%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN006-3 : 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 : n019.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 10:19:06 AM UTC 2026
% Result : Unsatisfiable 2.70s 1.05s
% Output : Refutation 2.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 16 unt; 0 def)
% Number of atoms : 33 ( 10 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 : 23 ( 23 !; 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(divide(a,b),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_divide_b_LE_d) ).
fof(f9,negated_conjecture,
~ less_equal(divide(a,d),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_divide_d_LE_b) ).
fof(f15,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ less_equal(X2,X1)
| less_equal(divide(divide(X0,X1),zero),divide(divide(X0,X2),X1)) ),
inference(superposition,[],[f4,f1]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ less_equal(divide(X0,X2),X1)
| less_equal(divide(divide(X0,X1),divide(X2,X1)),zero) ),
inference(superposition,[],[f4,f1]) ).
fof(f46,plain,
! [X0] : zero = divide(zero,X0),
inference(resolution,[],[f15,f3]) ).
fof(f77,plain,
! [X2,X0,X1] : less_equal(divide(divide(X0,X1),zero),divide(divide(X0,divide(X1,X2)),X1)),
inference(resolution,[],[f31,f3]) ).
fof(f139,plain,
less_equal(divide(divide(a,d),divide(b,d)),zero),
inference(resolution,[],[f34,f8]) ).
fof(f232,plain,
zero = divide(divide(a,d),divide(b,d)),
inference(resolution,[],[f139,f15]) ).
fof(f707,plain,
less_equal(divide(divide(divide(a,d),b),zero),divide(zero,b)),
inference(superposition,[],[f77,f232]) ).
fof(f743,plain,
less_equal(divide(divide(divide(a,d),b),zero),zero),
inference(forward_demodulation,[],[f707,f46]) ).
fof(f1072,plain,
zero = divide(divide(divide(a,d),b),zero),
inference(resolution,[],[f743,f15]) ).
fof(f1720,plain,
( zero != zero
| less_equal(divide(divide(a,d),b),zero) ),
inference(superposition,[],[f2,f1072]) ).
fof(f1756,plain,
less_equal(divide(divide(a,d),b),zero),
inference(trivial_inequality_removal,[],[f1720]) ).
fof(f1819,plain,
zero = divide(divide(a,d),b),
inference(resolution,[],[f1756,f15]) ).
fof(f1872,plain,
( zero != zero
| less_equal(divide(a,d),b) ),
inference(superposition,[],[f2,f1819]) ).
fof(f1909,plain,
less_equal(divide(a,d),b),
inference(trivial_inequality_removal,[],[f1872]) ).
fof(f1929,plain,
$false,
inference(forward_subsumption_resolution,[],[f1909,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n019.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 10:50:54 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.70/1.05 % (2908191)Input is clausal, will run a generic CNF schedule.
% 2.70/1.05 % (2908201)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1607914345:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.70/1.05 % (2908199)lrs+10_1_sil=8000:sp=occurrence:random_seed=2822725663:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.70/1.05 % (2908197)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=937388496:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.70/1.05 % (2908196)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=2580667378:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.70/1.05 % (2908200)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1092711921:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.70/1.05 % (2908198)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4190067062:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.70/1.05 % (2908202)dis-21_1_sil=8000:lcm=predicate:random_seed=3271043162: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)
% 2.70/1.05 % (2908200)Refutation not found, incomplete strategy
% 2.70/1.05 % (2908200)------------------------------
% 2.70/1.05 % (2908200)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.05 % (2908200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.05 % (2908200)CaDiCaL version: 2.1.3
% 2.70/1.05 % (2908200)Termination reason: Refutation not found, incomplete strategy
% 2.70/1.05 % (2908200)Time elapsed: 0.001 s
% 2.70/1.05 % (2908200)Peak memory usage: 87 MB
% 2.70/1.05 % (2908202)Refutation not found, incomplete strategy
% 2.70/1.05 % (2908202)------------------------------
% 2.70/1.05 % (2908202)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.05 % (2908202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.05 % (2908202)CaDiCaL version: 2.1.3
% 2.70/1.05 % (2908202)Termination reason: Refutation not found, incomplete strategy
% 2.70/1.05 % (2908202)Time elapsed: 0.001 s
% 2.70/1.05 % (2908202)Peak memory usage: 88 MB
% 2.70/1.05 % (2908201)First to succeed.
% 2.70/1.05 % (2908201)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2908191"
% 2.70/1.05 % (2908199)Also succeeded, but the first one will report.
% 2.70/1.05 % (2908201)Refutation found. Thanks to Tanya!
% 2.70/1.05 % SZS status Unsatisfiable for theBenchmark
% 2.70/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 2.70/1.05 % (2908201)------------------------------
% 2.70/1.05 % (2908201)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.05 % (2908201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.05 % (2908201)CaDiCaL version: 2.1.3
% 2.70/1.05 % (2908201)Termination reason: Refutation
% 2.70/1.05 % (2908201)Time elapsed: 0.018 s
% 2.70/1.05 % (2908201)Peak memory usage: 89 MB
% 2.70/1.05 % (2908201)Instructions burned: 54 (million)
% 2.70/1.05 % (2908201)------------------------------
% 2.70/1.05 % (2908201)------------------------------
% 2.70/1.05 % (2908191)Success in time 0.336 s
% 2.70/1.05 % Vampire exiting
%------------------------------------------------------------------------------