%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN055+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 : n014.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 12:26:59 PM UTC 2026
% Result : Theorem 0.12s 0.46s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 22 unt; 0 def)
% Number of atoms : 170 ( 34 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 207 ( 91 ~; 70 |; 46 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 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 : 145 ( 117 !; 28 ?)
% 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(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(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(f12,conjecture,
? [X0] :
( ? [X1] :
( ? [X2] :
( r2(X2,X1)
& ? [X3] :
( r1(X3)
& r2(X3,X2) ) )
& ? [X4] :
( r1(X4)
& r3(X4,X1,X0) ) )
& ? [X5] :
( X0 = X5
& ? [X6] :
( r2(X6,X5)
& ? [X7] :
( r1(X7)
& r2(X7,X6) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zeroplustwoeqtwo) ).
fof(f13,negated_conjecture,
~ ? [X0] :
( ? [X1] :
( ? [X2] :
( r2(X2,X1)
& ? [X3] :
( r1(X3)
& r2(X3,X2) ) )
& ? [X4] :
( r1(X4)
& r3(X4,X1,X0) ) )
& ? [X5] :
( X0 = X5
& ? [X6] :
( r2(X6,X5)
& ? [X7] :
( r1(X7)
& r2(X7,X6) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ~ r2(X2,X1)
| ! [X3] :
( ~ r1(X3)
| ~ r2(X3,X2) ) )
| ! [X4] :
( ~ r1(X4)
| ~ r3(X4,X1,X0) ) )
| ! [X5] :
( X0 != X5
| ! [X6] :
( ~ r2(X6,X5)
| ! [X7] :
( ~ r1(X7)
| ~ r2(X7,X6) ) ) ) ),
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(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,X6,X7,X4,X5] :
( ~ r2(X2,X1)
| ~ r1(X3)
| ~ r2(X3,X2)
| ~ r1(X4)
| ~ r3(X4,X1,X0)
| X0 != X5
| ~ r2(X6,X5)
| ~ r1(X7)
| ~ r2(X7,X6) ),
inference(cnf_transformation,[],[f14]) ).
fof(f64,plain,
! [X0,X1] : r2(sK7(X0,X1),sK5(X0,X1)),
inference(definition_unfolding,[],[f41,f42]) ).
fof(f67,plain,
r1(sK0),
inference(equality_resolution,[],[f25]) ).
fof(f69,plain,
! [X0] : r2(X0,sK1(X0)),
inference(equality_resolution,[],[f29]) ).
fof(f77,plain,
! [X2,X3,X1,X6,X7,X4,X5] :
( ~ r3(X4,X1,X5)
| ~ r1(X3)
| ~ r2(X3,X2)
| ~ r1(X4)
| ~ r2(X2,X1)
| ~ r2(X6,X5)
| ~ r1(X7)
| ~ r2(X7,X6) ),
inference(equality_resolution,[],[f63]) ).
fof(f79,plain,
! [X0] : sK0 = sK13(X0),
inference(resolution,[],[f26,f53]) ).
fof(f89,plain,
! [X0] : r3(X0,sK13(X0),X0),
inference(forward_demodulation,[],[f52,f51]) ).
fof(f90,plain,
! [X0] : r3(X0,sK0,X0),
inference(forward_demodulation,[],[f89,f79]) ).
fof(f96,plain,
! [X0,X1] : sK1(X0) = sK6(X1,X0),
inference(resolution,[],[f30,f44]) ).
fof(f105,plain,
! [X0,X1] : r3(X0,sK1(X1),sK5(X0,X1)),
inference(forward_demodulation,[],[f43,f96]) ).
fof(f106,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r2(X4,sK5(X2,X3))
| ~ r2(X0,X1)
| ~ r1(X2)
| ~ r2(X1,sK1(X3))
| ~ r1(X0)
| ~ r1(X5)
| ~ r2(X5,X4) ),
inference(resolution,[],[f105,f77]) ).
