%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW246+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 01:29:56 PM UTC 2026
% Result : ContradictoryAxioms 5.93s 1.68s
% Output : Refutation 5.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 7 unt; 2 def)
% Number of atoms : 63 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 55 ( 26 ~; 22 |; 0 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 33 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__0) ).
fof(f22,axiom,
! [X0,X1,X2] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
<=> ! [X3,X4] : hAPP(X0,X3) = hAPP(X0,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_constant__def) ).
fof(f67,axiom,
( class_Rings_Oidom(t_a)
=> ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C0_C) ).
fof(f1007,axiom,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Rings_Ocomm__semiring__0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ocomm__semiring__0) ).
fof(f1200,axiom,
class_Rings_Oidom(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
fof(f1201,plain,
! [X0,X1,X2] :
( ! [X3,X4] : hAPP(X0,X3) = hAPP(X0,X4)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0) ),
inference(unused_predicate_definition_removal,[],[f22]) ).
fof(f1253,plain,
( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ~ class_Rings_Oidom(t_a) ),
inference(ennf_transformation,[],[f67]) ).
fof(f1262,plain,
! [X0,X1] :
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f1296,plain,
! [X0,X1,X2] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
| ? [X3,X4] : hAPP(X0,X3) != hAPP(X0,X4) ),
inference(ennf_transformation,[],[f1201]) ).
fof(f1359,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1007]) ).
fof(f1597,plain,
! [X0,X1,X2] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
| hAPP(X0,sK3(X0)) != hAPP(X0,sK4(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X3,sK3(X0)),skolemize(X4,sK4(X0))],[f1296]) ).
fof(f1687,plain,
class_Rings_Oidom(t_a),
inference(cnf_transformation,[],[f1200]) ).
fof(f1689,plain,
( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ~ class_Rings_Oidom(t_a) ),
inference(cnf_transformation,[],[f1253]) ).
fof(f1700,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) ),
inference(cnf_transformation,[],[f1262]) ).
fof(f1813,plain,
! [X2,X0,X1] :
( hAPP(X0,sK3(X0)) != hAPP(X0,sK4(X0))
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0) ),
inference(cnf_transformation,[],[f1597]) ).
fof(f1904,plain,
! [X0] :
( ~ class_Rings_Oidom(X0)
| class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f1359]) ).
fof(f2401,definition,
( spl14_1
<=> class_Rings_Oidom(t_a) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f2402,plain,
( class_Rings_Oidom(t_a)
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f2401]) ).
fof(f2410,definition,
( spl14_3
<=> c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
fof(f2412,plain,
( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| spl14_3 ),
inference(avatar_component_clause,[],[f2410]) ).
fof(f2413,plain,
( ~ spl14_1
| ~ spl14_3 ),
inference(avatar_split_clause,[],[f1689,f2410,f2401]) ).
fof(f2414,plain,
spl14_1,
inference(avatar_split_clause,[],[f1687,f2401]) ).
fof(f2431,plain,
( class_Rings_Ocomm__semiring__0(t_a)
| ~ spl14_1 ),
inference(resolution,[],[f1904,f2402]) ).
fof(f2743,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(t_a) = hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),X0)
| ~ spl14_1 ),
inference(resolution,[],[f1700,f2431]) ).
fof(f4685,plain,
( ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(t_a) != hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),sK3(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))))
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X0,X1,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) )
| ~ spl14_1 ),
inference(superposition,[],[f1813,f2743]) ).
fof(f4698,plain,
( ! [X0,X1] : c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X0,X1,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ~ spl14_1 ),
inference(forward_subsumption_resolution,[],[f4685,f2743]) ).
fof(f4798,plain,
( $false
| ~ spl14_1
| spl14_3 ),
inference(resolution,[],[f4698,f2412]) ).
fof(f4799,plain,
( ~ spl14_1
| spl14_3 ),
inference(avatar_contradiction_clause,[],[f4798]) ).
cnf(s2,plain,
( ~ spl14_1
| ~ spl14_3 ),
inference(sat_conversion,[],[f2413]) ).
cnf(s3,plain,
spl14_1,
inference(sat_conversion,[],[f2414]) ).
cnf(s37,plain,
( ~ spl14_1
| spl14_3 ),
inference(sat_conversion,[],[f4799]) ).
cnf(s38,plain,
spl14_3,
inference(rat,[],[s37,s3]) ).
cnf(s39,plain,
$false,
inference(rat,[],[s2,s38,s3]) ).
fof(f4800,plain,
$false,
inference(avatar_sat_refutation,[],[s39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW246+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n020.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 13:25:04 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 4.72/1.48 % (157484)Detected formulas, will run a generic FOF schedule.
% 4.72/1.48 % (157490)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=3232196494:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.72/1.48 % (157495)dis-21_1_sil=8000:lcm=predicate:random_seed=2337264282: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)
% 4.72/1.48 % (157492)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2536357799:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.72/1.48 % (157491)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=885722963:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.72/1.48 % (157493)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2214561692:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.72/1.48 % (157489)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=2729679930:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.72/1.48 % (157494)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4126664092:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.72/1.48 % (157492)Refutation not found, incomplete strategy
% 4.72/1.48 % (157492)------------------------------
% 4.72/1.48 % (157492)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.72/1.48 % (157492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.72/1.48 % (157492)CaDiCaL version: 2.1.3
% 4.72/1.48 % (157492)Termination reason: Refutation not found, incomplete strategy
% 4.72/1.48 % (157492)Time elapsed: 0.012 s
% 4.72/1.48 % (157492)Peak memory usage: 89 MB
% 4.72/1.48 % (157492)Instructions burned: 19 (million)
% 4.72/1.48 % (157495)Instruction limit reached!
