%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN076+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:26:45 PM UTC 2026
% Result : Theorem 4.19s 1.71s
% Output : Refutation 4.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 22 unt; 2 def)
% Number of atoms : 140 ( 32 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 150 ( 66 ~; 44 |; 38 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 1 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn 99 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( ~ r1(X1)
& X1 != X0 )
| ( r1(X1)
& X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( ~ r2(X0,X2)
& X2 != X1 )
| ( r2(X0,X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
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/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).
fof(f8,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r3(X0,X2,X1) )
& X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).
fof(f9,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r4(X0,X2,X1) )
& ? [X3] :
( r1(X3)
& X1 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5a) ).
fof(f12,conjecture,
? [X0,X1,X2] :
( ? [X3] :
( X3 = X0
& ? [X4] :
( r4(X4,X1,X3)
& ? [X5] :
( r2(X5,X4)
& ? [X6] :
( r1(X6)
& r2(X6,X5) ) ) ) )
& ? [X7] :
( r3(X1,X2,X7)
& X7 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thereexistsanevennumber) ).
fof(f13,negated_conjecture,
~ ? [X0,X1,X2] :
( ? [X3] :
( X3 = X0
& ? [X4] :
( r4(X4,X1,X3)
& ? [X5] :
( r2(X5,X4)
& ? [X6] :
( r1(X6)
& r2(X6,X5) ) ) ) )
& ? [X7] :
( r3(X1,X2,X7)
& X7 = X0 ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ! [X3] :
( X0 != X3
| ! [X4] :
( ~ r4(X4,X1,X3)
| ! [X5] :
( ~ r2(X5,X4)
| ! [X6] :
( ~ r1(X6)
| ~ r2(X6,X5) ) ) ) )
| ! [X7] :
( ~ r3(X1,X2,X7)
| X0 != X7 ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
! [X1] :
( ( ~ r1(X1)
& sK0 != X1 )
| ( r1(X1)
& sK0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f1]) ).
fof(f16,plain,
! [X0,X2] :
( ( ~ r2(X0,X2)
& sK1(X0) != X2 )
| ( r2(X0,X2)
& sK1(X0) = X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f2]) ).
fof(f19,plain,
! [X0,X1] :
( r2(X1,sK6(X0,X1))
& r3(X0,sK6(X0,X1),sK5(X0,X1))
& sK4(X0,X1) = sK5(X0,X1)
& r2(sK7(X0,X1),sK4(X0,X1))
& r3(X0,X1,sK7(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X2,sK4(X0,X1)),skolemize(X3,sK5(X0,X1)),skolemize(X4,sK6(X0,X1)),skolemize(X5,sK7(X0,X1))],[f5]) ).
fof(f21,plain,
! [X0] :
( r1(sK13(X0))
& r3(X0,sK13(X0),sK12(X0))
& sK12(X0) = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X1,sK12(X0)),skolemize(X2,sK13(X0))],[f8]) ).
fof(f22,plain,
! [X0] :
( r1(sK15(X0))
& r4(X0,sK15(X0),sK14(X0))
& r1(sK16(X0))
& sK14(X0) = sK16(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X1,sK14(X0)),skolemize(X2,sK15(X0)),skolemize(X3,sK16(X0))],[f9]) ).
fof(f26,plain,
! [X1] :
( ~ r1(X1)
| sK0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X2,X0] :
( sK1(X0) != X2
| r2(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| sK1(X0) = X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f44,plain,
! [X0,X1] : r2(X1,sK6(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f51,plain,
! [X0] : sK12(X0) = X0,
inference(cnf_transformation,[],[f21]) ).
fof(f52,plain,
! [X0] : r3(X0,sK13(X0),sK12(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f53,plain,
! [X0] : r1(sK13(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f54,plain,
! [X0] : sK14(X0) = sK16(X0),
inference(cnf_transformation,[],[f22]) ).
fof(f55,plain,
! [X0] : r1(sK16(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f56,plain,
! [X0] : r4(X0,sK15(X0),sK14(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f57,plain,
! [X0] : r1(sK15(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f63,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( X0 != X3
| ~ r4(X4,X1,X3)
| ~ r2(X5,X4)
| ~ r1(X6)
| ~ r2(X6,X5)
| ~ r3(X1,X2,X7)
| X0 != X7 ),
inference(cnf_transformation,[],[f14]) ).
fof(f66,plain,
! [X0] : r2(X0,sK1(X0)),
inference(equality_resolution,[],[f29]) ).
