%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN005-3 : 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 : n010.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 10:19:05 AM UTC 2026
% Result : Unsatisfiable 3.77s 1.52s
% Output : Refutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 23 ( 13 unt; 0 def)
% Number of atoms : 34 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 12 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 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 : 27 ( 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( divide(X0,X1) = zero
| ~ less_equal(X0,X1) ),
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(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_equal_and_equal) ).
fof(f8,axiom,
less_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_LE_b) ).
fof(f9,axiom,
less_equal(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_LE_c) ).
fof(f10,negated_conjecture,
~ less_equal(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_LE_c) ).
fof(f15,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f41,plain,
! [X2,X0,X1] :
( less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(zero,X1))
| ~ less_equal(X0,X2) ),
inference(superposition,[],[f4,f1]) ).
fof(f44,plain,
! [X0] : zero = divide(zero,X0),
inference(resolution,[],[f15,f3]) ).
fof(f90,plain,
! [X2,X0,X1] :
( less_equal(divide(divide(X0,X1),divide(X2,X1)),zero)
| ~ less_equal(X0,X2) ),
inference(forward_demodulation,[],[f41,f44]) ).
fof(f92,plain,
! [X2,X0,X1] :
( ~ less_equal(X0,X1)
| zero = divide(divide(X0,X2),divide(X1,X2)) ),
inference(resolution,[],[f90,f15]) ).
fof(f118,plain,
! [X0] : zero = divide(divide(a,X0),divide(b,X0)),
inference(resolution,[],[f92,f8]) ).
fof(f153,plain,
! [X0] :
( zero != zero
| less_equal(divide(a,X0),divide(b,X0)) ),
inference(superposition,[],[f2,f118]) ).
fof(f170,plain,
! [X0] : less_equal(divide(a,X0),divide(b,X0)),
inference(trivial_inequality_removal,[],[f153]) ).
fof(f185,plain,
! [X0] :
( ~ less_equal(b,X0)
| less_equal(divide(a,X0),zero) ),
inference(superposition,[],[f170,f1]) ).
fof(f196,plain,
less_equal(divide(a,c),zero),
inference(resolution,[],[f185,f9]) ).
fof(f199,plain,
zero = divide(a,c),
inference(resolution,[],[f196,f15]) ).
fof(f237,plain,
( zero != zero
| less_equal(a,c) ),
inference(superposition,[],[f2,f199]) ).
fof(f256,plain,
less_equal(a,c),
inference(trivial_inequality_removal,[],[f237]) ).
fof(f265,plain,
$false,
inference(forward_subsumption_resolution,[],[f256,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN005-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n010.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 10:50:06 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 3.77/1.52 % (785920)Input is clausal, will run a generic CNF schedule.
% 3.77/1.52 % (786004)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3614016070:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.77/1.52 % (786005)lrs+10_1_sil=8000:sp=occurrence:random_seed=4183927420:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.77/1.52 % (786007)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3621012188:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.77/1.52 % (786001)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=2284364917:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.77/1.52 % (786008)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1495156287:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.77/1.52 % (786003)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2904864955:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.77/1.52 % (786009)dis-21_1_sil=8000:lcm=predicate:random_seed=4052494833: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)
% 3.77/1.52 % (786005)Refutation not found, incomplete strategy
% 3.77/1.52 % (786005)------------------------------
% 3.77/1.52 % (786005)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.52 % (786007)Refutation not found, incomplete strategy
% 3.77/1.52 % (786007)------------------------------
% 3.77/1.52 % (786007)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.52 % (786007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.52 % (786005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.52 % (786007)CaDiCaL version: 2.1.3
% 3.77/1.52 % (786005)CaDiCaL version: 2.1.3
% 3.77/1.52 % (786007)Termination reason: Refutation not found, incomplete strategy
% 3.77/1.52 % (786007)Time elapsed: 0.001 s
% 3.77/1.52 % (786005)Termination reason: Refutation not found, incomplete strategy
% 3.77/1.52 % (786005)Time elapsed: 0.001 s
% 3.77/1.52 % (786007)Peak memory usage: 86 MB
% 3.77/1.52 % (786005)Peak memory usage: 86 MB
% 3.77/1.52 % (786009)Refutation not found, incomplete strategy
% 3.77/1.52 % (786009)------------------------------
% 3.77/1.52 % (786009)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.52 % (786009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.52 % (786009)CaDiCaL version: 2.1.3
% 3.77/1.52 % (786009)Termination reason: Refutation not found, incomplete strategy
% 3.77/1.52 % (786009)Time elapsed: 0.001 s
% 3.77/1.52 % (786009)Peak memory usage: 88 MB
% 3.77/1.52 % (786008)First to succeed.
% 3.77/1.52 % (786008)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-785920"
% 3.77/1.52 % (786009)------------------------------
% 3.77/1.52 % (786009)------------------------------
% 3.77/1.52 % (786007)------------------------------
% 3.77/1.52 % (786007)------------------------------
% 3.77/1.52 % (786005)------------------------------
% 3.77/1.52 % (786005)------------------------------
% 3.77/1.52 % (786008)Refutation found. Thanks to Tanya!
% 3.77/1.52 % SZS status Unsatisfiable for theBenchmark
% 3.77/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 3.77/1.52 % (786008)------------------------------
% 3.77/1.52 % (786008)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.52 % (786008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.52 % (786008)CaDiCaL version: 2.1.3
% 3.77/1.52 % (786008)Termination reason: Refutation
% 3.77/1.52 % (786008)Time elapsed: 0.008 s
% 3.77/1.52 % (786008)Peak memory usage: 88 MB
% 3.77/1.52 % (786008)Instructions burned: 9 (million)
% 3.77/1.52 % (786008)------------------------------
% 3.77/1.52 % (786008)------------------------------
% 3.77/1.52 % (785920)Success in time 0.444 s
% 3.77/1.52 % Vampire exiting
%------------------------------------------------------------------------------