%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN060+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:26:41 PM UTC 2026
% Result : Theorem 5.82s 1.95s
% Output : Refutation 5.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 10 unt; 4 def)
% Number of atoms : 126 ( 18 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 159 ( 74 ~; 49 |; 32 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 0 con; 1-2 aty)
% Number of variables : 119 ( 95 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( ~ r2(X0,X2)
& X2 != X1 )
| ( r2(X0,X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f3,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ r3(X0,X1,X3)
& X3 != X2 )
| ( r3(X0,X1,X3)
& X3 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f5,axiom,
! [X0,X1] :
? [X2] :
( ? [X3] :
( ? [X4] :
( r2(X1,X4)
& r3(X0,X4,X3) )
& X3 = X2 )
& ? [X5] :
( r2(X5,X2)
& r3(X0,X1,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1a) ).
fof(f8,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r3(X0,X2,X1) )
& X1 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4a) ).
fof(f12,conjecture,
? [X0,X1,X2] :
( X2 = X0
& ? [X3] :
( r3(X1,X3,X2)
& ? [X4] :
( r2(X4,X3)
& ? [X5] :
( r2(X5,X4)
& ? [X6] :
( r2(X6,X5)
& ? [X7] :
( r1(X7)
& r2(X7,X6) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greq4) ).
fof(f13,negated_conjecture,
~ ? [X0,X1,X2] :
( X2 = X0
& ? [X3] :
( r3(X1,X3,X2)
& ? [X4] :
( r2(X4,X3)
& ? [X5] :
( r2(X5,X4)
& ? [X6] :
( r2(X6,X5)
& ? [X7] :
( r1(X7)
& r2(X7,X6) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( X0 != X2
| ! [X3] :
( ~ r3(X1,X3,X2)
| ! [X4] :
( ~ r2(X4,X3)
| ! [X5] :
( ~ r2(X5,X4)
| ! [X6] :
( ~ r2(X6,X5)
| ! [X7] :
( ~ r1(X7)
| ~ r2(X7,X6) ) ) ) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f17,plain,
! [X0,X2] :
( ( ~ r2(X0,X2)
& sK4(X0) != X2 )
| ( r2(X0,X2)
& sK4(X0) = X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f2]) ).
fof(f18,plain,
! [X0] :
( r1(sK6(X0))
& r3(X0,sK6(X0),sK5(X0))
& sK5(X0) = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X1,sK5(X0)),skolemize(X2,sK6(X0))],[f8]) ).
fof(f19,plain,
! [X0,X1] :
( r2(X1,sK9(X0,X1))
& r3(X0,sK9(X0,X1),sK8(X0,X1))
& sK7(X0,X1) = sK8(X0,X1)
& r2(sK10(X0,X1),sK7(X0,X1))
& r3(X0,X1,sK10(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10]),skolemize(X2,sK7(X0,X1)),skolemize(X3,sK8(X0,X1)),skolemize(X4,sK9(X0,X1)),skolemize(X5,sK10(X0,X1))],[f5]) ).
fof(f20,plain,
! [X0,X1,X3] :
( ( ~ r3(X0,X1,X3)
& sK11(X0,X1) != X3 )
| ( r3(X0,X1,X3)
& sK11(X0,X1) = X3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f3]) ).
fof(f21,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( X0 != X2
| ~ r3(X1,X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ r1(X7)
| ~ r2(X7,X6) ),
inference(cnf_transformation,[],[f14]) ).
fof(f33,plain,
! [X2,X0] :
( sK4(X0) != X2
| r2(X0,X2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f38,plain,
! [X0] : r1(sK6(X0)),
inference(cnf_transformation,[],[f18]) ).
fof(f43,plain,
! [X0,X1] : r2(X1,sK9(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f45,plain,
! [X3,X0,X1] :
( sK11(X0,X1) != X3
| r3(X0,X1,X3) ),
inference(cnf_transformation,[],[f20]) ).
fof(f53,plain,
! [X2,X3,X1,X6,X7,X4,X5] :
( ~ r3(X1,X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ r1(X7)
| ~ r2(X7,X6) ),
inference(equality_resolution,[],[f21]) ).
fof(f56,plain,
! [X0] : r2(X0,sK4(X0)),
inference(equality_resolution,[],[f33]) ).
fof(f58,plain,
! [X0,X1] : r3(X0,X1,sK11(X0,X1)),
inference(equality_resolution,[],[f45]) ).
fof(f60,plain,
! [X6,X7] :
( ~ r2(X7,X6)
| ~ r1(X7)
| sP14(X6) ),
inference(cnf_transformation,[],[f60_D]) ).
fof(f60_D,definition,
! [X6] :
( ! [X7] :
( ~ r2(X7,X6)
| ~ r1(X7) )
<=> ~ sP14(X6) ),
introduced(definition,[new_symbols(definition,[sP14])],[general_splitting_component_introduction]) ).
fof(f61,plain,
! [X2,X3,X1,X6,X4,X5] :
( ~ r3(X1,X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ sP14(X6) ),
inference(general_splitting,[],[f53,f60_D]) ).
fof(f62,plain,
! [X6,X5] :
( ~ r2(X6,X5)
| ~ sP14(X6)
| sP15(X5) ),
inference(cnf_transformation,[],[f62_D]) ).
