%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN006-1 : 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 : n003.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 7.93s 2.07s
% Output : Refutation 7.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 26 ( 21 unt; 0 def)
% Number of atoms : 36 ( 4 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 25 ( 25 !; 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(f10,axiom,
quotient(x,y,xQy),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQy) ).
fof(f11,axiom,
less_equal(xQy,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQyLEz) ).
fof(f12,axiom,
quotient(x,z,xQz),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQz) ).
fof(f13,negated_conjecture,
~ less_equal(xQz,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_xQzLEy) ).
fof(f16,plain,
quotient(xQy,z,zero),
inference(unit_resulting_resolution,[],[f1,f11]) ).
fof(f31,plain,
less_equal(divide(xQz,divide(y,z)),zero),
inference(unit_resulting_resolution,[],[f4,f12,f16,f10,f8,f8]) ).
fof(f108,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(unit_resulting_resolution,[],[f3,f8]) ).
fof(f109,plain,
! [X0,X1] : quotient(divide(X0,X1),X0,zero),
inference(unit_resulting_resolution,[],[f1,f108]) ).
fof(f150,plain,
zero = divide(xQz,divide(y,z)),
inference(unit_resulting_resolution,[],[f6,f31,f5]) ).
fof(f156,plain,
! [X0] : quotient(zero,X0,zero),
inference(unit_resulting_resolution,[],[f1,f5]) ).
fof(f163,plain,
quotient(xQz,divide(y,z),zero),
inference(superposition,[],[f8,f150]) ).
fof(f376,plain,
~ quotient(xQz,y,zero),
inference(unit_resulting_resolution,[],[f2,f13]) ).
fof(f382,plain,
less_equal(divide(divide(xQz,y),zero),zero),
inference(unit_resulting_resolution,[],[f4,f156,f8,f8,f109,f163]) ).
fof(f442,plain,
zero = divide(divide(xQz,y),zero),
inference(unit_resulting_resolution,[],[f6,f5,f382]) ).
fof(f449,plain,
quotient(divide(xQz,y),zero,zero),
inference(superposition,[],[f8,f442]) ).
fof(f450,plain,
less_equal(divide(xQz,y),zero),
inference(unit_resulting_resolution,[],[f2,f449]) ).
fof(f544,plain,
zero = divide(xQz,y),
inference(unit_resulting_resolution,[],[f6,f5,f450]) ).
fof(f553,plain,
quotient(xQz,y,zero),
inference(superposition,[],[f8,f544]) ).
fof(f554,plain,
$false,
inference(forward_subsumption_resolution,[],[f553,f376]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 10:52:32 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 5.95/1.87 % (336430)Input is clausal, will run a generic CNF schedule.
% 5.95/1.87 % (336437)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4080032932:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.95/1.87 % (336436)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=802829570:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.95/1.87 % (336440)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=382921806:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.95/1.87 % (336435)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=138862988:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.95/1.87 % (336438)lrs+10_1_sil=8000:sp=occurrence:random_seed=3718168116:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.95/1.87 % (336439)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=434753028:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.95/1.87 % (336439)Refutation not found, incomplete strategy
% 5.95/1.87 % (336439)------------------------------
% 5.95/1.87 % (336439)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.95/1.87 % (336439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.95/1.87 % (336439)CaDiCaL version: 2.1.3
% 5.95/1.87 % (336439)Termination reason: Refutation not found, incomplete strategy
% 5.95/1.87 % (336439)Time elapsed: 0.003 s
% 5.95/1.87 % (336439)Peak memory usage: 88 MB
% 5.95/1.87 % (336439)Instructions burned: 3 (million)
% 5.95/1.87 % (336441)dis-21_1_sil=8000:lcm=predicate:random_seed=3821816519: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)
% 5.95/1.87 % (336441)Instruction limit reached!
% 5.95/1.87 % (336441)------------------------------
% 5.95/1.87 % (336441)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.95/1.87 % (336441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.95/1.87 % (336441)CaDiCaL version: 2.1.3
% 5.95/1.87 % (336441)Termination reason: Instruction limit
% 5.95/1.87 % (336441)Termination phase: Saturation
% 5.95/1.87 % (336441)Time elapsed: 0.063 s
% 5.95/1.87 % (336441)Peak memory usage: 88 MB
% 5.95/1.87 % (336441)Instructions burned: 139 (million)
% 5.95/1.87 % (336438)Instruction limit reached!
% 5.95/1.87 % (336438)------------------------------
% 5.95/1.87 % (336438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.95/1.87 % (336438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.95/1.87 % (336438)CaDiCaL version: 2.1.3
% 5.95/1.87 % (336438)Termination reason: Instruction limit
% 5.95/1.87 % (336438)Termination phase: Saturation
% 5.95/1.87 % (336438)Time elapsed: 0.069 s
% 5.95/1.87 % (336438)Peak memory usage: 89 MB
% 5.95/1.87 % (336438)Instructions burned: 107 (million)
% 5.95/1.87 % (336440)Instruction limit reached!
