%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN005-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 8.68s 2.26s
% Output : Refutation 8.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 33 ( 20 unt; 0 def)
% Number of atoms : 58 ( 10 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 51 ( 26 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 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 : 49 ( 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal) ).
fof(f2,axiom,
! [X0,X1] :
( ~ quotient(X0,X1,zero)
| less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_equal_quotient) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| less_equal(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divisor_existence) ).
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/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(f8,axiom,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2)
| X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_defined) ).
fof(f10,axiom,
less_equal(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xLEy) ).
fof(f11,axiom,
less_equal(y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',yLEz) ).
fof(f12,negated_conjecture,
~ less_equal(x,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_transitivity_of_less_equal) ).
fof(f14,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[],[f3,f8]) ).
fof(f17,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f41,plain,
! [X0] : zero = divide(zero,X0),
inference(resolution,[],[f17,f14]) ).
fof(f43,plain,
! [X0] : quotient(zero,X0,zero),
inference(superposition,[],[f8,f41]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| divide(X0,X1) = X2 ),
inference(resolution,[],[f9,f8]) ).
fof(f54,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| zero = divide(X0,X1) ),
inference(resolution,[],[f47,f1]) ).
fof(f59,plain,
zero = divide(x,y),
inference(resolution,[],[f54,f10]) ).
fof(f60,plain,
zero = divide(y,z),
inference(resolution,[],[f54,f11]) ).
fof(f63,plain,
quotient(x,y,zero),
inference(superposition,[],[f8,f59]) ).
fof(f70,plain,
quotient(y,z,zero),
inference(superposition,[],[f8,f60]) ).
fof(f128,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ quotient(X5,X1,X6)
| ~ quotient(X3,X1,X4)
| ~ quotient(X3,X0,X5)
| ~ quotient(X0,X1,X2)
| less_equal(divide(X4,X2),X6) ),
inference(resolution,[],[f4,f8]) ).
fof(f138,plain,
! [X2,X3,X0,X1,X4] :
( ~ quotient(X3,X1,X4)
| ~ quotient(X0,X3,zero)
| ~ quotient(X0,X1,X2)
| less_equal(divide(X2,X4),zero) ),
inference(resolution,[],[f128,f43]) ).
fof(f148,plain,
! [X0,X1] :
( ~ quotient(X0,z,X1)
| ~ quotient(X0,y,zero)
| less_equal(divide(X1,zero),zero) ),
inference(resolution,[],[f138,f70]) ).
fof(f244,plain,
! [X0] :
( ~ quotient(X0,y,zero)
| less_equal(divide(divide(X0,z),zero),zero) ),
inference(resolution,[],[f148,f8]) ).
fof(f253,plain,
less_equal(divide(divide(x,z),zero),zero),
inference(resolution,[],[f244,f63]) ).
fof(f255,plain,
zero = divide(divide(x,z),zero),
inference(resolution,[],[f253,f17]) ).
fof(f266,plain,
quotient(divide(x,z),zero,zero),
inference(superposition,[],[f8,f255]) ).
fof(f267,plain,
less_equal(divide(x,z),zero),
inference(resolution,[],[f266,f2]) ).
fof(f275,plain,
zero = divide(x,z),
inference(resolution,[],[f267,f17]) ).
fof(f295,plain,
quotient(x,z,zero),
inference(superposition,[],[f8,f275]) ).
fof(f297,plain,
less_equal(x,z),
inference(resolution,[],[f295,f2]) ).
fof(f305,plain,
$false,
inference(forward_subsumption_resolution,[],[f297,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN005-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n009.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 10:49:50 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 8.68/2.26 % (1855241)Input is clausal, will run a generic CNF schedule.
% 8.68/2.26 % (1855297)lrs+10_1_sil=8000:sp=occurrence:random_seed=2317800022:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 8.68/2.26 % (1855297)Refutation not found, incomplete strategy
% 8.68/2.26 % (1855297)------------------------------
% 8.68/2.26 % (1855297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.26 % (1855297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.26 % (1855297)CaDiCaL version: 2.1.3
% 8.68/2.26 % (1855297)Termination reason: Refutation not found, incomplete strategy
% 8.68/2.26 % (1855297)Time elapsed: 0.0000 s
% 8.68/2.26 % (1855297)Peak memory usage: 87 MB
% 8.68/2.26 % (1855294)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=923195872:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 8.68/2.26 % (1855296)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1335928831:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 8.68/2.26 % (1855295)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=175437842:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 8.68/2.26 % (1855300)dis-21_1_sil=8000:lcm=predicate:random_seed=494766446: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)
% 8.68/2.26 % (1855299)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1794143116:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 8.68/2.26 % (1855300)Refutation not found, incomplete strategy
% 8.68/2.26 % (1855300)------------------------------
% 8.68/2.26 % (1855300)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.26 % (1855300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.26 % (1855300)CaDiCaL version: 2.1.3
% 8.68/2.26 % (1855300)Termination reason: Refutation not found, incomplete strategy
% 8.68/2.26 % (1855300)Time elapsed: 0.005 s
% 8.68/2.26 % (1855300)Peak memory usage: 88 MB
% 8.68/2.26 % (1855300)Instructions burned: 6 (million)
% 8.68/2.26 % (1855298)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2269132988:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 8.68/2.26 % (1855298)Refutation not found, incomplete strategy
% 8.68/2.26 % (1855298)------------------------------
% 8.68/2.26 % (1855298)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.26 % (1855298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.26 % (1855298)CaDiCaL version: 2.1.3
% 8.68/2.26 % (1855298)Termination reason: Refutation not found, incomplete strategy
% 8.68/2.26 % (1855298)Time elapsed: 0.001 s
% 8.68/2.26 % (1855298)Peak memory usage: 87 MB
% 8.68/2.26 % (1855297)------------------------------
% 8.68/2.26 % (1855297)------------------------------
% 8.68/2.26 % (1855299)Instruction limit reached!
