%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : HEN003-1 : 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 : n006.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 10:19:12 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.47s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 15 unt; 0 def)
% Number of atoms : 51 ( 7 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 50 ( 26 ~; 24 |; 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 : 65 ( 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ less_equal(X0,X1)
| quotient(X0,X1,zero) ),
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(X0,X1,X2)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X3,X5)
| ~ quotient(X5,X4,X6)
| ~ 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(X0,X1)
| ~ less_equal(X1,X0)
| 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,X2)
| ~ quotient(X0,X1,X3)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',well_defined) ).
fof(f10,negated_conjecture,
~ quotient(x,x,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_x_divide_x_is_zero) ).
fof(f14,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[],[f3,f8]) ).
fof(f18,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f21,plain,
! [X0,X1] : quotient(divide(X0,X1),X0,zero),
inference(resolution,[],[f14,f1]) ).
fof(f22,plain,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| divide(X0,X1) = X2 ),
inference(resolution,[],[f9,f8]) ).
fof(f27,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ quotient(X4,X2,X5)
| ~ quotient(X3,X1,X4)
| ~ quotient(X0,X1,X2)
| ~ quotient(divide(X3,X0),X1,X6)
| less_equal(X5,X6) ),
inference(resolution,[],[f4,f8]) ).
fof(f41,plain,
! [X0,X1] : zero = divide(divide(X0,X1),X0),
inference(resolution,[],[f22,f21]) ).
fof(f45,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ quotient(divide(X0,X3),X1,X5)
| ~ quotient(X3,X1,X4)
| ~ quotient(X0,X1,X2)
| less_equal(divide(X2,X4),X5) ),
inference(resolution,[],[f27,f8]) ).
fof(f61,plain,
! [X2,X0,X1] : less_equal(divide(divide(X0,X1),X0),X2),
inference(superposition,[],[f5,f41]) ).
fof(f86,plain,
! [X2,X0,X1] : quotient(divide(divide(X0,X1),X0),X2,zero),
inference(resolution,[],[f61,f1]) ).
fof(f118,plain,
! [X2,X3,X0,X1] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X1,X1,X3)
| less_equal(divide(X3,X2),zero) ),
inference(resolution,[],[f45,f21]) ).
fof(f235,plain,
! [X0,X1] :
( ~ quotient(X0,X0,X1)
| less_equal(divide(X1,zero),zero) ),
inference(resolution,[],[f118,f86]) ).
fof(f312,plain,
! [X0] : less_equal(divide(divide(X0,X0),zero),zero),
inference(resolution,[],[f235,f8]) ).
fof(f325,plain,
! [X0] : zero = divide(divide(X0,X0),zero),
inference(resolution,[],[f312,f18]) ).
fof(f360,plain,
! [X0] : quotient(divide(X0,X0),zero,zero),
inference(superposition,[],[f8,f325]) ).
fof(f387,plain,
! [X0] : less_equal(divide(X0,X0),zero),
inference(resolution,[],[f360,f2]) ).
fof(f416,plain,
! [X0] : zero = divide(X0,X0),
inference(resolution,[],[f387,f18]) ).
fof(f442,plain,
! [X0] : ~ quotient(x,x,divide(X0,X0)),
inference(superposition,[],[f10,f416]) ).
fof(f493,plain,
$false,
inference(resolution,[],[f442,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n006.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 10:49:10 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 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
% 0.23/0.47 % (2798240)Will run a generic schedule for satisfiability detection.
% 0.23/0.47 % (2798245)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3402781773_2999 on theBenchmark for (2999ds/0Mi)
% 0.23/0.47 % TRYING [1]
% 0.23/0.47 % TRYING [2]
% 0.23/0.47 % TRYING [3]
% 0.23/0.47 % TRYING [4]
% 0.23/0.47 % (2798246)% WARNING: option uhcvi not known.
% 0.23/0.47 % TRYING [5]
% 0.23/0.47 % (2798246)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1943114828:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.23/0.47 % (2798247)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2528230243:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.23/0.47 % (2798248)dis+10_1_sil=32000:sp=arity:random_seed=1816633986:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.23/0.47 % (2798249)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=664365426:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.23/0.47 % (2798251)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=171129230:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.23/0.47 % (2798250)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=840501662:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.23/0.47 % TRYING [6]
% 0.23/0.47 % (2798250) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2798240-2798250"...
% 0.23/0.47 % (2798248) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2798240-2798248"...
% 0.23/0.47 % (2798250)...printing done.
% 0.23/0.47 % (2798250)Refutation found. Thanks to Tanya!
% 0.23/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.47 % (2798250)------------------------------
% 0.23/0.47 % (2798250)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.47 % (2798250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.47 % (2798250)CaDiCaL version: 2.1.3
% 0.23/0.47 % (2798250)Termination reason: Refutation
% 0.23/0.47 % (2798250)Time elapsed: 0.011 s
% 0.23/0.47 % (2798250)Peak memory usage: 11 MB
% 0.23/0.47 % (2798250)Instructions burned: 15 (million)
% 0.23/0.47 % (2798240)Success in time 0.044 s
% 0.23/0.47 % Vampire exiting
%------------------------------------------------------------------------------