%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP019+5 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 11:28:34 AM UTC 2026
% Result : Theorem 12.53s 5.75s
% Output : Refutation 12.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 15 unt; 0 def)
% Number of atoms : 36 ( 26 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 13 ~; 2 |; 6 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 7 ( 5 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1248,axiom,
c_2Earithmetic_2EZERO = c_2Enum_2E0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Earithmetic_2EALT__ZERO) ).
fof(f16821,axiom,
ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__0) ).
fof(f16823,axiom,
! [X0] :
( mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__inv,X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__INV) ).
fof(f16826,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/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
fof(f16827,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)],[f16826]) ).
fof(f16914,plain,
? [X0] :
( ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = ap(c_2Ecomplex_2Ecomplex__inv,X0)
& X0 != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(ennf_transformation,[],[f16827]) ).
fof(f16915,plain,
? [X0] :
( ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = ap(c_2Ecomplex_2Ecomplex__inv,X0)
& X0 != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(flattening,[],[f16914]) ).
fof(f16919,plain,
! [X0] :
( ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__inv,X0)) = X0
| ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(ennf_transformation,[],[f16823]) ).
fof(f17483,plain,
( ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = ap(c_2Ecomplex_2Ecomplex__inv,sK88)
& ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != sK88
& mem(sK88,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(X0,sK88)],[f16915]) ).
fof(f18057,plain,
mem(sK88,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
inference(cnf_transformation,[],[f17483]) ).
fof(f18058,plain,
ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != sK88,
inference(cnf_transformation,[],[f17483]) ).
fof(f18059,plain,
ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = ap(c_2Ecomplex_2Ecomplex__inv,sK88),
inference(cnf_transformation,[],[f17483]) ).
fof(f18066,plain,
! [X0] :
( ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
| ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__inv,X0)) = X0 ),
inference(cnf_transformation,[],[f16919]) ).
fof(f18068,plain,
ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),
inference(cnf_transformation,[],[f16821]) ).
fof(f18170,plain,
c_2Enum_2E0 = c_2Earithmetic_2EZERO,
inference(cnf_transformation,[],[f1248]) ).
fof(f19435,plain,
ap(c_2Ecomplex_2Ecomplex__inv,sK88) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Earithmetic_2EZERO),
inference(definition_unfolding,[],[f18059,f18170]) ).
fof(f19436,plain,
sK88 != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Earithmetic_2EZERO),
inference(definition_unfolding,[],[f18058,f18170]) ).
fof(f19440,plain,
ap(c_2Ecomplex_2Ecomplex__of__num,c_2Earithmetic_2EZERO) = ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__of__num,c_2Earithmetic_2EZERO)),
inference(definition_unfolding,[],[f18068,f18170,f18170]) ).
fof(f19901,plain,
sK88 != ap(c_2Ecomplex_2Ecomplex__inv,sK88),
inference(superposition,[],[f19436,f19435]) ).
fof(f20076,plain,
ap(c_2Ecomplex_2Ecomplex__inv,sK88) = ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__inv,sK88)),
inference(superposition,[],[f19440,f19435]) ).
fof(f20660,plain,
sK88 = ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__inv,sK88)),
inference(resolution,[],[f18066,f18057]) ).
fof(f20684,plain,
sK88 = ap(c_2Ecomplex_2Ecomplex__inv,sK88),
inference(superposition,[],[f20076,f20660]) ).
fof(f20689,plain,
$false,
inference(forward_subsumption_resolution,[],[f20684,f19901]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP019+5 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.45 % Computer : n001.cluster.edu
% 0.14/0.45 % Model : x86_64 x86_64
% 0.14/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.45 % Memory : 8046.5625MB
% 0.14/0.45 % OS : Linux 6.8.0-71-generic
% 0.14/0.46 % CPULimit : 300
% 0.14/0.46 % WCLimit : 300
% 0.14/0.46 % DateTime : Sun Sep 27 12:11:35 UTC 2026
% 0.14/0.46 % CPUTime :
% 0.14/0.46 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.51 Running first-order theorem proving
% 0.17/0.51 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
% 12.53/5.75 % (3447626)Detected formulas, will run a generic FOF schedule.
% 12.53/5.75 % (3447637)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=2614228889:i=141193_2967 on theBenchmark for (2967ds/141193Mi)
% 12.53/5.75 % (3447640)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2981796081:i=109:sd=1:ins=1:gsp=on:ss=axioms_2967 on theBenchmark for (2967ds/109Mi)
% 12.53/5.75 % (3447639)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=808582521:i=141695:sd=1:nm=32:gsp=on:ss=included_2967 on theBenchmark for (2967ds/141695Mi)
% 12.53/5.75 % (3447638)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=3462187834:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2967 on theBenchmark for (2967ds/134677Mi)
% 12.53/5.75 % (3447640)Instruction limit reached!
% 12.53/5.75 % (3447640)------------------------------
% 12.53/5.75 % (3447640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.53/5.75 % (3447640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.53/5.75 % (3447640)CaDiCaL version: 2.1.3
% 12.53/5.75 % (3447640)Termination reason: Instruction limit
% 12.53/5.75 % (3447640)Termination phase: SInE selection
% 12.53/5.75 % (3447640)Time elapsed: 0.080 s
% 12.53/5.75 % (3447640)Peak memory usage: 120 MB
% 12.53/5.75 % (3447640)Instructions burned: 110 (million)
% 12.53/5.75 % (3447641)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2288762942:i=119:av=off:ss=axioms_2967 on theBenchmark for (2967ds/119Mi)
% 12.53/5.75 % (3447642)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=211134481:s2a=on:i=139:gtg=position_2967 on theBenchmark for (2967ds/139Mi)
% 12.53/5.75 % (3447643)dis-21_1_sil=8000:lcm=predicate:random_seed=1384764746:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2967 on theBenchmark for (2967ds/129Mi)
% 12.53/5.75 % (3447642)Instruction limit reached!
