%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW272+1 : TPTP v9.3.1. Released v5.2.0.
% 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 01:29:59 PM UTC 2026
% Result : Theorem 0.19s 1.71s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 18 unt; 1 def)
% Number of atoms : 66 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 56 ( 29 ~; 22 |; 0 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 22 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
v_pa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pne) ).
fof(f59,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
=> X0 = c_Groups_Ozero__class_Ozero(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__0__left) ).
fof(f62,axiom,
v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_s) ).
fof(f176,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__triv__right) ).
fof(f1121,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(f1174,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(f1206,conjecture,
v_s____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1207,negated_conjecture,
~ ( v_s____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(negated_conjecture,[status(cth)],[f1206]) ).
fof(f1210,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_s____,
inference(flattening,[],[f1207]) ).
fof(f1300,plain,
! [X0,X1] :
( X0 = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f59]) ).
fof(f1301,plain,
! [X0,X1] :
( X0 = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(flattening,[],[f1300]) ).
fof(f1461,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f176]) ).
fof(f2382,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1174]) ).
fof(f2732,plain,
v_pa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cnf_transformation,[],[f2]) ).
fof(f2815,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f1301]) ).
fof(f2820,plain,
v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____),
inference(cnf_transformation,[],[f62]) ).
fof(f2988,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(cnf_transformation,[],[f1461]) ).
fof(f4186,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1121]) ).
fof(f4239,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2382]) ).
fof(f4271,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_s____,
inference(cnf_transformation,[],[f1210]) ).
fof(f4286,plain,
v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_s____))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____),
inference(superposition,[],[f2820,f4271]) ).
fof(f4287,plain,
v_pa____ != v_s____,
inference(superposition,[],[f2732,f4271]) ).
fof(f4313,definition,
( spl23_3
<=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
introduced(definition,[new_symbols(definition,[spl23_3])],[avatar_definition]) ).
fof(f4314,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ spl23_3 ),
inference(avatar_component_clause,[],[f4313]) ).
fof(f4315,plain,
( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| spl23_3 ),
inference(avatar_component_clause,[],[f4313]) ).
fof(f4325,plain,
( ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| spl23_3 ),
inference(unit_resulting_resolution,[],[f4239,f4315]) ).
fof(f4328,plain,
( $false
| spl23_3 ),
inference(forward_subsumption_resolution,[],[f4325,f4186]) ).
fof(f4329,plain,
spl23_3,
inference(avatar_contradiction_clause,[],[f4328]) ).
fof(f4649,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),X0))
| v_s____ = X0
| ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(superposition,[],[f2815,f4271]) ).
fof(f4650,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),X0))
| v_s____ = X0 )
| ~ spl23_3 ),
inference(forward_subsumption_resolution,[],[f4649,f4314]) ).
fof(f4688,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_pa____))
| ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(superposition,[],[f2988,f4286]) ).
fof(f4692,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_pa____))
| ~ spl23_3 ),
inference(forward_subsumption_resolution,[],[f4688,f4314]) ).
fof(f4735,plain,
( v_pa____ = v_s____
| ~ spl23_3 ),
inference(unit_resulting_resolution,[],[f4650,f4692]) ).
fof(f4742,plain,
( $false
| ~ spl23_3 ),
inference(forward_subsumption_resolution,[],[f4735,f4287]) ).
fof(f4743,plain,
~ spl23_3,
inference(avatar_contradiction_clause,[],[f4742]) ).
cnf(s5,plain,
spl23_3,
inference(sat_conversion,[],[f4329]) ).
cnf(s10,plain,
~ spl23_3,
inference(sat_conversion,[],[f4743]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s5,s10]) ).
fof(f4744,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW272+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 % Computer : n016.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Mon Sep 28 13:33:43 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.25 Running first-order theorem proving
% 0.10/0.25 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
% 3.31/1.51 % (3624043)Detected formulas, will run a generic FOF schedule.
% 3.31/1.51 % (3624048)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=273885709:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.31/1.51 % (3624053)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1419680518:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.31/1.51 % (3624049)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2689846778:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.31/1.51 % (3624052)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=97205133:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.31/1.51 % (3624050)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2352198164:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.31/1.51 % (3624054)dis-21_1_sil=8000:lcm=predicate:random_seed=2009903450:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.31/1.51 % (3624051)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3822021222:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.31/1.51 % (3624051)Refutation not found, incomplete strategy
% 3.31/1.51 % (3624051)------------------------------
% 3.31/1.51 % (3624051)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.51 % (3624051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.51 % (3624051)CaDiCaL version: 2.1.3
% 3.31/1.51 % (3624051)Termination reason: Refutation not found, incomplete strategy
% 3.31/1.51 % (3624051)Time elapsed: 0.004 s
% 3.31/1.51 % (3624051)Peak memory usage: 89 MB
% 3.31/1.51 % (3624051)Instructions burned: 4 (million)
% 3.31/1.51 % (3624054)Instruction limit reached!
