%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG367-1 : 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 : n015.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 09:19:52 AM UTC 2026
% Result : Unsatisfiable 3.84s 1.33s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 11 unt; 2 def)
% Number of atoms : 49 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 31 ~; 21 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 29 ( 0 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f835,axiom,
! [X2,X0,X1] : c_Polynomial_Opoly(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(X0,X1),X2,tc_Complex_Ocomplex) = c_Polynomial_Opoly(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__offset_1) ).
fof(f890,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X0),X3,X0) = c_Polynomial_Opoly(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__offset__poly_0) ).
fof(f891,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X0),X0) = c_Polynomial_Odegree(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_degree__offset__poly_0) ).
fof(f892,plain,
! [X2,X0,X1] :
( c_Polynomial_Odegree(X1,X0) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ),
inference(reorient_equations,[],[f891]) ).
fof(f937,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f938,negated_conjecture,
! [X0] :
( c_Polynomial_Opoly(X0,v_q(X0),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_p,c_HOL_Oplus__class_Oplus(v_z,v_q(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| c_Polynomial_Odegree(X0,tc_Complex_Ocomplex) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1046,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1119,definition,
( spl0_1
<=> v_thesis____ ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f1123,definition,
( spl0_2
<=> ! [X0] :
( c_Polynomial_Opoly(X0,v_q(X0),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_p,c_HOL_Oplus__class_Oplus(v_z,v_q(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| c_Polynomial_Odegree(X0,tc_Complex_Ocomplex) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f1124,plain,
( ! [X0] :
( c_Polynomial_Opoly(X0,v_q(X0),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_p,c_HOL_Oplus__class_Oplus(v_z,v_q(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| c_Polynomial_Odegree(X0,tc_Complex_Ocomplex) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f1123]) ).
fof(f1125,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f938,f1123,f1119]) ).
fof(f1126,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f937,f1119]) ).
fof(f1132,plain,
( ! [X0] :
( c_Polynomial_Opoly(X0,v_q(X0),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(v_z,v_p),v_q(X0),tc_Complex_Ocomplex)
| c_Polynomial_Odegree(X0,tc_Complex_Ocomplex) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) )
| ~ spl0_2 ),
inference(superposition,[],[f1124,f835]) ).
fof(f1136,plain,
! [X2,X0,X1] : c_Polynomial_Opoly(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),
inference(resolution,[],[f890,f1046]) ).
fof(f1137,plain,
! [X2,X0,X1] : c_Polynomial_Opoly(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(X1,X0),X2,tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),
inference(forward_demodulation,[],[f1136,f835]) ).
fof(f1528,plain,
( ! [X0,X1] :
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(X0,X1),v_q(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X0,tc_Complex_Ocomplex)),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(v_z,v_p),v_q(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X0,tc_Complex_Ocomplex)),tc_Complex_Ocomplex) )
| ~ spl0_2 ),
inference(superposition,[],[f1132,f1137]) ).
fof(f1595,plain,
( ! [X0,X1] :
( c_Polynomial_Odegree(X0,tc_Complex_Ocomplex) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(v_z,v_p),v_q(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_Complex_Ocomplex)),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(X1,X0),v_q(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) )
| ~ spl0_2 ),
inference(superposition,[],[f1528,f892]) ).
fof(f1596,plain,
( ! [X0,X1] :
( c_Polynomial_Opoly(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(v_z,v_p),v_q(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_Complex_Ocomplex)),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(X1,X0),v_q(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
| c_Polynomial_Odegree(X0,tc_Complex_Ocomplex) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1595,f1046]) ).
fof(f1600,plain,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)
| ~ spl0_2 ),
inference(equality_resolution,[],[f1596]) ).
fof(f1601,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f1600]) ).
fof(f1602,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f1601]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f1125]) ).
cnf(s2,plain,
~ spl0_1,
inference(sat_conversion,[],[f1126]) ).
cnf(s8,plain,
~ spl0_2,
inference(sat_conversion,[],[f1602]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s8,s2]) ).
fof(f1603,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG367-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n015.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 20:17:02 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 3.84/1.33 % (2962467)Input is clausal, will run a generic CNF schedule.