% 12.53/5.75 % (3447642)------------------------------
% 12.53/5.75 % (3447642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.53/5.75 % (3447642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.53/5.75 % (3447642)CaDiCaL version: 2.1.3
% 12.53/5.75 % (3447642)Termination reason: Instruction limit
% 12.53/5.75 % (3447642)Termination phase: Property scanning
% 12.53/5.75 % (3447642)Time elapsed: 0.111 s
% 12.53/5.75 % (3447642)Peak memory usage: 120 MB
% 12.53/5.75 % (3447642)Instructions burned: 139 (million)
% 12.53/5.75 % (3447641)Instruction limit reached!
% 12.53/5.75 % (3447641)------------------------------
% 12.53/5.75 % (3447641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.53/5.75 % (3447641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.53/5.75 % (3447641)CaDiCaL version: 2.1.3
% 12.53/5.75 % (3447641)Termination reason: Instruction limit
% 12.53/5.75 % (3447641)Termination phase: SInE selection
% 12.53/5.75 % (3447641)Time elapsed: 0.113 s
% 12.53/5.75 % (3447641)Peak memory usage: 119 MB
% 12.53/5.75 % (3447641)Instructions burned: 119 (million)
% 12.53/5.75 % (3447643)Instruction limit reached!
% 12.53/5.75 % (3447643)------------------------------
% 12.53/5.75 % (3447643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.53/5.75 % (3447643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.53/5.75 % (3447643)CaDiCaL version: 2.1.3
% 12.53/5.75 % (3447643)Termination reason: Instruction limit
% 12.53/5.75 % (3447643)Termination phase: SInE selection
% 12.53/5.75 % (3447643)Time elapsed: 0.115 s
% 12.53/5.75 % (3447643)Peak memory usage: 119 MB
% 12.53/5.75 % (3447643)Instructions burned: 129 (million)
% 12.53/5.75 % (3447648)lrs+10_1_sil=8000:sp=occurrence:random_seed=3654958738:i=285:sd=3:ss=axioms:sgt=8_2965 on theBenchmark for (2965ds/285Mi)
% 12.53/5.75 % (3447654)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1571800489:s2a=on:i=248:s2at=1.23:gtg=position_2964 on theBenchmark for (2964ds/248Mi)
% 12.53/5.75 % (3447653)lrs+1011_1_sil=32000:sp=occurrence:random_seed=345109828:i=325:sd=1:ss=axioms:sgt=32_2964 on theBenchmark for (2964ds/325Mi)
% 12.53/5.75 % (3447652)lrs+10_1_sil=32000:urr=on:br=off:random_seed=372700943:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2964 on theBenchmark for (2964ds/157Mi)
% 12.53/5.75 % (3447654)Instruction limit reached!
% 12.53/5.75 % (3447654)------------------------------
% 12.53/5.75 % (3447654)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.53/5.75 % (3447654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.53/5.75 % (3447654)CaDiCaL version: 2.1.3
% 12.53/5.75 % (3447654)Termination reason: Instruction limit
% 12.53/5.75 % (3447654)Termination phase: Property scanning
% 12.53/5.75 % (3447654)Time elapsed: 0.105 s
% 12.53/5.75 % (3447654)Peak memory usage: 120 MB
% 12.53/5.75 % (3447654)Instructions burned: 250 (million)
% 12.53/5.75 % (3447648)First to succeed.
% 12.53/5.75 % (3447648)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3447626"
% 12.53/5.75 % (3447652)Instruction limit reached!
% 12.53/5.75 % (3447652)------------------------------
% 12.53/5.75 % (3447652)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.53/5.75 % (3447652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.53/5.75 % (3447652)CaDiCaL version: 2.1.3
% 12.53/5.75 % (3447652)Termination reason: Instruction limit
% 12.53/5.75 % (3447652)Termination phase: Property scanning
% 12.53/5.75 % (3447652)Time elapsed: 0.124 s
% 12.53/5.75 % (3447652)Peak memory usage: 120 MB
% 12.53/5.75 % (3447652)Instructions burned: 157 (million)
% 12.53/5.75 % (3447653)Also succeeded, but the first one will report.
% 12.53/5.75 % (3447659)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3649682995:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2961 on theBenchmark for (2961ds/294Mi)
% 12.53/5.75 % (3447660)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4132265710:i=2350_2960 on theBenchmark for (2960ds/2350Mi)
% 12.53/5.75 % (3447648)Refutation found. Thanks to Tanya!
% 12.53/5.75 % SZS status Theorem for theBenchmark
% 12.53/5.75 % SZS output start Proof for theBenchmark
% See solution above
% 12.53/5.75 % (3447648)------------------------------
% 12.53/5.75 % (3447648)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.53/5.75 % (3447648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.53/5.75 % (3447648)CaDiCaL version: 2.1.3
% 12.53/5.75 % (3447648)Termination reason: Refutation
% 12.53/5.75 % (3447648)Time elapsed: 0.284 s
% 12.53/5.75 % (3447648)Peak memory usage: 126 MB
% 12.53/5.75 % (3447648)Instructions burned: 286 (million)
% 12.53/5.75 % (3447648)------------------------------
% 12.53/5.75 % (3447648)------------------------------
% 12.53/5.75 % (3447626)Success in time 4.425 s
% 12.53/5.75 % Vampire exiting
%------------------------------------------------------------------------------