%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN009-4 : 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 : n018.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 10:19:08 AM UTC 2026
% Result : Unsatisfiable 3.66s 1.45s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 12 unt; 3 def)
% Number of atoms : 56 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 23 ~; 20 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( divide(X0,X1) != zero
| less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal2) ).
fof(f6,axiom,
! [X0,X1] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_equal_and_equal) ).
fof(f12,axiom,
! [X0] : divide(X0,X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
fof(f13,plain,
! [X0] : zero = divide(X0,X0),
inference(reorient_equations,[],[f12]) ).
fof(f17,axiom,
! [X2,X0,X1] :
( less_equal(divide(X0,X2),X1)
| ~ less_equal(divide(X0,X1),X2) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',property_of_divide2) ).
fof(f20,negated_conjecture,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f21,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f24,plain,
! [X0] : sQ0_eqProxy(zero,divide(X0,X0)),
inference(equality_proxy_replacement,[],[f13,f21]) ).
fof(f26,plain,
~ sQ0_eqProxy(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))),
inference(equality_proxy_replacement,[],[f20,f21]) ).
fof(f27,plain,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(equality_proxy_replacement,[],[f6,f21]) ).
fof(f28,plain,
! [X0,X1] :
( ~ sQ0_eqProxy(divide(X0,X1),zero)
| less_equal(X0,X1) ),
inference(equality_proxy_replacement,[],[f2,f21]) ).
fof(f31,plain,
! [X0,X1] :
( sQ0_eqProxy(X1,X0)
| ~ sQ0_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f21]) ).
fof(f34,plain,
! [X0,X1] :
( ~ sQ0_eqProxy(zero,divide(X0,X1))
| less_equal(X0,X1) ),
inference(resolution,[],[f28,f31]) ).
fof(f37,plain,
! [X0] : less_equal(X0,X0),
inference(resolution,[],[f34,f24]) ).
fof(f40,plain,
( ~ less_equal(divide(identity,divide(identity,divide(identity,a))),divide(identity,a))
| ~ less_equal(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) ),
inference(resolution,[],[f27,f26]) ).
fof(f45,definition,
( spl1_1
<=> less_equal(divide(identity,divide(identity,divide(identity,a))),divide(identity,a)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f46,plain,
( ~ less_equal(divide(identity,divide(identity,divide(identity,a))),divide(identity,a))
| spl1_1 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f48,definition,
( spl1_2
<=> less_equal(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f49,plain,
( ~ less_equal(divide(identity,a),divide(identity,divide(identity,divide(identity,a))))
| spl1_2 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f51,plain,
( ~ spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f40,f45,f48]) ).
fof(f116,plain,
( ~ less_equal(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))
| spl1_1 ),
inference(resolution,[],[f17,f46]) ).
fof(f132,plain,
( $false
| spl1_1 ),
inference(resolution,[],[f116,f37]) ).
fof(f133,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f132]) ).
fof(f177,plain,
( ~ less_equal(divide(identity,divide(identity,a)),a)
| spl1_2 ),
inference(resolution,[],[f18,f49]) ).
fof(f185,plain,
( ~ less_equal(divide(identity,a),divide(identity,a))
| spl1_2 ),
inference(resolution,[],[f177,f17]) ).
fof(f195,plain,
( $false
| spl1_2 ),
inference(resolution,[],[f185,f37]) ).
fof(f196,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f195]) ).
cnf(s2,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f51]) ).
cnf(s4,plain,
spl1_1,
inference(sat_conversion,[],[f133]) ).
cnf(s5,plain,
spl1_2,
inference(sat_conversion,[],[f196]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s2,s5,s4]) ).
fof(f197,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : HEN009-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 % Computer : n018.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 27 10:53:23 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 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
% 3.66/1.45 % (2157683)Input is clausal, will run a generic CNF schedule.