fof(f108,plain,
! [X2,X3,X0,X1,X4] :
( ~ r2(X4,sK7(X2,X3))
| ~ r1(X2)
| ~ r2(X1,sK1(X3))
| ~ r1(X0)
| ~ r1(X4)
| ~ r2(X0,X1) ),
inference(resolution,[],[f106,f64]) ).
fof(f113,plain,
! [X0,X1] : sK2(X0,X1) = sK7(X0,X1),
inference(resolution,[],[f34,f40]) ).
fof(f115,plain,
! [X0] : sK2(X0,sK0) = X0,
inference(resolution,[],[f34,f90]) ).
fof(f116,plain,
! [X0,X1] : sK5(X0,X1) = sK2(X0,sK1(X1)),
inference(resolution,[],[f34,f105]) ).
fof(f138,plain,
! [X2,X3,X0,X1,X4] :
( ~ r2(X2,sK2(X0,X1))
| ~ r1(X0)
| ~ r2(X3,sK1(X1))
| ~ r1(X4)
| ~ r1(X2)
| ~ r2(X4,X3) ),
inference(superposition,[],[f108,f113]) ).
fof(f172,plain,
! [X2,X3,X0,X1,X4] :
( ~ r2(X3,sK1(sK1(X1)))
| ~ r1(X0)
| ~ r2(X2,sK5(X0,X1))
| ~ r1(X4)
| ~ r1(X2)
| ~ r2(X4,X3) ),
inference(superposition,[],[f138,f116]) ).
fof(f175,plain,
! [X2,X3,X0,X1] :
( ~ r2(X1,sK5(X0,X2))
| ~ r1(X0)
| ~ r1(X3)
| ~ r1(X1)
| ~ r2(X3,sK1(X2)) ),
inference(resolution,[],[f172,f69]) ).
fof(f177,plain,
! [X2,X0,X1] :
( ~ r1(X0)
| ~ r1(X1)
| ~ r1(sK7(X0,X2))
| ~ r2(X1,sK1(X2)) ),
inference(resolution,[],[f175,f64]) ).
fof(f178,plain,
! [X2,X0,X1] :
( ~ r2(X1,sK1(X2))
| ~ r1(X0)
| ~ r1(X1)
| ~ r1(sK2(X0,X2)) ),
inference(forward_demodulation,[],[f177,f113]) ).
fof(f196,plain,
! [X0,X1] :
( ~ r1(sK2(X0,X1))
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[],[f178,f69]) ).
fof(f209,plain,
! [X0] :
( ~ r1(X0)
| ~ r1(sK0)
| ~ r1(X0) ),
inference(superposition,[],[f196,f115]) ).
fof(f211,plain,
! [X0] :
( ~ r1(X0)
| ~ r1(sK0) ),
inference(duplicate_literal_removal,[],[f209]) ).
fof(f212,plain,
! [X0] : ~ r1(X0),
inference(forward_subsumption_resolution,[],[f211,f67]) ).
fof(f220,plain,
$false,
inference(resolution,[],[f212,f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN055+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n014.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 21:51:46 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.12/0.46 % (1208753)Will run a generic schedule for satisfiability detection.
% 0.12/0.46 % (1208763)dis+10_1_sil=32000:sp=arity:random_seed=3881624293:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.46 % (1208761)% WARNING: option uhcvi not known.
% 0.12/0.46 % (1208763) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1208753-1208763"...
% 0.12/0.46 % (1208763)...printing done.
% 0.12/0.46 % (1208763)Refutation found. Thanks to Tanya!
% 0.12/0.46 % SZS status Theorem for theBenchmark
% 0.12/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.46 % (1208763)------------------------------
% 0.12/0.46 % (1208763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.46 % (1208763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.46 % (1208763)CaDiCaL version: 2.1.3
% 0.12/0.46 % (1208763)Termination reason: Refutation
% 0.12/0.46 % (1208763)Time elapsed: 0.004 s
% 0.12/0.46 % (1208763)Peak memory usage: 11 MB
% 0.12/0.46 % (1208763)Instructions burned: 9 (million)
% 0.12/0.46 % (1208753)Success in time 0.03 s
% 0.12/0.46 % Vampire exiting
%------------------------------------------------------------------------------