%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN005-2 : 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 : n009.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 0.16s 1.91s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of formulae : 18 ( 14 unt; 0 def)
% Number of atoms : 27 ( 2 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal) ).
fof(f2,axiom,
! [X0,X1] :
( ~ quotient(X0,X1,zero)
| less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_quotient) ).
fof(f4,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ quotient(X5,X4,X6)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X3,X5)
| ~ quotient(X0,X1,X2)
| ~ quotient(X2,X3,X7)
| less_equal(X6,X7) ),
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,axiom,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure) ).
fof(f11,axiom,
! [X0] : quotient(zero,X0,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
fof(f13,axiom,
! [X0] : quotient(X0,zero,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
fof(f14,axiom,
less_equal(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xLEy) ).
fof(f15,axiom,
less_equal(y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',yLEz) ).
fof(f16,negated_conjecture,
~ less_equal(x,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_transitivity_of_less_equal) ).
fof(f17,plain,
~ quotient(x,z,zero),
inference(unit_resulting_resolution,[],[f2,f16]) ).
fof(f39,plain,
quotient(x,y,zero),
inference(unit_resulting_resolution,[],[f1,f14]) ).
fof(f40,plain,
quotient(y,z,zero),
inference(unit_resulting_resolution,[],[f1,f15]) ).
fof(f305,plain,
less_equal(divide(x,z),zero),
inference(unit_resulting_resolution,[],[f4,f39,f11,f8,f13,f40]) ).
fof(f502,plain,
zero = divide(x,z),
inference(unit_resulting_resolution,[],[f6,f5,f305]) ).
fof(f545,plain,
quotient(x,z,zero),
inference(superposition,[],[f8,f502]) ).
fof(f546,plain,
$false,
inference(forward_subsumption_resolution,[],[f545,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN005-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n009.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sun Sep 27 10:49:50 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 0.16/1.91 % (1855289)Input is clausal, will run a generic CNF schedule.
% 0.16/1.91 % (1855320)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1750736134:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.16/1.91 % (1855321)dis-21_1_sil=8000:lcm=predicate:random_seed=707268242: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)
% 0.16/1.91 % (1855318)lrs+10_1_sil=8000:sp=occurrence:random_seed=3118668055:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.16/1.91 % (1855318)Refutation not found, incomplete strategy
% 0.16/1.91 % (1855318)------------------------------
% 0.16/1.91 % (1855318)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.91 % (1855318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.91 % (1855318)CaDiCaL version: 2.1.3
% 0.16/1.91 % (1855318)Termination reason: Refutation not found, incomplete strategy
% 0.16/1.91 % (1855318)Time elapsed: 0.001 s
% 0.16/1.91 % (1855318)Peak memory usage: 87 MB
% 0.16/1.91 % (1855316)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2106568472:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.16/1.91 % (1855319)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1874654769:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.16/1.91 % (1855321)Instruction limit reached!
% 0.16/1.91 % (1855321)------------------------------
% 0.16/1.91 % (1855321)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.91 % (1855321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.91 % (1855315)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=3474173900:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.16/1.91 % (1855317)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1393010853:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.16/1.91 % (1855321)CaDiCaL version: 2.1.3
% 0.16/1.91 % (1855321)Termination reason: Instruction limit
% 0.16/1.91 % (1855321)Termination phase: Saturation
% 0.16/1.91 % (1855321)Time elapsed: 0.077 s
% 0.16/1.91 % (1855321)Peak memory usage: 88 MB
% 0.16/1.91 % (1855321)Instructions burned: 118 (million)
% 0.16/1.91 % (1855320)Instruction limit reached!
