%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : HEN006-2 : 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 10:19:15 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.52s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 30 ( 14 unt; 0 def)
% Number of atoms : 60 ( 7 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 61 ( 31 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 53 ( 53 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).
fof(f2,axiom,
! [X0,X1] :
( ~ quotient(X0,X1,zero)
| less_equal(X0,X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
fof(f4,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ quotient(X2,X3,X7)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X3,X5)
| ~ quotient(X5,X4,X6)
| ~ quotient(X0,X1,X2)
| less_equal(X6,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
fof(f5,axiom,
! [X0] : less_equal(zero,X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
fof(f8,axiom,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/HEN001-0.ax',well_defined) ).
fof(f14,axiom,
! [X2,X0,X1] :
( ~ less_equal(X1,X2)
| ~ less_equal(X0,X1)
| less_equal(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
fof(f15,axiom,
quotient(x,y,xQy),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQy) ).
fof(f16,axiom,
less_equal(xQy,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQyLEz) ).
fof(f17,axiom,
quotient(x,z,xQz),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQz) ).
fof(f18,negated_conjecture,
~ less_equal(xQz,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_xQzLEy) ).
fof(f30,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[],[f3,f8]) ).
fof(f34,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ~ less_equal(X0,X1)
| zero = X2
| ~ quotient(X0,X1,X2) ),
inference(resolution,[],[f9,f1]) ).
fof(f74,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ quotient(X3,X0,X6)
| ~ quotient(X3,X1,X4)
| ~ quotient(X4,X2,X5)
| ~ quotient(X0,X1,X2)
| less_equal(X5,divide(X6,X1)) ),
inference(resolution,[],[f4,f8]) ).
fof(f87,plain,
! [X2,X0,X1] :
( ~ less_equal(X0,divide(X1,X2))
| less_equal(X0,X1) ),
inference(resolution,[],[f30,f14]) ).
fof(f180,plain,
! [X0] :
( ~ quotient(xQy,z,X0)
| zero = X0 ),
inference(resolution,[],[f64,f16]) ).
fof(f212,plain,
! [X2,X3,X0,X1] :
( ~ quotient(y,X0,X2)
| ~ quotient(X1,X2,X3)
| ~ quotient(x,X0,X1)
| less_equal(X3,divide(xQy,X0)) ),
inference(resolution,[],[f74,f15]) ).
fof(f246,plain,
zero = divide(xQy,z),
inference(resolution,[],[f180,f8]) ).
fof(f617,plain,
! [X2,X0,X1] :
( ~ quotient(x,X1,X0)
| ~ quotient(X0,divide(y,X1),X2)
| less_equal(X2,divide(xQy,X1)) ),
inference(resolution,[],[f212,f8]) ).
fof(f1377,plain,
! [X0] :
( ~ quotient(xQz,divide(y,z),X0)
| less_equal(X0,divide(xQy,z)) ),
inference(resolution,[],[f617,f17]) ).
fof(f1386,plain,
! [X0] :
( ~ quotient(xQz,divide(y,z),X0)
| less_equal(X0,zero) ),
inference(forward_demodulation,[],[f1377,f246]) ).
fof(f1875,plain,
less_equal(divide(xQz,divide(y,z)),zero),
inference(resolution,[],[f1386,f8]) ).
fof(f2108,plain,
zero = divide(xQz,divide(y,z)),
inference(resolution,[],[f1875,f34]) ).
fof(f2288,plain,
quotient(xQz,divide(y,z),zero),
inference(superposition,[],[f8,f2108]) ).
fof(f2336,plain,
less_equal(xQz,divide(y,z)),
inference(resolution,[],[f2288,f2]) ).
fof(f2354,plain,
less_equal(xQz,y),
inference(resolution,[],[f2336,f87]) ).
fof(f2370,plain,
$false,
inference(forward_subsumption_resolution,[],[f2354,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN006-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n018.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 10:52:59 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.16/0.52 % (2156076)Will run a generic schedule for satisfiability detection.
% 0.16/0.52 % (2156081)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1739165122_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.52 % TRYING [1]
% 0.16/0.52 % TRYING [2]
% 0.16/0.52 % TRYING [3]
% 0.16/0.52 % TRYING [4]
% 0.16/0.52 % (2156082)% WARNING: option uhcvi not known.
% 0.16/0.52 % TRYING [5]
% 0.16/0.52 % (2156084)dis+10_1_sil=32000:sp=arity:random_seed=3126269877:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.52 % (2156082)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1587967748:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.52 % (2156083)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2363910659:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.52 % (2156086)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=250447844:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.52 % (2156085)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4117481659:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.52 % (2156087)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3636200154:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.52 % TRYING [6]
% 0.16/0.52 % TRYING [7]
% 0.16/0.52 % (2156085)Instruction limit reached!
% 0.16/0.52 % (2156085)------------------------------
% 0.16/0.52 % (2156085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (2156085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (2156085)CaDiCaL version: 2.1.3
% 0.16/0.52 % (2156085)Termination reason: Instruction limit
% 0.16/0.52 % (2156085)Termination phase: Saturation
% 0.16/0.52 % (2156085)Time elapsed: 0.060 s
% 0.16/0.52 % (2156085)Peak memory usage: 12 MB
% 0.16/0.52 % (2156085)Instructions burned: 117 (million)
% 0.16/0.52 % TRYING [8]
% 0.16/0.52 % (2156082) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2156076-2156082"...
% 0.16/0.52 % (2156082)...printing done.
% 0.16/0.52 % (2156084)Instruction limit reached!
% 0.16/0.52 % (2156084)------------------------------
% 0.16/0.52 % (2156084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (2156084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (2156084)CaDiCaL version: 2.1.3
% 0.16/0.52 % (2156084)Termination reason: Instruction limit
% 0.16/0.52 % (2156084)Termination phase: Saturation
% 0.16/0.52 % (2156084)Time elapsed: 0.067 s
% 0.16/0.52 % (2156084)Peak memory usage: 12 MB
% 0.16/0.52 % (2156084)Instructions burned: 104 (million)
% 0.16/0.52 % (2156082)Refutation found. Thanks to Tanya!
% 0.16/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.52 % (2156082)------------------------------
% 0.16/0.52 % (2156082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (2156082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (2156082)CaDiCaL version: 2.1.3
% 0.16/0.52 % (2156082)Termination reason: Refutation
% 0.16/0.52 % (2156082)Time elapsed: 0.065 s
% 0.16/0.52 % (2156082)Peak memory usage: 12 MB
% 0.16/0.52 % (2156082)Instructions burned: 95 (million)
% 0.16/0.52 % (2156076)Success in time 0.09 s
% 0.16/0.52 % Vampire exiting
%------------------------------------------------------------------------------