%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP010+4 : 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 : n017.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 11:27:59 AM UTC 2026
% Result : Theorem 8.53s 4.39s
% Output : Refutation 8.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 3 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 25 ( 14 ~; 6 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 16 ( 8 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10764,conjecture,
! [X0,X1,X2,X3] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
<=> ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecardinal_2ECARD__NOT__LE) ).
fof(f10765,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
<=> ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) ),
inference(negated_conjecture,[status(cth)],[f10764]) ).
fof(f10773,plain,
? [X0,X1,X2,X3] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
<~> ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) ),
inference(ennf_transformation,[],[f10765]) ).
fof(f11066,plain,
? [X0,X1,X2,X3] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
| p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))) ) ),
inference(nnf_transformation,[],[f10773]) ).
fof(f11067,plain,
( ( p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK32,tyop_2Emin_2Ebool),sK34),s(tyop_2Emin_2Efun(sK33,tyop_2Emin_2Ebool),sK35))))
| p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK32,tyop_2Emin_2Ebool),sK34),s(tyop_2Emin_2Efun(sK33,tyop_2Emin_2Ebool),sK35)))) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK32,tyop_2Emin_2Ebool),sK34),s(tyop_2Emin_2Efun(sK33,tyop_2Emin_2Ebool),sK35))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK32,tyop_2Emin_2Ebool),sK34),s(tyop_2Emin_2Efun(sK33,tyop_2Emin_2Ebool),sK35)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32,sK33,sK34,sK35]),skolemize(X0,sK32),skolemize(X1,sK33),skolemize(X2,sK34),skolemize(X3,sK35)],[f11066]) ).
fof(f11463,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK32,tyop_2Emin_2Ebool),sK34),s(tyop_2Emin_2Efun(sK33,tyop_2Emin_2Ebool),sK35))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK32,tyop_2Emin_2Ebool),sK34),s(tyop_2Emin_2Efun(sK33,tyop_2Emin_2Ebool),sK35)))) ),
inference(cnf_transformation,[],[f11067]) ).
fof(f11464,plain,
( p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK32,tyop_2Emin_2Ebool),sK34),s(tyop_2Emin_2Efun(sK33,tyop_2Emin_2Ebool),sK35))))
| p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK32,tyop_2Emin_2Ebool),sK34),s(tyop_2Emin_2Efun(sK33,tyop_2Emin_2Ebool),sK35)))) ),
inference(cnf_transformation,[],[f11067]) ).
fof(f12370,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK32,tyop_2Emin_2Ebool),sK34),s(tyop_2Emin_2Efun(sK33,tyop_2Emin_2Ebool),sK35)))),
inference(duplicate_literal_removal,[],[f11463]) ).
fof(f12371,plain,
p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK32,tyop_2Emin_2Ebool),sK34),s(tyop_2Emin_2Efun(sK33,tyop_2Emin_2Ebool),sK35)))),
inference(duplicate_literal_removal,[],[f11464]) ).
fof(f12493,plain,
$false,
inference(forward_subsumption_resolution,[],[f12371,f12370]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP010+4 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n017.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 11:52:36 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 8.53/4.39 % (2417272)Detected formulas, will run a generic FOF schedule.
% 8.53/4.39 % (2417278)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=1931488651:i=141193_2974 on theBenchmark for (2974ds/141193Mi)
% 8.53/4.39 % (2417283)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1868318497:s2a=on:i=139:gtg=position_2974 on theBenchmark for (2974ds/139Mi)
% 8.53/4.39 % (2417279)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=835913156:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2974 on theBenchmark for (2974ds/134677Mi)
% 8.53/4.39 % (2417280)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=588982214:i=141695:sd=1:nm=32:gsp=on:ss=included_2974 on theBenchmark for (2974ds/141695Mi)
% 8.53/4.39 % (2417281)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2627682816:i=109:sd=1:ins=1:gsp=on:ss=axioms_2974 on theBenchmark for (2974ds/109Mi)
% 8.53/4.39 % (2417282)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=692209330:i=119:av=off:ss=axioms_2974 on theBenchmark for (2974ds/119Mi)
% 8.53/4.39 % (2417284)dis-21_1_sil=8000:lcm=predicate:random_seed=332590595:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2974 on theBenchmark for (2974ds/129Mi)
% 8.53/4.39 % (2417283)Instruction limit reached!
