%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : HEN005-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 10:19:14 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 30 ( 17 unt; 0 def)
% Number of atoms : 58 ( 9 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 57 ( 29 ~; 28 |; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 51 !; 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(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xLEy) ).
fof(f11,axiom,
less_equal(y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',yLEz) ).
fof(f12,negated_conjecture,
~ less_equal(x,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_transitivity_of_less_equal) ).
fof(f17,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| divide(X0,X1) = X2 ),
inference(resolution,[],[f9,f8]) ).
fof(f40,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(f47,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| zero = divide(X0,X1) ),
inference(resolution,[],[f38,f1]) ).
fof(f60,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,[],[f40,f1]) ).
fof(f68,plain,
zero = divide(x,y),
inference(resolution,[],[f47,f10]) ).
fof(f69,plain,
zero = divide(y,z),
inference(resolution,[],[f47,f11]) ).
fof(f71,plain,
quotient(x,y,zero),
inference(superposition,[],[f8,f68]) ).
fof(f96,plain,
! [X2,X3,X0,X1,X4] :
( ~ quotient(X0,X3,X4)
| ~ quotient(X0,X1,X2)
| less_equal(divide(X4,divide(X1,X3)),zero)
| ~ less_equal(X2,X3) ),
inference(resolution,[],[f60,f8]) ).
fof(f168,plain,
! [X2,X3,X0,X1] :
( ~ quotient(X0,X1,X2)
| less_equal(divide(divide(X0,X3),divide(X1,X3)),zero)
| ~ less_equal(X2,X3) ),
inference(resolution,[],[f96,f8]) ).
fof(f270,plain,
! [X0] :
( less_equal(divide(divide(x,X0),divide(y,X0)),zero)
| ~ less_equal(zero,X0) ),
inference(resolution,[],[f168,f71]) ).
fof(f273,plain,
! [X0] : less_equal(divide(divide(x,X0),divide(y,X0)),zero),
inference(forward_subsumption_resolution,[],[f270,f5]) ).
fof(f299,plain,
less_equal(divide(divide(x,z),zero),zero),
inference(superposition,[],[f273,f69]) ).
fof(f316,plain,
zero = divide(divide(x,z),zero),
inference(resolution,[],[f299,f17]) ).
fof(f333,plain,
quotient(divide(x,z),zero,zero),
inference(superposition,[],[f8,f316]) ).
fof(f353,plain,
less_equal(divide(x,z),zero),
inference(resolution,[],[f333,f2]) ).
fof(f380,plain,
zero = divide(x,z),
inference(resolution,[],[f353,f17]) ).
fof(f402,plain,
quotient(x,z,zero),
inference(superposition,[],[f8,f380]) ).
fof(f414,plain,
less_equal(x,z),
inference(resolution,[],[f402,f2]) ).
fof(f436,plain,
$false,
inference(forward_subsumption_resolution,[],[f414,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN005-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n015.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 10:53:05 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.18/0.47 % (1478917)Will run a generic schedule for satisfiability detection.
% 0.18/0.47 % (1478934)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3110852149:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.47 % (1478929)% WARNING: option uhcvi not known.
% 0.18/0.47 % (1478928)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=609889844_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.47 % (1478930)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2314878933:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.47 % (1478931)dis+10_1_sil=32000:sp=arity:random_seed=3083871768:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.47 % (1478932)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1170760796:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.47 % (1478929)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3614364594:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.47 % (1478935)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2441530839:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.47 % TRYING [1]
% 0.18/0.47 % TRYING [2]
% 0.18/0.47 % TRYING [3]
% 0.18/0.47 % TRYING [4]
% 0.18/0.47 % TRYING [5]
% 0.18/0.47 % (1478931) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1478917-1478931"...
% 0.18/0.47 % (1478931)...printing done.
% 0.18/0.47 % (1478931)Refutation found. Thanks to Tanya!
% 0.18/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.47 % (1478931)------------------------------
% 0.18/0.47 % (1478931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.47 % (1478931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.47 % (1478931)CaDiCaL version: 2.1.3
% 0.18/0.47 % (1478931)Termination reason: Refutation
% 0.18/0.47 % (1478931)Time elapsed: 0.010 s
% 0.18/0.47 % (1478931)Peak memory usage: 11 MB
% 0.18/0.47 % (1478931)Instructions burned: 14 (million)
% 0.18/0.47 % (1478917)Success in time 0.045 s
% 0.18/0.47 % Vampire exiting
%------------------------------------------------------------------------------