%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN068+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 12:27:02 PM UTC 2026
% Result : Theorem 0.33s 0.47s
% Output : Refutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 10 unt; 0 def)
% Number of atoms : 124 ( 52 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 117 ( 42 ~; 51 |; 24 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 82 ( 71 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( ~ r1(X1)
& X1 != X0 )
| ( r1(X1)
& X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
fof(f2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( ~ r2(X0,X2)
& X2 != X1 )
| ( r2(X0,X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
fof(f6,axiom,
! [X0,X1] :
? [X2] :
( ? [X3] :
( ? [X4] :
( r2(X1,X4)
& r4(X0,X4,X3) )
& X3 = X2 )
& ? [X5] :
( r3(X5,X0,X2)
& r4(X0,X1,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2a) ).
fof(f7,axiom,
! [X0,X1] :
( ! [X2] :
( ! [X3] :
( ~ r2(X0,X3)
| X3 != X2 )
| ~ r2(X1,X2) )
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_3a) ).
fof(f11,axiom,
! [X0,X1] :
( ! [X2] :
( ~ r1(X2)
| X2 != X1 )
| ~ r2(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_7a) ).
fof(f12,conjecture,
? [X0] :
( ! [X1] :
( ! [X2] :
( ~ r1(X2)
| ~ r2(X2,X1) )
| X0 != X1 )
& ! [X3] :
( ~ r1(X3)
| X0 != X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonzerosnononesexist) ).
fof(f13,negated_conjecture,
~ ? [X0] :
( ! [X1] :
( ! [X2] :
( ~ r1(X2)
| ~ r2(X2,X1) )
| X0 != X1 )
& ! [X3] :
( ~ r1(X3)
| X0 != X3 ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( r1(X2)
& r2(X2,X1) )
& X0 = X1 )
| ? [X3] :
( r1(X3)
& X0 = 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(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(f20,plain,
! [X0,X1] :
( r2(X1,sK10(X0,X1))
& r4(X0,sK10(X0,X1),sK9(X0,X1))
& sK8(X0,X1) = sK9(X0,X1)
& r3(sK11(X0,X1),X0,sK8(X0,X1))
& r4(X0,X1,sK11(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11]),skolemize(X2,sK8(X0,X1)),skolemize(X3,sK9(X0,X1)),skolemize(X4,sK10(X0,X1)),skolemize(X5,sK11(X0,X1))],[f6]) ).
fof(f24,plain,
! [X0] :
( ( r1(sK21(X0))
& r2(sK21(X0),sK20(X0))
& sK20(X0) = X0 )
| ( r1(sK22(X0))
& sK22(X0) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22]),skolemize(X1,sK20(X0)),skolemize(X2,sK21(X0)),skolemize(X3,sK22(X0))],[f14]) ).
fof(f26,plain,
! [X1] :
( sK0 != X1
| r1(X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
! [X1] :
( ~ r1(X1)
| sK0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X2,X0] :
( sK1(X0) != X2
| r2(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f50,plain,
! [X0,X1] : r2(X1,sK10(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f51,plain,
! [X2,X3,X0,X1] :
( ~ r2(X0,X3)
| X2 != X3
| ~ r2(X1,X2)
| X0 = X1 ),
inference(cnf_transformation,[],[f7]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ r1(X2)
| X1 != X2
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f64,plain,
! [X0] :
( sK22(X0) = X0
| sK20(X0) = X0 ),
inference(cnf_transformation,[],[f24]) ).
fof(f65,plain,
! [X0] :
( r1(sK22(X0))
| sK20(X0) = X0 ),
inference(cnf_transformation,[],[f24]) ).
fof(f66,plain,
! [X0] :
( r2(sK21(X0),sK20(X0))
| sK22(X0) = X0 ),
inference(cnf_transformation,[],[f24]) ).
fof(f67,plain,
! [X0] :
( r2(sK21(X0),sK20(X0))
| r1(sK22(X0)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f68,plain,
! [X0] :
( r1(sK21(X0))
| sK22(X0) = X0 ),
inference(cnf_transformation,[],[f24]) ).
fof(f69,plain,
! [X0] :
( r1(sK22(X0))
| r1(sK21(X0)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f73,plain,
r1(sK0),
inference(equality_resolution,[],[f26]) ).
fof(f75,plain,
! [X0] : r2(X0,sK1(X0)),
inference(equality_resolution,[],[f30]) ).
fof(f81,plain,
! [X3,X0,X1] :
( ~ r2(X1,X3)
| ~ r2(X0,X3)
| X0 = X1 ),
inference(equality_resolution,[],[f51]) ).
fof(f82,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| ~ r1(X2) ),
inference(equality_resolution,[],[f63]) ).
fof(f83,plain,
! [X0] :
( r1(X0)
| sK20(X0) = X0
| sK20(X0) = X0 ),
inference(superposition,[],[f65,f64]) ).
