%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN056+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 : n012.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 12:26:40 PM UTC 2026
% Result : Theorem 0.42s 0.83s
% Output : Refutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 23 unt; 0 def)
% Number of atoms : 210 ( 37 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 276 ( 125 ~; 101 |; 50 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-2 aty)
% Number of variables : 185 ( 153 !; 32 ?)
% 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(f3,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ r3(X0,X1,X3)
& X3 != X2 )
| ( r3(X0,X1,X3)
& X3 = X2 ) ),
file('/export/starexec/sandbox2/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/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] :
( X0 = X1
& ? [X2] :
( r2(X2,X1)
& ? [X3] :
( r2(X3,X2)
& ? [X4] :
( r1(X4)
& r2(X4,X3) ) ) ) )
& ? [X5] :
( ? [X6] :
( r3(X6,X5,X0)
& ? [X7] :
( r1(X7)
& r2(X7,X6) ) )
& ? [X8] :
( r2(X8,X5)
& ? [X9] :
( r1(X9)
& r2(X9,X8) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oneplustwoeqthree) ).
fof(f13,negated_conjecture,
~ ? [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r2(X2,X1)
& ? [X3] :
( r2(X3,X2)
& ? [X4] :
( r1(X4)
& r2(X4,X3) ) ) ) )
& ? [X5] :
( ? [X6] :
( r3(X6,X5,X0)
& ? [X7] :
( r1(X7)
& r2(X7,X6) ) )
& ? [X8] :
( r2(X8,X5)
& ? [X9] :
( r1(X9)
& r2(X9,X8) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0] :
( ! [X1] :
( X0 != X1
| ! [X2] :
( ~ r2(X2,X1)
| ! [X3] :
( ~ r2(X3,X2)
| ! [X4] :
( ~ r1(X4)
| ~ r2(X4,X3) ) ) ) )
| ! [X5] :
( ! [X6] :
( ~ r3(X6,X5,X0)
| ! [X7] :
( ~ r1(X7)
| ~ r2(X7,X6) ) )
| ! [X8] :
( ~ r2(X8,X5)
| ! [X9] :
( ~ r1(X9)
| ~ r2(X9,X8) ) ) ) ),
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(f17,plain,
! [X0,X1,X3] :
( ( ~ r3(X0,X1,X3)
& sK2(X0,X1) != X3 )
| ( r3(X0,X1,X3)
& sK2(X0,X1) = X3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f3]) ).
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(f25,plain,
! [X1] :
( sK0 != X1
| r1(X1) ),
inference(cnf_transformation,[],[f15]) ).
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(f33,plain,
! [X3,X0,X1] :
( sK2(X0,X1) != X3
| r3(X0,X1,X3) ),
inference(cnf_transformation,[],[f17]) ).
fof(f34,plain,
! [X3,X0,X1] :
( ~ r3(X0,X1,X3)
| sK2(X0,X1) = X3 ),
inference(cnf_transformation,[],[f17]) ).
fof(f40,plain,
! [X0,X1] : r3(X0,X1,sK7(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f41,plain,
! [X0,X1] : r2(sK7(X0,X1),sK4(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f42,plain,
! [X0,X1] : sK4(X0,X1) = sK5(X0,X1),
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
! [X0,X1] : r3(X0,sK6(X0,X1),sK5(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
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(f55,plain,
! [X0] : r1(sK16(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f63,plain,
! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( X0 != X1
| ~ r2(X2,X1)
| ~ r2(X3,X2)
| ~ r1(X4)
| ~ r2(X4,X3)
| ~ r3(X6,X5,X0)
| ~ r1(X7)
| ~ r2(X7,X6)
| ~ r2(X8,X5)
| ~ r1(X9)
| ~ r2(X9,X8) ),
inference(cnf_transformation,[],[f14]) ).
fof(f64,plain,
r1(sK0),
inference(equality_resolution,[],[f25]) ).
fof(f66,plain,
! [X0] : r2(X0,sK1(X0)),
inference(equality_resolution,[],[f29]) ).
fof(f68,plain,
! [X0,X1] : r3(X0,X1,sK2(X0,X1)),
inference(equality_resolution,[],[f33]) ).
fof(f74,plain,
! [X2,X3,X1,X8,X6,X9,X7,X4,X5] :
( ~ r2(X9,X8)
| ~ r2(X3,X2)
| ~ r1(X4)
| ~ r2(X4,X3)
| ~ r3(X6,X5,X1)
| ~ r1(X7)
| ~ r2(X7,X6)
| ~ r2(X8,X5)
| ~ r1(X9)
| ~ r2(X2,X1) ),
inference(equality_resolution,[],[f63]) ).
