%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS082+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 11:41:36 AM UTC 2026
% Result : Unsatisfiable 2.62s 1.23s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 4 unt; 0 def)
% Number of atoms : 200 ( 0 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 256 ( 102 ~; 83 |; 38 &)
% ( 4 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 147 ( 127 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( cUnsatisfiable(X0)
=> ? [X1] :
( rs(X0,X1)
& ? [X2] :
( rp(X1,X2)
& cowlThing(X2) )
& ! [X2] :
( rr(X1,X2)
=> cc(X2) )
& ! [X2] :
( rp(X1,X2)
=> ? [X3] :
( rr(X2,X3)
& cowlThing(X3) ) )
& ! [X2] :
( rp(X1,X2)
=> ? [X3] :
( rp(X2,X3)
& cowlThing(X3) ) )
& ! [X2] :
( rp(X1,X2)
=> ! [X3] :
( rr(X2,X3)
=> cc(X3) ) )
& ? [X2] :
( rr(X1,X2)
& cowlThing(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f4,axiom,
! [X0] :
( cUnsatisfiable(X0)
=> ca(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f5,axiom,
! [X0] :
( cc(X0)
<=> ! [X1] :
( rinvR(X0,X1)
=> ! [X2] :
( rinvP(X1,X2)
=> ! [X3] :
( rinvS(X2,X3)
=> ~ ca(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
fof(f6,axiom,
! [X0,X1] :
( rinvP(X0,X1)
<=> rp(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
fof(f7,axiom,
! [X0,X1] :
( rinvR(X0,X1)
<=> rr(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
fof(f8,axiom,
! [X0,X1] :
( rinvS(X0,X1)
<=> rs(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
fof(f10,axiom,
cUnsatisfiable(i2003_11_14_17_19_28752),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
fof(f11,plain,
! [X0] :
( cUnsatisfiable(X0)
=> ? [X1] :
( rs(X0,X1)
& ? [X2] :
( rp(X1,X2)
& cowlThing(X2) )
& ! [X3] :
( rr(X1,X3)
=> cc(X3) )
& ! [X4] :
( rp(X1,X4)
=> ? [X5] :
( rr(X4,X5)
& cowlThing(X5) ) )
& ! [X6] :
( rp(X1,X6)
=> ? [X7] :
( rp(X6,X7)
& cowlThing(X7) ) )
& ! [X8] :
( rp(X1,X8)
=> ! [X9] :
( rr(X8,X9)
=> cc(X9) ) )
& ? [X10] :
( rr(X1,X10)
& cowlThing(X10) ) ) ),
inference(rectify,[],[f3]) ).
fof(f12,plain,
! [X0] :
( cc(X0)
=> ! [X1] :
( rinvR(X0,X1)
=> ! [X2] :
( rinvP(X1,X2)
=> ! [X3] :
( rinvS(X2,X3)
=> ~ ca(X3) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f13,plain,
! [X0,X1] :
( rs(X1,X0)
=> rinvS(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f14,plain,
! [X0,X1] :
( rp(X1,X0)
=> rinvP(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f15,plain,
! [X0,X1] :
( rr(X1,X0)
=> rinvR(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f18,plain,
! [X0] :
( cUnsatisfiable(X0)
=> ? [X1] :
( rs(X0,X1)
& ? [X2] : rp(X1,X2)
& ! [X3] :
( rr(X1,X3)
=> cc(X3) )
& ! [X4] :
( rp(X1,X4)
=> ? [X5] : rr(X4,X5) )
& ! [X6] :
( rp(X1,X6)
=> ? [X7] : rp(X6,X7) )
& ! [X8] :
( rp(X1,X8)
=> ! [X9] :
( rr(X8,X9)
=> cc(X9) ) )
& ? [X10] : rr(X1,X10) ) ),
inference(pure_predicate_removal,[],[f11]) ).
