%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG387-1 : 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 : 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 09:19:55 AM UTC 2026
% Result : Unsatisfiable 5.36s 1.55s
% Output : Refutation 5.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 8 ( 5 unt; 0 def)
% Number of atoms : 11 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 5 ( 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f866,axiom,
! [X0,X1] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X1,c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ath_0) ).
fof(f870,axiom,
! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_v_0) ).
fof(f873,axiom,
! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_v0_0) ).
fof(f894,negated_conjecture,
! [X0] : ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1043,plain,
~ c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolution,[],[f894,f870]) ).
fof(f1044,plain,
~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(resolution,[],[f894,f873]) ).
fof(f1095,plain,
c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(resolution,[],[f1043,f866]) ).
fof(f1105,plain,
$false,
inference(forward_subsumption_resolution,[],[f1095,f1044]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG387-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n015.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Mon Sep 28 20:18:02 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running first-order theorem proving
% 0.10/0.23 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
% 5.36/1.55 % (2964619)Input is clausal, will run a generic CNF schedule.
% 5.36/1.55 % (2964626)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3241011891:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.36/1.55 % (2964628)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3868587864:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.36/1.55 % (2964629)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1482721879:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.36/1.55 % (2964624)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=499740567:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.36/1.55 % (2964630)dis-21_1_sil=8000:lcm=predicate:random_seed=2109394830: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)
% 5.36/1.55 % (2964627)lrs+10_1_sil=8000:sp=occurrence:random_seed=908190939:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.36/1.55 % (2964625)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=391605959:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.36/1.55 % (2964627)Instruction limit reached!
% 5.36/1.55 % (2964627)------------------------------
% 5.36/1.55 % (2964627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/1.55 % (2964627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.55 % (2964627)CaDiCaL version: 2.1.3
% 5.36/1.55 % (2964627)Termination reason: Instruction limit
% 5.36/1.55 % (2964627)Termination phase: Saturation
% 5.36/1.55 % (2964627)Time elapsed: 0.062 s
% 5.36/1.55 % (2964627)Peak memory usage: 89 MB
% 5.36/1.55 % (2964627)Instructions burned: 107 (million)
% 5.36/1.55 % (2964630)Instruction limit reached!
% 5.36/1.55 % (2964630)------------------------------
% 5.36/1.55 % (2964630)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/1.55 % (2964630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.55 % (2964630)CaDiCaL version: 2.1.3
% 5.36/1.55 % (2964630)Termination reason: Instruction limit
% 5.36/1.55 % (2964630)Termination phase: Saturation
% 5.36/1.55 % (2964630)Time elapsed: 0.073 s
% 5.36/1.55 % (2964630)Peak memory usage: 89 MB
% 5.36/1.55 % (2964630)Instructions burned: 117 (million)
% 5.36/1.55 % (2964628)Instruction limit reached!
% 5.36/1.55 % (2964628)------------------------------
% 5.36/1.55 % (2964628)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/1.55 % (2964628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.55 % (2964628)CaDiCaL version: 2.1.3
% 5.36/1.55 % (2964628)Termination reason: Instruction limit
% 5.36/1.55 % (2964628)Termination phase: Saturation
% 5.36/1.55 % (2964628)Time elapsed: 0.078 s
% 5.36/1.55 % (2964628)Peak memory usage: 89 MB
% 5.36/1.55 % (2964628)Instructions burned: 114 (million)
% 5.36/1.55 % (2964629)Instruction limit reached!
% 5.36/1.55 % (2964629)------------------------------
% 5.36/1.55 % (2964629)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/1.55 % (2964629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.55 % (2964629)CaDiCaL version: 2.1.3
% 5.36/1.55 % (2964629)Termination reason: Instruction limit
% 5.36/1.55 % (2964629)Termination phase: Saturation
% 5.36/1.55 % (2964629)Time elapsed: 0.122 s
% 5.36/1.55 % (2964629)Peak memory usage: 90 MB
% 5.36/1.55 % (2964629)Instructions burned: 181 (million)
% 5.36/1.55 % (2964638)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=1547665907:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.36/1.55 % (2964640)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3029823019:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.36/1.55 % (2964639)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2767652915: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)
% 5.36/1.55 % (2964638)First to succeed.
% 5.36/1.55 % (2964638)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2964619"
% 5.36/1.55 % (2964640)Also succeeded, but the first one will report.
% 5.36/1.55 % (2964639)Also succeeded, but the first one will report.
% 5.36/1.55 % (2964641)lrs+10_64_to=lpo:sil=8000:random_seed=700019311:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 5.36/1.55 % (2964641)Instruction limit reached!
% 5.36/1.55 % (2964641)------------------------------
% 5.36/1.55 % (2964641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/1.55 % (2964641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.55 % (2964641)CaDiCaL version: 2.1.3
% 5.36/1.55 % (2964641)Termination reason: Instruction limit
% 5.36/1.55 % (2964641)Termination phase: Saturation
% 5.36/1.55 % (2964641)Time elapsed: 0.084 s
% 5.36/1.55 % (2964641)Peak memory usage: 90 MB
% 5.36/1.55 % (2964641)Instructions burned: 127 (million)
% 5.36/1.55 % (2964626)Also succeeded, but the first one will report.
% 5.36/1.55 % (2964638)Refutation found. Thanks to Tanya!
% 5.36/1.55 % SZS status Unsatisfiable for theBenchmark
% 5.36/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 5.36/1.55 % (2964638)------------------------------
% 5.36/1.55 % (2964638)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/1.55 % (2964638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.55 % (2964638)CaDiCaL version: 2.1.3
% 5.36/1.55 % (2964638)Termination reason: Refutation
% 5.36/1.55 % (2964638)Time elapsed: 0.008 s
% 5.36/1.55 % (2964638)Peak memory usage: 89 MB
% 5.36/1.55 % (2964638)Instructions burned: 9 (million)
% 5.36/1.55 % (2964638)------------------------------
% 5.36/1.55 % (2964638)------------------------------
% 5.36/1.55 % (2964619)Success in time 0.692 s
% 5.36/1.55 % Vampire exiting
%------------------------------------------------------------------------------