%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN004-2 : 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 : n016.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 10:19:04 AM UTC 2026
% Result : Unsatisfiable 0.17s 1.81s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 26 ( 15 unt; 0 def)
% Number of atoms : 51 ( 10 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 51 ( 26 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 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 : 56 ( 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( ~ quotient(X0,X1,zero)
| less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_quotient) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| less_equal(X2,X0) ),
file('/export/starexec/sandbox/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/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(f12,axiom,
! [X0] : quotient(X0,X0,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
fof(f13,negated_conjecture,
~ quotient(x,zero,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_x_divde_zero_is_x) ).
fof(f23,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[],[f3,f8]) ).
fof(f27,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f30,plain,
! [X0,X1] :
( ~ less_equal(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[],[f6,f23]) ).
fof(f90,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( less_equal(divide(X4,X2),X6)
| ~ quotient(X3,X1,X4)
| ~ quotient(X3,X0,X5)
| ~ quotient(X5,X1,X6)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[],[f4,f8]) ).
fof(f93,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ quotient(X4,X1,zero)
| ~ quotient(X0,X3,X4)
| ~ quotient(X0,X1,X2)
| ~ quotient(X3,X1,X5)
| zero = divide(X2,X5) ),
inference(resolution,[],[f90,f27]) ).
fof(f100,plain,
! [X2,X3,X0,X1,X4] :
( ~ quotient(X1,X2,X4)
| ~ quotient(X0,X2,X3)
| ~ quotient(X0,X1,X2)
| zero = divide(X3,X4) ),
inference(resolution,[],[f93,f12]) ).
fof(f140,plain,
! [X2,X0,X1] :
( ~ quotient(X0,zero,X1)
| ~ quotient(X0,X1,X2)
| zero = divide(X2,zero) ),
inference(resolution,[],[f100,f11]) ).
fof(f155,plain,
! [X0,X1] :
( ~ quotient(X0,divide(X0,zero),X1)
| zero = divide(X1,zero) ),
inference(resolution,[],[f140,f8]) ).
fof(f161,plain,
! [X0] : zero = divide(divide(X0,divide(X0,zero)),zero),
inference(resolution,[],[f155,f8]) ).
fof(f172,plain,
! [X0] : quotient(divide(X0,divide(X0,zero)),zero,zero),
inference(superposition,[],[f8,f161]) ).
fof(f184,plain,
! [X0] : less_equal(divide(X0,divide(X0,zero)),zero),
inference(resolution,[],[f172,f2]) ).
fof(f200,plain,
! [X0] : zero = divide(X0,divide(X0,zero)),
inference(resolution,[],[f184,f27]) ).
fof(f221,plain,
! [X0] : quotient(X0,divide(X0,zero),zero),
inference(superposition,[],[f8,f200]) ).
fof(f232,plain,
! [X0] : less_equal(X0,divide(X0,zero)),
inference(resolution,[],[f221,f2]) ).
fof(f243,plain,
! [X0] : divide(X0,zero) = X0,
inference(resolution,[],[f232,f30]) ).
fof(f273,plain,
! [X0] : quotient(X0,zero,X0),
inference(superposition,[],[f8,f243]) ).
fof(f290,plain,
$false,
inference(resolution,[],[f273,f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n016.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 10:54:37 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.43 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
% 0.17/1.81 % (2445106)Input is clausal, will run a generic CNF schedule.
% 0.17/1.81 % (2445153)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2079220086:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.17/1.81 % (2445150)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1673851074:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.17/1.81 % (2445151)lrs+10_1_sil=8000:sp=occurrence:random_seed=476967927:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.17/1.81 % (2445154)dis-21_1_sil=8000:lcm=predicate:random_seed=2121123674: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)
% 0.17/1.81 % (2445149)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3191047987:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.17/1.81 % (2445148)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=2670337095:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.17/1.81 % (2445154)Refutation not found, incomplete strategy
% 0.17/1.81 % (2445154)------------------------------
% 0.17/1.81 % (2445154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.81 % (2445154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.81 % (2445154)CaDiCaL version: 2.1.3
% 0.17/1.81 % (2445154)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.81 % (2445154)Time elapsed: 0.001 s
% 0.17/1.81 % (2445154)Peak memory usage: 88 MB
% 0.17/1.81 % (2445151)Refutation not found, incomplete strategy
% 0.17/1.81 % (2445151)------------------------------
% 0.17/1.81 % (2445151)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.81 % (2445151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.81 % (2445151)CaDiCaL version: 2.1.3
% 0.17/1.81 % (2445151)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.81 % (2445151)Time elapsed: 0.002 s
% 0.17/1.81 % (2445151)Peak memory usage: 87 MB
% 0.17/1.81 % (2445151)Instructions burned: 1 (million)
% 0.17/1.81 % (2445152)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3315966520:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.17/1.81 % (2445152)Refutation not found, incomplete strategy
% 0.17/1.81 % (2445152)------------------------------
% 0.17/1.81 % (2445152)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.81 % (2445152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.81 % (2445152)CaDiCaL version: 2.1.3
% 0.17/1.81 % (2445152)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.81 % (2445152)Time elapsed: 0.001 s
% 0.17/1.81 % (2445152)Peak memory usage: 87 MB
% 0.17/1.81 % (2445152)Instructions burned: 3 (million)
% 0.17/1.81 % (2445153)Instruction limit reached!
