%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWW246+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 01:39:42 PM UTC 2026
% Result : ContradictoryAxioms 1.22s 0.56s
% Output : Refutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 5 unt; 0 def)
% Number of atoms : 54 ( 30 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 61 ( 29 ~; 22 |; 4 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 39 ( 37 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact__C0_C) ).
fof(f69,axiom,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( hAPP(c_Polynomial_Opoly(X2,X1),X0) = c_Groups_Ozero__class_Ozero(X2)
<=> ( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Oorder(X2,X0,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__root) ).
fof(f1200,axiom,
class_Rings_Oidom(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
fof(f1202,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(f1422,plain,
! [X0,X1,X2] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
| ? [X3,X4] : hAPP(X0,X3) != hAPP(X0,X4) ),
inference(ennf_transformation,[],[f1202]) ).
fof(f1471,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(f1473,plain,
! [X0,X1,X2] :
( ( hAPP(c_Polynomial_Opoly(X2,X1),X0) = c_Groups_Ozero__class_Ozero(X2)
<=> ( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Oorder(X2,X0,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Oidom(X2) ),
inference(ennf_transformation,[],[f69]) ).
fof(f2296,plain,
! [X0,X1,X2] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
| hAPP(X0,sK2(X0)) != hAPP(X0,sK3(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X3,sK2(X0)),skolemize(X4,sK3(X0))],[f1422]) ).
fof(f2308,plain,
! [X0,X1,X2] :
( ( ( hAPP(c_Polynomial_Opoly(X2,X1),X0) = c_Groups_Ozero__class_Ozero(X2)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Oorder(X2,X0,X1) ) )
& ( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Oorder(X2,X0,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X1),X0) ) )
| ~ class_Rings_Oidom(X2) ),
inference(nnf_transformation,[],[f1473]) ).
fof(f2309,plain,
! [X0,X1,X2] :
( ( ( hAPP(c_Polynomial_Opoly(X2,X1),X0) = c_Groups_Ozero__class_Ozero(X2)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Oorder(X2,X0,X1) ) )
& ( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Oorder(X2,X0,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X1),X0) ) )
| ~ class_Rings_Oidom(X2) ),
inference(flattening,[],[f2308]) ).
fof(f2564,plain,
! [X2,X0,X1] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
| hAPP(X0,sK2(X0)) != hAPP(X0,sK3(X0)) ),
inference(cnf_transformation,[],[f2296]) ).
fof(f2618,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,[],[f1471]) ).
fof(f2624,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f2309]) ).
fof(f3830,plain,
class_Rings_Oidom(t_a),
inference(cnf_transformation,[],[f1200]) ).
fof(f3849,plain,
! [X2,X0] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0) ),
inference(equality_resolution,[],[f2624]) ).
fof(f6356,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),
inference(resolution,[],[f3849,f3830]) ).
fof(f6651,plain,
( hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),sK2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(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)))))
| ~ class_Rings_Oidom(t_a) ),
inference(resolution,[],[f2564,f2618]) ).
fof(f6652,plain,
( c_Groups_Ozero__class_Ozero(t_a) != hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),sK2(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))))
| ~ class_Rings_Oidom(t_a) ),
inference(forward_demodulation,[],[f6651,f6356]) ).
fof(f6653,plain,
( c_Groups_Ozero__class_Ozero(t_a) != c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Rings_Oidom(t_a) ),
inference(forward_demodulation,[],[f6652,f6356]) ).
fof(f6654,plain,
~ class_Rings_Oidom(t_a),
inference(trivial_inequality_removal,[],[f6653]) ).
fof(f6655,plain,
$false,
inference(resolution,[],[f6654,f3830]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW246+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n011.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 13:24:15 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.22/0.56 % (3380132)Will run a generic schedule for satisfiability detection.
% 1.22/0.56 % (3380141)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2215998688:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.22/0.56 % (3380138)% WARNING: option uhcvi not known.
% 1.22/0.56 % (3380139)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1907467317:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.22/0.56 % (3380140)dis+10_1_sil=32000:sp=arity:random_seed=1690838207:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.22/0.56 % (3380142)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=931095479:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.22/0.56 % (3380138)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=302914243:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.22/0.56 % (3380143)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1091290115:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.22/0.56 % (3380141)Instruction limit reached!