% 3.84/1.33 % (2962476)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1306726171:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.84/1.33 % (2962475)lrs+10_1_sil=8000:sp=occurrence:random_seed=3320586130:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.84/1.33 % (2962478)dis-21_1_sil=8000:lcm=predicate:random_seed=3239537637: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)
% 3.84/1.33 % (2962474)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=634723781:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.84/1.33 % (2962472)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=133030052:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.84/1.33 % (2962477)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3185825252:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.84/1.33 % (2962473)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2484004270:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.84/1.33 % (2962476)Instruction limit reached!
% 3.84/1.33 % (2962476)------------------------------
% 3.84/1.33 % (2962476)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.33 % (2962476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.33 % (2962476)CaDiCaL version: 2.1.3
% 3.84/1.33 % (2962476)Termination reason: Instruction limit
% 3.84/1.33 % (2962476)Termination phase: Saturation
% 3.84/1.33 % (2962476)Time elapsed: 0.039 s
% 3.84/1.33 % (2962476)Peak memory usage: 89 MB
% 3.84/1.33 % (2962476)Instructions burned: 117 (million)
% 3.84/1.33 % (2962477)First to succeed.
% 3.84/1.33 % (2962477)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2962467"
% 3.84/1.33 % (2962478)Instruction limit reached!
% 3.84/1.33 % (2962478)------------------------------
% 3.84/1.33 % (2962478)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.33 % (2962478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.33 % (2962478)CaDiCaL version: 2.1.3
% 3.84/1.33 % (2962478)Termination reason: Instruction limit
% 3.84/1.33 % (2962478)Termination phase: Saturation
% 3.84/1.33 % (2962478)Time elapsed: 0.069 s
% 3.84/1.33 % (2962478)Peak memory usage: 89 MB
% 3.84/1.33 % (2962478)Instructions burned: 117 (million)
% 3.84/1.33 % (2962475)Instruction limit reached!
% 3.84/1.33 % (2962475)------------------------------
% 3.84/1.33 % (2962475)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.33 % (2962475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.33 % (2962475)CaDiCaL version: 2.1.3
% 3.84/1.33 % (2962475)Termination reason: Instruction limit
% 3.84/1.33 % (2962475)Termination phase: Saturation
% 3.84/1.33 % (2962475)Time elapsed: 0.072 s
% 3.84/1.33 % (2962475)Peak memory usage: 90 MB
% 3.84/1.33 % (2962475)Instructions burned: 107 (million)
% 3.84/1.33 % (2962486)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=2932888068:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.84/1.33 % (2962486)Also succeeded, but the first one will report.
% 3.84/1.33 % (2962488)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1202566036:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.84/1.33 % (2962487)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3209322488: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)
% 3.84/1.33 % (2962488)Also succeeded, but the first one will report.
% 3.84/1.33 % (2962477)Refutation found. Thanks to Tanya!
% 3.84/1.33 % SZS status Unsatisfiable for theBenchmark
% 3.84/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.84/1.33 % (2962477)------------------------------
% 3.84/1.33 % (2962477)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.33 % (2962477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.33 % (2962477)CaDiCaL version: 2.1.3
% 3.84/1.33 % (2962477)Termination reason: Refutation
% 3.84/1.33 % (2962477)Time elapsed: 0.040 s
% 3.84/1.33 % (2962477)Peak memory usage: 90 MB
% 3.84/1.33 % (2962477)Instructions burned: 62 (million)
% 3.84/1.33 % (2962477)------------------------------
% 3.84/1.33 % (2962477)------------------------------
% 3.84/1.33 % (2962467)Success in time 0.484 s
% 3.84/1.33 % Vampire exiting
%------------------------------------------------------------------------------