%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG347-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 09:19:50 AM UTC 2026
% Result : Unsatisfiable 0.21s 1.41s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 11 unt; 2 def)
% Number of atoms : 65 ( 24 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 63 ( 31 ~; 30 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 15 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1295,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X0) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_offset__poly__eq__0__iff_0) ).
fof(f1296,plain,
! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1 ),
inference(reorient_equations,[],[f1295]) ).
fof(f1306,axiom,
! [X2,X0,X1] :
( ~ class_HOL_Ozero(X0)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X1,X2,X0),X0) = c_Suc(c_Polynomial_Odegree(X2,X0))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_degree__pCons__eq_0) ).
fof(f1307,plain,
! [X2,X0,X1] :
( ~ class_HOL_Ozero(X0)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X1,X2,X0),X0) = c_Suc(c_Polynomial_Odegree(X2,X0))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 ),
inference(reorient_equations,[],[f1306]) ).
fof(f1310,negated_conjecture,
class_Ring__and__Field_Ocomm__semiring__0(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f1311,negated_conjecture,
c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a) = c_Polynomial_Odegree(v_pa,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1312,negated_conjecture,
v_pa != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1313,negated_conjecture,
c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) != c_Suc(c_Polynomial_Odegree(v_pa,t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1322,axiom,
! [X0] :
( class_HOL_Ozero(X0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_HOL_Ozero) ).
fof(f1563,definition,
( spl0_5
<=> class_HOL_Ozero(t_a) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f1564,plain,
( class_HOL_Ozero(t_a)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f1563]) ).
fof(f1565,plain,
( ~ class_HOL_Ozero(t_a)
| spl0_5 ),
inference(avatar_component_clause,[],[f1563]) ).
fof(f1578,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| spl0_5 ),
inference(resolution,[],[f1565,f1322]) ).
fof(f1579,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f1578,f1310]) ).
fof(f1580,plain,
spl0_5,
inference(avatar_contradiction_clause,[],[f1579]) ).
fof(f1868,definition,
( spl0_11
<=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f1870,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f1868]) ).
fof(f1922,plain,
( ! [X0,X1] :
( c_Polynomial_Odegree(c_Polynomial_OpCons(X0,X1,t_a),t_a) = c_Suc(c_Polynomial_Odegree(X1,t_a))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = X1 )
| ~ spl0_5 ),
inference(resolution,[],[f1307,f1564]) ).
fof(f2382,plain,
( c_Suc(c_Polynomial_Odegree(v_pa,t_a)) != c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ spl0_5 ),
inference(superposition,[],[f1313,f1922]) ).
fof(f2395,plain,
( c_Suc(c_Polynomial_Odegree(v_pa,t_a)) != c_Suc(c_Polynomial_Odegree(v_pa,t_a))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ spl0_5 ),
inference(forward_demodulation,[],[f2382,f1311]) ).
fof(f2396,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f2395]) ).
fof(f2398,plain,
( spl0_11
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f2396,f1563,f1868]) ).
fof(f2405,plain,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ spl0_11 ),
inference(superposition,[],[f1296,f1870]) ).
fof(f2406,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f2405]) ).
fof(f2407,plain,
( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f2406,f1310]) ).
fof(f2415,plain,
( $false
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f2407,f1312]) ).
fof(f2416,plain,
~ spl0_11,
inference(avatar_contradiction_clause,[],[f2415]) ).
cnf(s4,plain,
spl0_5,
inference(sat_conversion,[],[f1580]) ).
cnf(s9,plain,
( ~ spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f2398]) ).
cnf(s11,plain,
~ spl0_11,
inference(sat_conversion,[],[f2416]) ).
cnf(s12,plain,
~ spl0_5,
inference(rat,[],[s9,s11]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s4,s12]) ).
fof(f2420,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG347-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n013.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 20:08:06 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 0.21/1.41 % (1509896)Input is clausal, will run a generic CNF schedule.
% 0.21/1.41 % (1509905)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1984983872:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.21/1.41 % (1509902)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1001586955:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.21/1.41 % (1509903)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1319855907:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.21/1.41 % (1509904)lrs+10_1_sil=8000:sp=occurrence:random_seed=1189573333:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.21/1.41 % (1509901)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=648563039:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.21/1.41 % (1509905)Instruction limit reached!
