%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN012-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 10:19:11 AM UTC 2026
% Result : Unsatisfiable 2.64s 1.33s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 18 ( 12 unt; 0 def)
% Number of atoms : 25 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 8 ~; 7 |; 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ less_equal(X0,X1)
| divide(X0,X1) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal1) ).
fof(f2,axiom,
! [X0,X1] :
( divide(X0,X1) != zero
| less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal2) ).
fof(f3,axiom,
! [X0,X1] : less_equal(divide(X0,X1),X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',quotient_property) ).
fof(f5,axiom,
! [X0] : less_equal(zero,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_smallest) ).
fof(f6,axiom,
! [X0,X1] :
( ~ less_equal(X1,X0)
| ~ less_equal(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_and_equal) ).
fof(f8,negated_conjecture,
~ less_equal(a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_LE_a) ).
fof(f11,plain,
! [X0,X1] : zero = divide(divide(X0,X1),X0),
inference(resolution,[],[f1,f3]) ).
fof(f15,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f45,plain,
! [X0,X1] : less_equal(divide(divide(X0,X0),divide(X1,X0)),zero),
inference(superposition,[],[f4,f11]) ).
fof(f114,plain,
! [X0] : less_equal(divide(divide(X0,X0),zero),zero),
inference(superposition,[],[f45,f11]) ).
fof(f165,plain,
! [X0] : zero = divide(divide(X0,X0),zero),
inference(resolution,[],[f114,f15]) ).
fof(f200,plain,
! [X0] :
( zero != zero
| less_equal(divide(X0,X0),zero) ),
inference(superposition,[],[f2,f165]) ).
fof(f216,plain,
! [X0] : less_equal(divide(X0,X0),zero),
inference(trivial_inequality_removal,[],[f200]) ).
fof(f255,plain,
! [X0] : zero = divide(X0,X0),
inference(resolution,[],[f216,f15]) ).
fof(f335,plain,
! [X0] :
( zero != zero
| less_equal(X0,X0) ),
inference(superposition,[],[f2,f255]) ).
fof(f367,plain,
! [X0] : less_equal(X0,X0),
inference(trivial_inequality_removal,[],[f335]) ).
fof(f467,plain,
$false,
inference(resolution,[],[f367,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN012-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n008.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 10:52:09 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.64/1.33 % (1047299)Input is clausal, will run a generic CNF schedule.
% 2.64/1.33 % (1047307)lrs+10_1_sil=8000:sp=occurrence:random_seed=1509659965:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.64/1.33 % (1047307)First to succeed.
% 2.64/1.33 % (1047307)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1047299"
% 2.64/1.33 % (1047309)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1307796408:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.64/1.33 % (1047308)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4272238318:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.64/1.33 % (1047305)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1340616075:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.64/1.33 % (1047310)dis-21_1_sil=8000:lcm=predicate:random_seed=1780830823: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)
% 2.64/1.33 % (1047304)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=1946951232:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.64/1.33 % (1047306)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=961605754:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.64/1.33 % (1047308)Refutation not found, incomplete strategy
% 2.64/1.33 % (1047308)------------------------------
% 2.64/1.33 % (1047308)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.33 % (1047308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.33 % (1047308)CaDiCaL version: 2.1.3
% 2.64/1.33 % (1047308)Termination reason: Refutation not found, incomplete strategy
% 2.64/1.33 % (1047308)Time elapsed: 0.0000 s
% 2.64/1.33 % (1047308)Peak memory usage: 86 MB
% 2.64/1.33 % (1047310)Refutation not found, incomplete strategy
% 2.64/1.33 % (1047310)------------------------------
% 2.64/1.33 % (1047310)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.33 % (1047310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.33 % (1047310)CaDiCaL version: 2.1.3
% 2.64/1.33 % (1047310)Termination reason: Refutation not found, incomplete strategy
% 2.64/1.33 % (1047310)Time elapsed: 0.001 s
% 2.64/1.33 % (1047310)Peak memory usage: 87 MB
% 2.64/1.33 % (1047309)Also succeeded, but the first one will report.
% 2.64/1.33 % (1047307)Refutation found. Thanks to Tanya!
% 2.64/1.33 % SZS status Unsatisfiable for theBenchmark
% 2.64/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.64/1.33 % (1047307)------------------------------
% 2.64/1.33 % (1047307)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.33 % (1047307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.33 % (1047307)CaDiCaL version: 2.1.3
% 2.64/1.33 % (1047307)Termination reason: Refutation
% 2.64/1.33 % (1047307)Time elapsed: 0.005 s
% 2.64/1.33 % (1047307)Peak memory usage: 88 MB
% 2.64/1.33 % (1047307)Instructions burned: 13 (million)
% 2.64/1.33 % (1047307)------------------------------
% 2.64/1.33 % (1047307)------------------------------
% 2.64/1.33 % (1047299)Success in time 0.287 s
% 2.64/1.33 % Vampire exiting
%------------------------------------------------------------------------------