% 0.16/1.91 % (1855320)------------------------------
% 0.16/1.91 % (1855320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.91 % (1855320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.91 % (1855320)CaDiCaL version: 2.1.3
% 0.16/1.91 % (1855320)Termination reason: Instruction limit
% 0.16/1.91 % (1855320)Termination phase: Saturation
% 0.16/1.91 % (1855320)Time elapsed: 0.080 s
% 0.16/1.91 % (1855320)Peak memory usage: 88 MB
% 0.16/1.91 % (1855320)Instructions burned: 181 (million)
% 0.16/1.91 % (1855319)Refutation not found, incomplete strategy
% 0.16/1.91 % (1855319)------------------------------
% 0.16/1.91 % (1855319)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.91 % (1855319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.91 % (1855319)CaDiCaL version: 2.1.3
% 0.16/1.91 % (1855319)Termination reason: Refutation not found, incomplete strategy
% 0.16/1.91 % (1855319)Time elapsed: 0.006 s
% 0.16/1.91 % (1855319)Peak memory usage: 87 MB
% 0.16/1.91 % (1855319)Instructions burned: 7 (million)
% 0.16/1.91 % (1855332)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1036281487:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.16/1.91 % (1855332)Refutation not found, incomplete strategy
% 0.16/1.91 % (1855332)------------------------------
% 0.16/1.91 % (1855332)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.91 % (1855332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.91 % (1855332)CaDiCaL version: 2.1.3
% 0.16/1.91 % (1855332)Termination reason: Refutation not found, incomplete strategy
% 0.16/1.91 % (1855332)Time elapsed: 0.001 s
% 0.16/1.91 % (1855332)Peak memory usage: 88 MB
% 0.16/1.91 % (1855333)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=4077665300:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 0.16/1.91 % (1855333)First to succeed.
% 0.16/1.91 % (1855333)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1855289"
% 0.16/1.91 % (1855319)------------------------------
% 0.16/1.91 % (1855319)------------------------------
% 0.16/1.91 % (1855318)------------------------------
% 0.16/1.91 % (1855318)------------------------------
% 0.16/1.91 % (1855332)------------------------------
% 0.16/1.91 % (1855332)------------------------------
% 0.16/1.91 % (1855340)lrs+10_64_to=lpo:sil=8000:random_seed=879111707:i=126:bd=preordered_2993 on theBenchmark for (2993ds/126Mi)
% 0.16/1.91 % (1855340)Also succeeded, but the first one will report.
% 0.16/1.91 % (1855341)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2718573594:avsq=on:i=194:fgj=on:bd=preordered_2993 on theBenchmark for (2993ds/194Mi)
% 0.16/1.91 % (1855339)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2439549896:st=4:i=219:sd=3:ss=axioms_2993 on theBenchmark for (2993ds/219Mi)
% 0.16/1.91 % (1855339)Refutation not found, incomplete strategy
% 0.16/1.91 % (1855339)------------------------------
% 0.16/1.91 % (1855339)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.91 % (1855339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.91 % (1855339)CaDiCaL version: 2.1.3
% 0.16/1.91 % (1855339)Termination reason: Refutation not found, incomplete strategy
% 0.16/1.91 % (1855339)Time elapsed: 0.001 s
% 0.16/1.91 % (1855339)Peak memory usage: 87 MB
% 0.16/1.91 % (1855333)Refutation found. Thanks to Tanya!
% 0.16/1.91 % SZS status Unsatisfiable for theBenchmark
% 0.16/1.91 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.91 % (1855333)------------------------------
% 0.16/1.91 % (1855333)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.91 % (1855333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.91 % (1855333)CaDiCaL version: 2.1.3
% 0.16/1.91 % (1855333)Termination reason: Refutation
% 0.16/1.91 % (1855333)Time elapsed: 0.028 s
% 0.16/1.91 % (1855333)Peak memory usage: 88 MB
% 0.16/1.91 % (1855333)Instructions burned: 29 (million)
% 0.16/1.91 % (1855333)------------------------------
% 0.16/1.91 % (1855333)------------------------------
% 0.16/1.91 % (1855289)Success in time 0.788 s
% 0.16/1.91 % Vampire exiting
%------------------------------------------------------------------------------