%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG372-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 09:30:25 AM UTC 2026
% Result : Unsatisfiable 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 12 unt; 3 def)
% Number of atoms : 49 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 17 ~; 16 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 5 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f840,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__zero_0) ).
fof(f841,plain,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0) ),
inference(reorient_equations,[],[f840]) ).
fof(f862,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rp_0) ).
fof(f914,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
fof(f926,negated_conjecture,
( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1027,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
fof(f1052,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f1127,definition,
( spl0_1
<=> c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f1129,plain,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| spl0_1 ),
inference(avatar_component_clause,[],[f1127]) ).
fof(f1131,definition,
( spl0_2
<=> c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f1133,plain,
( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_2 ),
inference(avatar_component_clause,[],[f1131]) ).
fof(f1134,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f926,f1131,f1127]) ).
fof(f1136,definition,
( spl0_3
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f1138,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f1136]) ).
fof(f1143,plain,
spl0_3,
inference(avatar_split_clause,[],[f862,f1136]) ).
fof(f1215,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolution,[],[f841,f1052]) ).
fof(f1223,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| spl0_1 ),
inference(superposition,[],[f1129,f1215]) ).
fof(f1229,plain,
( $false
| spl0_1
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f1223,f1138]) ).
fof(f1230,plain,
( spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f1229]) ).
fof(f1233,plain,
! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0,
inference(resolution,[],[f914,f1027]) ).
fof(f1237,plain,
( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| spl0_2 ),
inference(superposition,[],[f1133,f1233]) ).
fof(f1238,plain,
( $false
| spl0_2 ),
inference(trivial_inequality_removal,[],[f1237]) ).
fof(f1239,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f1238]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f1134]) ).
cnf(s3,plain,
spl0_3,
inference(sat_conversion,[],[f1143]) ).
cnf(s5,plain,
( spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f1230]) ).
cnf(s6,plain,
spl0_2,
inference(sat_conversion,[],[f1239]) ).
cnf(s7,plain,
spl0_1,
inference(rat,[],[s5,s3]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s6,s7]) ).
fof(f1240,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG372-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n015.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 20:17:17 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.31 % (2962904)Will run a generic schedule for satisfiability detection.
% 0.21/0.31 % (2962912)dis+10_1_sil=32000:sp=arity:random_seed=340424675:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.31 % (2962910)% WARNING: option uhcvi not known.
% 0.21/0.31 % (2962909)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2933889157_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.31 % (2962910)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3881685567:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.31 % (2962911)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3595907665:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.31 % (2962913)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1880384551:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.31 % (2962912) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2962904-2962912"...
% 0.21/0.31 % (2962914)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1437260768:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.31 % (2962915)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3049795308:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.31 % (2962912)...printing done.
% 0.21/0.31 % (2962912)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.31 % (2962912)------------------------------
% 0.21/0.31 % (2962912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (2962912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (2962912)CaDiCaL version: 2.1.3
% 0.21/0.31 % (2962912)Termination reason: Refutation
% 0.21/0.31 % (2962912)Time elapsed: 0.008 s
% 0.21/0.31 % (2962912)Peak memory usage: 13 MB
% 0.21/0.31 % (2962912)Instructions burned: 20 (million)
% 0.21/0.31 % (2962904)Success in time 0.07 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------