%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG439-1 : 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 : n008.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 09:20:01 AM UTC 2026
% Result : Unsatisfiable 4.03s 1.61s
% Output : Refutation 4.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 5 unt; 2 def)
% Number of atoms : 46 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 18 ~; 19 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 2 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f941,axiom,
! [X0,X1] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_resolve__eq__raw_I2_J_0) ).
fof(f944,negated_conjecture,
( v_c != v_y
| c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) != v_y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f945,plain,
( v_c != v_y
| v_y != c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) ),
inference(reorient_equations,[],[f944]) ).
fof(f946,negated_conjecture,
( c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = v_y
| v_c = v_y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f947,plain,
( v_y = c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| v_c = v_y ),
inference(reorient_equations,[],[f946]) ).
fof(f1130,definition,
( spl0_1
<=> v_c = v_y ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f1131,plain,
( v_c != v_y
| spl0_1 ),
inference(avatar_component_clause,[],[f1130]) ).
fof(f1134,definition,
( spl0_2
<=> v_y = c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f1135,plain,
( v_y != c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| spl0_2 ),
inference(avatar_component_clause,[],[f1134]) ).
fof(f1136,plain,
( v_y = c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f1134]) ).
fof(f1137,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f947,f1134,f1130]) ).
fof(f1138,plain,
( ~ spl0_2
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f945,f1130,f1134]) ).
fof(f1189,plain,
( v_c = v_y
| ~ spl0_2 ),
inference(superposition,[],[f941,f1136]) ).
fof(f1193,plain,
( $false
| spl0_1
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1189,f1131]) ).
fof(f1194,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f1193]) ).
fof(f1195,plain,
( v_c != v_y
| spl0_2 ),
inference(forward_demodulation,[],[f1135,f941]) ).
fof(f1196,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f1195,f1134,f1130]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f1137]) ).
cnf(s2,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f1138]) ).
cnf(s12,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f1194]) ).
cnf(s13,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f1196]) ).
cnf(s14,plain,
spl0_1,
inference(rat,[],[s1,s12]) ).
cnf(s15,plain,
spl0_2,
inference(rat,[],[s13,s14]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s2,s15,s14]) ).
fof(f1197,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG439-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 % Computer : n008.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Mon Sep 28 20:25:24 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.28 Running first-order theorem proving
% 0.10/0.28 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
% 4.03/1.61 % (2587444)Input is clausal, will run a generic CNF schedule.
% 4.03/1.61 % (2587454)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4266836345:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.03/1.61 % (2587453)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1099174932:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.03/1.61 % (2587454)First to succeed.
% 4.03/1.61 % (2587454)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2587444"
% 4.03/1.61 % (2587453)Also succeeded, but the first one will report.
% 4.03/1.61 % (2587455)dis-21_1_sil=8000:lcm=predicate:random_seed=220660748: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)
% 4.03/1.61 % (2587452)lrs+10_1_sil=8000:sp=occurrence:random_seed=3854542204:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.03/1.61 % (2587450)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3499026220:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.03/1.61 % (2587451)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2682229163:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.03/1.61 % (2587449)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=1012045834:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.03/1.61 % (2587452)Also succeeded, but the first one will report.
% 4.03/1.61 % (2587455)Instruction limit reached!
% 4.03/1.61 % (2587455)------------------------------
% 4.03/1.61 % (2587455)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.03/1.61 % (2587455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/1.61 % (2587455)CaDiCaL version: 2.1.3
% 4.03/1.61 % (2587455)Termination reason: Instruction limit
% 4.03/1.61 % (2587455)Termination phase: Saturation
% 4.03/1.61 % (2587455)Time elapsed: 0.095 s
% 4.03/1.61 % (2587455)Peak memory usage: 89 MB
% 4.03/1.61 % (2587455)Instructions burned: 117 (million)
% 4.03/1.61 % (2587454)Refutation found. Thanks to Tanya!
% 4.03/1.61 % SZS status Unsatisfiable for theBenchmark
% 4.03/1.61 % SZS output start Proof for theBenchmark
% See solution above
% 4.03/1.61 % (2587454)------------------------------
% 4.03/1.61 % (2587454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.03/1.61 % (2587454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/1.61 % (2587454)CaDiCaL version: 2.1.3
% 4.03/1.61 % (2587454)Termination reason: Refutation
% 4.03/1.61 % (2587454)Time elapsed: 0.014 s
% 4.03/1.61 % (2587454)Peak memory usage: 90 MB
% 4.03/1.61 % (2587454)Instructions burned: 29 (million)
% 4.03/1.61 % (2587454)------------------------------
% 4.03/1.61 % (2587454)------------------------------
% 4.03/1.61 % (2587444)Success in time 0.461 s
% 4.03/1.61 % Vampire exiting
%------------------------------------------------------------------------------