%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : HEN003-2 : 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 : n001.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 10:19:13 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 27 ( 13 unt; 0 def)
% Number of atoms : 53 ( 8 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 53 ( 27 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 63 ( 63 !; 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(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/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(f11,axiom,
! [X0] : quotient(zero,X0,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
fof(f12,negated_conjecture,
~ quotient(x,x,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_x_divide_x_is_zero) ).
fof(f20,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[],[f3,f8]) ).
fof(f21,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| divide(X0,X1) = X2 ),
inference(resolution,[],[f9,f8]) ).
fof(f35,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(f48,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| zero = divide(X0,X1) ),
inference(resolution,[],[f29,f1]) ).
fof(f58,plain,
! [X0,X1] : zero = divide(divide(X0,X1),X0),
inference(resolution,[],[f48,f20]) ).
fof(f62,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,[],[f35,f8]) ).
fof(f109,plain,
! [X2,X3,X0,X1] :
( ~ quotient(X0,zero,X1)
| ~ quotient(X0,X2,X3)
| less_equal(divide(X3,zero),divide(X1,X2)) ),
inference(resolution,[],[f62,f11]) ).
fof(f135,plain,
! [X2,X0,X1] :
( less_equal(divide(X2,zero),divide(divide(X0,zero),X1))
| ~ quotient(X0,X1,X2) ),
inference(resolution,[],[f109,f8]) ).
fof(f224,plain,
! [X0,X1] :
( ~ quotient(X1,X1,X0)
| less_equal(divide(X0,zero),zero) ),
inference(superposition,[],[f135,f58]) ).
fof(f232,plain,
! [X0] : less_equal(divide(divide(X0,X0),zero),zero),
inference(resolution,[],[f224,f8]) ).
fof(f240,plain,
! [X0] : zero = divide(divide(X0,X0),zero),
inference(resolution,[],[f232,f21]) ).
fof(f264,plain,
! [X0] : quotient(divide(X0,X0),zero,zero),
inference(superposition,[],[f8,f240]) ).
fof(f301,plain,
! [X0] : less_equal(divide(X0,X0),zero),
inference(resolution,[],[f264,f2]) ).
fof(f342,plain,
! [X0] : zero = divide(X0,X0),
inference(resolution,[],[f301,f21]) ).
fof(f365,plain,
! [X0] : quotient(X0,X0,zero),
inference(superposition,[],[f8,f342]) ).
fof(f400,plain,
$false,
inference(resolution,[],[f365,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 10:55:15 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.10/0.45 % (3381522)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (3381528)% WARNING: option uhcvi not known.
% 0.10/0.45 % (3381528)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1973922324:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.45 % (3381527)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=452638673_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.45 % (3381529)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2719958129:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.45 % (3381530)dis+10_1_sil=32000:sp=arity:random_seed=1977451807:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (3381531)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1343115959:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % (3381532)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2119237832:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.45 % TRYING [1]
% 0.10/0.45 % (3381533)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=889973817:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.45 % TRYING [2]
% 0.10/0.45 % TRYING [3]
% 0.10/0.45 % TRYING [4]
% 0.10/0.45 % TRYING [5]
% 0.10/0.45 % (3381530) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3381522-3381530"...
% 0.10/0.45 % (3381530)...printing done.
% 0.10/0.45 % (3381530)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (3381530)------------------------------
% 0.10/0.45 % (3381530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (3381530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (3381530)CaDiCaL version: 2.1.3
% 0.10/0.45 % (3381530)Termination reason: Refutation
% 0.10/0.45 % (3381530)Time elapsed: 0.010 s
% 0.10/0.45 % (3381530)Peak memory usage: 11 MB
% 0.10/0.45 % (3381530)Instructions burned: 13 (million)
% 0.10/0.45 % (3381522)Success in time 0.045 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------