%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG406-1 : 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 : n004.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 09:19:57 AM UTC 2026
% Result : Unsatisfiable 5.26s 1.42s
% Output : Refutation 5.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 34 ( 15 unt; 3 def)
% Number of atoms : 61 ( 1 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 54 ( 27 ~; 24 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 3 ( 1 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 : 8 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f35,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_t_I1_J_0) ).
fof(f430,axiom,
! [X0,X1] :
( c_lessequals(X0,X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_0) ).
fof(f627,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/sandbox/benchmark/theBenchmark.p',cls_norm__ge__zero_0) ).
fof(f634,axiom,
c_HOL_Oord__class_Oless(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_t_I2_J_0) ).
fof(f636,axiom,
! [X2,X0,X1] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
fof(f682,axiom,
! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__1_0) ).
fof(f690,negated_conjecture,
~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f759,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).
fof(f790,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f810,plain,
~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f690,f682]) ).
fof(f811,plain,
( ~ class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal)
| ~ c_lessequals(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(resolution,[],[f810,f636]) ).
fof(f815,plain,
( ~ c_lessequals(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(forward_subsumption_resolution,[],[f811,f759]) ).
fof(f817,definition,
( spl0_1
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f819,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| spl0_1 ),
inference(avatar_component_clause,[],[f817]) ).
fof(f821,definition,
( spl0_2
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f823,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal)
| spl0_2 ),
inference(avatar_component_clause,[],[f821]) ).
fof(f825,definition,
( spl0_3
<=> c_lessequals(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f827,plain,
( ~ c_lessequals(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_3 ),
inference(avatar_component_clause,[],[f825]) ).
fof(f828,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f815,f825,f821,f817]) ).
fof(f829,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| spl0_1 ),
inference(resolution,[],[f819,f627]) ).
fof(f833,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f829,f790]) ).
fof(f834,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f833]) ).
fof(f835,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal)
| spl0_2 ),
inference(resolution,[],[f823,f430]) ).
fof(f838,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f835,f35]) ).
fof(f839,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f838]) ).
fof(f854,plain,
( ~ c_HOL_Oord__class_Oless(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_3 ),
inference(resolution,[],[f827,f430]) ).
fof(f857,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f854,f634]) ).
fof(f858,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f857]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f828]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f834]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f839]) ).
cnf(s5,plain,
spl0_3,
inference(sat_conversion,[],[f858]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s5,s3,s2]) ).
fof(f859,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG406-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n004.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Mon Sep 28 20:19:07 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running first-order theorem proving
% 0.09/0.20 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
% 4.59/1.32 % (715631)Input is clausal, will run a generic CNF schedule.
% 4.59/1.32 % (715641)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4071992094:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.59/1.32 % (715636)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=4266270165:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.59/1.32 % (715639)lrs+10_1_sil=8000:sp=occurrence:random_seed=2686843458:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.59/1.32 % (715638)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4256593047:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.59/1.32 % (715640)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=855338676:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.59/1.32 % (715637)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3508486686:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.59/1.32 % (715642)dis-21_1_sil=8000:lcm=predicate:random_seed=3050539292: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)
% 4.59/1.32 % (715641)Instruction limit reached!
% 4.59/1.32 % (715641)------------------------------
% 4.59/1.32 % (715641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.32 % (715641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.32 % (715641)CaDiCaL version: 2.1.3
% 4.59/1.32 % (715641)Termination reason: Instruction limit
% 4.59/1.32 % (715641)Termination phase: Saturation
% 4.59/1.32 % (715641)Time elapsed: 0.064 s
% 4.59/1.32 % (715641)Peak memory usage: 90 MB
% 4.59/1.32 % (715641)Instructions burned: 181 (million)
% 4.59/1.32 % (715640)Instruction limit reached!
% 4.59/1.32 % (715640)------------------------------
% 4.59/1.32 % (715640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.32 % (715640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.32 % (715640)CaDiCaL version: 2.1.3
% 4.59/1.32 % (715640)Termination reason: Instruction limit
% 4.59/1.32 % (715640)Termination phase: Saturation
% 4.59/1.32 % (715640)Time elapsed: 0.067 s
% 4.59/1.32 % (715640)Peak memory usage: 88 MB
% 4.59/1.32 % (715640)Instructions burned: 116 (million)
% 4.59/1.32 % (715639)Instruction limit reached!
% 4.59/1.32 % (715639)------------------------------
% 4.59/1.32 % (715639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.32 % (715639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.32 % (715639)CaDiCaL version: 2.1.3
% 4.59/1.32 % (715639)Termination reason: Instruction limit
% 4.59/1.32 % (715639)Termination phase: Saturation
% 4.59/1.32 % (715639)Time elapsed: 0.068 s
% 4.59/1.32 % (715639)Peak memory usage: 89 MB
% 4.59/1.32 % (715639)Instructions burned: 107 (million)
% 4.59/1.32 % (715642)Instruction limit reached!
