%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG354-1 : 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 09:19:51 AM UTC 2026
% Result : Unsatisfiable 2.38s 0.73s
% Output : Refutation 2.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 15 unt; 6 def)
% Number of atoms : 71 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 61 ( 30 ~; 25 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 5 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f473,axiom,
! [X0] :
( v_thesis____
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_Power_Opower__class_Opower(X0,v_m____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).
fof(f475,axiom,
c_HOL_Oord__class_Oless(v_m____,v_na____,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f476,axiom,
v_m____ != c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f477,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != v_m____,
inference(reorient_equations,[],[f476]) ).
fof(f478,axiom,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_Power_Opower__class_Opower(v_sko__CHAINED__1(v_b,v_m____),v_m____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| v_m____ = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(v_m____,v_na____,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
fof(f479,plain,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_Power_Opower__class_Opower(v_sko__CHAINED__1(v_b,v_m____),v_m____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_nat) = v_m____
| ~ c_HOL_Oord__class_Oless(v_m____,v_na____,tc_nat) ),
inference(reorient_equations,[],[f478]) ).
fof(f480,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f584,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f794,plain,
~ sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_nat),v_m____),
inference(equality_proxy_replacement,[],[f477,f584]) ).
fof(f795,plain,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_Power_Opower__class_Opower(v_sko__CHAINED__1(v_b,v_m____),v_m____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_nat),v_m____)
| ~ c_HOL_Oord__class_Oless(v_m____,v_na____,tc_nat) ),
inference(equality_proxy_replacement,[],[f479,f584]) ).
fof(f799,definition,
( spl1_1
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_Power_Opower__class_Opower(X0,v_m____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f800,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_Power_Opower__class_Opower(X0,v_m____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f799]) ).
fof(f802,definition,
( spl1_2
<=> v_thesis____ ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f803,plain,
( v_thesis____
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f802]) ).
fof(f806,definition,
( spl1_3
<=> c_HOL_Oord__class_Oless(v_m____,v_na____,tc_nat) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f807,plain,
( ~ c_HOL_Oord__class_Oless(v_m____,v_na____,tc_nat)
| spl1_3 ),
inference(avatar_component_clause,[],[f806]) ).
fof(f809,definition,
( spl1_4
<=> sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_nat),v_m____) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f810,plain,
( sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_nat),v_m____)
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f809]) ).
fof(f812,definition,
( spl1_5
<=> c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_Power_Opower__class_Opower(v_sko__CHAINED__1(v_b,v_m____),v_m____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f813,plain,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_Power_Opower__class_Opower(v_sko__CHAINED__1(v_b,v_m____),v_m____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f812]) ).
fof(f814,plain,
( ~ spl1_3
| spl1_4
| spl1_5 ),
inference(avatar_split_clause,[],[f795,f812,f809,f806]) ).
fof(f815,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f473,f802,f799]) ).
fof(f816,plain,
( $false
| ~ spl1_2 ),
inference(resolution,[],[f803,f480]) ).
fof(f817,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f816]) ).
fof(f818,plain,
( $false
| spl1_3 ),
inference(resolution,[],[f475,f807]) ).
fof(f819,plain,
spl1_3,
inference(avatar_contradiction_clause,[],[f818]) ).
fof(f820,plain,
( $false
| ~ spl1_1
| ~ spl1_5 ),
inference(resolution,[],[f813,f800]) ).
fof(f821,plain,
( ~ spl1_1
| ~ spl1_5 ),
inference(avatar_contradiction_clause,[],[f820]) ).
fof(f822,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f794,f810]) ).
fof(f823,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f822]) ).
cnf(s2,plain,
( ~ spl1_3
| spl1_4
| spl1_5 ),
inference(sat_conversion,[],[f814]) ).
cnf(s3,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f815]) ).
cnf(s4,plain,
~ spl1_2,
inference(sat_conversion,[],[f817]) ).
cnf(s5,plain,
spl1_3,
inference(sat_conversion,[],[f819]) ).
cnf(s6,plain,
( ~ spl1_1
| ~ spl1_5 ),
inference(sat_conversion,[],[f821]) ).
cnf(s7,plain,
~ spl1_4,
inference(sat_conversion,[],[f823]) ).
cnf(s8,plain,
spl1_1,
inference(rat,[],[s3,s4]) ).
cnf(s9,plain,
~ spl1_5,
inference(rat,[],[s6,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s2,s9,s7,s5]) ).
fof(f824,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG354-1 : 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 20:09:19 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 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
% 2.38/0.73 % (3696627)Input is clausal, will run a generic CNF schedule.
% 2.38/0.73 % (3696634)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1272457404:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.38/0.73 % (3696638)dis-21_1_sil=8000:lcm=predicate:random_seed=1133132553: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)
% 2.38/0.73 % (3696636)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1736213215:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.38/0.73 % (3696637)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2210987633:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.38/0.73 % (3696633)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3985608783:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.38/0.73 % (3696632)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=2695635363:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.38/0.73 % (3696635)lrs+10_1_sil=8000:sp=occurrence:random_seed=1596335585:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.38/0.73 % (3696638)First to succeed.
% 2.38/0.73 % (3696638)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3696627"
% 2.38/0.73 % (3696637)Also succeeded, but the first one will report.
% 2.38/0.73 % (3696635)Also succeeded, but the first one will report.
% 2.38/0.73 % (3696636)Instruction limit reached!
% 2.38/0.73 % (3696636)------------------------------
% 2.38/0.73 % (3696636)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.38/0.73 % (3696636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.73 % (3696636)CaDiCaL version: 2.1.3
% 2.38/0.73 % (3696636)Termination reason: Instruction limit
% 2.38/0.73 % (3696636)Termination phase: Saturation
% 2.38/0.73 % (3696636)Time elapsed: 0.036 s
% 2.38/0.73 % (3696636)Peak memory usage: 88 MB
% 2.38/0.73 % (3696636)Instructions burned: 117 (million)
% 2.38/0.73 % (3696638)Refutation found. Thanks to Tanya!
% 2.38/0.73 % SZS status Unsatisfiable for theBenchmark
% 2.38/0.73 % SZS output start Proof for theBenchmark
% See solution above
% 2.38/0.73 % (3696638)------------------------------
% 2.38/0.73 % (3696638)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.38/0.73 % (3696638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.73 % (3696638)CaDiCaL version: 2.1.3
% 2.38/0.73 % (3696638)Termination reason: Refutation
% 2.38/0.73 % (3696638)Time elapsed: 0.004 s
% 2.38/0.73 % (3696638)Peak memory usage: 89 MB
% 2.38/0.73 % (3696638)Instructions burned: 14 (million)
% 2.38/0.73 % (3696638)------------------------------
% 2.38/0.73 % (3696638)------------------------------
% 2.38/0.73 % (3696627)Success in time 0.309 s
% 2.38/0.73 % Vampire exiting
%------------------------------------------------------------------------------