%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN009-5 : 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 : n005.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 3.47s 1.38s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 57 ( 15 unt; 5 def)
% Number of atoms : 109 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 102 ( 50 ~; 47 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : divide(divide(X0,X1),X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
fof(f4,axiom,
! [X0] : divide(zero,X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_is_smallest) ).
fof(f5,plain,
! [X0] : zero = divide(zero,X0),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X0,X1] :
( divide(X0,X1) != zero
| divide(X1,X0) != zero
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divide_and_equal) ).
fof(f7,plain,
! [X0,X1] :
( divide(X0,X1) != zero
| zero != divide(X1,X0)
| X0 = X1 ),
inference(reorient_equations,[],[f6]) ).
fof(f12,axiom,
! [X2,X0,X1] :
( divide(divide(X0,X1),X2) != zero
| divide(divide(X0,X2),X1) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide1) ).
fof(f13,plain,
! [X2,X0,X1] :
( zero != divide(divide(X0,X1),X2)
| zero = divide(divide(X0,X2),X1) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,axiom,
! [X2,X0,X1] :
( divide(X0,X1) != zero
| divide(divide(X2,X1),divide(X2,X0)) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide2) ).
fof(f15,plain,
! [X2,X0,X1] :
( divide(X0,X1) != zero
| zero = divide(divide(X2,X1),divide(X2,X0)) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f17,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f19,plain,
! [X2,X0,X1] :
( sQ0_eqProxy(zero,divide(divide(X0,X2),X1))
| ~ sQ0_eqProxy(zero,divide(divide(X0,X1),X2)) ),
inference(equality_proxy_replacement,[],[f13,f17,f17]) ).
fof(f20,plain,
! [X2,X0,X1] :
( sQ0_eqProxy(zero,divide(divide(X2,X1),divide(X2,X0)))
| ~ sQ0_eqProxy(divide(X0,X1),zero) ),
inference(equality_proxy_replacement,[],[f15,f17,f17]) ).
fof(f21,plain,
~ sQ0_eqProxy(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))),
inference(equality_proxy_replacement,[],[f16,f17]) ).
fof(f23,plain,
! [X0,X1] :
( ~ sQ0_eqProxy(divide(X0,X1),zero)
| ~ sQ0_eqProxy(zero,divide(X1,X0))
| sQ0_eqProxy(X0,X1) ),
inference(equality_proxy_replacement,[],[f7,f17,f17,f17]) ).
fof(f24,plain,
! [X0] : sQ0_eqProxy(zero,divide(zero,X0)),
inference(equality_proxy_replacement,[],[f5,f17]) ).
fof(f26,plain,
! [X0,X1] : sQ0_eqProxy(divide(divide(X0,X1),X0),zero),
inference(equality_proxy_replacement,[],[f1,f17]) ).
fof(f28,plain,
! [X0,X1] :
( sQ0_eqProxy(X1,X0)
| ~ sQ0_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f17]) ).
fof(f32,plain,
! [X0,X1] :
( sQ0_eqProxy(X1,X0)
| ~ sQ0_eqProxy(zero,divide(X0,X1))
| ~ sQ0_eqProxy(zero,divide(X1,X0)) ),
inference(resolution,[],[f23,f28]) ).
fof(f47,plain,
( ~ sQ0_eqProxy(zero,divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,a)))
| ~ sQ0_eqProxy(zero,divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a))))) ),
inference(resolution,[],[f32,f21]) ).
fof(f55,definition,
( spl1_1
<=> sQ0_eqProxy(zero,divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,a))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f56,plain,
( ~ sQ0_eqProxy(zero,divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,a)))
| spl1_1 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f58,definition,
( spl1_2
<=> sQ0_eqProxy(zero,divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a))))) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f59,plain,
( ~ sQ0_eqProxy(zero,divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))))
| spl1_2 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,plain,
( ~ spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f47,f55,f58]) ).
fof(f63,plain,
( ~ sQ0_eqProxy(zero,divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))))
| spl1_1 ),
inference(resolution,[],[f56,f19]) ).
fof(f87,plain,
( ~ sQ0_eqProxy(divide(divide(identity,a),divide(identity,a)),zero)
| spl1_1 ),
inference(resolution,[],[f63,f20]) ).
fof(f100,plain,
( ~ sQ0_eqProxy(zero,divide(divide(identity,a),divide(identity,a)))
| spl1_1 ),
inference(resolution,[],[f87,f28]) ).
fof(f111,plain,
( ~ sQ0_eqProxy(divide(a,a),zero)
| spl1_1 ),
inference(resolution,[],[f100,f20]) ).
