%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN003-1 : 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 : n026.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 10:19:03 AM UTC 2026
% Result : Unsatisfiable 3.89s 1.61s
% Output : Refutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 28 ( 14 unt; 0 def)
% Number of atoms : 54 ( 9 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 53 ( 27 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 64 !; 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,negated_conjecture,
~ quotient(x,x,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_x_divide_x_is_zero) ).
fof(f13,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[],[f3,f8]) ).
fof(f15,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f19,plain,
! [X0] : zero = divide(zero,X0),
inference(resolution,[],[f15,f13]) ).
fof(f20,plain,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| divide(X0,X1) = X2 ),
inference(resolution,[],[f9,f8]) ).
fof(f23,plain,
! [X0] : quotient(zero,X0,zero),
inference(superposition,[],[f8,f19]) ).
fof(f24,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(f35,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| zero = divide(X0,X1) ),
inference(resolution,[],[f20,f1]) ).
fof(f39,plain,
! [X0,X1] : zero = divide(divide(X0,X1),X0),
inference(resolution,[],[f35,f13]) ).
fof(f46,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ quotient(X3,X1,X5)
| ~ quotient(X0,X3,X4)
| ~ quotient(X0,X1,X2)
| less_equal(divide(X2,X5),divide(X4,X1)) ),
inference(resolution,[],[f24,f8]) ).
fof(f68,plain,
! [X2,X3,X0,X1] :
( ~ quotient(X0,zero,X1)
| ~ quotient(X0,X2,X3)
| less_equal(divide(X3,zero),divide(X1,X2)) ),
inference(resolution,[],[f46,f23]) ).
fof(f128,plain,
! [X2,X0,X1] :
( less_equal(divide(X2,zero),divide(divide(X0,zero),X1))
| ~ quotient(X0,X1,X2) ),
inference(resolution,[],[f68,f8]) ).
fof(f367,plain,
! [X0,X1] :
( ~ quotient(X1,X1,X0)
| less_equal(divide(X0,zero),zero) ),
inference(superposition,[],[f128,f39]) ).
fof(f373,plain,
! [X0] : less_equal(divide(divide(X0,X0),zero),zero),
inference(resolution,[],[f367,f8]) ).
fof(f396,plain,
! [X0] : zero = divide(divide(X0,X0),zero),
inference(resolution,[],[f373,f15]) ).
fof(f434,plain,
! [X0] : quotient(divide(X0,X0),zero,zero),
inference(superposition,[],[f8,f396]) ).
fof(f482,plain,
! [X0] : less_equal(divide(X0,X0),zero),
inference(resolution,[],[f434,f2]) ).
fof(f521,plain,
! [X0] : zero = divide(X0,X0),
inference(resolution,[],[f482,f15]) ).
fof(f549,plain,
! [X0] : quotient(X0,X0,zero),
inference(superposition,[],[f8,f521]) ).
fof(f637,plain,
$false,
inference(resolution,[],[f549,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 10:52:11 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.89/1.61 % (2657011)Input is clausal, will run a generic CNF schedule.
% 3.89/1.61 % (2657037)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1794991182:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.89/1.61 % (2657041)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=908569069:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.89/1.61 % (2657038)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4026756707:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.89/1.61 % (2657039)lrs+10_1_sil=8000:sp=occurrence:random_seed=3708993379:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.89/1.61 % (2657036)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=35758449:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.89/1.61 % (2657042)dis-21_1_sil=8000:lcm=predicate:random_seed=3551301375: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)
% 3.89/1.61 % (2657039)First to succeed.
% 3.89/1.61 % (2657039)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2657011"
% 3.89/1.61 % (2657040)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1870023634:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.89/1.61 % (2657040)Refutation not found, incomplete strategy
% 3.89/1.61 % (2657040)------------------------------
% 3.89/1.61 % (2657040)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.61 % (2657040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.61 % (2657040)CaDiCaL version: 2.1.3
% 3.89/1.61 % (2657040)Termination reason: Refutation not found, incomplete strategy
% 3.89/1.61 % (2657040)Time elapsed: 0.002 s
% 3.89/1.61 % (2657040)Peak memory usage: 87 MB
% 3.89/1.61 % (2657040)Instructions burned: 2 (million)
% 3.89/1.61 % (2657042)Instruction limit reached!
% 3.89/1.61 % (2657042)------------------------------
% 3.89/1.61 % (2657042)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.61 % (2657042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.61 % (2657042)CaDiCaL version: 2.1.3
% 3.89/1.61 % (2657042)Termination reason: Instruction limit
% 3.89/1.61 % (2657042)Termination phase: Saturation
% 3.89/1.61 % (2657042)Time elapsed: 0.053 s
% 3.89/1.61 % (2657042)Peak memory usage: 88 MB
% 3.89/1.61 % (2657042)Instructions burned: 119 (million)
% 3.89/1.61 % (2657041)Instruction limit reached!
% 3.89/1.61 % (2657041)------------------------------
% 3.89/1.61 % (2657041)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.61 % (2657041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.61 % (2657041)CaDiCaL version: 2.1.3
% 3.89/1.61 % (2657041)Termination reason: Instruction limit
% 3.89/1.61 % (2657041)Termination phase: Saturation
% 3.89/1.61 % (2657041)Time elapsed: 0.181 s
% 3.89/1.61 % (2657041)Peak memory usage: 89 MB
% 3.89/1.61 % (2657041)Instructions burned: 180 (million)
% 3.89/1.61 % (2657050)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=1940963382:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.89/1.61 % (2657050)Refutation not found, incomplete strategy
% 3.89/1.61 % (2657050)------------------------------
% 3.89/1.61 % (2657050)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.61 % (2657050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.61 % (2657050)CaDiCaL version: 2.1.3
% 3.89/1.61 % (2657050)Termination reason: Refutation not found, incomplete strategy
% 3.89/1.61 % (2657050)Time elapsed: 0.001 s
% 3.89/1.61 % (2657050)Peak memory usage: 88 MB
% 3.89/1.61 % (2657039)Refutation found. Thanks to Tanya!
% 3.89/1.61 % SZS status Unsatisfiable for theBenchmark
% 3.89/1.61 % SZS output start Proof for theBenchmark
% See solution above
% 3.89/1.61 % (2657039)------------------------------
% 3.89/1.61 % (2657039)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.61 % (2657039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.61 % (2657039)CaDiCaL version: 2.1.3
% 3.89/1.61 % (2657039)Termination reason: Refutation
% 3.89/1.61 % (2657039)Time elapsed: 0.015 s
% 3.89/1.61 % (2657039)Peak memory usage: 88 MB
% 3.89/1.61 % (2657039)Instructions burned: 20 (million)
% 3.89/1.61 % (2657039)------------------------------
% 3.89/1.61 % (2657039)------------------------------
% 3.89/1.61 % (2657011)Success in time 0.452 s
% 3.89/1.61 % Vampire exiting
%------------------------------------------------------------------------------