%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN067+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 0.09s 0.43s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of formulae : 86 ( 36 unt; 0 def)
% Number of atoms : 181 ( 69 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 154 ( 59 ~; 47 |; 48 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 1 con; 0-2 aty)
% Number of variables : 177 ( 154 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( ~ r1(X1)
& X1 != X0 )
| ( r1(X1)
& X1 = X0 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/NUM008+0.ax',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/Axioms/NUM008+0.ax',axiom_3) ).
fof(f4,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ r4(X0,X1,X3)
& X3 != X2 )
| ( r4(X0,X1,X3)
& X3 = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_4) ).
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/Axioms/NUM008+0.ax',axiom_1a) ).
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/sandbox/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/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_3a) ).
fof(f8,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r3(X0,X2,X1) )
& X1 = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).
fof(f9,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r4(X0,X2,X1) )
& ? [X3] :
( r1(X3)
& X1 = X3 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_5a) ).
fof(f10,axiom,
! [X0] :
( ? [X1] :
( r1(X1)
& X0 = X1 )
| ? [X2,X3] :
( r2(X2,X3)
& X0 = X3 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_6a) ).
fof(f11,axiom,
! [X0,X1] :
( ! [X2] :
( ~ r1(X2)
| X2 != X1 )
| ~ r2(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_7a) ).
fof(f12,conjecture,
? [X0] :
! [X1] :
( ~ r1(X1)
| X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonzerosexist) ).
fof(f13,negated_conjecture,
~ ? [X0] :
! [X1] :
( ~ r1(X1)
| X0 != X1 ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0] :
? [X1] :
( r1(X1)
& X0 = X1 ),
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(f18,plain,
! [X0,X1,X3] :
( ( ~ r4(X0,X1,X3)
& sK3(X0,X1) != X3 )
| ( r4(X0,X1,X3)
& sK3(X0,X1) = X3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f4]) ).
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(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(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(f23,plain,
! [X0] :
( ( r1(sK17(X0))
& sK17(X0) = X0 )
| ( r2(sK18(X0),sK19(X0))
& sK19(X0) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18,sK19]),skolemize(X1,sK17(X0)),skolemize(X2,sK18(X0)),skolemize(X3,sK19(X0))],[f10]) ).
fof(f24,plain,
! [X0] :
( r1(sK20(X0))
& sK20(X0) = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X1,sK20(X0))],[f14]) ).
fof(f25,plain,
! [X1] :
( sK0 != X1
| sK0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X1] :
( sK0 != X1
| r1(X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
! [X0] :
( ~ r1(X0)
| sK0 = X0 ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X0] :
( ~ r1(X0)
| r1(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X2,X0] :
( sK1(X0) != X2
| sK1(X0) = X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X2,X0] :
( sK1(X0) != X2
| r2(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
! [X0,X1] :
( ~ r2(X0,X1)
| sK1(X0) = X1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f32,plain,
! [X0,X1] :
( ~ r2(X0,X1)
| r2(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f33,plain,
! [X3,X0,X1] :
( sK2(X0,X1) != X3
| sK2(X0,X1) = X3 ),
inference(cnf_transformation,[],[f17]) ).
fof(f34,plain,
! [X3,X0,X1] :
( sK2(X0,X1) != X3
| r3(X0,X1,X3) ),
inference(cnf_transformation,[],[f17]) ).
fof(f35,plain,
! [X3,X0,X1] :
( ~ r3(X0,X1,X3)
| sK2(X0,X1) = X3 ),
inference(cnf_transformation,[],[f17]) ).
fof(f36,plain,
! [X3,X0,X1] :
( ~ r3(X0,X1,X3)
| r3(X0,X1,X3) ),
inference(cnf_transformation,[],[f17]) ).
fof(f37,plain,
! [X3,X0,X1] :
( sK3(X0,X1) != X3
| sK3(X0,X1) = X3 ),
inference(cnf_transformation,[],[f18]) ).
fof(f38,plain,
! [X3,X0,X1] :
( sK3(X0,X1) != X3
| r4(X0,X1,X3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ r4(X0,X1,X2)
| sK3(X0,X1) = X2 ),
inference(cnf_transformation,[],[f18]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ r4(X0,X1,X2)
| r4(X0,X1,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f41,plain,
! [X0,X1] : r3(X0,X1,sK7(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f42,plain,
! [X0,X1] : r2(sK7(X0,X1),sK4(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
! [X0,X1] : sK4(X0,X1) = sK5(X0,X1),
inference(cnf_transformation,[],[f19]) ).
fof(f44,plain,
! [X0,X1] : r3(X0,sK6(X0,X1),sK5(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f45,plain,
! [X0,X1] : r2(X1,sK6(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f46,plain,
! [X0,X1] : r4(X0,X1,sK11(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f47,plain,
! [X0,X1] : r3(sK11(X0,X1),X0,sK8(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f48,plain,
! [X0,X1] : sK8(X0,X1) = sK9(X0,X1),
inference(cnf_transformation,[],[f20]) ).
fof(f49,plain,
! [X0,X1] : r4(X0,sK10(X0,X1),sK9(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
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(f52,plain,
! [X0] : sK12(X0) = X0,
inference(cnf_transformation,[],[f21]) ).
fof(f53,plain,
! [X0] : r3(X0,sK13(X0),sK12(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f54,plain,
! [X0] : r1(sK13(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f55,plain,
! [X0] : sK14(X0) = sK16(X0),
inference(cnf_transformation,[],[f22]) ).