fof(f74,plain,
! [X2,X3,X1,X6,X7,X4,X5] :
( ~ r4(X4,X1,X3)
| ~ r2(X5,X4)
| ~ r1(X6)
| ~ r2(X6,X5)
| ~ r3(X1,X2,X7)
| X3 != X7 ),
inference(equality_resolution,[],[f63]) ).
fof(f75,plain,
! [X2,X1,X6,X7,X4,X5] :
( ~ r1(X6)
| ~ r2(X5,X4)
| ~ r4(X4,X1,X7)
| ~ r2(X6,X5)
| ~ r3(X1,X2,X7) ),
inference(equality_resolution,[],[f74]) ).
fof(f86,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r2(sK13(X4),X0)
| ~ r4(X1,X2,X3)
| ~ r2(X0,X1)
| ~ r3(X2,X5,X3) ),
inference(resolution,[],[f53,f75]) ).
fof(f95,plain,
! [X0] : sK0 = sK13(X0),
inference(resolution,[],[f26,f53]) ).
fof(f96,plain,
! [X0] : sK0 = sK15(X0),
inference(resolution,[],[f26,f57]) ).
fof(f99,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r4(X0,X1,X2)
| ~ r2(sK6(X3,sK13(X4)),X0)
| ~ r3(X1,X5,X2) ),
inference(resolution,[],[f44,f86]) ).
fof(f105,plain,
! [X0] : r1(sK14(X0)),
inference(superposition,[],[f55,f54]) ).
fof(f118,plain,
! [X0] : r3(X0,sK13(X0),X0),
inference(forward_demodulation,[],[f52,f51]) ).
fof(f119,plain,
! [X2,X3,X0,X1] :
( ~ r3(sK15(X2),X3,sK14(X2))
| ~ r2(sK6(X0,sK13(X1)),X2) ),
inference(resolution,[],[f56,f99]) ).
fof(f134,plain,
! [X0,X1] : sK1(X0) = sK6(X1,X0),
inference(resolution,[],[f30,f44]) ).
fof(f173,plain,
! [X0] : sK0 = sK14(X0),
inference(resolution,[],[f105,f26]) ).
fof(f179,plain,
! [X0] : r3(X0,sK0,X0),
inference(superposition,[],[f118,f95]) ).
fof(f356,plain,
! [X2,X3,X0,X1] :
( ~ r3(sK15(X0),X1,sK0)
| ~ r2(sK6(X2,sK13(X3)),X0) ),
inference(superposition,[],[f119,f173]) ).
fof(f372,definition,
( spl20_3
<=> ! [X1] : ~ r2(sK1(sK0),X1) ),
introduced(definition,[new_symbols(definition,[spl20_3])],[avatar_definition]) ).
fof(f373,plain,
( ! [X1] : ~ r2(sK1(sK0),X1)
| ~ spl20_3 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f375,definition,
( spl20_4
<=> ! [X0] : ~ r3(sK0,X0,sK0) ),
introduced(definition,[new_symbols(definition,[spl20_4])],[avatar_definition]) ).
fof(f376,plain,
( ! [X0] : ~ r3(sK0,X0,sK0)
| ~ spl20_4 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f384,plain,
! [X2,X3,X0,X1] :
( ~ r3(sK0,X1,sK0)
| ~ r2(sK6(X2,sK13(X3)),X0) ),
inference(forward_demodulation,[],[f356,f96]) ).
fof(f393,plain,
! [X3,X0,X1] :
( ~ r2(sK1(sK13(X3)),X0)
| ~ r3(sK0,X1,sK0) ),
inference(forward_demodulation,[],[f384,f134]) ).
fof(f398,plain,
! [X0,X1] :
( ~ r2(sK1(sK0),X0)
| ~ r3(sK0,X1,sK0) ),
inference(forward_demodulation,[],[f393,f95]) ).
fof(f399,plain,
( spl20_4
| spl20_3 ),
inference(avatar_split_clause,[],[f398,f372,f375]) ).
fof(f400,plain,
( $false
| ~ spl20_3 ),
inference(resolution,[],[f373,f66]) ).
fof(f405,plain,
~ spl20_3,
inference(avatar_contradiction_clause,[],[f400]) ).
fof(f407,plain,
( $false
| ~ spl20_4 ),
inference(resolution,[],[f376,f179]) ).
fof(f410,plain,
~ spl20_4,
inference(avatar_contradiction_clause,[],[f407]) ).
cnf(s10,plain,
( spl20_3
| spl20_4 ),
inference(sat_conversion,[],[f399]) ).
cnf(s13,plain,
~ spl20_3,
inference(sat_conversion,[],[f405]) ).
cnf(s15,plain,
~ spl20_4,
inference(sat_conversion,[],[f410]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s10,s15,s13]) ).
fof(f411,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN076+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n001.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 22:03:02 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 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
% 4.19/1.71 % (4002072)Detected formulas, will run a generic FOF schedule.
