peak memory usage: 12 MB
% 0.94/0.70 % (1856177)Instructions burned: 132 (million)
% 0.94/0.70 % TRYING [1]
% 0.94/0.70 % TRYING [2]
% 0.94/0.70 % TRYING [3]
% 0.94/0.70 % TRYING [4]
% 0.94/0.70 % (1856197)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1882399863:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 0.94/0.70 % TRYING [5]
% 0.94/0.70 % (1856204)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=2360183856:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.94/0.70 % TRYING [6]
% 0.94/0.70 % (1856178)Instruction limit reached!
% 0.94/0.70 % (1856178)------------------------------
% 0.94/0.70 % (1856178)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.70 % (1856178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.70 % (1856178)CaDiCaL version: 2.1.3
% 0.94/0.70 % (1856178)Termination reason: Instruction limit
% 0.94/0.70 % (1856178)Termination phase: Saturation
% 0.94/0.70 % (1856178)Time elapsed: 0.113 s
% 0.94/0.70 % (1856178)Peak memory usage: 13 MB
% 0.94/0.70 % (1856178)Instructions burned: 160 (million)
% 0.94/0.70 % (1856221)ott-21_1_sil=16000:fs=off:random_seed=779645964:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.94/0.70 % TRYING [9]
% 0.94/0.70 % TRYING [7]
% 0.94/0.70 % (1856197)Instruction limit reached!
% 0.94/0.70 % (1856197)------------------------------
% 0.94/0.70 % (1856197)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.70 % (1856197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.70 % (1856197)CaDiCaL version: 2.1.3
% 0.94/0.70 % (1856197)Termination reason: Instruction limit
% 0.94/0.70 % (1856197)Termination phase: Saturation
% 0.94/0.70 % (1856197)Time elapsed: 0.087 s
% 0.94/0.70 % (1856197)Peak memory usage: 13 MB
% 0.94/0.70 % (1856197)Instructions burned: 131 (million)
% 0.94/0.70 % (1856247)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1067499962:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 0.94/0.70 % (1856174) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1856167-1856174"...
% 0.94/0.70 % (1856174)...printing done.
% 0.94/0.70 % (1856174)Refutation found. Thanks to Tanya!
% 0.94/0.70 % SZS status Unsatisfiable for theBenchmark
% 0.94/0.70 % SZS output start Proof for theBenchmark
% See solution above
% 0.94/0.70 % (1856174)------------------------------
% 0.94/0.70 % (1856174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.70 % (1856174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.70 % (1856174)CaDiCaL version: 2.1.3
% 0.94/0.70 % (1856174)Termination reason: Refutation
% 0.94/0.70 % (1856174)Time elapsed: 0.203 s
% 0.94/0.70 % (1856174)Peak memory usage: 14 MB
% 0.94/0.70 % (1856174)Instructions burned: 305 (million)
% 0.94/0.70 % (1856167)Success in time 0.244 s
% 0.94/0.70 % Vampire exiting
%------------------------------------------------------------------------------