%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN059+2 : TPTP v9.3.1. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 5.50s 1.72s
% Output : Refutation 5.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 17 unt; 0 def)
% Number of atoms : 70 ( 18 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 65 ( 26 ~; 17 |; 22 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 69 ( 49 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( ~ r1(X1)
& X1 != X0 )
| ( r1(X1)
& X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
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] :
( ? [X4] :
( r4(X2,X2,X4)
& X3 = X4 )
& ? [X5] :
( r4(X1,X1,X5)
& ? [X6] :
( r4(X0,X0,X6)
& r3(X6,X5,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fermattothepoweroftwo) ).
fof(f13,negated_conjecture,
~ ? [X0,X1,X2,X3] :
( ? [X4] :
( r4(X2,X2,X4)
& X3 = X4 )
& ? [X5] :
( r4(X1,X1,X5)
& ? [X6] :
( r4(X0,X0,X6)
& r3(X6,X5,X3) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2,X3] :
( ! [X4] :
( ~ r4(X2,X2,X4)
| X3 != X4 )
| ! [X5] :
( ~ r4(X1,X1,X5)
| ! [X6] :
( ~ r4(X0,X0,X6)
| ~ r3(X6,X5,X3) ) ) ),
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(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(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,X4,X5] :
( ~ r4(X2,X2,X4)
| X3 != X4
| ~ r4(X1,X1,X5)
| ~ r4(X0,X0,X6)
| ~ r3(X6,X5,X3) ),
inference(cnf_transformation,[],[f14]) ).
fof(f74,plain,
! [X2,X0,X1,X6,X4,X5] :
( ~ r4(X2,X2,X4)
| ~ r4(X1,X1,X5)
| ~ r4(X0,X0,X6)
| ~ r3(X6,X5,X4) ),
inference(equality_resolution,[],[f63]) ).
fof(f75,plain,
! [X2,X3,X0,X1] :
( ~ r4(X0,X0,X1)
| ~ r4(X2,X2,X3)
| ~ r3(X3,X1,X1) ),
inference(factoring,[],[f74]) ).
fof(f77,plain,
! [X0,X1] :
( ~ r3(X1,X1,X1)
| ~ r4(X0,X0,X1) ),
inference(factoring,[],[f75]) ).
fof(f80,plain,
! [X0] : sK0 = sK13(X0),
inference(resolution,[],[f26,f53]) ).
fof(f81,plain,
! [X0] : sK0 = sK15(X0),
inference(resolution,[],[f26,f57]) ).
fof(f85,plain,
! [X0] : r1(sK14(X0)),
inference(superposition,[],[f55,f54]) ).
fof(f86,plain,
! [X0] : sK0 = sK14(X0),
inference(resolution,[],[f85,f26]) ).
fof(f96,plain,
! [X0] : r3(X0,sK13(X0),X0),
inference(forward_demodulation,[],[f52,f51]) ).
fof(f97,plain,
! [X0] : r3(X0,sK0,X0),
inference(forward_demodulation,[],[f96,f80]) ).
fof(f98,plain,
! [X0] : ~ r4(X0,X0,sK0),
inference(resolution,[],[f97,f77]) ).
fof(f100,plain,
! [X0] : r4(X0,sK0,sK14(X0)),
inference(forward_demodulation,[],[f56,f81]) ).
fof(f119,plain,
! [X0] : r4(X0,sK0,sK0),
inference(superposition,[],[f100,f86]) ).
fof(f139,plain,
$false,
inference(resolution,[],[f119,f98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUN059+2 : TPTP v9.3.1. Bugfixed v7.4.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n010.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 27 21:52:32 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.49 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
% 5.50/1.72 % (1347499)Detected formulas, will run a generic FOF schedule.
% 5.50/1.72 % (1347510)dis-21_1_sil=8000:lcm=predicate:random_seed=2502897432:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/129Mi)
% 5.50/1.72 % (1347510)Refutation not found, incomplete strategy
% 5.50/1.72 % (1347510)------------------------------
% 5.50/1.72 % (1347510)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.50/1.72 % (1347510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.50/1.72 % (1347510)CaDiCaL version: 2.1.3
% 5.50/1.72 % (1347510)Termination reason: Refutation not found, incomplete strategy
% 5.50/1.72 % (1347510)Time elapsed: 0.002 s
% 5.50/1.72 % (1347510)Peak memory usage: 88 MB
% 5.50/1.72 % (1347510)Instructions burned: 4 (million)
% 5.50/1.72 % (1347508)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1205220850:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 5.50/1.72 % (1347504)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=419010356:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 5.50/1.72 % (1347509)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3689874952:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 5.50/1.72 % (1347507)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=333149026:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 5.50/1.72 % (1347506)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=2773911500:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 5.50/1.72 % (1347505)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=2439518256:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 5.50/1.72 % (1347507)Refutation not found, incomplete strategy
% 5.50/1.72 % (1347507)------------------------------
% 5.50/1.72 % (1347507)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.50/1.72 % (1347507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.50/1.72 % (1347507)CaDiCaL version: 2.1.3
% 5.50/1.72 % (1347507)Termination reason: Refutation not found, incomplete strategy
% 5.50/1.72 % (1347507)Time elapsed: 0.004 s
% 5.50/1.72 % (1347507)Peak memory usage: 88 MB
% 5.50/1.72 % (1347507)Instructions burned: 1 (million)
% 5.50/1.72 % (1347509)First to succeed.
% 5.50/1.72 % (1347509)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1347499"
% 5.50/1.72 % (1347510)------------------------------
% 5.50/1.72 % (1347510)------------------------------
% 5.50/1.72 % (1347508)Instruction limit reached!
% 5.50/1.72 % (1347508)------------------------------
% 5.50/1.72 % (1347508)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.50/1.72 % (1347508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.50/1.72 % (1347508)CaDiCaL version: 2.1.3
% 5.50/1.72 % (1347508)Termination reason: Instruction limit
% 5.50/1.72 % (1347508)Termination phase: Saturation
% 5.50/1.72 % (1347508)Time elapsed: 0.116 s
% 5.50/1.72 % (1347508)Peak memory usage: 88 MB
% 5.50/1.72 % (1347508)Instructions burned: 119 (million)
% 5.50/1.72 % (1347518)lrs+10_1_sil=8000:sp=occurrence:random_seed=1140798997:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 5.50/1.72 % (1347518)Also succeeded, but the first one will report.
% 5.50/1.72 % (1347507)------------------------------
% 5.50/1.72 % (1347507)------------------------------
% 5.50/1.72 % (1347519)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1141096461:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 5.50/1.72 % (1347509)Refutation found. Thanks to Tanya!
% 5.50/1.72 % SZS status Theorem for theBenchmark
% 5.50/1.72 % SZS output start Proof for theBenchmark
% See solution above
% 5.50/1.72 % (1347509)------------------------------
% 5.50/1.72 % (1347509)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.50/1.72 % (1347509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.50/1.72 % (1347509)CaDiCaL version: 2.1.3
% 5.50/1.72 % (1347509)Termination reason: Refutation
% 5.50/1.72 % (1347509)Time elapsed: 0.009 s
% 5.50/1.72 % (1347509)Peak memory usage: 89 MB
% 5.50/1.72 % (1347509)Instructions burned: 5 (million)
% 5.50/1.72 % (1347509)------------------------------
% 5.50/1.72 % (1347509)------------------------------
% 5.50/1.72 % (1347499)Success in time 0.682 s
% 5.50/1.72 % Vampire exiting
%------------------------------------------------------------------------------