% 0.21/1.41 % (1509905)------------------------------
% 0.21/1.41 % (1509905)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.41 % (1509905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.41 % (1509905)CaDiCaL version: 2.1.3
% 0.21/1.41 % (1509905)Termination reason: Instruction limit
% 0.21/1.41 % (1509905)Termination phase: Saturation
% 0.21/1.41 % (1509905)Time elapsed: 0.042 s
% 0.21/1.41 % (1509905)Peak memory usage: 89 MB
% 0.21/1.41 % (1509905)Instructions burned: 116 (million)
% 0.21/1.41 % (1509907)dis-21_1_sil=8000:lcm=predicate:random_seed=3857000429: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)
% 0.21/1.41 % (1509906)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1774449894:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.21/1.41 % (1509904)Instruction limit reached!
% 0.21/1.41 % (1509904)------------------------------
% 0.21/1.41 % (1509904)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.41 % (1509904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.41 % (1509904)CaDiCaL version: 2.1.3
% 0.21/1.41 % (1509904)Termination reason: Instruction limit
% 0.21/1.41 % (1509904)Termination phase: Saturation
% 0.21/1.41 % (1509904)Time elapsed: 0.074 s
% 0.21/1.41 % (1509904)Peak memory usage: 89 MB
% 0.21/1.41 % (1509904)Instructions burned: 107 (million)
% 0.21/1.41 % (1509906)First to succeed.
% 0.21/1.41 % (1509906)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1509896"
% 0.21/1.41 % (1509907)Instruction limit reached!
% 0.21/1.41 % (1509907)------------------------------
% 0.21/1.41 % (1509907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.41 % (1509907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.41 % (1509907)CaDiCaL version: 2.1.3
% 0.21/1.41 % (1509907)Termination reason: Instruction limit
% 0.21/1.41 % (1509907)Termination phase: Saturation
% 0.21/1.41 % (1509907)Time elapsed: 0.069 s
% 0.21/1.41 % (1509907)Peak memory usage: 90 MB
% 0.21/1.41 % (1509907)Instructions burned: 118 (million)
% 0.21/1.41 % (1509913)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=2303668656:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.21/1.41 % (1509913)Instruction limit reached!
% 0.21/1.41 % (1509913)------------------------------
% 0.21/1.41 % (1509913)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.41 % (1509913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.41 % (1509913)CaDiCaL version: 2.1.3
% 0.21/1.41 % (1509913)Termination reason: Instruction limit
% 0.21/1.41 % (1509913)Termination phase: Saturation
% 0.21/1.41 % (1509913)Time elapsed: 0.047 s
% 0.21/1.41 % (1509913)Peak memory usage: 90 MB
% 0.21/1.41 % (1509913)Instructions burned: 144 (million)
% 0.21/1.41 % (1509916)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=510148225: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)
% 0.21/1.41 % (1509917)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3412296134:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 0.21/1.41 % (1509917)Also succeeded, but the first one will report.
% 0.21/1.41 % (1509916)Also succeeded, but the first one will report.
% 0.21/1.41 % (1509919)lrs+10_64_to=lpo:sil=8000:random_seed=157941805:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 0.21/1.41 % (1509906)Refutation found. Thanks to Tanya!
% 0.21/1.41 % SZS status Unsatisfiable for theBenchmark
% 0.21/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.41 % (1509906)------------------------------
% 0.21/1.41 % (1509906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.41 % (1509906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.41 % (1509906)CaDiCaL version: 2.1.3
% 0.21/1.41 % (1509906)Termination reason: Refutation
% 0.21/1.41 % (1509906)Time elapsed: 0.060 s
% 0.21/1.41 % (1509906)Peak memory usage: 90 MB
% 0.21/1.41 % (1509906)Instructions burned: 89 (million)
% 0.21/1.41 % (1509906)------------------------------
% 0.21/1.41 % (1509906)------------------------------
% 0.21/1.41 % (1509896)Success in time 0.536 s
% 0.21/1.41 % Vampire exiting
%------------------------------------------------------------------------------