% 4.19/1.71 % (4002079)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=1977443029:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.19/1.71 % (4002083)dis-21_1_sil=8000:lcm=predicate:random_seed=274119702: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)
% 4.19/1.71 % (4002081)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1328084291:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.19/1.71 % (4002077)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=3135233732:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.19/1.71 % (4002078)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=1672957276:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.19/1.71 % (4002080)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1440427268:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.19/1.71 % (4002082)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3132648680:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.19/1.71 % (4002083)Refutation not found, incomplete strategy
% 4.19/1.71 % (4002083)------------------------------
% 4.19/1.71 % (4002083)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.71 % (4002080)Refutation not found, incomplete strategy
% 4.19/1.71 % (4002080)------------------------------
% 4.19/1.71 % (4002080)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.71 % (4002082)First to succeed.
% 4.19/1.71 % (4002081)Instruction limit reached!
% 4.19/1.71 % (4002081)------------------------------
% 4.19/1.71 % (4002081)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.71 % (4002083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.71 % (4002080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.71 % (4002081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.71 % (4002080)CaDiCaL version: 2.1.3
% 4.19/1.71 % (4002083)CaDiCaL version: 2.1.3
% 4.19/1.71 % (4002080)Termination reason: Refutation not found, incomplete strategy
% 4.19/1.71 % (4002080)Time elapsed: 0.205 s
% 4.19/1.71 % (4002081)CaDiCaL version: 2.1.3
% 4.19/1.71 % (4002083)Termination reason: Refutation not found, incomplete strategy
% 4.19/1.71 % (4002083)Time elapsed: 0.205 s
% 4.19/1.71 % (4002080)Peak memory usage: 88 MB
% 4.19/1.71 % (4002083)Peak memory usage: 88 MB
% 4.19/1.71 % (4002081)Termination reason: Instruction limit
% 4.19/1.71 % (4002081)Termination phase: Saturation
% 4.19/1.71 % (4002080)Instructions burned: 3 (million)
% 4.19/1.71 % (4002083)Instructions burned: 2 (million)
% 4.19/1.71 % (4002081)Time elapsed: 0.205 s
% 4.19/1.71 % (4002081)Peak memory usage: 89 MB
% 4.19/1.71 % (4002081)Instructions burned: 322 (million)
% 4.19/1.71 % (4002082)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4002072"
% 4.19/1.71 % (4002079)Refutation not found, incomplete strategy
% 4.19/1.71 % (4002079)------------------------------
% 4.19/1.71 % (4002079)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.71 % (4002079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.71 % (4002079)CaDiCaL version: 2.1.3
% 4.19/1.71 % (4002079)Termination reason: Refutation not found, incomplete strategy
% 4.19/1.71 % (4002079)Time elapsed: 0.340 s
% 4.19/1.71 % (4002079)Peak memory usage: 128 MB
% 4.19/1.71 % (4002079)Instructions burned: 917 (million)
% 4.19/1.71 % (4002091)lrs+10_1_sil=8000:sp=occurrence:random_seed=146149729:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 4.19/1.71 % (4002091)Also succeeded, but the first one will report.
% 4.19/1.71 % (4002080)------------------------------
% 4.19/1.71 % (4002080)------------------------------
% 4.19/1.71 % (4002083)------------------------------
% 4.19/1.71 % (4002083)------------------------------
% 4.19/1.71 % (4002079)------------------------------
% 4.19/1.71 % (4002079)------------------------------
% 4.19/1.71 % (4002082)Refutation found. Thanks to Tanya!
% 4.19/1.71 % SZS status Theorem for theBenchmark
% 4.19/1.71 % SZS output start Proof for theBenchmark
% See solution above
% 4.19/1.71 % (4002082)------------------------------
% 4.19/1.71 % (4002082)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.71 % (4002082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.71 % (4002082)CaDiCaL version: 2.1.3
% 4.19/1.71 % (4002082)Termination reason: Refutation
% 4.19/1.71 % (4002082)Time elapsed: 0.206 s
% 4.19/1.71 % (4002082)Peak memory usage: 89 MB
% 4.19/1.71 % (4002082)Instructions burned: 16 (million)
% 4.19/1.71 % (4002082)------------------------------
% 4.19/1.71 % (4002082)------------------------------
% 4.19/1.71 % (4002072)Success in time 0.638 s
% 4.19/1.71 % Vampire exiting
%------------------------------------------------------------------------------