%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP010+5 : 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 11:28:00 AM UTC 2026
% Result : Theorem 7.39s 3.17s
% Output : Refutation 7.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 3 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 54 ( 16 ~; 8 |; 19 &)
% ( 2 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 20 ( 8 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8598,conjecture,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( mem(X2,arr(X0,bool))
=> ! [X3] :
( mem(X3,arr(X1,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ecardinal_2ECARD__NOT__LE) ).
fof(f8599,negated_conjecture,
~ ! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( mem(X2,arr(X0,bool))
=> ! [X3] :
( mem(X3,arr(X1,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f8598]) ).
fof(f8655,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
<~> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) )
& mem(X2,arr(X0,bool)) )
& ne(X1) )
& ne(X0) ),
inference(ennf_transformation,[],[f8599]) ).
fof(f9083,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) )
& mem(X2,arr(X0,bool)) )
& ne(X1) )
& ne(X0) ),
inference(nnf_transformation,[],[f8655]) ).
fof(f9084,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) )
& mem(X2,arr(X0,bool)) )
& ne(X1) )
& ne(X0) ),
inference(flattening,[],[f9083]) ).
fof(f9085,plain,
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK77,sK78),sK79),sK80))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK77,sK78),sK79),sK80)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK77,sK78),sK79),sK80))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK77,sK78),sK79),sK80)) )
& mem(sK80,arr(sK78,bool))
& mem(sK79,arr(sK77,bool))
& ne(sK78)
& ne(sK77) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77,sK78,sK79,sK80]),skolemize(X0,sK77),skolemize(X1,sK78),skolemize(X2,sK79),skolemize(X3,sK80)],[f9084]) ).
fof(f9548,plain,
( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK77,sK78),sK79),sK80))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK77,sK78),sK79),sK80)) ),
inference(cnf_transformation,[],[f9085]) ).
fof(f9549,plain,
( p(ap(ap(c_2Ecardinal_2Ecardleq(sK77,sK78),sK79),sK80))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK77,sK78),sK79),sK80)) ),
inference(cnf_transformation,[],[f9085]) ).
fof(f10682,plain,
~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK77,sK78),sK79),sK80)),
inference(duplicate_literal_removal,[],[f9548]) ).
fof(f10683,plain,
p(ap(ap(c_2Ecardinal_2Ecardleq(sK77,sK78),sK79),sK80)),
inference(duplicate_literal_removal,[],[f9549]) ).
fof(f10912,plain,
$false,
inference(forward_subsumption_resolution,[],[f10683,f10682]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP010+5 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 11:56:57 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 7.39/3.17 % (3393908)Detected formulas, will run a generic FOF schedule.
% 7.39/3.17 % (3393915)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=1577718135:i=141695:sd=1:nm=32:gsp=on:ss=included_2986 on theBenchmark for (2986ds/141695Mi)
% 7.39/3.17 % (3393913)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=3456092300:i=141193_2986 on theBenchmark for (2986ds/141193Mi)
% 7.39/3.17 % (3393914)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=1331608109:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2986 on theBenchmark for (2986ds/134677Mi)
% 7.39/3.17 % (3393918)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2879765874:s2a=on:i=139:gtg=position_2986 on theBenchmark for (2986ds/139Mi)
% 7.39/3.17 % (3393916)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2514282150:i=109:sd=1:ins=1:gsp=on:ss=axioms_2986 on theBenchmark for (2986ds/109Mi)
% 7.39/3.17 % (3393917)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3211609073:i=119:av=off:ss=axioms_2986 on theBenchmark for (2986ds/119Mi)
% 7.39/3.17 % (3393919)dis-21_1_sil=8000:lcm=predicate:random_seed=1361651988:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2986 on theBenchmark for (2986ds/129Mi)
% 7.39/3.17 % (3393918)Instruction limit reached!
% 7.39/3.17 % (3393918)------------------------------
% 7.39/3.17 % (3393918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.39/3.17 % (3393918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/3.17 % (3393918)CaDiCaL version: 2.1.3
% 7.39/3.17 % (3393918)Termination reason: Instruction limit
% 7.39/3.17 % (3393918)Termination phase: Property scanning
% 7.39/3.17 % (3393918)Time elapsed: 0.057 s
% 7.39/3.17 % (3393918)Peak memory usage: 106 MB
% 7.39/3.17 % (3393918)Instructions burned: 141 (million)
% 7.39/3.17 % (3393919)Instruction limit reached!
% 7.39/3.17 % (3393919)------------------------------
% 7.39/3.17 % (3393919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.39/3.17 % (3393919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/3.17 % (3393919)CaDiCaL version: 2.1.3
% 7.39/3.17 % (3393919)Termination reason: Instruction limit
% 7.39/3.17 % (3393919)Termination phase: SInE selection
% 7.39/3.17 % (3393919)Time elapsed: 0.073 s
% 7.39/3.17 % (3393919)Peak memory usage: 105 MB
% 7.39/3.17 % (3393919)Instructions burned: 130 (million)
% 7.39/3.17 % (3393916)Instruction limit reached!