% 4.59/1.32 % (715642)------------------------------
% 4.59/1.32 % (715642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.32 % (715642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.32 % (715642)CaDiCaL version: 2.1.3
% 4.59/1.32 % (715642)Termination reason: Instruction limit
% 4.59/1.32 % (715642)Termination phase: Saturation
% 4.59/1.32 % (715642)Time elapsed: 0.067 s
% 4.59/1.32 % (715642)Peak memory usage: 89 MB
% 4.59/1.32 % (715642)Instructions burned: 119 (million)
% 4.59/1.32 % (715650)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=49655108:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.59/1.32 % (715650)Instruction limit reached!
% 4.59/1.32 % (715650)------------------------------
% 4.59/1.32 % (715650)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.32 % (715650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.32 % (715650)CaDiCaL version: 2.1.3
% 4.59/1.32 % (715650)Termination reason: Instruction limit
% 4.59/1.32 % (715650)Termination phase: Saturation
% 4.59/1.32 % (715650)Time elapsed: 0.044 s
% 4.59/1.32 % (715650)Peak memory usage: 89 MB
% 4.59/1.32 % (715650)Instructions burned: 148 (million)
% 4.59/1.32 % (715653)lrs+10_64_to=lpo:sil=8000:random_seed=2127135426:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 5.26/1.42 % (715651)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=629837173: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)
% 5.26/1.42 % (715652)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2744551148:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.26/1.42 % (715652)First to succeed.
% 5.26/1.42 % (715652)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-715631"
% 5.26/1.42 % (715653)Instruction limit reached!
% 5.26/1.42 % (715653)------------------------------
% 5.26/1.42 % (715653)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.26/1.42 % (715653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.26/1.42 % (715653)CaDiCaL version: 2.1.3
% 5.26/1.42 % (715653)Termination reason: Instruction limit
% 5.26/1.42 % (715653)Termination phase: Saturation
% 5.26/1.42 % (715653)Time elapsed: 0.071 s
% 5.26/1.42 % (715653)Peak memory usage: 89 MB
% 5.26/1.42 % (715653)Instructions burned: 128 (million)
% 5.26/1.42 % (715651)Instruction limit reached!
% 5.26/1.42 % (715651)------------------------------
% 5.26/1.42 % (715651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.26/1.42 % (715651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.26/1.42 % (715651)CaDiCaL version: 2.1.3
% 5.26/1.42 % (715651)Termination reason: Instruction limit
% 5.26/1.42 % (715651)Termination phase: Saturation
% 5.26/1.42 % (715651)Time elapsed: 0.104 s
% 5.26/1.42 % (715651)Peak memory usage: 89 MB
% 5.26/1.42 % (715651)Instructions burned: 190 (million)
% 5.26/1.42 % (715655)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1605726054:avsq=on:i=194:fgj=on:bd=preordered_2996 on theBenchmark for (2996ds/194Mi)
% 5.26/1.42 % (715655)Instruction limit reached!
% 5.26/1.42 % (715655)------------------------------
% 5.26/1.42 % (715655)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.26/1.42 % (715655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.26/1.42 % (715655)CaDiCaL version: 2.1.3
% 5.26/1.42 % (715655)Termination reason: Instruction limit
% 5.26/1.42 % (715655)Termination phase: Saturation
% 5.26/1.42 % (715655)Time elapsed: 0.051 s
% 5.26/1.42 % (715655)Peak memory usage: 89 MB
% 5.26/1.42 % (715655)Instructions burned: 196 (million)
% 5.26/1.42 % (715659)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=4066787207:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 5.26/1.42 % (715661)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3639842604:i=3394:sd=4:ss=included:sgt=64_2994 on theBenchmark for (2994ds/3394Mi)
% 5.26/1.42 % (715652)Refutation found. Thanks to Tanya!
% 5.26/1.42 % SZS status Unsatisfiable for theBenchmark
% 5.26/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 5.26/1.42 % (715652)------------------------------
% 5.26/1.42 % (715652)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.26/1.42 % (715652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.26/1.42 % (715652)CaDiCaL version: 2.1.3
% 5.26/1.42 % (715652)Termination reason: Refutation
% 5.26/1.42 % (715652)Time elapsed: 0.013 s
% 5.26/1.42 % (715652)Peak memory usage: 90 MB
% 5.26/1.42 % (715652)Instructions burned: 19 (million)
% 5.26/1.42 % (715652)------------------------------
% 5.26/1.42 % (715652)------------------------------
% 5.26/1.43 % (715631)Success in time 0.684 s
% 5.26/1.43 % Vampire exiting
%------------------------------------------------------------------------------