% 3.31/1.51 % (3624054)------------------------------
% 3.31/1.51 % (3624054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.51 % (3624054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.51 % (3624054)CaDiCaL version: 2.1.3
% 3.31/1.51 % (3624054)Termination reason: Instruction limit
% 3.31/1.51 % (3624054)Termination phase: Saturation
% 3.31/1.51 % (3624054)Time elapsed: 0.068 s
% 3.31/1.51 % (3624054)Peak memory usage: 90 MB
% 3.31/1.51 % (3624054)Instructions burned: 129 (million)
% 3.31/1.51 % (3624052)Instruction limit reached!
% 3.31/1.51 % (3624052)------------------------------
% 3.31/1.51 % (3624052)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.51 % (3624052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.51 % (3624052)CaDiCaL version: 2.1.3
% 3.31/1.51 % (3624052)Termination reason: Instruction limit
% 3.31/1.51 % (3624052)Termination phase: Saturation
% 3.31/1.51 % (3624052)Time elapsed: 0.072 s
% 3.31/1.51 % (3624052)Peak memory usage: 89 MB
% 3.31/1.51 % (3624052)Instructions burned: 120 (million)
% 3.31/1.51 % (3624053)Instruction limit reached!
% 3.31/1.51 % (3624053)------------------------------
% 3.31/1.51 % (3624053)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.51 % (3624053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.51 % (3624053)CaDiCaL version: 2.1.3
% 3.31/1.51 % (3624053)Termination reason: Instruction limit
% 3.31/1.51 % (3624053)Termination phase: Saturation
% 3.31/1.51 % (3624053)Time elapsed: 0.080 s
% 3.31/1.51 % (3624053)Peak memory usage: 91 MB
% 3.31/1.51 % (3624053)Instructions burned: 140 (million)
% 3.31/1.51 % (3624063)lrs+10_1_sil=32000:urr=on:br=off:random_seed=442388129:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.31/1.51 % (3624062)lrs+10_1_sil=8000:sp=occurrence:random_seed=3159411689:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.31/1.51 % (3624063)Refutation not found, incomplete strategy
% 3.31/1.51 % (3624063)------------------------------
% 3.31/1.51 % (3624063)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.51 % (3624063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.51 % (3624063)CaDiCaL version: 2.1.3
% 3.31/1.51 % (3624063)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.71 % (3624063)Time elapsed: 0.010 s
% 0.19/1.71 % (3624063)Peak memory usage: 89 MB
% 0.19/1.71 % (3624063)Instructions burned: 17 (million)
% 0.19/1.71 % (3624051)------------------------------
% 0.19/1.71 % (3624051)------------------------------
% 0.19/1.71 % (3624064)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1734141842:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 0.19/1.71 % (3624064)Refutation not found, incomplete strategy
% 0.19/1.71 % (3624064)------------------------------
% 0.19/1.71 % (3624064)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.71 % (3624064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.71 % (3624064)CaDiCaL version: 2.1.3
% 0.19/1.71 % (3624064)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.71 % (3624064)Time elapsed: 0.004 s
% 0.19/1.71 % (3624064)Peak memory usage: 89 MB
% 0.19/1.71 % (3624064)Instructions burned: 4 (million)
% 0.19/1.71 % (3624068)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2427903448:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 0.19/1.71 % (3624062)Instruction limit reached!
% 0.19/1.71 % (3624062)------------------------------
% 0.19/1.71 % (3624062)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.71 % (3624062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.71 % (3624062)CaDiCaL version: 2.1.3
% 0.19/1.71 % (3624062)Termination reason: Instruction limit
% 0.19/1.71 % (3624062)Termination phase: Saturation
% 0.19/1.71 % (3624062)Time elapsed: 0.185 s
% 0.19/1.71 % (3624062)Peak memory usage: 92 MB
% 0.19/1.71 % (3624062)Instructions burned: 286 (million)
% 0.19/1.71 % (3624068)First to succeed.
% 0.19/1.71 % (3624068)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3624043"
% 0.19/1.71 % (3624063)------------------------------
% 0.19/1.71 % (3624063)------------------------------
% 0.19/1.71 % (3624064)------------------------------
% 0.19/1.71 % (3624064)------------------------------
% 0.19/1.71 % (3624070)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=79913849:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 0.19/1.71 % (3624068)Refutation found. Thanks to Tanya!
% 0.19/1.71 % SZS status Theorem for theBenchmark
% 0.19/1.71 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.71 % (3624068)------------------------------
% 0.19/1.71 % (3624068)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.71 % (3624068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.71 % (3624068)CaDiCaL version: 2.1.3
% 0.19/1.71 % (3624068)Termination reason: Refutation
% 0.19/1.71 % (3624068)Time elapsed: 0.027 s
% 0.19/1.71 % (3624068)Peak memory usage: 92 MB
% 0.19/1.71 % (3624068)Instructions burned: 88 (million)
% 0.19/1.71 % (3624068)------------------------------
% 0.19/1.71 % (3624068)------------------------------
% 0.19/1.71 % (3624043)Success in time 0.818 s
% 0.19/1.71 % Vampire exiting
%------------------------------------------------------------------------------