% 8.68/2.26 % (1855299)------------------------------
% 8.68/2.26 % (1855299)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.26 % (1855299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.26 % (1855299)CaDiCaL version: 2.1.3
% 8.68/2.26 % (1855299)Termination reason: Instruction limit
% 8.68/2.26 % (1855299)Termination phase: Saturation
% 8.68/2.26 % (1855299)Time elapsed: 0.115 s
% 8.68/2.26 % (1855299)Peak memory usage: 89 MB
% 8.68/2.26 % (1855299)Instructions burned: 180 (million)
% 8.68/2.26 % (1855308)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=3372129279:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 8.68/2.26 % (1855308)Refutation not found, incomplete strategy
% 8.68/2.26 % (1855308)------------------------------
% 8.68/2.26 % (1855308)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.26 % (1855308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.26 % (1855308)CaDiCaL version: 2.1.3
% 8.68/2.26 % (1855308)Termination reason: Refutation not found, incomplete strategy
% 8.68/2.26 % (1855308)Time elapsed: 0.001 s
% 8.68/2.26 % (1855308)Peak memory usage: 88 MB
% 8.68/2.26 % (1855300)------------------------------
% 8.68/2.26 % (1855300)------------------------------
% 8.68/2.26 % (1855309)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3782442962: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)
% 8.68/2.26 % (1855298)------------------------------
% 8.68/2.26 % (1855298)------------------------------
% 8.68/2.26 % (1855308)------------------------------
% 8.68/2.26 % (1855308)------------------------------
% 8.68/2.26 % (1855309)Instruction limit reached!
% 8.68/2.26 % (1855309)------------------------------
% 8.68/2.26 % (1855309)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.26 % (1855309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.26 % (1855309)CaDiCaL version: 2.1.3
% 8.68/2.26 % (1855309)Termination reason: Instruction limit
% 8.68/2.26 % (1855309)Termination phase: Saturation
% 8.68/2.26 % (1855309)Time elapsed: 0.142 s
% 8.68/2.26 % (1855309)Peak memory usage: 89 MB
% 8.68/2.26 % (1855309)Instructions burned: 192 (million)
% 8.68/2.26 % (1855311)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3545754433:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 8.68/2.26 % (1855311)Refutation not found, incomplete strategy
% 8.68/2.26 % (1855311)------------------------------
% 8.68/2.26 % (1855311)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.26 % (1855311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.26 % (1855311)CaDiCaL version: 2.1.3
% 8.68/2.26 % (1855311)Termination reason: Refutation not found, incomplete strategy
% 8.68/2.26 % (1855311)Time elapsed: 0.002 s
% 8.68/2.26 % (1855311)Peak memory usage: 88 MB
% 8.68/2.26 % (1855313)lrs+10_64_to=lpo:sil=8000:random_seed=85098049:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 8.68/2.26 % (1855313)First to succeed.
% 8.68/2.26 % (1855313)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1855241"
% 8.68/2.26 % (1855322)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2100155295:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 8.68/2.26 % (1855322)Also succeeded, but the first one will report.
% 8.68/2.26 % (1855323)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=1151581463:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 8.68/2.26 % (1855323)Also succeeded, but the first one will report.
% 8.68/2.26 % (1855295)Also succeeded, but the first one will report.
% 8.68/2.26 % (1855294)Also succeeded, but the first one will report.
% 8.68/2.26 % (1855296)Also succeeded, but the first one will report.
% 8.68/2.26 % (1855311)------------------------------
% 8.68/2.26 % (1855311)------------------------------
% 8.68/2.26 % (1855313)Refutation found. Thanks to Tanya!
% 8.68/2.26 % SZS status Unsatisfiable for theBenchmark
% 8.68/2.26 % SZS output start Proof for theBenchmark
% See solution above
% 8.68/2.26 % (1855313)------------------------------
% 8.68/2.26 % (1855313)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.26 % (1855313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.26 % (1855313)CaDiCaL version: 2.1.3
% 8.68/2.26 % (1855313)Termination reason: Refutation
% 8.68/2.26 % (1855313)Time elapsed: 0.014 s
% 8.68/2.26 % (1855313)Peak memory usage: 88 MB
% 8.68/2.26 % (1855313)Instructions burned: 11 (million)
% 8.68/2.26 % (1855313)------------------------------
% 8.68/2.26 % (1855313)------------------------------
% 8.68/2.26 % (1855241)Success in time 1.165 s
% 8.68/2.26 % Vampire exiting
%------------------------------------------------------------------------------