%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP020+1 : 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 11:28:36 AM UTC 2026
% Result : Theorem 3.54s 6.60s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 9 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 11 ~; 7 |; 3 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 39 ( 30 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f47,axiom,
! [X0,X1,X2,X3] :
( ? [X4] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X0,X1),X4),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
<=> ? [X5] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X1,X0),X5),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EBIJ__SYM) ).
fof(f58,axiom,
? [X0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eutil__prob_2ENUM__2D__BIJ) ).
fof(f59,conjecture,
? [X0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eutil__prob_2ENUM__2D__BIJ__INV) ).
fof(f60,negated_conjecture,
~ ? [X0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))),
inference(negated_conjecture,[status(cth)],[f59]) ).
fof(f61,plain,
! [X0] : ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))),
inference(ennf_transformation,[],[f60]) ).
fof(f104,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X0,X1),X4),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
| ! [X5] : ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X1,X0),X5),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))) )
& ( ? [X5] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X1,X0),X5),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))
| ! [X4] : ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X0,X1),X4),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f105,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X0,X1),X4),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
| ! [X5] : ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X1,X0),X5),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))) )
& ( ? [X6] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X1,X0),X6),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))
| ! [X7] : ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X0,X1),X7),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) ) ),
inference(rectify,[],[f104]) ).
fof(f106,plain,
! [X0,X1,X2,X3] :
( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X0,X1),sK7(X0,X1,X2,X3)),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
| ! [X5] : ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X1,X0),X5),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))) )
& ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X1,X0),sK8(X0,X1,X2,X3)),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))
| ! [X7] : ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X0,X1),X7),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X4,sK7(X0,X1,X2,X3)),skolemize(X6,sK8(X0,X1,X2,X3))],[f105]) ).
fof(f107,plain,
p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sK9),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f58]) ).
fof(f108,plain,
! [X0] : ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))),
inference(cnf_transformation,[],[f61]) ).
fof(f176,plain,
! [X2,X3,X0,X1,X7] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X1,X0),sK8(X0,X1,X2,X3)),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X0,X1),X7),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) ),
inference(cnf_transformation,[],[f106]) ).
fof(f178,plain,
p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sK9),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))),
inference(cnf_transformation,[],[f107]) ).
fof(f191,plain,
! [X0] : ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))),
inference(resolution,[],[f108,f176]) ).
fof(f192,plain,
$false,
inference(resolution,[],[f191,f178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP020+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/5.53 % Computer : n001.cluster.edu
% 0.13/5.53 % Model : x86_64 x86_64
% 0.13/5.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.53 % Memory : 8046.5625MB
% 0.13/5.53 % OS : Linux 6.8.0-71-generic
% 0.13/5.53 % CPULimit : 300
% 0.13/5.53 % WCLimit : 300
% 0.13/5.53 % DateTime : Sun Sep 27 12:12:06 UTC 2026
% 0.13/5.53 % CPUTime :
% 0.13/5.53 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/5.57 Running first-order theorem proving
% 0.13/5.57 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
% 3.54/6.60 % (3449222)Detected formulas, will run a generic FOF schedule.
% 3.54/6.60 % (3449232)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1533606428:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.54/6.60 % (3449228)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=2446460797:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.54/6.60 % (3449230)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1624050095:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.54/6.60 % (3449229)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=27689176:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.54/6.60 % (3449227)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=2321170210:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.54/6.60 % (3449231)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=382634129:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.54/6.60 % (3449230)First to succeed.
% 3.54/6.60 % (3449230)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3449222"
% 3.54/6.60 % (3449231)Also succeeded, but the first one will report.
% 3.54/6.60 % (3449232)Instruction limit reached!
% 3.54/6.60 % (3449232)------------------------------
% 3.54/6.60 % (3449232)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/6.60 % (3449232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/6.60 % (3449232)CaDiCaL version: 2.1.3
% 3.54/6.60 % (3449232)Termination reason: Instruction limit
% 3.54/6.60 % (3449232)Termination phase: Saturation
% 3.54/6.60 % (3449232)Time elapsed: 0.044 s
% 3.54/6.60 % (3449232)Peak memory usage: 89 MB
% 3.54/6.60 % (3449232)Instructions burned: 140 (million)
% 3.54/6.60 % (3449233)dis-21_1_sil=8000:lcm=predicate:random_seed=2803292181: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)
% 3.54/6.60 % (3449233)Instruction limit reached!
% 3.54/6.60 % (3449233)------------------------------
% 3.54/6.60 % (3449233)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/6.60 % (3449233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/6.60 % (3449233)CaDiCaL version: 2.1.3
% 3.54/6.60 % (3449233)Termination reason: Instruction limit
% 3.54/6.60 % (3449233)Termination phase: Saturation
% 3.54/6.60 % (3449233)Time elapsed: 0.067 s
% 3.54/6.60 % (3449233)Peak memory usage: 90 MB
% 3.54/6.60 % (3449233)Instructions burned: 131 (million)
% 3.54/6.60 % (3449241)lrs+10_1_sil=8000:sp=occurrence:random_seed=3207796060:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.54/6.60 % (3449241)Also succeeded, but the first one will report.
% 3.54/6.60 % (3449242)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2093525624:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.54/6.60 % (3449230)Refutation found. Thanks to Tanya!
% 3.54/6.60 % SZS status Theorem for theBenchmark
% 3.54/6.60 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/6.60 % (3449230)------------------------------
% 3.68/6.60 % (3449230)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/6.60 % (3449230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/6.60 % (3449230)CaDiCaL version: 2.1.3
% 3.68/6.60 % (3449230)Termination reason: Refutation
% 3.68/6.60 % (3449230)Time elapsed: 0.006 s
% 3.68/6.60 % (3449230)Peak memory usage: 88 MB
% 3.68/6.60 % (3449230)Instructions burned: 9 (million)
% 3.68/6.60 % (3449230)------------------------------
% 3.68/6.60 % (3449230)------------------------------
% 3.68/6.60 % (3449222)Success in time 0.432 s
% 3.68/6.60 % Vampire exiting
%------------------------------------------------------------------------------