fof(f19,plain,
! [X0] :
( ? [X1] :
( rs(X0,X1)
& ? [X2] : rp(X1,X2)
& ! [X3] :
( cc(X3)
| ~ rr(X1,X3) )
& ! [X4] :
( ? [X5] : rr(X4,X5)
| ~ rp(X1,X4) )
& ! [X6] :
( ? [X7] : rp(X6,X7)
| ~ rp(X1,X6) )
& ! [X8] :
( ! [X9] :
( cc(X9)
| ~ rr(X8,X9) )
| ~ rp(X1,X8) )
& ? [X10] : rr(X1,X10) )
| ~ cUnsatisfiable(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
! [X0] :
( ca(X0)
| ~ cUnsatisfiable(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f21,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ ca(X3)
| ~ rinvS(X2,X3) )
| ~ rinvP(X1,X2) )
| ~ rinvR(X0,X1) )
| ~ cc(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f22,plain,
! [X0,X1] :
( rinvP(X0,X1)
| ~ rp(X1,X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f23,plain,
! [X0,X1] :
( rinvR(X0,X1)
| ~ rr(X1,X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f24,plain,
! [X0,X1] :
( rinvS(X0,X1)
| ~ rs(X1,X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f27,plain,
! [X0] :
( ( rs(X0,sK0(X0))
& rp(sK0(X0),sK1(X0))
& ! [X3] :
( cc(X3)
| ~ rr(sK0(X0),X3) )
& ! [X4] :
( rr(X4,sK2(X4))
| ~ rp(sK0(X0),X4) )
& ! [X6] :
( rp(X6,sK3(X6))
| ~ rp(sK0(X0),X6) )
& ! [X8] :
( ! [X9] :
( cc(X9)
| ~ rr(X8,X9) )
| ~ rp(sK0(X0),X8) )
& rr(sK0(X0),sK4(X0)) )
| ~ cUnsatisfiable(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X1,sK0(X0)),skolemize(X2,sK1(X0)),skolemize(X5,sK2(X4)),skolemize(X7,sK3(X6)),skolemize(X10,sK4(X0))],[f19]) ).
fof(f29,plain,
! [X0,X8,X9] :
( cc(X9)
| ~ rr(X8,X9)
| ~ rp(sK0(X0),X8)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f31,plain,
! [X0,X4] :
( rr(X4,sK2(X4))
| ~ rp(sK0(X0),X4)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f33,plain,
! [X0] :
( rp(sK0(X0),sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f34,plain,
! [X0] :
( rs(X0,sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f35,plain,
! [X0] :
( ca(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( ~ rinvS(X2,X3)
| ~ ca(X3)
| ~ rinvP(X1,X2)
| ~ rinvR(X0,X1)
| ~ cc(X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f37,plain,
! [X0,X1] :
( rinvP(X0,X1)
| ~ rp(X1,X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X0,X1] :
( rinvR(X0,X1)
| ~ rr(X1,X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f39,plain,
! [X0,X1] :
( rinvS(X0,X1)
| ~ rs(X1,X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f41,plain,
cUnsatisfiable(i2003_11_14_17_19_28752),
inference(cnf_transformation,[],[f10]) ).
fof(f42,plain,
! [X2,X3,X0,X1] :
( ~ rinvP(X1,X2)
| ~ ca(X0)
| ~ rinvR(X3,X1)
| ~ cc(X3)
| ~ rs(X0,X2) ),
inference(resolution,[],[f36,f39]) ).
fof(f43,plain,
! [X2,X3,X0,X1] :
( ~ rinvR(X1,X2)
| ~ ca(X0)
| ~ cc(X1)
| ~ rs(X0,X3)
| ~ rp(X3,X2) ),
inference(resolution,[],[f42,f37]) ).
fof(f44,plain,
! [X2,X3,X0,X1] :
( ~ ca(X0)
| ~ cc(X1)
| ~ rs(X0,X2)
| ~ rp(X2,X3)
| ~ rr(X3,X1) ),
inference(resolution,[],[f43,f38]) ).
fof(f45,plain,
! [X2,X3,X0,X1] :
( ~ rs(X1,X2)
| ~ cc(X0)
| ~ rp(X2,X3)
| ~ rr(X3,X0)
| ~ cUnsatisfiable(X1) ),
inference(resolution,[],[f44,f35]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ cc(X0)
| ~ rp(sK0(X1),X2)
| ~ rr(X2,X0)
| ~ cUnsatisfiable(X1)
| ~ cUnsatisfiable(X1) ),
inference(resolution,[],[f45,f34]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ cc(X0)
| ~ rp(sK0(X1),X2)
| ~ rr(X2,X0)
| ~ cUnsatisfiable(X1) ),
inference(duplicate_literal_removal,[],[f46]) ).
fof(f48,plain,
! [X2,X3,X0,X1,X4] :
( ~ rr(X1,X2)
| ~ rr(X3,X2)
| ~ cUnsatisfiable(X0)
| ~ rp(sK0(X0),X1)
| ~ rp(sK0(X4),X3)
| ~ cUnsatisfiable(X4) ),
inference(resolution,[],[f47,f29]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( ~ rr(X0,X1)
| ~ cUnsatisfiable(X2)
| ~ rp(sK0(X2),X0)
| ~ rp(sK0(X3),X0)
| ~ cUnsatisfiable(X3) ),
inference(factoring,[],[f48]) ).
