%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN007-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 10:19:07 AM UTC 2026
% Result : Unsatisfiable 3.51s 1.38s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 18 ( 9 unt; 1 def)
% Number of atoms : 28 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 14 ~; 9 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( divide(X0,X1) != zero
| less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal2) ).
fof(f12,axiom,
! [X0] : divide(X0,X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
fof(f13,plain,
! [X0] : zero = divide(X0,X0),
inference(reorient_equations,[],[f12]) ).
fof(f16,axiom,
! [X2,X0,X1] :
( less_equal(X0,X2)
| ~ less_equal(X1,X2)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
fof(f17,axiom,
! [X2,X0,X1] :
( less_equal(divide(X0,X2),X1)
| ~ less_equal(divide(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide1) ).
fof(f18,axiom,
less_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_LE_b) ).
fof(f19,negated_conjecture,
~ less_equal(divide(c,b),divide(c,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_divide_b_LE_c_divide_a) ).
fof(f20,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f23,plain,
! [X0] : sQ0_eqProxy(zero,divide(X0,X0)),
inference(equality_proxy_replacement,[],[f13,f20]) ).
fof(f26,plain,
! [X0,X1] :
( ~ sQ0_eqProxy(divide(X0,X1),zero)
| less_equal(X0,X1) ),
inference(equality_proxy_replacement,[],[f2,f20]) ).
fof(f29,plain,
! [X0,X1] :
( sQ0_eqProxy(X1,X0)
| ~ sQ0_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f20]) ).
fof(f30,plain,
! [X0,X1] :
( ~ sQ0_eqProxy(zero,divide(X0,X1))
| less_equal(X0,X1) ),
inference(resolution,[],[f26,f29]) ).
fof(f40,plain,
~ less_equal(divide(c,divide(c,a)),b),
inference(resolution,[],[f17,f19]) ).
fof(f45,plain,
! [X0] :
( ~ less_equal(divide(c,divide(c,a)),X0)
| ~ less_equal(X0,b) ),
inference(resolution,[],[f40,f16]) ).
fof(f47,plain,
! [X0] : less_equal(X0,X0),
inference(resolution,[],[f30,f23]) ).
fof(f70,plain,
! [X0] :
( ~ less_equal(divide(c,X0),divide(c,a))
| ~ less_equal(X0,b) ),
inference(resolution,[],[f45,f17]) ).
fof(f152,plain,
~ less_equal(a,b),
inference(resolution,[],[f70,f47]) ).
fof(f153,plain,
$false,
inference(resolution,[],[f152,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN007-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n004.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 10:50:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.51/1.38 % (3337011)Input is clausal, will run a generic CNF schedule.
% 3.51/1.38 % (3337017)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=298219679:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.51/1.38 % (3337016)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=4109630063:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.51/1.38 % (3337020)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3169242203:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.51/1.38 % (3337019)lrs+10_1_sil=8000:sp=occurrence:random_seed=1098765461:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.51/1.38 % (3337022)dis-21_1_sil=8000:lcm=predicate:random_seed=2828717027:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.51/1.38 % (3337018)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1413603362:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.51/1.38 % (3337021)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2930214966:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.51/1.38 % (3337022)First to succeed.
% 3.51/1.38 % (3337022)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3337011"
% 3.51/1.38 % (3337021)Also succeeded, but the first one will report.
% 3.51/1.38 % (3337020)Also succeeded, but the first one will report.
% 3.51/1.38 % (3337019)Also succeeded, but the first one will report.
% 3.51/1.38 % (3337022)Refutation found. Thanks to Tanya!
% 3.51/1.38 % SZS status Unsatisfiable for theBenchmark
% 3.51/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.38 % (3337022)------------------------------
% 3.51/1.38 % (3337022)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.38 % (3337022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.38 % (3337022)CaDiCaL version: 2.1.3
% 3.51/1.38 % (3337022)Termination reason: Refutation
% 3.51/1.38 % (3337022)Time elapsed: 0.004 s
% 3.51/1.38 % (3337022)Peak memory usage: 88 MB
% 3.51/1.38 % (3337022)Instructions burned: 4 (million)
% 3.51/1.38 % (3337022)------------------------------
% 3.51/1.38 % (3337022)------------------------------
% 3.51/1.38 % (3337011)Success in time 0.432 s
% 3.51/1.38 % Vampire exiting
%------------------------------------------------------------------------------