%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN008-4 : 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 : n003.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 10:19:08 AM UTC 2026
% Result : Unsatisfiable 2.62s 1.32s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 28 ( 20 unt; 0 def)
% Number of atoms : 37 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 10 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ less_equal(X0,X1)
| divide(X0,X1) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal1) ).
fof(f2,axiom,
! [X0,X1] :
( divide(X0,X1) != zero
| less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal2) ).
fof(f3,axiom,
! [X0,X1] : less_equal(divide(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
fof(f4,axiom,
! [X2,X0,X1] : less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_property) ).
fof(f5,axiom,
! [X0] : less_equal(zero,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_is_smallest) ).
fof(f6,axiom,
! [X0,X1] :
( ~ less_equal(X1,X0)
| ~ less_equal(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_equal_and_equal) ).
fof(f10,axiom,
! [X0] : divide(zero,X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
fof(f11,plain,
! [X0] : zero = divide(zero,X0),
inference(reorient_equations,[],[f10]) ).
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(f17,axiom,
! [X2,X0,X1] :
( ~ less_equal(divide(X0,X1),X2)
| less_equal(divide(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide1) ).
fof(f19,axiom,
less_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_LE_b) ).
fof(f20,negated_conjecture,
~ less_equal(divide(a,c),divide(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_divide_c_LE_b_divide_c) ).
fof(f28,plain,
zero = divide(a,b),
inference(resolution,[],[f1,f19]) ).
fof(f31,plain,
! [X0] :
( zero != zero
| less_equal(X0,X0) ),
inference(superposition,[],[f2,f13]) ).
fof(f35,plain,
! [X0] : less_equal(X0,X0),
inference(trivial_inequality_removal,[],[f31]) ).
fof(f49,plain,
! [X0,X1] :
( ~ less_equal(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[],[f6,f3]) ).
fof(f50,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f70,plain,
! [X0,X1] : less_equal(divide(X0,divide(X0,X1)),X1),
inference(resolution,[],[f17,f35]) ).
fof(f107,plain,
! [X2,X0,X1] : less_equal(divide(divide(X0,X1),divide(divide(X0,X2),X1)),divide(X2,X1)),
inference(resolution,[],[f4,f17]) ).
fof(f193,plain,
! [X0] : zero = divide(X0,divide(X0,zero)),
inference(resolution,[],[f70,f50]) ).
fof(f609,plain,
! [X0] : less_equal(divide(divide(a,X0),divide(zero,X0)),divide(b,X0)),
inference(superposition,[],[f107,f28]) ).
fof(f625,plain,
! [X0] : less_equal(divide(divide(a,X0),zero),divide(b,X0)),
inference(forward_demodulation,[],[f609,f11]) ).
fof(f831,plain,
! [X0] :
( zero != zero
| less_equal(X0,divide(X0,zero)) ),
inference(superposition,[],[f2,f193]) ).
fof(f864,plain,
! [X0] : less_equal(X0,divide(X0,zero)),
inference(trivial_inequality_removal,[],[f831]) ).
fof(f919,plain,
! [X0] : divide(X0,zero) = X0,
inference(resolution,[],[f864,f49]) ).
fof(f1830,plain,
! [X0] : less_equal(divide(a,X0),divide(b,X0)),
inference(superposition,[],[f625,f919]) ).
fof(f1854,plain,
$false,
inference(resolution,[],[f1830,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN008-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n003.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 10:52:41 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
% 2.62/1.32 % (336868)Input is clausal, will run a generic CNF schedule.
% 2.62/1.32 % (336876)lrs+10_1_sil=8000:sp=occurrence:random_seed=2959059858:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.62/1.32 % (336876)First to succeed.
% 2.62/1.32 % (336876)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-336868"
% 2.62/1.32 % (336878)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1618882602:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.62/1.32 % (336873)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=4233297368:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.62/1.32 % (336874)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3308607836:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.62/1.32 % (336875)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2281787922:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.62/1.32 % (336879)dis-21_1_sil=8000:lcm=predicate:random_seed=1787613439: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)
% 2.62/1.32 % (336877)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=962860884:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.62/1.32 % (336878)Also succeeded, but the first one will report.
% 2.62/1.32 % (336877)Instruction limit reached!
% 2.62/1.32 % (336877)------------------------------
% 2.62/1.32 % (336877)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.32 % (336877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.32 % (336877)CaDiCaL version: 2.1.3
% 2.62/1.32 % (336877)Termination reason: Instruction limit
% 2.62/1.32 % (336877)Termination phase: Saturation
% 2.62/1.32 % (336877)Time elapsed: 0.071 s
% 2.62/1.32 % (336877)Peak memory usage: 88 MB
% 2.62/1.32 % (336877)Instructions burned: 115 (million)
% 2.62/1.32 % (336879)Instruction limit reached!
% 2.62/1.32 % (336879)------------------------------
% 2.62/1.32 % (336879)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.32 % (336879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.32 % (336879)CaDiCaL version: 2.1.3
% 2.62/1.32 % (336879)Termination reason: Instruction limit
% 2.62/1.32 % (336879)Termination phase: Saturation
% 2.62/1.32 % (336879)Time elapsed: 0.075 s
% 2.62/1.32 % (336879)Peak memory usage: 88 MB
% 2.62/1.32 % (336879)Instructions burned: 119 (million)
% 2.62/1.32 % (336876)Refutation found. Thanks to Tanya!
% 2.62/1.32 % SZS status Unsatisfiable for theBenchmark
% 2.62/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/1.32 % (336876)------------------------------
% 2.62/1.32 % (336876)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.32 % (336876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.32 % (336876)CaDiCaL version: 2.1.3
% 2.62/1.32 % (336876)Termination reason: Refutation
% 2.62/1.32 % (336876)Time elapsed: 0.018 s
% 2.62/1.32 % (336876)Peak memory usage: 89 MB
% 2.62/1.32 % (336876)Instructions burned: 48 (million)
% 2.62/1.32 % (336876)------------------------------
% 2.62/1.32 % (336876)------------------------------
% 2.62/1.32 % (336868)Success in time 0.28 s
% 2.62/1.32 % Vampire exiting
%------------------------------------------------------------------------------