%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN010-4 : 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 : n006.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 10:19:09 AM UTC 2026
% Result : Unsatisfiable 2.22s 1.71s
% Output : Refutation 4.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 69 ( 21 unt; 7 def)
% Number of atoms : 142 ( 6 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 140 ( 67 ~; 66 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( divide(X0,X1) != zero
| less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal2) ).
fof(f3,axiom,
! [X0,X1] : less_equal(divide(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
fof(f4,axiom,
! [X2,X0,X1] : less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
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(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_and_equal) ).
fof(f12,axiom,
! [X0] : divide(X0,X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
fof(f13,plain,
! [X0] : zero = divide(X0,X0),
inference(reorient_equations,[],[f12]) ).
fof(f16,axiom,
! [X2,X0,X1] :
( less_equal(X0,X2)
| ~ less_equal(X1,X2)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
fof(f17,axiom,
! [X2,X0,X1] :
( less_equal(divide(X0,X2),X1)
| ~ less_equal(divide(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide1) ).
fof(f18,axiom,
! [X2,X0,X1] :
( less_equal(divide(X2,X1),divide(X2,X0))
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide2) ).
fof(f22,negated_conjecture,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_of_inversion) ).
fof(f23,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f26,plain,
! [X0] : sQ0_eqProxy(zero,divide(X0,X0)),
inference(equality_proxy_replacement,[],[f13,f23]) ).
fof(f29,plain,
~ sQ0_eqProxy(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),
inference(equality_proxy_replacement,[],[f22,f23]) ).
fof(f30,plain,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(equality_proxy_replacement,[],[f6,f23]) ).
fof(f31,plain,
! [X0,X1] :
( ~ sQ0_eqProxy(divide(X0,X1),zero)
| less_equal(X0,X1) ),
inference(equality_proxy_replacement,[],[f2,f23]) ).
fof(f34,plain,
! [X0,X1] :
( sQ0_eqProxy(X1,X0)
| ~ sQ0_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f23]) ).
fof(f37,plain,
! [X0,X1] :
( ~ sQ0_eqProxy(zero,divide(X0,X1))
| less_equal(X0,X1) ),
inference(resolution,[],[f31,f34]) ).
fof(f40,plain,
! [X0] : less_equal(X0,X0),
inference(resolution,[],[f37,f26]) ).
fof(f43,plain,
( ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a))
| ~ less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) ),
inference(resolution,[],[f30,f29]) ).
fof(f45,plain,
! [X0,X1] :
( ~ less_equal(divide(X0,X1),zero)
| ~ less_equal(zero,divide(X0,X1))
| less_equal(X0,X1) ),
inference(resolution,[],[f30,f31]) ).
fof(f48,definition,
( spl1_1
<=> less_equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f49,plain,
( ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a))
| spl1_1 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f51,definition,
( spl1_2
<=> less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f52,plain,
( ~ less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a))))
| spl1_2 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f54,plain,
( ~ spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f43,f48,f51]) ).
fof(f55,plain,
( $false
| spl1_1 ),
inference(resolution,[],[f49,f3]) ).
fof(f57,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f55]) ).
fof(f58,plain,
( ! [X0] :
( ~ less_equal(X0,divide(divide(identity,a),divide(identity,divide(identity,a))))
| ~ less_equal(divide(identity,a),X0) )
| spl1_2 ),
inference(resolution,[],[f52,f16]) ).
fof(f60,plain,
( ! [X0,X1] :
( ~ less_equal(divide(identity,a),X0)
| ~ less_equal(X1,divide(divide(identity,a),divide(identity,divide(identity,a))))
| ~ less_equal(X0,X1) )
| spl1_2 ),
inference(resolution,[],[f58,f16]) ).
fof(f186,plain,
( ! [X0,X1] :
( ~ less_equal(divide(identity,divide(identity,a)),X0)
| ~ less_equal(X1,divide(divide(identity,a),X0))
| ~ less_equal(divide(identity,a),X1) )
| spl1_2 ),
inference(resolution,[],[f18,f60]) ).
fof(f338,definition,
( spl1_7
<=> less_equal(divide(identity,divide(identity,a)),a) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f339,plain,
( ~ less_equal(divide(identity,divide(identity,a)),a)
| spl1_7 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f350,plain,
( ~ less_equal(divide(identity,a),divide(identity,a))
| spl1_7 ),
inference(resolution,[],[f339,f17]) ).
fof(f359,plain,
( $false
| spl1_7 ),
inference(resolution,[],[f350,f40]) ).