% 0.17/1.81 % (2445153)------------------------------
% 0.17/1.81 % (2445153)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.81 % (2445153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.81 % (2445153)CaDiCaL version: 2.1.3
% 0.17/1.81 % (2445153)Termination reason: Instruction limit
% 0.17/1.81 % (2445153)Termination phase: Saturation
% 0.17/1.81 % (2445153)Time elapsed: 0.097 s
% 0.17/1.81 % (2445153)Peak memory usage: 88 MB
% 0.17/1.81 % (2445153)Instructions burned: 180 (million)
% 0.17/1.81 % (2445152)------------------------------
% 0.17/1.81 % (2445152)------------------------------
% 0.17/1.81 % (2445151)------------------------------
% 0.17/1.81 % (2445151)------------------------------
% 0.17/1.81 % (2445154)------------------------------
% 0.17/1.81 % (2445154)------------------------------
% 0.17/1.81 % (2445175)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=2776217282:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.17/1.81 % (2445175)Refutation not found, incomplete strategy
% 0.17/1.81 % (2445175)------------------------------
% 0.17/1.81 % (2445175)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.81 % (2445175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.81 % (2445175)CaDiCaL version: 2.1.3
% 0.17/1.81 % (2445175)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.81 % (2445175)Time elapsed: 0.001 s
% 0.17/1.81 % (2445175)Peak memory usage: 87 MB
% 0.17/1.81 % (2445176)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1231448483:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 0.17/1.81 % (2445176)Refutation not found, incomplete strategy
% 0.17/1.81 % (2445176)------------------------------
% 0.17/1.81 % (2445176)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.81 % (2445176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.81 % (2445176)CaDiCaL version: 2.1.3
% 0.17/1.81 % (2445176)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.81 % (2445176)Time elapsed: 0.001 s
% 0.17/1.81 % (2445176)Peak memory usage: 88 MB
% 0.17/1.81 % (2445177)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3927760901:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 0.17/1.81 % (2445179)lrs+10_64_to=lpo:sil=8000:random_seed=4161988808:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 0.17/1.81 % (2445177)Refutation not found, incomplete strategy
% 0.17/1.81 % (2445177)------------------------------
% 0.17/1.81 % (2445177)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.81 % (2445177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.81 % (2445177)CaDiCaL version: 2.1.3
% 0.17/1.81 % (2445177)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.81 % (2445177)Time elapsed: 0.001 s
% 0.17/1.81 % (2445177)Peak memory usage: 87 MB
% 0.17/1.81 % (2445179)First to succeed.
% 0.17/1.81 % (2445179)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2445106"
% 0.17/1.81 % (2445176)------------------------------
% 0.17/1.81 % (2445176)------------------------------
% 0.17/1.81 % (2445175)------------------------------
% 0.17/1.81 % (2445175)------------------------------
% 0.17/1.81 % (2445183)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3451114771:avsq=on:i=194:fgj=on:bd=preordered_2993 on theBenchmark for (2993ds/194Mi)
% 0.17/1.81 % (2445183)Instruction limit reached!
% 0.17/1.81 % (2445183)------------------------------
% 0.17/1.81 % (2445183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.81 % (2445183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.81 % (2445183)CaDiCaL version: 2.1.3
% 0.17/1.81 % (2445183)Termination reason: Instruction limit
% 0.17/1.81 % (2445183)Termination phase: Saturation
% 0.17/1.81 % (2445183)Time elapsed: 0.058 s
% 0.17/1.81 % (2445183)Peak memory usage: 88 MB
% 0.17/1.81 % (2445183)Instructions burned: 195 (million)
% 0.17/1.81 % (2445177)------------------------------
% 0.17/1.81 % (2445177)------------------------------
% 0.17/1.81 % (2445184)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=4008590366:i=157:gtg=all_2993 on theBenchmark for (2993ds/157Mi)
% 0.17/1.81 % (2445184)Also succeeded, but the first one will report.
% 0.17/1.81 % (2445179)Refutation found. Thanks to Tanya!
% 0.17/1.81 % SZS status Unsatisfiable for theBenchmark
% 0.17/1.81 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.81 % (2445179)------------------------------
% 0.17/1.81 % (2445179)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.81 % (2445179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.81 % (2445179)CaDiCaL version: 2.1.3
% 0.17/1.81 % (2445179)Termination reason: Refutation
% 0.17/1.81 % (2445179)Time elapsed: 0.008 s
% 0.17/1.81 % (2445179)Peak memory usage: 87 MB
% 0.17/1.81 % (2445179)Instructions burned: 10 (million)
% 0.17/1.81 % (2445179)------------------------------
% 0.17/1.81 % (2445179)------------------------------
% 0.17/1.81 % (2445106)Success in time 0.871 s
% 0.17/1.81 % Vampire exiting
%------------------------------------------------------------------------------