% 1.22/0.56 % (3380141)------------------------------
% 1.22/0.56 % (3380141)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.56 % (3380141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.56 % (3380141)CaDiCaL version: 2.1.3
% 1.22/0.56 % (3380141)Termination reason: Instruction limit
% 1.22/0.56 % (3380141)Termination phase: Saturation
% 1.22/0.56 % (3380141)Time elapsed: 0.035 s
% 1.22/0.56 % (3380141)Peak memory usage: 14 MB
% 1.22/0.56 % (3380141)Instructions burned: 124 (million)
% 1.22/0.56 % (3380137)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3843720244_2999 on theBenchmark for (2999ds/0Mi)
% 1.22/0.56 % (3380150)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1176729295:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 1.22/0.56 % (3380140)Instruction limit reached!
% 1.22/0.56 % (3380140)------------------------------
% 1.22/0.56 % (3380140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.56 % (3380140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.56 % (3380140)CaDiCaL version: 2.1.3
% 1.22/0.56 % (3380140)Termination reason: Instruction limit
% 1.22/0.56 % (3380140)Termination phase: Saturation
% 1.22/0.56 % (3380140)Time elapsed: 0.056 s
% 1.22/0.56 % (3380140)Peak memory usage: 14 MB
% 1.22/0.56 % (3380140)Instructions burned: 103 (million)
% 1.22/0.56 % (3380142)Instruction limit reached!
% 1.22/0.56 % (3380142)------------------------------
% 1.22/0.56 % (3380142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.56 % (3380142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.56 % (3380142)CaDiCaL version: 2.1.3
% 1.22/0.56 % (3380142)Termination reason: Instruction limit
% 1.22/0.56 % (3380142)Termination phase: Saturation
% 1.22/0.56 % (3380142)Time elapsed: 0.077 s
% 1.22/0.56 % (3380142)Peak memory usage: 15 MB
% 1.22/0.56 % (3380142)Instructions burned: 132 (million)
% 1.22/0.56 % (3380153)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2033030664:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.22/0.56 % (3380155)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=976779126:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.22/0.56 % (3380143)Instruction limit reached!
% 1.22/0.56 % (3380143)------------------------------
% 1.22/0.56 % (3380143)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.56 % (3380143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.56 % (3380143)CaDiCaL version: 2.1.3
% 1.22/0.56 % (3380143)Termination reason: Instruction limit
% 1.22/0.56 % (3380143)Termination phase: Saturation
% 1.22/0.56 % (3380143)Time elapsed: 0.099 s
% 1.22/0.56 % (3380143)Peak memory usage: 16 MB
% 1.22/0.56 % (3380143)Instructions burned: 160 (million)
% 1.22/0.56 % (3380160)ott-21_1_sil=16000:fs=off:random_seed=700272314:i=180:av=off:fsr=off_2997 on theBenchmark for (2997ds/180Mi)
% 1.22/0.56 % (3380153)Instruction limit reached!
% 1.22/0.56 % (3380153)------------------------------
% 1.22/0.56 % (3380153)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.56 % (3380153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.56 % (3380153)CaDiCaL version: 2.1.3
% 1.22/0.56 % (3380153)Termination reason: Instruction limit
% 1.22/0.56 % (3380153)Termination phase: Saturation
% 1.22/0.56 % (3380153)Time elapsed: 0.065 s
% 1.22/0.56 % (3380153)Peak memory usage: 14 MB
% 1.22/0.56 % (3380153)Instructions burned: 132 (million)
% 1.22/0.56 % (3380171)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3534675534:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 1.22/0.56 % (3380160) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3380132-3380160"...
% 1.22/0.56 % (3380160)...printing done.
% 1.22/0.56 % (3380160)Refutation found. Thanks to Tanya!
% 1.22/0.56 % SZS status ContradictoryAxioms for theBenchmark
% 1.22/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 1.22/0.56 % (3380160)------------------------------
% 1.22/0.56 % (3380160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.56 % (3380160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.56 % (3380160)CaDiCaL version: 2.1.3
% 1.22/0.56 % (3380160)Termination reason: Refutation
% 1.22/0.56 % (3380160)Time elapsed: 0.079 s
% 1.22/0.56 % (3380160)Peak memory usage: 14 MB
% 1.22/0.56 % (3380160)Instructions burned: 156 (million)
% 1.22/0.56 % (3380132)Success in time 0.306 s
% 1.22/0.56 % Vampire exiting
%------------------------------------------------------------------------------