% 4.72/1.48 % (157495)------------------------------
% 4.72/1.48 % (157495)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.72/1.48 % (157495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.72/1.48 % (157495)CaDiCaL version: 2.1.3
% 4.72/1.48 % (157495)Termination reason: Instruction limit
% 4.72/1.48 % (157495)Termination phase: Saturation
% 4.72/1.48 % (157495)Time elapsed: 0.068 s
% 4.72/1.48 % (157495)Peak memory usage: 90 MB
% 4.72/1.48 % (157495)Instructions burned: 130 (million)
% 4.72/1.48 % (157493)Instruction limit reached!
% 4.72/1.48 % (157493)------------------------------
% 4.72/1.48 % (157493)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.72/1.48 % (157493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.72/1.48 % (157493)CaDiCaL version: 2.1.3
% 4.72/1.48 % (157493)Termination reason: Instruction limit
% 4.72/1.48 % (157493)Termination phase: Saturation
% 4.72/1.48 % (157493)Time elapsed: 0.071 s
% 4.72/1.48 % (157493)Peak memory usage: 89 MB
% 4.72/1.48 % (157493)Instructions burned: 119 (million)
% 4.72/1.48 % (157494)Instruction limit reached!
% 4.72/1.48 % (157494)------------------------------
% 4.72/1.48 % (157494)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.72/1.48 % (157494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.72/1.48 % (157494)CaDiCaL version: 2.1.3
% 4.72/1.48 % (157494)Termination reason: Instruction limit
% 4.72/1.48 % (157494)Termination phase: Saturation
% 4.72/1.48 % (157494)Time elapsed: 0.074 s
% 4.72/1.48 % (157494)Peak memory usage: 91 MB
% 4.72/1.48 % (157494)Instructions burned: 140 (million)
% 4.72/1.48 % (157503)lrs+10_1_sil=8000:sp=occurrence:random_seed=2827648841:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 4.72/1.48 % (157505)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4123019584:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 4.72/1.48 % (157504)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2736346784:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 4.72/1.48 % (157492)------------------------------
% 4.72/1.48 % (157492)------------------------------
% 4.72/1.48 % (157504)Instruction limit reached!
% 4.72/1.48 % (157504)------------------------------
% 4.72/1.48 % (157504)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.72/1.48 % (157504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.68 % (157504)CaDiCaL version: 2.1.3
% 5.93/1.68 % (157504)Termination reason: Instruction limit
% 5.93/1.68 % (157504)Termination phase: Saturation
% 5.93/1.68 % (157504)Time elapsed: 0.083 s
% 5.93/1.68 % (157504)Peak memory usage: 90 MB
% 5.93/1.68 % (157504)Instructions burned: 157 (million)
% 5.93/1.68 % (157503)First to succeed.
% 5.93/1.68 % (157503)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-157484"
% 5.93/1.68 % (157505)Instruction limit reached!
% 5.93/1.68 % (157505)------------------------------
% 5.93/1.68 % (157505)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.68 % (157505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.68 % (157505)CaDiCaL version: 2.1.3
% 5.93/1.68 % (157505)Termination reason: Instruction limit
% 5.93/1.68 % (157505)Termination phase: Saturation
% 5.93/1.68 % (157505)Time elapsed: 0.175 s
% 5.93/1.68 % (157505)Peak memory usage: 91 MB
% 5.93/1.68 % (157505)Instructions burned: 325 (million)
% 5.93/1.68 % (157509)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=791097586:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 5.93/1.68 % (157510)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3554897621:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 5.93/1.68 % (157490)Also succeeded, but the first one will report.
% 5.93/1.68 % (157509)Instruction limit reached!
% 5.93/1.68 % (157509)------------------------------
% 5.93/1.68 % (157509)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.68 % (157509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.68 % (157509)CaDiCaL version: 2.1.3
% 5.93/1.68 % (157509)Termination reason: Instruction limit
% 5.93/1.68 % (157509)Termination phase: Saturation
% 5.93/1.68 % (157509)Time elapsed: 0.145 s
% 5.93/1.68 % (157509)Peak memory usage: 92 MB
% 5.93/1.68 % (157509)Instructions burned: 249 (million)
% 5.93/1.68 % (157511)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3368033408:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 5.93/1.68 % (157503)Refutation found. Thanks to Tanya!
% 5.93/1.68 % SZS status ContradictoryAxioms for theBenchmark
% 5.93/1.68 % SZS output start Proof for theBenchmark
% See solution above
% 5.93/1.68 % (157503)------------------------------
% 5.93/1.68 % (157503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.68 % (157503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.68 % (157503)CaDiCaL version: 2.1.3
% 5.93/1.68 % (157503)Termination reason: Refutation
% 5.93/1.68 % (157503)Time elapsed: 0.096 s
% 5.93/1.68 % (157503)Peak memory usage: 92 MB
% 5.93/1.68 % (157503)Instructions burned: 152 (million)
% 5.93/1.68 % (157503)------------------------------
% 5.93/1.68 % (157503)------------------------------
% 5.93/1.68 % (157484)Success in time 0.813 s
% 5.93/1.68 % Vampire exiting
%------------------------------------------------------------------------------