%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : HEN005-2 : 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 : n011.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 0.16s 0.49s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 28 ( 15 unt; 0 def)
% Number of atoms : 53 ( 9 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 51 ( 26 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 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 : 43 ( 43 !; 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(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(f13,axiom,
! [X0] : quotient(X0,zero,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
fof(f14,axiom,
less_equal(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xLEy) ).
fof(f15,axiom,
less_equal(y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',yLEz) ).
fof(f16,negated_conjecture,
~ less_equal(x,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_transitivity_of_less_equal) ).
fof(f81,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f350,plain,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| divide(X0,X1) = X2 ),
inference(resolution,[],[f9,f8]) ).
fof(f450,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| zero = divide(X0,X1) ),
inference(resolution,[],[f350,f1]) ).
fof(f483,plain,
zero = divide(x,y),
inference(resolution,[],[f450,f14]) ).
fof(f484,plain,
zero = divide(y,z),
inference(resolution,[],[f450,f15]) ).
fof(f487,plain,
quotient(x,y,zero),
inference(superposition,[],[f8,f483]) ).
fof(f494,plain,
quotient(y,z,zero),
inference(superposition,[],[f8,f484]) ).
fof(f606,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ quotient(X4,X1,X5)
| ~ quotient(X2,X1,X3)
| ~ quotient(X2,X0,X4)
| ~ quotient(X0,X1,zero)
| less_equal(X3,X5) ),
inference(resolution,[],[f4,f13]) ).
fof(f611,plain,
! [X2,X3,X0,X1] :
( ~ quotient(X3,X1,zero)
| ~ quotient(X0,X3,zero)
| ~ quotient(X0,X1,X2)
| less_equal(X2,zero) ),
inference(resolution,[],[f606,f11]) ).
fof(f2350,plain,
! [X0,X1] :
( ~ quotient(X0,z,X1)
| ~ quotient(X0,y,zero)
| less_equal(X1,zero) ),
inference(resolution,[],[f611,f494]) ).
fof(f2571,plain,
! [X0] :
( less_equal(divide(X0,z),zero)
| ~ quotient(X0,y,zero) ),
inference(resolution,[],[f2350,f8]) ).
fof(f2577,plain,
! [X0] :
( ~ quotient(X0,y,zero)
| zero = divide(X0,z) ),
inference(resolution,[],[f2571,f81]) ).
fof(f2591,plain,
zero = divide(x,z),
inference(resolution,[],[f2577,f487]) ).
fof(f2604,plain,
quotient(x,z,zero),
inference(superposition,[],[f8,f2591]) ).
fof(f2628,plain,
less_equal(x,z),
inference(resolution,[],[f2604,f2]) ).
fof(f2638,plain,
$false,
inference(forward_subsumption_resolution,[],[f2628,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN005-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n011.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 10:49:50 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.42 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
% 0.16/0.49 % (2214873)Will run a generic schedule for satisfiability detection.
% 0.16/0.49 % (2214880)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1751160092:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.49 % (2214878)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2636365932_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.49 % TRYING [1]
% 0.16/0.49 % TRYING [2]
% 0.16/0.49 % (2214882)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1509227508:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.49 % TRYING [3]
% 0.16/0.49 % (2214881)dis+10_1_sil=32000:sp=arity:random_seed=1647713480:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.49 % TRYING [4]
% 0.16/0.49 % (2214879)% WARNING: option uhcvi not known.
% 0.16/0.49 % TRYING [5]
% 0.16/0.49 % (2214879)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=841209637:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.49 % (2214880) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2214873-2214880"...
% 0.16/0.49 % (2214884)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3136303593:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.49 % (2214880)...printing done.
% 0.16/0.49 % (2214880)Refutation found. Thanks to Tanya!
% 0.16/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.49 % (2214880)------------------------------
% 0.16/0.49 % (2214880)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.49 % (2214880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.49 % (2214880)CaDiCaL version: 2.1.3
% 0.16/0.49 % (2214880)Termination reason: Refutation
% 0.16/0.49 % (2214880)Time elapsed: 0.027 s
% 0.16/0.49 % (2214880)Peak memory usage: 12 MB
% 0.16/0.49 % (2214880)Instructions burned: 69 (million)
% 0.16/0.49 % (2214873)Success in time 0.066 s
% 0.16/0.49 % Vampire exiting
%------------------------------------------------------------------------------