% 8.53/4.39 % (2417283)------------------------------
% 8.53/4.39 % (2417283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/4.39 % (2417283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/4.39 % (2417283)CaDiCaL version: 2.1.3
% 8.53/4.39 % (2417283)Termination reason: Instruction limit
% 8.53/4.39 % (2417283)Termination phase: Property scanning
% 8.53/4.39 % (2417283)Time elapsed: 0.053 s
% 8.53/4.39 % (2417283)Peak memory usage: 103 MB
% 8.53/4.39 % (2417283)Instructions burned: 139 (million)
% 8.53/4.39 % (2417281)Instruction limit reached!
% 8.53/4.39 % (2417281)------------------------------
% 8.53/4.39 % (2417281)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/4.39 % (2417281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/4.39 % (2417281)CaDiCaL version: 2.1.3
% 8.53/4.39 % (2417281)Termination reason: Instruction limit
% 8.53/4.39 % (2417281)Termination phase: SInE selection
% 8.53/4.39 % (2417281)Time elapsed: 0.061 s
% 8.53/4.39 % (2417281)Peak memory usage: 103 MB
% 8.53/4.39 % (2417281)Instructions burned: 109 (million)
% 8.53/4.39 % (2417282)Instruction limit reached!
% 8.53/4.39 % (2417282)------------------------------
% 8.53/4.39 % (2417282)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/4.39 % (2417282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/4.39 % (2417282)CaDiCaL version: 2.1.3
% 8.53/4.39 % (2417282)Termination reason: Instruction limit
% 8.53/4.39 % (2417282)Termination phase: SInE selection
% 8.53/4.39 % (2417282)Time elapsed: 0.065 s
% 8.53/4.39 % (2417282)Peak memory usage: 103 MB
% 8.53/4.39 % (2417282)Instructions burned: 120 (million)
% 8.53/4.39 % (2417284)Instruction limit reached!
% 8.53/4.39 % (2417284)------------------------------
% 8.53/4.39 % (2417284)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/4.39 % (2417284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/4.39 % (2417284)CaDiCaL version: 2.1.3
% 8.53/4.39 % (2417284)Termination reason: Instruction limit
% 8.53/4.39 % (2417284)Termination phase: SInE selection
% 8.53/4.39 % (2417284)Time elapsed: 0.068 s
% 8.53/4.39 % (2417284)Peak memory usage: 103 MB
% 8.53/4.39 % (2417284)Instructions burned: 131 (million)
% 8.53/4.39 % (2417293)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2601997622:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2972 on theBenchmark for (2972ds/157Mi)
% 8.53/4.39 % (2417292)lrs+10_1_sil=8000:sp=occurrence:random_seed=1896898674:i=285:sd=3:ss=axioms:sgt=8_2972 on theBenchmark for (2972ds/285Mi)
% 8.53/4.39 % (2417294)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2811367721:i=325:sd=1:ss=axioms:sgt=32_2972 on theBenchmark for (2972ds/325Mi)
% 8.53/4.39 % (2417295)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=1470379529:s2a=on:i=248:s2at=1.23:gtg=position_2972 on theBenchmark for (2972ds/248Mi)
% 8.53/4.39 % (2417293)Instruction limit reached!
% 8.53/4.39 % (2417293)------------------------------
% 8.53/4.39 % (2417293)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/4.39 % (2417293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/4.39 % (2417293)CaDiCaL version: 2.1.3
% 8.53/4.39 % (2417293)Termination reason: Instruction limit
% 8.53/4.39 % (2417293)Termination phase: Property scanning
% 8.53/4.39 % (2417293)Time elapsed: 0.060 s
% 8.53/4.39 % (2417293)Peak memory usage: 103 MB
% 8.53/4.39 % (2417293)Instructions burned: 159 (million)
% 8.53/4.39 % (2417295)Instruction limit reached!