fof(f122,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ r2(sK1(X7),X4)
| ~ r1(X2)
| ~ r2(X2,X0)
| ~ r3(X3,X4,X5)
| ~ r1(X6)
| ~ r2(X6,X3)
| ~ r2(X0,X1)
| ~ r1(X7)
| ~ r2(X1,X5) ),
inference(resolution,[],[f66,f74]) ).
fof(f124,plain,
! [X0] : sK0 = sK13(X0),
inference(resolution,[],[f26,f53]) ).
fof(f154,plain,
! [X0] : r3(X0,sK13(X0),X0),
inference(forward_demodulation,[],[f52,f51]) ).
fof(f165,plain,
! [X0,X1] : sK1(X0) = sK6(X1,X0),
inference(resolution,[],[f30,f44]) ).
fof(f179,plain,
! [X0,X1] : r3(X0,sK6(X0,X1),sK4(X0,X1)),
inference(forward_demodulation,[],[f43,f42]) ).
fof(f186,plain,
! [X0,X1] : sK2(X0,X1) = sK7(X0,X1),
inference(resolution,[],[f34,f40]) ).
fof(f188,plain,
! [X0] : sK2(X0,sK13(X0)) = X0,
inference(resolution,[],[f34,f154]) ).
fof(f189,plain,
! [X0,X1] : sK4(X0,X1) = sK2(X0,sK6(X0,X1)),
inference(resolution,[],[f34,f179]) ).
fof(f216,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ r3(X2,sK1(sK1(X3)),X4)
| ~ r2(X0,X1)
| ~ r1(X0)
| ~ r1(X5)
| ~ r2(X5,X2)
| ~ r2(X1,X6)
| ~ r1(X3)
| ~ r2(X6,X4) ),
inference(resolution,[],[f122,f66]) ).
fof(f224,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r2(X4,sK2(X3,sK1(sK1(X5))))
| ~ r1(X0)
| ~ r1(X2)
| ~ r2(X2,X3)
| ~ r2(X1,X4)
| ~ r1(X5)
| ~ r2(X0,X1) ),
inference(resolution,[],[f216,f68]) ).
fof(f293,plain,
! [X0] : sK2(X0,sK0) = X0,
inference(forward_demodulation,[],[f188,f124]) ).
fof(f373,plain,
! [X0,X1] : sK4(X0,X1) = sK2(X0,sK1(X1)),
inference(forward_demodulation,[],[f189,f165]) ).
fof(f384,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r2(X2,sK4(X0,sK1(X1)))
| ~ r1(X3)
| ~ r1(X4)
| ~ r2(X4,X0)
| ~ r2(X5,X2)
| ~ r1(X1)
| ~ r2(X3,X5) ),
inference(superposition,[],[f224,f373]) ).
fof(f412,plain,
! [X2,X3,X0,X1,X4] :
( ~ r1(X0)
| ~ r1(X1)
| ~ r2(X1,X2)
| ~ r2(X3,sK7(X2,sK1(X4)))
| ~ r1(X4)
| ~ r2(X0,X3) ),
inference(resolution,[],[f384,f41]) ).
fof(f416,plain,
! [X2,X3,X0,X1,X4] :
( ~ r2(X3,sK2(X2,sK1(X4)))
| ~ r1(X0)
| ~ r1(X1)
| ~ r2(X1,X2)
| ~ r1(X4)
| ~ r2(X0,X3) ),
inference(forward_demodulation,[],[f412,f186]) ).
fof(f417,plain,
! [X2,X3,X0,X1,X4] :
( ~ r2(X3,sK4(X2,X4))
| ~ r1(X0)
| ~ r1(X1)
| ~ r2(X1,X2)
| ~ r1(X4)
| ~ r2(X0,X3) ),
inference(forward_demodulation,[],[f416,f373]) ).
fof(f418,plain,
! [X2,X3,X0,X1] :
( ~ r1(X0)
| ~ r1(X1)
| ~ r2(X1,X2)
| ~ r1(X3)
| ~ r2(X0,sK7(X2,X3)) ),
inference(resolution,[],[f417,f41]) ).
fof(f420,plain,
! [X2,X3,X0,X1] :
( ~ r2(X0,sK2(X2,X3))
| ~ r1(X0)
| ~ r1(X1)
| ~ r2(X1,X2)
| ~ r1(X3) ),
inference(forward_demodulation,[],[f418,f186]) ).