fof(f62_D,definition,
! [X5] :
( ! [X6] :
( ~ r2(X6,X5)
| ~ sP14(X6) )
<=> ~ sP15(X5) ),
introduced(definition,[new_symbols(definition,[sP15])],[general_splitting_component_introduction]) ).
fof(f63,plain,
! [X2,X3,X1,X4,X5] :
( ~ r3(X1,X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ sP15(X5) ),
inference(general_splitting,[],[f61,f62_D]) ).
fof(f64,plain,
! [X4,X5] :
( ~ r2(X5,X4)
| ~ sP15(X5)
| sP16(X4) ),
inference(cnf_transformation,[],[f64_D]) ).
fof(f64_D,definition,
! [X4] :
( ! [X5] :
( ~ r2(X5,X4)
| ~ sP15(X5) )
<=> ~ sP16(X4) ),
introduced(definition,[new_symbols(definition,[sP16])],[general_splitting_component_introduction]) ).
fof(f65,plain,
! [X2,X3,X1,X4] :
( ~ r3(X1,X3,X2)
| ~ r2(X4,X3)
| ~ sP16(X4) ),
inference(general_splitting,[],[f63,f64_D]) ).
fof(f66,plain,
! [X3,X4] :
( ~ r2(X4,X3)
| ~ sP16(X4)
| sP17(X3) ),
inference(cnf_transformation,[],[f66_D]) ).
fof(f66_D,definition,
! [X3] :
( ! [X4] :
( ~ r2(X4,X3)
| ~ sP16(X4) )
<=> ~ sP17(X3) ),
introduced(definition,[new_symbols(definition,[sP17])],[general_splitting_component_introduction]) ).
fof(f67,plain,
! [X2,X3,X1] :
( ~ r3(X1,X3,X2)
| ~ sP17(X3) ),
inference(general_splitting,[],[f65,f66_D]) ).
fof(f71,plain,
! [X0] : ~ sP17(X0),
inference(resolution,[],[f67,f58]) ).
fof(f75,plain,
! [X0,X1] :
( sP14(sK9(X1,X0))
| ~ r1(X0) ),
inference(resolution,[],[f60,f43]) ).
fof(f79,plain,
! [X0] :
( sP15(sK4(X0))
| ~ sP14(X0) ),
inference(resolution,[],[f62,f56]) ).
fof(f85,plain,
! [X0] :
( sP16(sK4(X0))
| ~ sP15(X0) ),
inference(resolution,[],[f64,f56]) ).
fof(f92,plain,
! [X0,X1] :
( ~ sP16(X0)
| sP17(sK9(X1,X0)) ),
inference(resolution,[],[f66,f43]) ).
fof(f95,plain,
! [X0] : ~ sP16(X0),
inference(forward_subsumption_resolution,[],[f92,f71]) ).
fof(f99,plain,
! [X0] : ~ sP15(X0),
inference(resolution,[],[f85,f95]) ).
fof(f101,plain,
! [X0] : ~ sP14(X0),
inference(resolution,[],[f99,f79]) ).
fof(f104,plain,
! [X0] : ~ r1(X0),
inference(resolution,[],[f101,f75]) ).
fof(f106,plain,
$false,
inference(resolution,[],[f104,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUN060+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.44 % Computer : n006.cluster.edu
% 0.15/0.44 % Model : x86_64 x86_64
% 0.15/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.44 % Memory : 8046.5625MB
% 0.15/0.44 % OS : Linux 6.8.0-71-generic
% 0.15/0.44 % CPULimit : 300
% 0.15/0.44 % WCLimit : 300
% 0.15/0.44 % DateTime : Sun Sep 27 21:51:40 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 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
% 5.82/1.95 % (3357136)Detected formulas, will run a generic FOF schedule.
% 5.82/1.95 % (3357143)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=1986099296:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.82/1.95 % (3357142)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=2193698937:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.82/1.95 % (3357141)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=3209559070:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.82/1.95 % (3357144)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3394798563:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.82/1.95 % (3357144)First to succeed.
% 5.82/1.95 % (3357144)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3357136"
% 5.82/1.95 % (3357146)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3077603652:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.82/1.95 % (3357145)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3908865453:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.82/1.95 % (3357147)dis-21_1_sil=8000:lcm=predicate:random_seed=2301747062: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)
% 5.82/1.95 % (3357145)Also succeeded, but the first one will report.
% 5.82/1.95 % (3357146)Also succeeded, but the first one will report.
% 5.82/1.95 % (3357147)Also succeeded, but the first one will report.
% 5.82/1.95 % (3357144)Refutation found. Thanks to Tanya!
% 5.82/1.95 % SZS status Theorem for theBenchmark
% 5.82/1.95 % SZS output start Proof for theBenchmark
% See solution above
% 5.82/1.95 % (3357144)------------------------------
% 5.82/1.95 % (3357144)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.82/1.95 % (3357144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.82/1.95 % (3357144)CaDiCaL version: 2.1.3
% 5.82/1.95 % (3357144)Termination reason: Refutation
% 5.82/1.95 % (3357144)Time elapsed: 0.006 s
% 5.82/1.95 % (3357144)Peak memory usage: 88 MB
% 5.82/1.95 % (3357144)Instructions burned: 3 (million)
% 5.82/1.95 % (3357144)------------------------------
% 5.82/1.95 % (3357144)------------------------------
% 5.82/1.95 % (3357136)Success in time 0.711 s
% 5.82/1.95 % Vampire exiting
%------------------------------------------------------------------------------