% 7.39/3.17 % (3393916)------------------------------
% 7.39/3.17 % (3393916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.39/3.17 % (3393916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/3.17 % (3393916)CaDiCaL version: 2.1.3
% 7.39/3.17 % (3393916)Termination reason: Instruction limit
% 7.39/3.17 % (3393916)Termination phase: Property scanning
% 7.39/3.17 % (3393916)Time elapsed: 0.078 s
% 7.39/3.17 % (3393916)Peak memory usage: 108 MB
% 7.39/3.17 % (3393916)Instructions burned: 110 (million)
% 7.39/3.17 % (3393917)Instruction limit reached!
% 7.39/3.17 % (3393917)------------------------------
% 7.39/3.17 % (3393917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.39/3.17 % (3393917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/3.17 % (3393917)CaDiCaL version: 2.1.3
% 7.39/3.17 % (3393917)Termination reason: Instruction limit
% 7.39/3.17 % (3393917)Termination phase: Preprocessing 3
% 7.39/3.17 % (3393917)Time elapsed: 0.086 s
% 7.39/3.17 % (3393917)Peak memory usage: 108 MB
% 7.39/3.17 % (3393917)Instructions burned: 120 (million)
% 7.39/3.17 % (3393927)lrs+10_1_sil=8000:sp=occurrence:random_seed=1801787840:i=285:sd=3:ss=axioms:sgt=8_2984 on theBenchmark for (2984ds/285Mi)
% 7.39/3.17 % (3393928)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3676211543:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2984 on theBenchmark for (2984ds/157Mi)
% 7.39/3.17 % (3393929)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1977515248:i=325:sd=1:ss=axioms:sgt=32_2984 on theBenchmark for (2984ds/325Mi)
% 7.39/3.17 % (3393930)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=3649853840:s2a=on:i=248:s2at=1.23:gtg=position_2983 on theBenchmark for (2983ds/248Mi)
% 7.39/3.17 % (3393928)Instruction limit reached!
% 7.39/3.17 % (3393928)------------------------------
% 7.39/3.17 % (3393928)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.39/3.17 % (3393928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/3.17 % (3393928)CaDiCaL version: 2.1.3
% 7.39/3.17 % (3393928)Termination reason: Instruction limit
% 7.39/3.17 % (3393928)Termination phase: Property scanning
% 7.39/3.17 % (3393928)Time elapsed: 0.061 s
% 7.39/3.17 % (3393928)Peak memory usage: 106 MB
% 7.39/3.17 % (3393928)Instructions burned: 158 (million)
% 7.39/3.17 % (3393929)First to succeed.
% 7.39/3.17 % (3393929)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3393908"
% 7.39/3.17 % (3393930)Instruction limit reached!
% 7.39/3.17 % (3393930)------------------------------
% 7.39/3.17 % (3393930)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.39/3.17 % (3393930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/3.17 % (3393930)CaDiCaL version: 2.1.3
% 7.39/3.17 % (3393930)Termination reason: Instruction limit
% 7.39/3.17 % (3393930)Termination phase: Property scanning
% 7.39/3.17 % (3393930)Time elapsed: 0.095 s
% 7.39/3.17 % (3393930)Peak memory usage: 106 MB
% 7.39/3.17 % (3393930)Instructions burned: 249 (million)
% 7.39/3.17 % (3393927)Instruction limit reached!
% 7.39/3.17 % (3393927)------------------------------
% 7.39/3.17 % (3393927)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.39/3.17 % (3393927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/3.17 % (3393927)CaDiCaL version: 2.1.3
% 7.39/3.17 % (3393927)Termination reason: Instruction limit
% 7.39/3.17 % (3393927)Termination phase: Saturation
% 7.39/3.17 % (3393927)Time elapsed: 0.171 s
% 7.39/3.17 % (3393927)Peak memory usage: 113 MB
% 7.39/3.17 % (3393927)Instructions burned: 285 (million)
% 7.39/3.17 % (3393935)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3308398029:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2981 on theBenchmark for (2981ds/294Mi)
% 7.39/3.17 % (3393936)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1047222542:i=2350_2981 on theBenchmark for (2981ds/2350Mi)
% 7.39/3.17 % (3393937)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3979358671:cts=off:i=113:fsr=off:ss=included:sgt=4_2980 on theBenchmark for (2980ds/113Mi)
% 7.39/3.17 % (3393929)Refutation found. Thanks to Tanya!
% 7.39/3.17 % SZS status Theorem for theBenchmark
% 7.39/3.17 % SZS output start Proof for theBenchmark
% See solution above
% 7.39/3.17 % (3393929)------------------------------
% 7.39/3.17 % (3393929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.39/3.17 % (3393929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/3.17 % (3393929)CaDiCaL version: 2.1.3
% 7.39/3.17 % (3393929)Termination reason: Refutation
% 7.39/3.17 % (3393929)Time elapsed: 0.103 s
% 7.39/3.17 % (3393929)Peak memory usage: 111 MB
% 7.39/3.17 % (3393929)Instructions burned: 158 (million)
% 7.39/3.17 % (3393929)------------------------------
% 7.39/3.17 % (3393929)------------------------------
% 7.39/3.17 % (3393908)Success in time 2.112 s
% 7.39/3.17 % Vampire exiting
%------------------------------------------------------------------------------