fof(f421,plain,
! [X2,X0,X1] :
( ~ r2(X1,X0)
| ~ r1(X1)
| ~ r1(X2)
| ~ r2(X2,X0)
| ~ r1(sK0) ),
inference(superposition,[],[f420,f293]) ).
fof(f424,plain,
! [X2,X0,X1] :
( ~ r2(X1,X0)
| ~ r1(X1)
| ~ r1(X2)
| ~ r2(X2,X0) ),
inference(forward_subsumption_resolution,[],[f421,f64]) ).
fof(f433,plain,
! [X0,X1] :
( ~ r2(X0,X1)
| ~ r1(X0)
| ~ r1(X0) ),
inference(factoring,[],[f424]) ).
fof(f434,plain,
! [X0,X1] :
( ~ r2(X0,X1)
| ~ r1(X0) ),
inference(duplicate_literal_removal,[],[f433]) ).
fof(f442,plain,
! [X0] : ~ r1(X0),
inference(resolution,[],[f434,f66]) ).
fof(f452,plain,
$false,
inference(resolution,[],[f442,f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUN056+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 21:51:19 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.33 Running first-order theorem proving
% 0.08/0.33 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
% 0.42/0.83 % (2791041)Detected formulas, will run a generic FOF schedule.
% 0.42/0.83 % (2791052)dis-21_1_sil=8000:lcm=predicate:random_seed=3047998870: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)
% 0.42/0.83 % (2791051)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1660285709:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.42/0.83 % (2791048)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=1586342235:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.42/0.83 % (2791049)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2611888569:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.42/0.83 % (2791046)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=812370652:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.42/0.83 % (2791050)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2254426024:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.42/0.83 % (2791047)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=4258356070:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.42/0.83 % (2791049)Refutation not found, incomplete strategy
% 0.42/0.83 % (2791049)------------------------------
% 0.42/0.83 % (2791049)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.42/0.83 % (2791049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.83 % (2791049)CaDiCaL version: 2.1.3
% 0.42/0.83 % (2791049)Termination reason: Refutation not found, incomplete strategy
% 0.42/0.83 % (2791049)Time elapsed: 0.002 s
% 0.42/0.83 % (2791049)Peak memory usage: 88 MB
% 0.42/0.83 % (2791049)Instructions burned: 4 (million)
% 0.42/0.83 % (2791051)First to succeed.
% 0.42/0.83 % (2791051)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2791041"
% 0.42/0.83 % (2791050)Also succeeded, but the first one will report.
% 0.42/0.83 % (2791052)Instruction limit reached!
% 0.42/0.83 % (2791052)------------------------------
% 0.42/0.83 % (2791052)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.42/0.83 % (2791052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.83 % (2791052)CaDiCaL version: 2.1.3
% 0.42/0.83 % (2791052)Termination reason: Instruction limit
% 0.42/0.83 % (2791052)Termination phase: Saturation
% 0.42/0.83 % (2791052)Time elapsed: 0.030 s
% 0.42/0.83 % (2791052)Peak memory usage: 88 MB
% 0.42/0.83 % (2791052)Instructions burned: 134 (million)
% 0.42/0.83 % (2791049)------------------------------
% 0.42/0.83 % (2791049)------------------------------
% 0.42/0.83 % (2791060)lrs+10_1_sil=8000:sp=occurrence:random_seed=1170997812:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.42/0.83 % (2791051)Refutation found. Thanks to Tanya!
% 0.42/0.83 % SZS status Theorem for theBenchmark
% 0.42/0.83 % SZS output start Proof for theBenchmark
% See solution above
% 2.37/0.93 % (2791051)------------------------------
% 2.37/0.93 % (2791051)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.37/0.93 % (2791051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.37/0.93 % (2791051)CaDiCaL version: 2.1.3
% 2.37/0.93 % (2791051)Termination reason: Refutation
% 2.37/0.93 % (2791051)Time elapsed: 0.012 s
% 2.37/0.93 % (2791051)Peak memory usage: 88 MB
% 2.37/0.93 % (2791051)Instructions burned: 33 (million)
% 2.37/0.93 % (2791051)------------------------------
% 2.37/0.93 % (2791051)------------------------------
% 2.37/0.93 % (2791041)Success in time 0.304 s
% 2.37/0.93 % Vampire exiting
%------------------------------------------------------------------------------