fof(f360,plain,
spl1_7,
inference(avatar_contradiction_clause,[],[f359]) ).
fof(f533,plain,
( ! [X0] :
( ~ less_equal(divide(identity,a),divide(divide(identity,X0),divide(a,X0)))
| ~ less_equal(divide(identity,divide(identity,a)),X0) )
| spl1_2 ),
inference(resolution,[],[f4,f186]) ).
fof(f614,plain,
! [X0,X1] :
( ~ less_equal(divide(X0,zero),X1)
| less_equal(X0,X1)
| ~ less_equal(zero,divide(X0,X1)) ),
inference(resolution,[],[f45,f17]) ).
fof(f615,plain,
! [X2,X0,X1] :
( ~ less_equal(divide(X0,X1),X2)
| less_equal(X0,X1)
| ~ less_equal(X2,zero)
| ~ less_equal(zero,divide(X0,X1)) ),
inference(resolution,[],[f45,f16]) ).
fof(f721,plain,
! [X0,X1] :
( ~ less_equal(zero,divide(X0,divide(X0,X1)))
| less_equal(X0,divide(X0,X1))
| ~ less_equal(X1,zero) ),
inference(resolution,[],[f614,f18]) ).
fof(f791,plain,
! [X0,X1] :
( ~ less_equal(zero,divide(X0,X1))
| ~ less_equal(X0,zero)
| less_equal(X0,X1) ),
inference(resolution,[],[f615,f3]) ).
fof(f858,plain,
! [X0,X1] :
( less_equal(X0,X1)
| ~ less_equal(X0,zero) ),
inference(resolution,[],[f791,f5]) ).
fof(f1275,plain,
! [X0,X1] :
( ~ less_equal(zero,zero)
| less_equal(X0,divide(X0,X1))
| ~ less_equal(X1,zero) ),
inference(resolution,[],[f858,f721]) ).
fof(f1431,definition,
( spl1_16
<=> ! [X0,X1] :
( less_equal(X0,divide(X0,X1))
| ~ less_equal(X1,zero) ) ),
introduced(definition,[new_symbols(definition,[spl1_16])],[avatar_definition]) ).
fof(f1432,plain,
( ! [X0,X1] :
( less_equal(X0,divide(X0,X1))
| ~ less_equal(X1,zero) )
| ~ spl1_16 ),
inference(avatar_component_clause,[],[f1431]) ).
fof(f1434,definition,
( spl1_17
<=> less_equal(zero,zero) ),
introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition]) ).
fof(f1435,plain,
( ~ less_equal(zero,zero)
| spl1_17 ),
inference(avatar_component_clause,[],[f1434]) ).
fof(f1436,plain,
( spl1_16
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f1275,f1434,f1431]) ).
fof(f1501,plain,
( $false
| spl1_17 ),
inference(resolution,[],[f1435,f5]) ).
fof(f1506,plain,
spl1_17,
inference(avatar_contradiction_clause,[],[f1501]) ).
fof(f1588,plain,
( ~ less_equal(divide(a,a),zero)
| ~ less_equal(divide(identity,divide(identity,a)),a)
| spl1_2
| ~ spl1_16 ),
inference(resolution,[],[f1432,f533]) ).
fof(f1641,definition,
( spl1_30
<=> less_equal(divide(a,a),zero) ),
introduced(definition,[new_symbols(definition,[spl1_30])],[avatar_definition]) ).
fof(f1642,plain,
( ~ less_equal(divide(a,a),zero)
| spl1_30 ),
inference(avatar_component_clause,[],[f1641]) ).
fof(f1643,plain,
( ~ spl1_7
| ~ spl1_30
| spl1_2
| ~ spl1_16 ),
inference(avatar_split_clause,[],[f1588,f1431,f51,f1641,f338]) ).
fof(f1687,plain,
( ~ less_equal(divide(a,zero),a)
| spl1_30 ),
inference(resolution,[],[f1642,f17]) ).
fof(f1711,plain,
( $false
| spl1_30 ),
inference(resolution,[],[f1687,f3]) ).
fof(f1715,plain,
spl1_30,
inference(avatar_contradiction_clause,[],[f1711]) ).
cnf(s2,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f54]) ).
cnf(s3,plain,
spl1_1,
inference(sat_conversion,[],[f57]) ).
cnf(s13,plain,
spl1_7,
inference(sat_conversion,[],[f360]) ).
cnf(s29,plain,
( spl1_16
| ~ spl1_17 ),
inference(sat_conversion,[],[f1436]) ).
cnf(s45,plain,
spl1_17,
inference(sat_conversion,[],[f1506]) ).
