%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : HEN004-2 : 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 : n002.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 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 26 ( 16 unt; 0 def)
% Number of atoms : 47 ( 6 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 43 ( 22 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 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 : 51 ( 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f11,axiom,
! [X0] : quotient(zero,X0,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
fof(f12,axiom,
! [X0] : quotient(X0,X0,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
fof(f13,negated_conjecture,
~ quotient(x,zero,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_x_divde_zero_is_x) ).
fof(f22,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[],[f3,f8]) ).
fof(f23,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f26,plain,
! [X0,X1] :
( ~ less_equal(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[],[f22,f6]) ).
fof(f33,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ quotient(X3,X0,X1)
| ~ quotient(X3,X1,X4)
| ~ quotient(X4,X2,X5)
| ~ quotient(X0,X1,X2)
| less_equal(X5,zero) ),
inference(resolution,[],[f4,f12]) ).
fof(f87,plain,
! [X2,X3,X0,X1,X4] :
( ~ quotient(X2,X3,X4)
| ~ quotient(X0,divide(X0,X1),X2)
| ~ quotient(X1,divide(X0,X1),X3)
| less_equal(X4,zero) ),
inference(resolution,[],[f33,f8]) ).
fof(f227,plain,
! [X2,X3,X0,X1] :
( ~ quotient(X1,divide(X0,X1),X3)
| ~ quotient(X0,divide(X0,X1),X2)
| less_equal(divide(X2,X3),zero) ),
inference(resolution,[],[f87,f8]) ).
fof(f370,plain,
! [X0,X1] :
( ~ quotient(X0,divide(X0,zero),X1)
| less_equal(divide(X1,zero),zero) ),
inference(resolution,[],[f227,f11]) ).
fof(f428,plain,
! [X0] : less_equal(divide(divide(X0,divide(X0,zero)),zero),zero),
inference(resolution,[],[f370,f8]) ).
fof(f528,plain,
! [X0] : zero = divide(divide(X0,divide(X0,zero)),zero),
inference(resolution,[],[f428,f23]) ).
fof(f690,plain,
! [X0] : quotient(divide(X0,divide(X0,zero)),zero,zero),
inference(superposition,[],[f8,f528]) ).
fof(f737,plain,
! [X0] : less_equal(divide(X0,divide(X0,zero)),zero),
inference(resolution,[],[f690,f2]) ).
fof(f770,plain,
! [X0] : zero = divide(X0,divide(X0,zero)),
inference(resolution,[],[f737,f23]) ).
fof(f793,plain,
! [X0] : quotient(X0,divide(X0,zero),zero),
inference(superposition,[],[f8,f770]) ).
fof(f821,plain,
! [X0] : less_equal(X0,divide(X0,zero)),
inference(resolution,[],[f793,f2]) ).
fof(f852,plain,
! [X0] : divide(X0,zero) = X0,
inference(resolution,[],[f821,f26]) ).
fof(f903,plain,
! [X0] : quotient(X0,zero,X0),
inference(superposition,[],[f8,f852]) ).
fof(f1006,plain,
$false,
inference(backward_subsumption_resolution,[],[f13,f903]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n002.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 10:52:26 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.16/0.47 % (3359413)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (3359419)% WARNING: option uhcvi not known.
% 0.16/0.47 % (3359419)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2410956236:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (3359418)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3490727809_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % (3359422)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1436073960:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (3359420)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=272166687:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (3359421)dis+10_1_sil=32000:sp=arity:random_seed=1678578381:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (3359424)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=846194743:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % (3359423)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2703767020:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % TRYING [1]
% 0.16/0.47 % TRYING [2]
% 0.16/0.47 % TRYING [3]
% 0.16/0.47 % TRYING [4]
% 0.16/0.47 % (3359419) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3359413-3359419"...
% 0.16/0.47 % (3359419)...printing done.
% 0.16/0.47 % (3359419)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (3359419)------------------------------
% 0.16/0.47 % (3359419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (3359419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (3359419)CaDiCaL version: 2.1.3
% 0.16/0.47 % (3359419)Termination reason: Refutation
% 0.16/0.47 % (3359419)Time elapsed: 0.015 s
% 0.16/0.47 % (3359419)Peak memory usage: 11 MB
% 0.16/0.47 % (3359419)Instructions burned: 40 (million)
% 0.16/0.47 % (3359413)Success in time 0.043 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------