% 5.95/1.87 % (336440)------------------------------
% 5.95/1.87 % (336440)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.95/1.87 % (336440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.95/1.87 % (336440)CaDiCaL version: 2.1.3
% 5.95/1.87 % (336440)Termination reason: Instruction limit
% 5.95/1.87 % (336440)Termination phase: Saturation
% 5.95/1.87 % (336440)Time elapsed: 0.112 s
% 5.95/1.87 % (336440)Peak memory usage: 89 MB
% 5.95/1.87 % (336440)Instructions burned: 181 (million)
% 5.95/1.87 % (336450)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=403575209: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)
% 5.95/1.87 % (336449)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=3458380128:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.95/1.87 % (336449)Refutation not found, incomplete strategy
% 5.95/1.87 % (336449)------------------------------
% 5.95/1.87 % (336449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.95/1.87 % (336449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.95/1.87 % (336449)CaDiCaL version: 2.1.3
% 5.95/1.87 % (336449)Termination reason: Refutation not found, incomplete strategy
% 7.93/2.07 % (336449)Time elapsed: 0.004 s
% 7.93/2.07 % (336449)Peak memory usage: 88 MB
% 7.93/2.07 % (336449)Instructions burned: 4 (million)
% 7.93/2.07 % (336451)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2721975818:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 7.93/2.07 % (336439)------------------------------
% 7.93/2.07 % (336439)------------------------------
% 7.93/2.07 % (336451)Refutation not found, incomplete strategy
% 7.93/2.07 % (336451)------------------------------
% 7.93/2.07 % (336451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.93/2.07 % (336451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.93/2.07 % (336451)CaDiCaL version: 2.1.3
% 7.93/2.07 % (336451)Termination reason: Refutation not found, incomplete strategy
% 7.93/2.07 % (336451)Time elapsed: 0.004 s
% 7.93/2.07 % (336451)Peak memory usage: 88 MB
% 7.93/2.07 % (336451)Instructions burned: 4 (million)
% 7.93/2.07 % (336450)Instruction limit reached!
% 7.93/2.07 % (336450)------------------------------
% 7.93/2.07 % (336450)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.93/2.07 % (336450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.93/2.07 % (336450)CaDiCaL version: 2.1.3
% 7.93/2.07 % (336450)Termination reason: Instruction limit
% 7.93/2.07 % (336450)Termination phase: Saturation
% 7.93/2.07 % (336450)Time elapsed: 0.103 s
% 7.93/2.07 % (336450)Peak memory usage: 89 MB
% 7.93/2.07 % (336450)Instructions burned: 189 (million)
% 7.93/2.07 % (336455)lrs+10_64_to=lpo:sil=8000:random_seed=422211261:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 7.93/2.07 % (336456)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=537138292:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 7.93/2.07 % (336449)------------------------------
% 7.93/2.07 % (336449)------------------------------
% 7.93/2.07 % (336455)Instruction limit reached!
% 7.93/2.07 % (336455)------------------------------
% 7.93/2.07 % (336455)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.93/2.07 % (336455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.93/2.07 % (336455)CaDiCaL version: 2.1.3
% 7.93/2.07 % (336455)Termination reason: Instruction limit
% 7.93/2.07 % (336455)Termination phase: Saturation
% 7.93/2.07 % (336455)Time elapsed: 0.081 s
% 7.93/2.07 % (336455)Peak memory usage: 88 MB
% 7.93/2.07 % (336455)Instructions burned: 127 (million)
% 7.93/2.07 % (336451)------------------------------
% 7.93/2.07 % (336451)------------------------------
% 7.93/2.07 % (336456)Instruction limit reached!
% 7.93/2.07 % (336456)------------------------------
% 7.93/2.07 % (336456)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.93/2.07 % (336456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.93/2.07 % (336456)CaDiCaL version: 2.1.3
% 7.93/2.07 % (336456)Termination reason: Instruction limit
% 7.93/2.07 % (336456)Termination phase: Saturation
% 7.93/2.07 % (336456)Time elapsed: 0.115 s
% 7.93/2.07 % (336456)Peak memory usage: 89 MB
% 7.93/2.07 % (336456)Instructions burned: 195 (million)
% 7.93/2.07 % (336459)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3694902043:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 7.93/2.07 % (336460)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=1236989722:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 7.93/2.07 % (336461)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=4186772622:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 7.93/2.07 % (336436)First to succeed.
% 7.93/2.07 % (336436)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-336430"
% 7.93/2.07 % (336461)Also succeeded, but the first one will report.
% 7.93/2.07 % (336435)Also succeeded, but the first one will report.
% 7.93/2.07 % (336459)Also succeeded, but the first one will report.
% 7.93/2.07 % (336462)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=46219883:i=107_2993 on theBenchmark for (2993ds/107Mi)
% 7.93/2.07 % (336462)Refutation not found, incomplete strategy
% 7.93/2.07 % (336462)------------------------------
% 7.93/2.07 % (336462)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.93/2.07 % (336462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.93/2.07 % (336462)CaDiCaL version: 2.1.3
% 7.93/2.07 % (336462)Termination reason: Refutation not found, incomplete strategy
% 7.93/2.07 % (336462)Time elapsed: 0.006 s
% 7.93/2.07 % (336462)Peak memory usage: 88 MB
% 7.93/2.07 % (336462)Instructions burned: 8 (million)
% 7.93/2.07 % (336436)Refutation found. Thanks to Tanya!
% 7.93/2.07 % SZS status Unsatisfiable for theBenchmark
% 7.93/2.07 % SZS output start Proof for theBenchmark
% See solution above
% 7.93/2.07 % (336436)------------------------------
% 7.93/2.07 % (336436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.93/2.07 % (336436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.93/2.07 % (336436)CaDiCaL version: 2.1.3
% 7.93/2.07 % (336436)Termination reason: Refutation
% 7.93/2.07 % (336436)Time elapsed: 0.642 s
% 7.93/2.07 % (336436)Peak memory usage: 128 MB
% 7.93/2.07 % (336436)Instructions burned: 955 (million)
% 7.93/2.07 % (336436)------------------------------
% 7.93/2.07 % (336436)------------------------------
% 7.93/2.07 % (336430)Success in time 1.042 s
% 7.93/2.07 % Vampire exiting
%------------------------------------------------------------------------------