% 3.66/1.45 % (2157791)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=950633006:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.66/1.45 % (2157795)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3155180001:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.66/1.45 % (2157792)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1077802026:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.66/1.45 % (2157793)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1591847904:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.66/1.45 % (2157796)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3908348297:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.66/1.45 % (2157794)lrs+10_1_sil=8000:sp=occurrence:random_seed=31834298:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.66/1.45 % (2157797)dis-21_1_sil=8000:lcm=predicate:random_seed=2022506593: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)
% 3.66/1.45 % (2157797)First to succeed.
% 3.66/1.45 % (2157797)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2157683"
% 3.66/1.45 % (2157794)Instruction limit reached!
% 3.66/1.45 % (2157794)------------------------------
% 3.66/1.45 % (2157794)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.45 % (2157794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.45 % (2157794)CaDiCaL version: 2.1.3
% 3.66/1.45 % (2157794)Termination reason: Instruction limit
% 3.66/1.45 % (2157794)Termination phase: Saturation
% 3.66/1.45 % (2157794)Time elapsed: 0.070 s
% 3.66/1.45 % (2157794)Peak memory usage: 88 MB
% 3.66/1.45 % (2157794)Instructions burned: 108 (million)
% 3.66/1.45 % (2157795)Instruction limit reached!
% 3.66/1.45 % (2157795)------------------------------
% 3.66/1.45 % (2157795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.45 % (2157795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.45 % (2157795)CaDiCaL version: 2.1.3
% 3.66/1.45 % (2157795)Termination reason: Instruction limit
% 3.66/1.45 % (2157795)Termination phase: Saturation
% 3.66/1.45 % (2157795)Time elapsed: 0.071 s
% 3.66/1.45 % (2157795)Peak memory usage: 88 MB
% 3.66/1.45 % (2157795)Instructions burned: 115 (million)
% 3.66/1.45 % (2157796)Instruction limit reached!
% 3.66/1.45 % (2157796)------------------------------
% 3.66/1.45 % (2157796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.45 % (2157796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.45 % (2157796)CaDiCaL version: 2.1.3
% 3.66/1.45 % (2157796)Termination reason: Instruction limit
% 3.66/1.45 % (2157796)Termination phase: Saturation
% 3.66/1.45 % (2157796)Time elapsed: 0.110 s
% 3.66/1.45 % (2157796)Peak memory usage: 89 MB
% 3.66/1.45 % (2157796)Instructions burned: 181 (million)
% 3.66/1.45 % (2157806)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1445738104: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)
% 3.66/1.45 % (2157805)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=562142785:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.66/1.45 % (2157805)Refutation not found, incomplete strategy
% 3.66/1.45 % (2157805)------------------------------
% 3.66/1.45 % (2157805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.45 % (2157805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.45 % (2157805)CaDiCaL version: 2.1.3
% 3.66/1.45 % (2157805)Termination reason: Refutation not found, incomplete strategy
% 3.66/1.45 % (2157805)Time elapsed: 0.002 s
% 3.66/1.45 % (2157805)Peak memory usage: 88 MB
% 3.66/1.45 % (2157805)Instructions burned: 1 (million)
% 3.66/1.45 % (2157797)Refutation found. Thanks to Tanya!
% 3.66/1.45 % SZS status Unsatisfiable for theBenchmark
% 3.66/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.66/1.45 % (2157797)------------------------------
% 3.66/1.45 % (2157797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.45 % (2157797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.45 % (2157797)CaDiCaL version: 2.1.3
% 3.66/1.45 % (2157797)Termination reason: Refutation
% 3.66/1.45 % (2157797)Time elapsed: 0.005 s
% 3.66/1.45 % (2157797)Peak memory usage: 89 MB
% 3.66/1.45 % (2157797)Instructions burned: 5 (million)
% 3.66/1.45 % (2157797)------------------------------
% 3.66/1.45 % (2157797)------------------------------
% 3.66/1.45 % (2157683)Success in time 0.433 s
% 3.66/1.45 % Vampire exiting
%------------------------------------------------------------------------------