%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW288+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 : n019.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 01:30:02 PM UTC 2026
% Result : Theorem 0.20s 1.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 38 ( 15 unt; 3 def)
% Number of atoms : 69 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 31 ~; 24 |; 1 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 9 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
( ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
=> v_p = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096p_A_061_A_091_058poly_Ap_A_I0_058_058_Ha_J_058_093_096) ).
fof(f32,axiom,
! [X0,X1] :
( class_Groups_Ozero(X1)
=> c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__pCons__0) ).
fof(f1012,axiom,
! [X0] :
( class_Int_Oring__char__0(X0)
=> class_Groups_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Int_Oring__char__0__Groups_Ozero) ).
fof(f1216,conjecture,
c_Polynomial_Odegree(t_a,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1217,negated_conjecture,
c_Polynomial_Odegree(t_a,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(negated_conjecture,[status(cth)],[f1216]) ).
fof(f1218,axiom,
class_Int_Oring__char__0(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
fof(f1219,axiom,
class_Rings_Oidom(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_1) ).
fof(f1221,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Odegree(t_a,v_p),
inference(flattening,[],[f1217]) ).
fof(f1365,plain,
( v_p = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
| ~ class_Int_Oring__char__0(t_a)
| ~ class_Rings_Oidom(t_a) ),
inference(ennf_transformation,[],[f14]) ).
fof(f1366,plain,
( v_p = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
| ~ class_Int_Oring__char__0(t_a)
| ~ class_Rings_Oidom(t_a) ),
inference(flattening,[],[f1365]) ).
fof(f1387,plain,
! [X0,X1] :
( c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f2344,plain,
! [X0] :
( class_Groups_Ozero(X0)
| ~ class_Int_Oring__char__0(X0) ),
inference(ennf_transformation,[],[f1012]) ).
fof(f2753,plain,
( v_p = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
| ~ class_Int_Oring__char__0(t_a)
| ~ class_Rings_Oidom(t_a) ),
inference(cnf_transformation,[],[f1366]) ).
fof(f2782,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))
| ~ class_Groups_Ozero(X1) ),
inference(cnf_transformation,[],[f1387]) ).
fof(f3955,plain,
! [X0] :
( ~ class_Int_Oring__char__0(X0)
| class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f2344]) ).
fof(f4159,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Odegree(t_a,v_p),
inference(cnf_transformation,[],[f1221]) ).
fof(f4160,plain,
class_Int_Oring__char__0(t_a),
inference(cnf_transformation,[],[f1218]) ).
fof(f4161,plain,
class_Rings_Oidom(t_a),
inference(cnf_transformation,[],[f1219]) ).
fof(f4370,definition,
( spl13_3
<=> class_Rings_Oidom(t_a) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f4374,definition,
( spl13_4
<=> class_Int_Oring__char__0(t_a) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f4375,plain,
( class_Int_Oring__char__0(t_a)
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f4374]) ).
fof(f4378,definition,
( spl13_5
<=> v_p = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
fof(f4380,plain,
( v_p = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
| ~ spl13_5 ),
inference(avatar_component_clause,[],[f4378]) ).
fof(f4381,plain,
( ~ spl13_3
| ~ spl13_4
| spl13_5 ),
inference(avatar_split_clause,[],[f2753,f4378,f4374,f4370]) ).
fof(f4401,plain,
spl13_4,
inference(avatar_split_clause,[],[f4160,f4374]) ).
fof(f4402,plain,
spl13_3,
inference(avatar_split_clause,[],[f4161,f4370]) ).
fof(f4413,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(t_a,v_p)
| ~ class_Groups_Ozero(t_a)
| ~ spl13_5 ),
inference(superposition,[],[f2782,f4380]) ).
fof(f4414,plain,
( ~ class_Groups_Ozero(t_a)
| ~ spl13_5 ),
inference(forward_subsumption_resolution,[],[f4413,f4159]) ).
fof(f4456,plain,
( class_Groups_Ozero(t_a)
| ~ spl13_4 ),
inference(resolution,[],[f3955,f4375]) ).
fof(f4458,plain,
( $false
| ~ spl13_4
| ~ spl13_5 ),
inference(forward_subsumption_resolution,[],[f4456,f4414]) ).
fof(f4459,plain,
( ~ spl13_4
| ~ spl13_5 ),
inference(avatar_contradiction_clause,[],[f4458]) ).
cnf(s3,plain,
( ~ spl13_3
| ~ spl13_4
| spl13_5 ),
inference(sat_conversion,[],[f4381]) ).
cnf(s8,plain,
spl13_4,
inference(sat_conversion,[],[f4401]) ).
cnf(s9,plain,
spl13_3,
inference(sat_conversion,[],[f4402]) ).
cnf(s10,plain,
( ~ spl13_4
| ~ spl13_5 ),
inference(sat_conversion,[],[f4459]) ).
cnf(s11,plain,
~ spl13_5,
inference(rat,[],[s10,s8]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s3,s11,s8,s9]) ).
fof(f4460,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW288+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n019.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 13:30:18 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 0.20/1.30 % (4002397)Detected formulas, will run a generic FOF schedule.
