%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG372-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 09:19:53 AM UTC 2026
% Result : Unsatisfiable 3.64s 1.23s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 35 ( 11 unt; 4 def)
% Number of atoms : 62 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 52 ( 25 ~; 23 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 13 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f862,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rp_0) ).
fof(f868,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__le__zero__iff_1) ).
fof(f878,axiom,
! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X0,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__trans_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1027,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
fof(f1052,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f1125,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f1490,plain,
! [X0,X1] :
( sQ0_eqProxy(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0),X1)
| ~ class_OrderedGroup_Ogroup__add(X0) ),
inference(equality_proxy_replacement,[],[f914,f1125]) ).
fof(f1494,plain,
( ~ sQ0_eqProxy(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) ),
inference(equality_proxy_replacement,[],[f926,f1125]) ).
fof(f1496,plain,
! [X0,X1] :
( sQ0_eqProxy(X1,X0)
| ~ sQ0_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f1125]) ).
fof(f1499,definition,
( spl1_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,[spl1_1])],[avatar_definition]) ).
fof(f1500,plain,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| spl1_1 ),
inference(avatar_component_clause,[],[f1499]) ).
fof(f1502,definition,
( spl1_2
<=> sQ0_eqProxy(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,[spl1_2])],[avatar_definition]) ).
fof(f1503,plain,
( ~ sQ0_eqProxy(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))
| spl1_2 ),
inference(avatar_component_clause,[],[f1502]) ).
fof(f1504,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f1494,f1502,f1499]) ).
fof(f1506,definition,
( spl1_3
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f1507,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f1506]) ).
fof(f1512,plain,
spl1_3,
inference(avatar_split_clause,[],[f862,f1506]) ).
fof(f1650,plain,
c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolution,[],[f868,f1052]) ).
fof(f1727,plain,
( ! [X0] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,v_r,tc_RealDef_Oreal) )
| spl1_1 ),
inference(resolution,[],[f878,f1500]) ).
fof(f1729,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| spl1_1 ),
inference(resolution,[],[f1727,f1650]) ).
fof(f1741,plain,
( $false
| spl1_1
| ~ spl1_3 ),
inference(resolution,[],[f1729,f1507]) ).
fof(f1744,plain,
( spl1_1
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f1741]) ).
fof(f1746,plain,
( ~ sQ0_eqProxy(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_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex))
| spl1_2 ),
inference(resolution,[],[f1503,f1496]) ).
fof(f1754,plain,
( ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| spl1_2 ),
inference(resolution,[],[f1746,f1490]) ).
fof(f1760,plain,
( $false
| spl1_2 ),
inference(resolution,[],[f1754,f1027]) ).
fof(f1761,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f1760]) ).
cnf(s1,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f1504]) ).
cnf(s3,plain,
spl1_3,
inference(sat_conversion,[],[f1512]) ).
cnf(s4,plain,
( spl1_1
| ~ spl1_3 ),
inference(sat_conversion,[],[f1744]) ).
cnf(s7,plain,
spl1_2,
inference(sat_conversion,[],[f1761]) ).
cnf(s8,plain,
spl1_1,
inference(rat,[],[s4,s3]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s7,s8]) ).
fof(f1762,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG372-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n011.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
% 0.08/0.20 % DateTime : Mon Sep 28 20:14:01 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.64/1.23 % (3720861)Input is clausal, will run a generic CNF schedule.
% 3.64/1.23 % (3720870)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1913525477:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.64/1.23 % (3720869)lrs+10_1_sil=8000:sp=occurrence:random_seed=2576781625:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.64/1.23 % (3720871)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4123231313:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.64/1.23 % (3720867)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=409561422:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.64/1.23 % (3720868)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2944805434:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.64/1.23 % (3720866)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=3687737732:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.64/1.23 % (3720872)dis-21_1_sil=8000:lcm=predicate:random_seed=195496536: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)
% 3.64/1.23 % (3720870)Instruction limit reached!
% 3.64/1.23 % (3720870)------------------------------
% 3.64/1.23 % (3720870)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.23 % (3720870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.23 % (3720870)CaDiCaL version: 2.1.3
% 3.64/1.23 % (3720870)Termination reason: Instruction limit
% 3.64/1.23 % (3720870)Termination phase: Saturation
% 3.64/1.23 % (3720870)Time elapsed: 0.039 s
% 3.64/1.23 % (3720870)Peak memory usage: 89 MB
% 3.64/1.23 % (3720870)Instructions burned: 114 (million)
% 3.64/1.23 % (3720872)First to succeed.
% 3.64/1.23 % (3720872)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3720861"
% 3.64/1.23 % (3720869)Instruction limit reached!
% 3.64/1.23 % (3720869)------------------------------
% 3.64/1.23 % (3720869)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.23 % (3720869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.23 % (3720869)CaDiCaL version: 2.1.3
% 3.64/1.23 % (3720869)Termination reason: Instruction limit
% 3.64/1.23 % (3720869)Termination phase: Saturation
% 3.64/1.23 % (3720869)Time elapsed: 0.071 s
% 3.64/1.23 % (3720869)Peak memory usage: 89 MB
% 3.64/1.23 % (3720869)Instructions burned: 108 (million)
% 3.64/1.23 % (3720871)Instruction limit reached!
% 3.64/1.23 % (3720871)------------------------------
% 3.64/1.23 % (3720871)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.23 % (3720871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.23 % (3720871)CaDiCaL version: 2.1.3
% 3.64/1.23 % (3720871)Termination reason: Instruction limit
% 3.64/1.23 % (3720871)Termination phase: Saturation
% 3.64/1.23 % (3720871)Time elapsed: 0.097 s
% 3.64/1.23 % (3720871)Peak memory usage: 89 MB
% 3.64/1.23 % (3720871)Instructions burned: 180 (million)
% 3.64/1.23 % (3720880)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=3252544925:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.64/1.23 % (3720880)Refutation not found, incomplete strategy
% 3.64/1.23 % (3720880)------------------------------
% 3.64/1.23 % (3720880)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.23 % (3720880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.23 % (3720880)CaDiCaL version: 2.1.3
% 3.64/1.23 % (3720880)Termination reason: Refutation not found, incomplete strategy
% 3.64/1.23 % (3720880)Time elapsed: 0.006 s
% 3.64/1.23 % (3720880)Peak memory usage: 89 MB
% 3.64/1.23 % (3720880)Instructions burned: 7 (million)
% 3.64/1.23 % (3720881)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=4038159486: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)
% 3.64/1.23 % (3720881)Also succeeded, but the first one will report.
% 3.64/1.23 % (3720882)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2682579040:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.64/1.23 % (3720882)Also succeeded, but the first one will report.
% 3.64/1.23 % (3720872)Refutation found. Thanks to Tanya!
% 3.64/1.23 % SZS status Unsatisfiable for theBenchmark
% 3.64/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 3.64/1.23 % (3720872)------------------------------
% 3.64/1.23 % (3720872)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.23 % (3720872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.23 % (3720872)CaDiCaL version: 2.1.3
% 3.64/1.23 % (3720872)Termination reason: Refutation
% 3.64/1.23 % (3720872)Time elapsed: 0.020 s
% 3.64/1.23 % (3720872)Peak memory usage: 90 MB
% 3.64/1.23 % (3720872)Instructions burned: 36 (million)
% 3.64/1.23 % (3720872)------------------------------
% 3.64/1.23 % (3720872)------------------------------
% 3.64/1.23 % (3720861)Success in time 0.464 s
% 3.64/1.23 % Vampire exiting
%------------------------------------------------------------------------------