fof(f130,plain,
( ~ sQ0_eqProxy(zero,divide(a,a))
| spl1_1 ),
inference(resolution,[],[f111,f28]) ).
fof(f132,definition,
( spl1_13
<=> sQ0_eqProxy(zero,divide(divide(a,a),zero)) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
fof(f133,plain,
( ~ sQ0_eqProxy(zero,divide(divide(a,a),zero))
| spl1_13 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f135,definition,
( spl1_14
<=> sQ0_eqProxy(zero,divide(zero,divide(a,a))) ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
fof(f136,plain,
( ~ sQ0_eqProxy(zero,divide(zero,divide(a,a)))
| spl1_14 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f150,plain,
( ~ sQ0_eqProxy(zero,divide(divide(a,a),zero))
| ~ sQ0_eqProxy(zero,divide(zero,divide(a,a)))
| spl1_1 ),
inference(resolution,[],[f130,f32]) ).
fof(f152,plain,
( ~ spl1_14
| ~ spl1_13
| spl1_1 ),
inference(avatar_split_clause,[],[f150,f55,f132,f135]) ).
fof(f189,plain,
( ~ sQ0_eqProxy(zero,divide(divide(a,zero),a))
| spl1_13 ),
inference(resolution,[],[f133,f19]) ).
fof(f215,plain,
( ~ sQ0_eqProxy(divide(divide(a,zero),a),zero)
| spl1_13 ),
inference(resolution,[],[f189,f28]) ).
fof(f248,plain,
( $false
| spl1_13 ),
inference(resolution,[],[f215,f26]) ).
fof(f251,plain,
spl1_13,
inference(avatar_contradiction_clause,[],[f248]) ).
fof(f256,plain,
( $false
| spl1_14 ),
inference(resolution,[],[f136,f24]) ).
fof(f260,plain,
spl1_14,
inference(avatar_contradiction_clause,[],[f256]) ).
fof(f268,plain,
( ~ sQ0_eqProxy(divide(divide(identity,divide(identity,a)),a),zero)
| spl1_2 ),
inference(resolution,[],[f59,f20]) ).
fof(f281,plain,
( ~ sQ0_eqProxy(zero,divide(divide(identity,divide(identity,a)),a))
| spl1_2 ),
inference(resolution,[],[f268,f28]) ).
fof(f300,plain,
( ~ sQ0_eqProxy(zero,divide(divide(identity,a),divide(identity,a)))
| spl1_2 ),
inference(resolution,[],[f281,f19]) ).
fof(f335,plain,
( ~ sQ0_eqProxy(divide(a,a),zero)
| spl1_2 ),
inference(resolution,[],[f300,f20]) ).
fof(f352,plain,
( ~ sQ0_eqProxy(zero,divide(zero,divide(a,a)))
| ~ sQ0_eqProxy(zero,divide(divide(a,a),zero))
| spl1_2 ),
inference(resolution,[],[f335,f32]) ).
fof(f354,plain,
( ~ spl1_13
| ~ spl1_14
| spl1_2 ),
inference(avatar_split_clause,[],[f352,f58,f135,f132]) ).
cnf(s2,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f61]) ).
cnf(s14,plain,
( spl1_1
| ~ spl1_13
| ~ spl1_14 ),
inference(sat_conversion,[],[f152]) ).
cnf(s26,plain,
spl1_13,
inference(sat_conversion,[],[f251]) ).
cnf(s29,plain,
spl1_14,
inference(sat_conversion,[],[f260]) ).
cnf(s42,plain,
( spl1_2
| ~ spl1_13
| ~ spl1_14 ),
inference(sat_conversion,[],[f354]) ).
cnf(s45,plain,
spl1_2,
inference(rat,[],[s42,s29,s26]) ).
cnf(s49,plain,
spl1_1,
inference(rat,[],[s14,s29,s26]) ).
cnf(s50,plain,
$false,
inference(rat,[],[s2,s45,s49]) ).
fof(f355,plain,
$false,
inference(avatar_sat_refutation,[],[s50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 % Computer : n005.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 27 10:51:02 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.44 Running first-order theorem proving
% 0.15/0.44 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
% 2.43/1.28 % (3813102)Input is clausal, will run a generic CNF schedule.
% 2.43/1.28 % (3813244)lrs+10_1_sil=8000:sp=occurrence:random_seed=2931403885:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.43/1.28 % (3813243)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3995209468:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.43/1.28 % (3813240)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=1440566534:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.43/1.28 % (3813244)Instruction limit reached!
