%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG342-1 : 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 : n012.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 09:19:49 AM UTC 2026
% Result : Unsatisfiable 2.35s 0.73s
% Output : Refutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 7 ( 3 unt; 0 def)
% Number of atoms : 11 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 3 ( 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f520,axiom,
! [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_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f521,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f522,negated_conjecture,
! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f523,negated_conjecture,
! [X0] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_x(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f795,plain,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[],[f520,f523]) ).
fof(f797,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_subsumption_resolution,[],[f795,f522]) ).
fof(f798,plain,
$false,
inference(forward_subsumption_resolution,[],[f797,f521]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG342-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Mon Sep 28 20:09:04 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running first-order theorem proving
% 0.08/0.12 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
% 2.35/0.73 % (3696191)Input is clausal, will run a generic CNF schedule.
% 2.35/0.73 % (3696200)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3138425587:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.35/0.73 % (3696197)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=441589947:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.35/0.73 % (3696202)dis-21_1_sil=8000:lcm=predicate:random_seed=1434039903: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)
% 2.35/0.73 % (3696199)lrs+10_1_sil=8000:sp=occurrence:random_seed=2435539277:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.35/0.73 % (3696196)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=709745272:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.35/0.73 % (3696201)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1698830228:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.35/0.73 % (3696198)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4200784973:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.35/0.73 % (3696201)First to succeed.
% 2.35/0.73 % (3696201)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3696191"
% 2.35/0.73 % (3696202)Instruction limit reached!
% 2.35/0.73 % (3696202)------------------------------
% 2.35/0.73 % (3696202)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/0.73 % (3696202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.73 % (3696202)CaDiCaL version: 2.1.3
% 2.35/0.73 % (3696202)Termination reason: Instruction limit
% 2.35/0.73 % (3696202)Termination phase: Saturation
% 2.35/0.73 % (3696202)Time elapsed: 0.025 s
% 2.35/0.73 % (3696202)Peak memory usage: 89 MB
% 2.35/0.73 % (3696202)Instructions burned: 117 (million)
% 2.35/0.73 % (3696200)Instruction limit reached!
% 2.35/0.73 % (3696200)------------------------------
% 2.35/0.73 % (3696200)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/0.73 % (3696200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.73 % (3696200)CaDiCaL version: 2.1.3
% 2.35/0.73 % (3696200)Termination reason: Instruction limit
% 2.35/0.73 % (3696200)Termination phase: Saturation
% 2.35/0.73 % (3696200)Time elapsed: 0.037 s
% 2.35/0.73 % (3696200)Peak memory usage: 88 MB
% 2.35/0.73 % (3696200)Instructions burned: 116 (million)
% 2.35/0.73 % (3696199)Instruction limit reached!
% 2.35/0.73 % (3696199)------------------------------
% 2.35/0.73 % (3696199)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/0.73 % (3696199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.73 % (3696199)CaDiCaL version: 2.1.3
% 2.35/0.73 % (3696199)Termination reason: Instruction limit
% 2.35/0.73 % (3696199)Termination phase: Saturation
% 2.35/0.73 % (3696199)Time elapsed: 0.038 s
% 2.35/0.73 % (3696199)Peak memory usage: 89 MB
% 2.35/0.73 % (3696199)Instructions burned: 107 (million)
% 2.35/0.73 % (3696212)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=381848219:st=4:i=219:sd=3:ss=axioms_2998 on theBenchmark for (2998ds/219Mi)
% 2.35/0.73 % (3696211)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3159953743:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2998 on theBenchmark for (2998ds/189Mi)
% 2.35/0.73 % (3696210)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=3533771776:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.35/0.73 % (3696210)Also succeeded, but the first one will report.
% 2.35/0.73 % (3696212)Also succeeded, but the first one will report.
% 2.35/0.73 % (3696211)Also succeeded, but the first one will report.
% 2.35/0.73 % (3696201)Refutation found. Thanks to Tanya!
% 2.35/0.73 % SZS status Unsatisfiable for theBenchmark
% 2.35/0.73 % SZS output start Proof for theBenchmark
% See solution above
% 2.35/0.73 % (3696201)------------------------------
% 2.35/0.73 % (3696201)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/0.73 % (3696201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.73 % (3696201)CaDiCaL version: 2.1.3
% 2.35/0.73 % (3696201)Termination reason: Refutation
% 2.35/0.73 % (3696201)Time elapsed: 0.010 s
% 2.35/0.73 % (3696201)Peak memory usage: 89 MB
% 2.35/0.73 % (3696201)Instructions burned: 29 (million)
% 2.35/0.73 % (3696201)------------------------------
% 2.35/0.73 % (3696201)------------------------------
% 2.35/0.73 % (3696191)Success in time 0.317 s
% 2.35/0.73 % Vampire exiting
%------------------------------------------------------------------------------