fof(f72,plain,
! [X2,X3,X0,X1] :
( ~ rp(sK0(X0),X1)
| ~ rp(sK0(X2),X1)
| ~ rp(sK0(X3),X1)
| ~ cUnsatisfiable(X2)
| ~ cUnsatisfiable(X0)
| ~ cUnsatisfiable(X3) ),
inference(resolution,[],[f62,f31]) ).
fof(f110,plain,
! [X2,X0,X1] :
( ~ rp(sK0(X2),X1)
| ~ rp(sK0(X0),X1)
| ~ cUnsatisfiable(X0)
| ~ cUnsatisfiable(X2)
| ~ cUnsatisfiable(X0) ),
inference(factoring,[],[f72]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ rp(sK0(X2),X1)
| ~ rp(sK0(X0),X1)
| ~ cUnsatisfiable(X0)
| ~ cUnsatisfiable(X2) ),
inference(duplicate_literal_removal,[],[f110]) ).
fof(f123,plain,
! [X0,X1] :
( ~ rp(sK0(X0),X1)
| ~ cUnsatisfiable(X0)
| ~ cUnsatisfiable(X0) ),
inference(factoring,[],[f111]) ).
fof(f124,plain,
! [X0,X1] :
( ~ rp(sK0(X0),X1)
| ~ cUnsatisfiable(X0) ),
inference(duplicate_literal_removal,[],[f123]) ).
fof(f127,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f124,f33]) ).
fof(f130,plain,
! [X0] : ~ cUnsatisfiable(X0),
inference(duplicate_literal_removal,[],[f127]) ).
fof(f131,plain,
$false,
inference(resolution,[],[f130,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS082+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n018.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 27 13:22:23 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 2.62/1.23 % (2353941)Detected formulas, will run a generic FOF schedule.
% 2.62/1.23 % (2353952)dis-21_1_sil=8000:lcm=predicate:random_seed=3302121282: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)
% 2.62/1.23 % (2353952)First to succeed.
% 2.62/1.23 % (2353952)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2353941"
% 2.62/1.23 % (2353946)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=2289251044:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.62/1.23 % (2353949)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=864001106:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.62/1.23 % (2353947)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=4184248175:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.62/1.23 % (2353948)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=2337938629:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.62/1.23 % (2353950)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1726294102:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.62/1.23 % (2353951)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1250415602:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.62/1.23 % (2353950)Refutation not found, incomplete strategy
% 2.62/1.23 % (2353950)------------------------------
% 2.62/1.23 % (2353950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.23 % (2353949)Refutation not found, incomplete strategy
% 2.62/1.23 % (2353949)------------------------------
% 2.62/1.23 % (2353949)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.23 % (2353949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.23 % (2353950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.23 % (2353949)CaDiCaL version: 2.1.3
% 2.62/1.23 % (2353949)Termination reason: Refutation not found, incomplete strategy
% 2.62/1.23 % (2353949)Time elapsed: 0.0000 s
% 2.62/1.23 % (2353949)Peak memory usage: 86 MB
% 2.62/1.23 % (2353950)CaDiCaL version: 2.1.3
% 2.62/1.23 % (2353950)Termination reason: Refutation not found, incomplete strategy
% 2.62/1.23 % (2353950)Time elapsed: 0.0000 s
% 2.62/1.23 % (2353950)Peak memory usage: 86 MB
% 2.62/1.23 % (2353951)Also succeeded, but the first one will report.
% 2.62/1.23 % (2353952)Refutation found. Thanks to Tanya!
% 2.62/1.23 % SZS status Unsatisfiable for theBenchmark
% 2.62/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/1.23 % (2353952)------------------------------
% 2.62/1.23 % (2353952)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.23 % (2353952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.23 % (2353952)CaDiCaL version: 2.1.3
% 2.62/1.23 % (2353952)Termination reason: Refutation
% 2.62/1.23 % (2353952)Time elapsed: 0.003 s
% 2.62/1.23 % (2353952)Peak memory usage: 88 MB
% 2.62/1.23 % (2353952)Instructions burned: 5 (million)
% 2.62/1.23 % (2353952)------------------------------
% 2.62/1.23 % (2353952)------------------------------
% 2.62/1.23 % (2353941)Success in time 0.297 s
% 2.62/1.23 % Vampire exiting
%------------------------------------------------------------------------------