% 2.43/1.28 % (3813244)------------------------------
% 2.43/1.28 % (3813244)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.43/1.28 % (3813244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/1.28 % (3813244)CaDiCaL version: 2.1.3
% 2.43/1.28 % (3813244)Termination reason: Instruction limit
% 2.43/1.28 % (3813244)Termination phase: Saturation
% 2.43/1.28 % (3813244)Time elapsed: 0.035 s
% 2.43/1.28 % (3813244)Peak memory usage: 89 MB
% 2.43/1.28 % (3813244)Instructions burned: 109 (million)
% 2.43/1.28 % (3813242)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3733001491:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.43/1.28 % (3813246)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1948942874:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.43/1.28 % (3813245)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4186784590:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.43/1.28 % (3813247)dis-21_1_sil=8000:lcm=predicate:random_seed=2565631611: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)
% 2.43/1.28 % (3813247)First to succeed.
% 2.43/1.28 % (3813247)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3813102"
% 2.43/1.28 % (3813245)Instruction limit reached!
% 2.43/1.28 % (3813245)------------------------------
% 2.43/1.28 % (3813245)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.43/1.28 % (3813245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/1.28 % (3813245)CaDiCaL version: 2.1.3
% 2.43/1.28 % (3813245)Termination reason: Instruction limit
% 2.43/1.28 % (3813245)Termination phase: Saturation
% 2.43/1.28 % (3813245)Time elapsed: 0.069 s
% 2.43/1.28 % (3813245)Peak memory usage: 88 MB
% 2.43/1.28 % (3813245)Instructions burned: 116 (million)
% 2.43/1.28 % (3813251)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=2631702548:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.43/1.28 % (3813251)Refutation not found, incomplete strategy
% 2.43/1.28 % (3813251)------------------------------
% 2.43/1.28 % (3813251)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.43/1.28 % (3813251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/1.28 % (3813251)CaDiCaL version: 2.1.3
% 2.43/1.28 % (3813251)Termination reason: Refutation not found, incomplete strategy
% 2.43/1.28 % (3813251)Time elapsed: 0.0000 s
% 2.43/1.29 % (3813251)Peak memory usage: 87 MB
% 2.43/1.29 % (3813246)Instruction limit reached!
% 2.43/1.29 % (3813246)------------------------------
% 2.43/1.29 % (3813246)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.43/1.29 % (3813246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/1.29 % (3813246)CaDiCaL version: 2.1.3
% 2.43/1.29 % (3813246)Termination reason: Instruction limit
% 2.43/1.29 % (3813246)Termination phase: Saturation
% 2.43/1.29 % (3813246)Time elapsed: 0.100 s
% 2.43/1.29 % (3813246)Peak memory usage: 89 MB
% 2.43/1.29 % (3813246)Instructions burned: 181 (million)
% 2.43/1.29 % (3813256)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3423971251: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)
% 2.43/1.29 % (3813256)Refutation not found, incomplete strategy
% 2.43/1.29 % (3813256)------------------------------
% 2.43/1.29 % (3813256)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.43/1.29 % (3813256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.38 % (3813256)CaDiCaL version: 2.1.3
% 3.47/1.38 % (3813256)Termination reason: Refutation not found, incomplete strategy
% 3.47/1.38 % (3813256)Time elapsed: 0.001 s
% 3.47/1.38 % (3813256)Peak memory usage: 88 MB
% 3.47/1.38 % (3813256)Instructions burned: 1 (million)
% 3.47/1.38 % (3813258)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2511710627:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.47/1.38 % (3813251)------------------------------
% 3.47/1.38 % (3813251)------------------------------
% 3.47/1.38 % (3813247)Refutation found. Thanks to Tanya!
% 3.47/1.38 % SZS status Unsatisfiable for theBenchmark
% 3.47/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.38 % (3813247)------------------------------
% 3.47/1.38 % (3813247)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.38 % (3813247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.38 % (3813247)CaDiCaL version: 2.1.3
% 3.47/1.38 % (3813247)Termination reason: Refutation
% 3.47/1.38 % (3813247)Time elapsed: 0.006 s
% 3.47/1.38 % (3813247)Peak memory usage: 89 MB
% 3.47/1.38 % (3813247)Instructions burned: 6 (million)
% 3.47/1.38 % (3813247)------------------------------
% 3.47/1.38 % (3813247)------------------------------
% 3.47/1.38 % (3813102)Success in time 0.414 s
% 3.47/1.38 % Vampire exiting
%------------------------------------------------------------------------------