%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG371-1 : 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 : n010.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 0.21s 1.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 29 ( 9 unt; 2 def)
% Number of atoms : 54 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 52 ( 27 ~; 23 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f456,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/sandbox2/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
fof(f460,axiom,
! [X0,X1] :
( c_lessequals(X0,X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_0) ).
fof(f469,axiom,
! [X0,X1] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__ge__zero_0) ).
fof(f494,axiom,
! [X0,X1] :
( ~ c_lessequals(X1,X0,tc_RealDef_Oreal)
| X0 = X1
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
fof(f501,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/sandbox2/benchmark/theBenchmark.p',cls_norm__not__less__zero_0) ).
fof(f512,negated_conjecture,
c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f513,negated_conjecture,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f573,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f702,definition,
( spl0_4
<=> v_r = c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f703,plain,
( v_r = c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f702]) ).
fof(f705,plain,
( v_r = c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex)
| ~ c_lessequals(v_r,c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(resolution,[],[f494,f513]) ).
fof(f713,definition,
( spl0_5
<=> c_lessequals(v_r,c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f714,plain,
( ~ c_lessequals(v_r,c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| spl0_5 ),
inference(avatar_component_clause,[],[f713]) ).
fof(f715,plain,
( ~ spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f705,f702,f713]) ).
fof(f747,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(v_r,X0,tc_RealDef_Oreal) )
| spl0_5 ),
inference(resolution,[],[f456,f714]) ).
fof(f753,plain,
( ~ c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| spl0_5 ),
inference(resolution,[],[f747,f469]) ).
fof(f754,plain,
( ~ c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f753,f573]) ).
fof(f757,plain,
( ~ c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_5 ),
inference(resolution,[],[f754,f460]) ).
fof(f759,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f757,f512]) ).
fof(f760,plain,
spl0_5,
inference(avatar_contradiction_clause,[],[f759]) ).
fof(f775,plain,
( ~ c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ spl0_4 ),
inference(superposition,[],[f501,f703]) ).
fof(f778,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f775,f512]) ).
fof(f782,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f778,f573]) ).
fof(f783,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f782]) ).
cnf(s3,plain,
( spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f715]) ).
cnf(s5,plain,
spl0_5,
inference(sat_conversion,[],[f760]) ).
cnf(s9,plain,
~ spl0_4,
inference(sat_conversion,[],[f783]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s3,s5,s9]) ).
fof(f789,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG371-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.20 % Computer : n010.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Mon Sep 28 20:14:03 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 Running first-order theorem proving
% 0.11/0.24 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
% 0.21/1.30 % (2266488)Input is clausal, will run a generic CNF schedule.
% 0.21/1.30 % (2266496)lrs+10_1_sil=8000:sp=occurrence:random_seed=2821830689:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.21/1.30 % (2266496)Instruction limit reached!
% 0.21/1.30 % (2266496)------------------------------
% 0.21/1.30 % (2266496)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (2266496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (2266496)CaDiCaL version: 2.1.3
% 0.21/1.30 % (2266496)Termination reason: Instruction limit
% 0.21/1.30 % (2266496)Termination phase: Saturation
% 0.21/1.30 % (2266496)Time elapsed: 0.037 s
% 0.21/1.30 % (2266496)Peak memory usage: 89 MB
% 0.21/1.30 % (2266496)Instructions burned: 108 (million)
% 0.21/1.30 % (2266498)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3192825320:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.21/1.30 % (2266494)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3200583968:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.21/1.30 % (2266495)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2331274988:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.21/1.30 % (2266493)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=3252929248:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.21/1.30 % (2266497)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1838532192:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.21/1.30 % (2266499)dis-21_1_sil=8000:lcm=predicate:random_seed=2219046858: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)
% 0.21/1.30 % (2266497)First to succeed.
% 0.21/1.30 % (2266498)Also succeeded, but the first one will report.
% 0.21/1.30 % (2266497)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2266488"
% 0.21/1.30 % (2266499)Instruction limit reached!
% 0.21/1.30 % (2266499)------------------------------
% 0.21/1.30 % (2266499)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (2266499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (2266499)CaDiCaL version: 2.1.3
% 0.21/1.30 % (2266499)Termination reason: Instruction limit
% 0.21/1.30 % (2266499)Termination phase: Saturation
% 0.21/1.30 % (2266499)Time elapsed: 0.050 s
% 0.21/1.30 % (2266499)Peak memory usage: 89 MB
% 0.21/1.30 % (2266499)Instructions burned: 120 (million)
% 0.21/1.30 % (2266501)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=682552533:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 0.21/1.30 % (2266501)Also succeeded, but the first one will report.
% 0.21/1.30 % (2266508)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1452317760: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)
% 0.21/1.30 % (2266508)Also succeeded, but the first one will report.
% 0.21/1.30 % (2266497)Refutation found. Thanks to Tanya!
% 0.21/1.30 % SZS status Unsatisfiable for theBenchmark
% 0.21/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.30 % (2266497)------------------------------
% 0.21/1.30 % (2266497)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (2266497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (2266497)CaDiCaL version: 2.1.3
% 0.21/1.30 % (2266497)Termination reason: Refutation
% 0.21/1.30 % (2266497)Time elapsed: 0.012 s
% 0.21/1.30 % (2266497)Peak memory usage: 90 MB
% 0.21/1.30 % (2266497)Instructions burned: 15 (million)
% 0.21/1.30 % (2266497)------------------------------
% 0.21/1.30 % (2266497)------------------------------
% 0.21/1.30 % (2266488)Success in time 0.441 s
% 0.21/1.30 % Vampire exiting
%------------------------------------------------------------------------------