cnf(s47,plain,
( spl1_2
| ~ spl1_7
| ~ spl1_16
| ~ spl1_30 ),
inference(sat_conversion,[],[f1643]) ).
cnf(s58,plain,
spl1_30,
inference(sat_conversion,[],[f1715]) ).
cnf(s59,plain,
( spl1_2
| ~ spl1_7
| ~ spl1_16 ),
inference(rat,[],[s47,s58]) ).
cnf(s70,plain,
spl1_16,
inference(rat,[],[s29,s45]) ).
cnf(s76,plain,
spl1_2,
inference(rat,[],[s59,s70,s13]) ).
cnf(s77,plain,
$false,
inference(rat,[],[s2,s76,s3]) ).
fof(f1716,plain,
$false,
inference(avatar_sat_refutation,[],[s77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n006.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 10:50:55 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.44 Running first-order theorem proving
% 0.16/0.44 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
% 2.22/1.71 % (2801640)Input is clausal, will run a generic CNF schedule.
% 2.22/1.71 % (2801651)dis-21_1_sil=8000:lcm=predicate:random_seed=3132940251: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)
% 2.22/1.71 % (2801651)First to succeed.
% 2.22/1.71 % (2801651)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2801640"
% 2.22/1.71 % (2801646)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2309075093:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.22/1.71 % (2801645)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=2491857898:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.22/1.71 % (2801647)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=534348704:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.22/1.71 % (2801648)lrs+10_1_sil=8000:sp=occurrence:random_seed=3344752667:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.22/1.71 % (2801649)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2589364009:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.22/1.71 % (2801650)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=868833895:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.22/1.71 % (2801648)Instruction limit reached!
% 2.22/1.71 % (2801648)------------------------------
% 2.22/1.71 % (2801648)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.22/1.71 % (2801648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.22/1.71 % (2801648)CaDiCaL version: 2.1.3
% 2.22/1.71 % (2801648)Termination reason: Instruction limit
% 2.22/1.71 % (2801648)Termination phase: Saturation
% 2.22/1.71 % (2801648)Time elapsed: 0.111 s
% 2.22/1.71 % (2801648)Peak memory usage: 88 MB
% 2.22/1.71 % (2801648)Instructions burned: 107 (million)
% 2.22/1.71 % (2801649)Instruction limit reached!
% 2.22/1.71 % (2801649)------------------------------
% 2.22/1.71 % (2801649)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.22/1.71 % (2801649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.22/1.71 % (2801649)CaDiCaL version: 2.1.3
% 2.22/1.71 % (2801649)Termination reason: Instruction limit
% 2.22/1.71 % (2801649)Termination phase: Saturation
% 2.22/1.71 % (2801649)Time elapsed: 0.118 s
% 2.22/1.71 % (2801649)Peak memory usage: 88 MB
% 2.22/1.71 % (2801649)Instructions burned: 114 (million)
% 2.22/1.71 % (2801650)Instruction limit reached!
% 2.22/1.71 % (2801650)------------------------------
% 2.22/1.71 % (2801650)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.22/1.71 % (2801650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.22/1.71 % (2801650)CaDiCaL version: 2.1.3
% 2.22/1.71 % (2801650)Termination reason: Instruction limit
% 2.22/1.71 % (2801650)Termination phase: Saturation
% 2.22/1.71 % (2801650)Time elapsed: 0.176 s
% 2.22/1.71 % (2801650)Peak memory usage: 89 MB
% 2.22/1.71 % (2801650)Instructions burned: 181 (million)
% 2.22/1.71 % (2801651)Refutation found. Thanks to Tanya!
% 2.22/1.71 % SZS status Unsatisfiable for theBenchmark
% 2.22/1.71 % SZS output start Proof for theBenchmark
% See solution above
% 4.51/2.02 % (2801651)------------------------------
% 4.51/2.02 % (2801651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.51/2.02 % (2801651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.51/2.02 % (2801651)CaDiCaL version: 2.1.3
% 4.51/2.02 % (2801651)Termination reason: Refutation
% 4.51/2.02 % (2801651)Time elapsed: 0.025 s
% 4.51/2.02 % (2801651)Peak memory usage: 89 MB
% 4.51/2.02 % (2801651)Instructions burned: 40 (million)
% 4.51/2.02 % (2801651)------------------------------
% 4.51/2.02 % (2801651)------------------------------
% 4.51/2.02 % (2801640)Success in time 0.508 s
% 4.51/2.02 % Vampire exiting
%------------------------------------------------------------------------------