fof(f85,plain,
! [X0] :
( r1(X0)
| sK20(X0) = X0 ),
inference(duplicate_literal_removal,[],[f83]) ).
fof(f91,plain,
! [X0] :
( sK22(X0) = X0
| sK0 = sK21(X0) ),
inference(resolution,[],[f27,f68]) ).
fof(f99,plain,
! [X0] : ~ r1(sK1(X0)),
inference(resolution,[],[f82,f75]) ).
fof(f101,plain,
! [X0,X1] : ~ r1(sK10(X0,X1)),
inference(resolution,[],[f82,f50]) ).
fof(f107,plain,
! [X0] :
( r1(X0)
| r1(sK21(X0))
| sK0 = sK21(X0) ),
inference(superposition,[],[f69,f91]) ).
fof(f108,plain,
! [X0] :
( r1(X0)
| sK0 = sK21(X0) ),
inference(forward_subsumption_resolution,[],[f107,f27]) ).
fof(f218,plain,
! [X0,X1] :
( ~ r2(X0,sK1(X1))
| X0 = X1 ),
inference(resolution,[],[f81,f75]) ).
fof(f269,plain,
! [X0] : sK0 = sK21(sK1(X0)),
inference(resolution,[],[f99,f108]) ).
fof(f270,plain,
! [X0] : sK1(X0) = sK20(sK1(X0)),
inference(resolution,[],[f99,f85]) ).
fof(f287,plain,
! [X0] :
( r2(sK21(sK1(X0)),sK1(X0))
| sK1(X0) = sK22(sK1(X0)) ),
inference(superposition,[],[f66,f270]) ).
fof(f288,plain,
! [X0] :
( r2(sK21(sK1(X0)),sK1(X0))
| r1(sK22(sK1(X0))) ),
inference(superposition,[],[f67,f270]) ).
fof(f303,plain,
! [X0] :
( r2(sK0,sK1(X0))
| r1(sK22(sK1(X0))) ),
inference(forward_demodulation,[],[f288,f269]) ).
fof(f304,plain,
! [X0] :
( r2(sK0,sK1(X0))
| sK1(X0) = sK22(sK1(X0)) ),
inference(forward_demodulation,[],[f287,f269]) ).
fof(f429,plain,
! [X0] :
( sK1(X0) = sK22(sK1(X0))
| sK0 = X0 ),
inference(resolution,[],[f218,f304]) ).
fof(f431,plain,
! [X0] :
( r1(sK22(sK1(X0)))
| sK0 = X0 ),
inference(resolution,[],[f218,f303]) ).
fof(f498,plain,
! [X0] :
( r1(sK1(X0))
| sK0 = X0
| sK0 = X0 ),
inference(superposition,[],[f431,f429]) ).
fof(f507,plain,
! [X0] :
( r1(sK1(X0))
| sK0 = X0 ),
inference(duplicate_literal_removal,[],[f498]) ).
fof(f515,plain,
! [X0] : sK0 = X0,
inference(forward_subsumption_resolution,[],[f507,f99]) ).
fof(f579,plain,
~ r1(sK0),
inference(superposition,[],[f101,f515]) ).
fof(f663,plain,
$false,
inference(forward_subsumption_resolution,[],[f579,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN068+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 21:55:51 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.33/0.47 % (3927415)Will run a generic schedule for satisfiability detection.
% 0.33/0.47 % (3927425)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=772898278:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.33/0.47 % (3927421)% WARNING: option uhcvi not known.
% 0.33/0.47 % (3927420)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3204740233_2999 on theBenchmark for (2999ds/0Mi)
% 0.33/0.47 % (3927422)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2665936133:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.33/0.47 % (3927426)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3823927758:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.33/0.47 % (3927423)dis+10_1_sil=32000:sp=arity:random_seed=2348499343:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.33/0.47 % (3927424)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=508215311:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.33/0.47 % (3927421)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=449317563:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.33/0.47 % TRYING [1]
% 0.33/0.47 % TRYING [2]
% 0.33/0.47 % TRYING [3]
% 0.33/0.47 % TRYING [4]
% 0.33/0.47 % TRYING [5]
% 0.33/0.47 % (3927423) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3927415-3927423"...
% 0.33/0.47 % (3927423)...printing done.
% 0.33/0.47 % (3927423)Refutation found. Thanks to Tanya!
% 0.33/0.47 % SZS status Theorem for theBenchmark
% 0.33/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.33/0.47 % (3927423)------------------------------
% 0.33/0.47 % (3927423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.47 % (3927423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.47 % (3927423)CaDiCaL version: 2.1.3
% 0.33/0.47 % (3927423)Termination reason: Refutation
% 0.33/0.47 % (3927423)Time elapsed: 0.015 s
% 0.33/0.47 % (3927423)Peak memory usage: 11 MB
% 0.33/0.47 % (3927423)Instructions burned: 23 (million)
% 0.33/0.47 % (3927415)Success in time 0.051 s
% 0.33/0.47 % Vampire exiting
%------------------------------------------------------------------------------