% 8.53/4.39 % (2417295)------------------------------
% 8.53/4.39 % (2417295)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/4.39 % (2417295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/4.39 % (2417295)CaDiCaL version: 2.1.3
% 8.53/4.39 % (2417295)Termination reason: Instruction limit
% 8.53/4.39 % (2417295)Termination phase: Property scanning
% 8.53/4.39 % (2417295)Time elapsed: 0.093 s
% 8.53/4.39 % (2417295)Peak memory usage: 103 MB
% 8.53/4.39 % (2417295)Instructions burned: 250 (million)
% 8.53/4.39 % (2417294)First to succeed.
% 8.53/4.39 % (2417294)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2417272"
% 8.53/4.39 % (2417292)Instruction limit reached!
% 8.53/4.39 % (2417292)------------------------------
% 8.53/4.39 % (2417292)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/4.39 % (2417292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/4.39 % (2417292)CaDiCaL version: 2.1.3
% 8.53/4.39 % (2417292)Termination reason: Instruction limit
% 8.53/4.39 % (2417292)Termination phase: Saturation
% 8.53/4.39 % (2417292)Time elapsed: 0.159 s
% 8.53/4.39 % (2417292)Peak memory usage: 108 MB
% 8.53/4.39 % (2417292)Instructions burned: 287 (million)
% 8.53/4.39 % (2417300)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=243533011:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2970 on theBenchmark for (2970ds/294Mi)
% 8.53/4.39 % (2417301)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2214721396:i=2350_2969 on theBenchmark for (2969ds/2350Mi)
% 8.53/4.39 % (2417302)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3054965053:cts=off:i=113:fsr=off:ss=included:sgt=4_2969 on theBenchmark for (2969ds/113Mi)
% 8.53/4.39 % (2417300)Instruction limit reached!
% 8.53/4.39 % (2417300)------------------------------
% 8.53/4.39 % (2417300)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/4.39 % (2417300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/4.39 % (2417300)CaDiCaL version: 2.1.3
% 8.53/4.39 % (2417300)Termination reason: Instruction limit
% 8.53/4.39 % (2417300)Termination phase: Preprocessing 3
% 8.53/4.39 % (2417300)Time elapsed: 0.160 s
% 8.53/4.39 % (2417300)Peak memory usage: 106 MB
% 8.53/4.39 % (2417300)Instructions burned: 294 (million)
% 8.53/4.39 % (2417302)Instruction limit reached!
% 8.53/4.39 % (2417302)------------------------------
% 8.53/4.39 % (2417302)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/4.39 % (2417302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/4.39 % (2417302)CaDiCaL version: 2.1.3
% 8.53/4.39 % (2417302)Termination reason: Instruction limit
% 8.53/4.39 % (2417302)Termination phase: SInE selection
% 8.53/4.39 % (2417302)Time elapsed: 0.063 s
% 8.53/4.39 % (2417302)Peak memory usage: 103 MB
% 8.53/4.39 % (2417302)Instructions burned: 115 (million)
% 8.53/4.39 % (2417294)Refutation found. Thanks to Tanya!
% 8.53/4.39 % SZS status Theorem for theBenchmark
% 8.53/4.39 % SZS output start Proof for theBenchmark
% See solution above
% 8.53/4.39 % (2417294)------------------------------
% 8.53/4.39 % (2417294)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/4.39 % (2417294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/4.39 % (2417294)CaDiCaL version: 2.1.3
% 8.53/4.39 % (2417294)Termination reason: Refutation
% 8.53/4.39 % (2417294)Time elapsed: 0.116 s
% 8.53/4.39 % (2417294)Peak memory usage: 107 MB
% 8.53/4.39 % (2417294)Instructions burned: 199 (million)
% 8.53/4.39 % (2417294)------------------------------
% 8.53/4.39 % (2417294)------------------------------
% 8.53/4.39 % (2417272)Success in time 3.303 s
% 8.53/4.39 % Vampire exiting
%------------------------------------------------------------------------------