% 0.20/1.30 % (4002403)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=2874094779:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.20/1.30 % (4002408)dis-21_1_sil=8000:lcm=predicate:random_seed=645866050: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)
% 0.20/1.30 % (4002405)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=668065840:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.20/1.30 % (4002407)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2122892444:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.20/1.30 % (4002402)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=1408664852:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.20/1.30 % (4002406)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3791513491:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.20/1.30 % (4002404)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=1949545866:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.20/1.30 % (4002405)Refutation not found, incomplete strategy
% 0.20/1.30 % (4002405)------------------------------
% 0.20/1.30 % (4002405)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.30 % (4002405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.30 % (4002405)CaDiCaL version: 2.1.3
% 0.20/1.30 % (4002405)Termination reason: Refutation not found, incomplete strategy
% 0.20/1.30 % (4002405)Time elapsed: 0.006 s
% 0.20/1.30 % (4002405)Peak memory usage: 89 MB
% 0.20/1.30 % (4002405)Instructions burned: 7 (million)
% 0.20/1.30 % (4002407)First to succeed.
% 0.20/1.30 % (4002407)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4002397"
% 0.20/1.30 % (4002408)Instruction limit reached!
% 0.20/1.30 % (4002408)------------------------------
% 0.20/1.30 % (4002408)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.30 % (4002408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.30 % (4002408)CaDiCaL version: 2.1.3
% 0.20/1.30 % (4002408)Termination reason: Instruction limit
% 0.20/1.30 % (4002408)Termination phase: Saturation
% 0.20/1.30 % (4002408)Time elapsed: 0.069 s
% 0.20/1.30 % (4002408)Peak memory usage: 90 MB
% 0.20/1.30 % (4002408)Instructions burned: 130 (million)
% 0.20/1.30 % (4002406)Instruction limit reached!
% 0.20/1.30 % (4002406)------------------------------
% 0.20/1.30 % (4002406)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.30 % (4002406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.30 % (4002406)CaDiCaL version: 2.1.3
% 0.20/1.30 % (4002406)Termination reason: Instruction limit
% 0.20/1.30 % (4002406)Termination phase: Saturation
% 0.20/1.30 % (4002406)Time elapsed: 0.071 s
% 0.20/1.30 % (4002406)Peak memory usage: 89 MB
% 0.20/1.30 % (4002406)Instructions burned: 119 (million)
% 0.20/1.30 % (4002417)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3053959703:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 0.20/1.30 % (4002416)lrs+10_1_sil=8000:sp=occurrence:random_seed=1954057248:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.20/1.30 % (4002405)------------------------------
% 0.20/1.30 % (4002405)------------------------------
% 0.20/1.30 % (4002417)Refutation not found, incomplete strategy
% 0.20/1.30 % (4002417)------------------------------
% 0.20/1.30 % (4002417)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.30 % (4002417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.30 % (4002417)CaDiCaL version: 2.1.3
% 0.20/1.30 % (4002417)Termination reason: Refutation not found, incomplete strategy
% 0.20/1.30 % (4002417)Time elapsed: 0.010 s
% 0.20/1.30 % (4002417)Peak memory usage: 89 MB
% 0.20/1.30 % (4002417)Instructions burned: 18 (million)
% 0.20/1.30 % (4002407)Refutation found. Thanks to Tanya!
% 0.20/1.30 % SZS status Theorem for theBenchmark
% 0.20/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.30 % (4002407)------------------------------
% 0.20/1.30 % (4002407)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.30 % (4002407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.30 % (4002407)CaDiCaL version: 2.1.3
% 0.20/1.30 % (4002407)Termination reason: Refutation
% 0.20/1.30 % (4002407)Time elapsed: 0.048 s
% 0.20/1.30 % (4002407)Peak memory usage: 91 MB
% 0.20/1.30 % (4002407)Instructions burned: 92 (million)
% 0.20/1.30 % (4002407)------------------------------
% 0.20/1.30 % (4002407)------------------------------
% 0.20/1.30 % (4002397)Success in time 0.537 s
% 0.20/1.30 % Vampire exiting
%------------------------------------------------------------------------------