fof(f56,plain,
! [X0] : r1(sK16(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f57,plain,
! [X0] : r4(X0,sK15(X0),sK14(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f58,plain,
! [X0] : r1(sK15(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f59,plain,
! [X0] :
( sK17(X0) = X0
| sK19(X0) = X0 ),
inference(cnf_transformation,[],[f23]) ).
fof(f60,plain,
! [X0] :
( sK17(X0) = X0
| r2(sK18(X0),sK19(X0)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f61,plain,
! [X0] :
( r1(sK17(X0))
| sK19(X0) = X0 ),
inference(cnf_transformation,[],[f23]) ).
fof(f62,plain,
! [X0] :
( r1(sK17(X0))
| r2(sK18(X0),sK19(X0)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ r1(X2)
| X1 != X2
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f64,plain,
! [X0] : sK20(X0) = X0,
inference(cnf_transformation,[],[f24]) ).
fof(f65,plain,
! [X0] : r1(sK20(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f66,plain,
! [X0,X1] : r2(sK7(X0,X1),sK5(X0,X1)),
inference(definition_unfolding,[],[f42,f43]) ).
fof(f67,plain,
! [X0,X1] : r3(sK11(X0,X1),X0,sK9(X0,X1)),
inference(definition_unfolding,[],[f47,f48]) ).
fof(f68,plain,
! [X0] : r4(X0,sK15(X0),sK16(X0)),
inference(definition_unfolding,[],[f57,f55]) ).
fof(f69,plain,
r1(sK0),
inference(equality_resolution,[],[f26]) ).
fof(f70,plain,
sK0 = sK0,
inference(equality_resolution,[],[f25]) ).
fof(f71,plain,
! [X0] : r2(X0,sK1(X0)),
inference(equality_resolution,[],[f30]) ).
fof(f72,plain,
! [X0] : sK1(X0) = sK1(X0),
inference(equality_resolution,[],[f29]) ).
fof(f73,plain,
! [X0,X1] : r3(X0,X1,sK2(X0,X1)),
inference(equality_resolution,[],[f34]) ).
fof(f74,plain,
! [X0,X1] : sK2(X0,X1) = sK2(X0,X1),
inference(equality_resolution,[],[f33]) ).
fof(f75,plain,
! [X0,X1] : r4(X0,X1,sK3(X0,X1)),
inference(equality_resolution,[],[f38]) ).
fof(f76,plain,
! [X0,X1] : sK3(X0,X1) = sK3(X0,X1),
inference(equality_resolution,[],[f37]) ).
fof(f77,plain,
! [X2,X0,X1] :
( ~ r2(X0,X1)
| ~ r2(X2,X1)
| X0 = X2 ),
inference(equality_resolution,[],[f51]) ).
fof(f78,plain,
! [X0,X1] :
( ~ r1(X0)
| ~ r2(X1,X0) ),
inference(equality_resolution,[],[f63]) ).
fof(f79,plain,
! [X2,X0,X1] :
( r3(X0,X1,X2)
| ~ r3(X0,X1,X2) ),
inference(consistent_polarity_flipping,[],[f36]) ).
fof(f80,plain,
! [X2,X0,X1] :
( r3(X0,X1,X2)
| sK2(X0,X1) = X2 ),
inference(consistent_polarity_flipping,[],[f35]) ).
fof(f81,plain,
! [X0,X1] : ~ r3(X0,X1,sK2(X0,X1)),
inference(consistent_polarity_flipping,[],[f73]) ).
fof(f82,plain,
! [X0,X1] : ~ r3(X0,sK6(X0,X1),sK5(X0,X1)),
inference(consistent_polarity_flipping,[],[f44]) ).
fof(f83,plain,
! [X0,X1] : ~ r3(X0,X1,sK7(X0,X1)),
inference(consistent_polarity_flipping,[],[f41]) ).
fof(f84,plain,
! [X0,X1] : ~ r3(sK11(X0,X1),X0,sK9(X0,X1)),
inference(consistent_polarity_flipping,[],[f67]) ).
fof(f85,plain,
! [X0] : ~ r3(X0,sK13(X0),sK12(X0)),
inference(consistent_polarity_flipping,[],[f53]) ).
fof(f113,plain,
$false,
inference(finite_model_not_found_(exhaustively_excluded_all_possible_domain_size_assignments),[],[f28,f27,f69,f70,f32,f31,f71,f72,f79,f80,f81,f74,f40,f39,f75,f76,f45,f82,f66,f83,f50,f49,f84,f46,f77,f54,f85,f52,f58,f68,f56,f62,f61,f60,f59,f78,f65,f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN067+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 21:56:46 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.43 % (2049101)Will run a generic schedule for satisfiability detection.
% 0.09/0.43 % (2049106)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4257840358_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.43 % TRYING [1]
% 0.09/0.43 % TRYING [2]
% 0.09/0.43 % (2049106) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2049101-2049106"...
% 0.09/0.43 % (2049106)...printing done.
% 0.09/0.43 % (2049106)Refutation found. Thanks to Tanya!
% 0.09/0.43 % SZS status Theorem for theBenchmark
% 0.09/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.44 % (2049106)------------------------------
% 0.09/0.44 % (2049106)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.44 % (2049106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.44 % (2049106)CaDiCaL version: 2.1.3
% 0.09/0.44 % (2049106)Termination reason: Refutation
% 0.09/0.44 % (2049106)Time elapsed: 0.002 s
% 0.09/0.44 % (2049106)Peak memory usage: 11 MB
% 0.09/0.44 % (2049106)Instructions burned: 5 (million)
% 0.09/0.44 % (2049101)Success in time 0.026 s
% 0.09/0.44 % Vampire exiting
%------------------------------------------------------------------------------