%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP019+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 11:28:30 AM UTC 2026
% Result : Theorem 2.62s 1.39s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 6 unt; 0 def)
% Number of atoms : 43 ( 28 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 47 ( 22 ~; 11 |; 7 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 10 ( 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f32,axiom,
! [X0] :
( mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ( ap(c_2Ecomplex_2Ecomplex__inv,X0) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
<=> X0 = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
fof(f33,conjecture,
! [X0] :
( mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ( X0 != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
=> ap(c_2Ecomplex_2Ecomplex__inv,X0) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
fof(f34,negated_conjecture,
~ ! [X0] :
( mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ( X0 != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
=> ap(c_2Ecomplex_2Ecomplex__inv,X0) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f37,plain,
? [X0] :
( ap(c_2Ecomplex_2Ecomplex__inv,X0) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& X0 != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(ennf_transformation,[],[f34]) ).
fof(f38,plain,
? [X0] :
( ap(c_2Ecomplex_2Ecomplex__inv,X0) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& X0 != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(flattening,[],[f37]) ).
fof(f44,plain,
! [X0] :
( ( ap(c_2Ecomplex_2Ecomplex__inv,X0) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
<=> X0 = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) )
| ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(ennf_transformation,[],[f32]) ).
fof(f49,plain,
( ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = ap(c_2Ecomplex_2Ecomplex__inv,sK0)
& ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != sK0
& mem(sK0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f38]) ).
fof(f52,plain,
! [X0] :
( ( ( ap(c_2Ecomplex_2Ecomplex__inv,X0) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != X0 )
& ( X0 = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| ap(c_2Ecomplex_2Ecomplex__inv,X0) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) ) )
| ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(nnf_transformation,[],[f44]) ).
fof(f58,plain,
mem(sK0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
inference(cnf_transformation,[],[f49]) ).
fof(f59,plain,
ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != sK0,
inference(cnf_transformation,[],[f49]) ).
fof(f60,plain,
ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = ap(c_2Ecomplex_2Ecomplex__inv,sK0),
inference(cnf_transformation,[],[f49]) ).
fof(f66,plain,
! [X0] :
( ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = X0
| ap(c_2Ecomplex_2Ecomplex__inv,X0) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f85,plain,
sK0 != ap(c_2Ecomplex_2Ecomplex__inv,sK0),
inference(superposition,[],[f59,f60]) ).
fof(f106,plain,
! [X0] :
( ap(c_2Ecomplex_2Ecomplex__inv,sK0) = X0
| ap(c_2Ecomplex_2Ecomplex__inv,X0) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(forward_demodulation,[],[f66,f60]) ).
fof(f107,plain,
! [X0] :
( ap(c_2Ecomplex_2Ecomplex__inv,X0) != ap(c_2Ecomplex_2Ecomplex__inv,sK0)
| ap(c_2Ecomplex_2Ecomplex__inv,sK0) = X0
| ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(forward_demodulation,[],[f106,f60]) ).
fof(f108,plain,
( sK0 = ap(c_2Ecomplex_2Ecomplex__inv,sK0)
| ~ mem(sK0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(equality_resolution,[],[f107]) ).
fof(f109,plain,
~ mem(sK0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
inference(forward_subsumption_resolution,[],[f108,f85]) ).
fof(f110,plain,
$false,
inference(forward_subsumption_resolution,[],[f109,f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP019+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 % Computer : n009.cluster.edu
% 0.12/0.42 % Model : x86_64 x86_64
% 0.12/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.42 % Memory : 8046.5625MB
% 0.12/0.42 % OS : Linux 6.8.0-71-generic
% 0.12/0.43 % CPULimit : 300
% 0.12/0.43 % WCLimit : 300
% 0.12/0.43 % DateTime : Sun Sep 27 12:05:46 UTC 2026
% 0.12/0.43 % CPUTime :
% 0.12/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.46 Running first-order theorem proving
% 0.16/0.46 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
% 2.62/1.39 % (1918847)Detected formulas, will run a generic FOF schedule.
% 2.62/1.39 % (1918856)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3097527427:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.62/1.39 % (1918856)First to succeed.
% 2.62/1.39 % (1918856)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1918847"
% 2.62/1.39 % (1918852)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=2830174278:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.62/1.39 % (1918854)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3675774853:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.62/1.39 % (1918855)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2658001137:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.62/1.39 % (1918853)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3044572731:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.62/1.39 % (1918855)Also succeeded, but the first one will report.
% 2.62/1.39 % (1918858)dis-21_1_sil=8000:lcm=predicate:random_seed=3314971648:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.62/1.39 % (1918857)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=685380302:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.62/1.39 % (1918857)Also succeeded, but the first one will report.
% 2.62/1.39 % (1918858)Also succeeded, but the first one will report.
% 2.62/1.39 % (1918856)Refutation found. Thanks to Tanya!
% 2.62/1.39 % SZS status Theorem for theBenchmark
% 2.62/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/1.40 % (1918856)------------------------------
% 2.62/1.40 % (1918856)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.40 % (1918856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.40 % (1918856)CaDiCaL version: 2.1.3
% 2.62/1.40 % (1918856)Termination reason: Refutation
% 2.62/1.40 % (1918856)Time elapsed: 0.002 s
% 2.62/1.40 % (1918856)Peak memory usage: 88 MB
% 2.62/1.40 % (1918856)Instructions burned: 3 (million)
% 2.62/1.40 % (1918856)------------------------------
% 2.62/1.40 % (1918856)------------------------------
% 2.62/1.40 % (1918847)Success in time 0.29 s
% 2.62/1.40 % Vampire exiting
%------------------------------------------------------------------------------