%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP019+1 : 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 : 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 11:28:30 AM UTC 2026
% Result : Theorem 3.40s 1.23s
% Output : Refutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 8 unt; 2 def)
% Number of atoms : 28 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 5 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 7 ( 6 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28,axiom,
! [X0] :
( s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
<=> s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
fof(f29,conjecture,
! [X0] :
( s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0) != s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
=> s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0))) != s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
fof(f30,negated_conjecture,
~ ! [X0] :
( s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0) != s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
=> s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0))) != s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
? [X0] :
( s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
& s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0) != s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ),
inference(ennf_transformation,[],[f30]) ).
fof(f34,plain,
( s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sK0)))
& s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) != s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f31]) ).
fof(f37,plain,
! [X0] :
( ( s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
| s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0) != s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
& ( s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
| s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0))) != s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f38,plain,
s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) != s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sK0),
inference(cnf_transformation,[],[f34]) ).
fof(f39,plain,
s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sK0))),
inference(cnf_transformation,[],[f34]) ).
fof(f43,plain,
! [X0] :
( s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
| s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0))) != s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ),
inference(cnf_transformation,[],[f37]) ).
fof(f45,definition,
~ sP2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))),
introduced(definition,[new_symbols(definition,[sP2])],[inequality_splitting_name_introduction]) ).
fof(f46,plain,
sP2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sK0)),
inference(inequality_splitting,[],[f38,f45]) ).
fof(f49,definition,
~ sP4(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f50,plain,
! [X0] :
( s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
| sP4(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0)))) ),
inference(inequality_splitting,[],[f43,f49]) ).
fof(f51,plain,
( sP2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))
| sP4(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sK0)))) ),
inference(superposition,[],[f46,f50]) ).
fof(f52,plain,
sP4(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sK0)))),
inference(forward_subsumption_resolution,[],[f51,f45]) ).
fof(f53,plain,
sP4(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))),
inference(forward_demodulation,[],[f52,f39]) ).
fof(f54,plain,
$false,
inference(forward_subsumption_resolution,[],[f53,f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP019+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n004.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 12:05:07 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 3.40/1.23 % (3400571)Detected formulas, will run a generic FOF schedule.
% 3.40/1.23 % (3400576)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=307138976:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.40/1.23 % (3400579)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3401645954:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.40/1.23 % (3400578)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=1505699650:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.40/1.23 % (3400580)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1143349292:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.40/1.23 % (3400577)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=3117395677:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.40/1.23 % (3400582)dis-21_1_sil=8000:lcm=predicate:random_seed=1033205969: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)
% 3.40/1.23 % (3400579)First to succeed.
% 3.40/1.23 % (3400580)Also succeeded, but the first one will report.
% 3.40/1.23 % (3400579)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3400571"
% 3.40/1.23 % (3400582)Also succeeded, but the first one will report.
% 3.40/1.23 % (3400581)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1588963662:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.40/1.23 % (3400581)Also succeeded, but the first one will report.
% 3.40/1.23 % (3400579)Refutation found. Thanks to Tanya!
% 3.40/1.23 % SZS status Theorem for theBenchmark
% 3.40/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 3.40/1.23 % (3400579)------------------------------
% 3.40/1.23 % (3400579)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.23 % (3400579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.23 % (3400579)CaDiCaL version: 2.1.3
% 3.40/1.23 % (3400579)Termination reason: Refutation
% 3.40/1.23 % (3400579)Time elapsed: 0.003 s
% 3.40/1.23 % (3400579)Peak memory usage: 88 MB
% 3.40/1.23 % (3400579)Instructions burned: 2 (million)
% 3.40/1.23 % (3400579)------------------------------
% 3.40/1.23 % (3400579)------------------------------
% 3.40/1.23 % (3400571)Success in time 0.426 s
% 3.40/1.23 % Vampire exiting
%------------------------------------------------------------------------------