%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG373-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 0.17s 0.26s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 31 ( 17 unt; 0 def)
% Number of atoms : 50 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 20 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 38 ( 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f35,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| X1 = c_HOL_Ozero__class_Ozero(X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).
fof(f36,plain,
! [X0,X1] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) ),
inference(reorient_equations,[],[f35]) ).
fof(f112,axiom,
! [X0,X1] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X1,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__le__zero_0) ).
fof(f219,axiom,
! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X0,X1),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__bound__exists_0) ).
fof(f284,axiom,
! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__abs__def_1) ).
fof(f316,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X1,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__not__less__zero_0) ).
fof(f348,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X0,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
fof(f356,axiom,
! [X0] : ~ c_HOL_Oord__class_Oless(X0,X0,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_1) ).
fof(f394,axiom,
! [X2,X0,X1] :
( c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
fof(f401,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/sandbox/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
fof(f419,negated_conjecture,
! [X0] : c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f420,negated_conjecture,
! [X0] : ~ c_HOL_Oord__class_Oless(v_x(X0),X0,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f469,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).
fof(f496,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
fof(f501,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
fof(f513,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f595,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(superposition,[],[f316,f419]) ).
fof(f596,plain,
! [X0] : ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_subsumption_resolution,[],[f595,f513]) ).
fof(f597,plain,
! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0,
inference(resolution,[],[f401,f496]) ).
fof(f731,plain,
! [X0] : c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolution,[],[f284,f596]) ).
fof(f963,plain,
! [X0] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(superposition,[],[f112,f731]) ).
fof(f968,plain,
! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_subsumption_resolution,[],[f963,f469]) ).
fof(f971,plain,
! [X0] : c_lessequals(v_x(X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f968,f597]) ).
fof(f1508,plain,
! [X0,X1] :
( ~ c_lessequals(X0,v_x(X1),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[],[f348,f971]) ).
fof(f1566,plain,
! [X0,X1] :
( c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(v_x(X1),X0,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(resolution,[],[f1508,f394]) ).
fof(f1572,plain,
! [X0,X1] :
( c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(v_x(X1),X0,tc_RealDef_Oreal) ),
inference(forward_subsumption_resolution,[],[f1566,f501]) ).
fof(f1715,plain,
! [X0] : c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolution,[],[f1572,f420]) ).
fof(f1757,plain,
! [X0] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(resolution,[],[f1715,f36]) ).
fof(f1771,plain,
! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0,
inference(forward_subsumption_resolution,[],[f1757,f469]) ).
fof(f2009,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(superposition,[],[f219,f1771]) ).
fof(f2320,plain,
$false,
inference(forward_subsumption_resolution,[],[f2009,f356]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG373-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.16 % Computer : n018.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Mon Sep 28 20:16:10 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 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
% 0.17/0.26 % (3721881)Will run a generic schedule for satisfiability detection.
% 0.17/0.26 % (3721889)dis+10_1_sil=32000:sp=arity:random_seed=2986658249:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.26 % (3721887)% WARNING: option uhcvi not known.
% 0.17/0.26 % (3721886)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1436559067_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.26 % (3721887)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1834925110:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.26 % (3721888)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1133715035:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.26 % (3721890)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1706532076:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.26 % (3721891)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1424365023:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.26 % (3721892)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2824715068:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.26 % (3721889) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3721881-3721889"...
% 0.17/0.26 % (3721889)...printing done.
% 0.17/0.26 % (3721889)Refutation found. Thanks to Tanya!
% 0.17/0.26 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.26 % (3721889)------------------------------
% 0.17/0.26 % (3721889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.26 % (3721889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.26 % (3721889)CaDiCaL version: 2.1.3
% 0.17/0.26 % (3721889)Termination reason: Refutation
% 0.17/0.26 % (3721889)Time elapsed: 0.019 s
% 0.17/0.26 % (3721889)Peak memory usage: 12 MB
% 0.17/0.26 % (3721889)Instructions burned: 52 (million)
% 0.17/0.26 % (3721881)Success in time 0.057 s
% 0.17/0.26 % Vampire exiting
%------------------------------------------------------------------------------