%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN057+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 : n026.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 12:27:00 PM UTC 2026
% Result : Theorem 0.17s 0.49s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 25 unt; 0 def)
% Number of atoms : 176 ( 28 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 212 ( 90 ~; 92 |; 30 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 163 ( 136 !; 27 ?)
% 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(f12,conjecture,
? [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r2(X2,X1)
& ? [X3] :
( r2(X3,X2)
& ? [X4] :
( r2(X4,X3)
& ? [X5] :
( r1(X5)
& r2(X5,X4) ) ) ) ) )
& ? [X6] :
( r3(X6,X6,X0)
& ? [X7] :
( r2(X7,X6)
& ? [X8] :
( r1(X8)
& r2(X8,X7) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',twoplustwoeqfour) ).
fof(f13,negated_conjecture,
~ ? [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r2(X2,X1)
& ? [X3] :
( r2(X3,X2)
& ? [X4] :
( r2(X4,X3)
& ? [X5] :
( r1(X5)
& r2(X5,X4) ) ) ) ) )
& ? [X6] :
( r3(X6,X6,X0)
& ? [X7] :
( r2(X7,X6)
& ? [X8] :
( r1(X8)
& r2(X8,X7) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0] :
( ! [X1] :
( X0 != X1
| ! [X2] :
( ~ r2(X2,X1)
| ! [X3] :
( ~ r2(X3,X2)
| ! [X4] :
( ~ r2(X4,X3)
| ! [X5] :
( ~ r1(X5)
| ~ r2(X5,X4) ) ) ) ) )
| ! [X6] :
( ~ r3(X6,X6,X0)
| ! [X7] :
( ~ r2(X7,X6)
| ! [X8] :
( ~ r1(X8)
| ~ r2(X8,X7) ) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
! [X1] :
( r1(X1)
| sK0 != X1 ),
inference(cnf_transformation,[],[f1]) ).
fof(f16,plain,
! [X1] :
( sK0 = X1
| ~ r1(X1) ),
inference(cnf_transformation,[],[f1]) ).
fof(f17,plain,
! [X2,X0] :
( r2(X0,X2)
| sK1(X0) != X2 ),
inference(cnf_transformation,[],[f2]) ).
fof(f18,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| sK1(X0) = X2 ),
inference(cnf_transformation,[],[f2]) ).
fof(f19,plain,
! [X3,X0,X1] :
( r3(X0,X1,X3)
| sK2(X0,X1) != X3 ),
inference(cnf_transformation,[],[f3]) ).
fof(f20,plain,
! [X3,X0,X1] :
( ~ r3(X0,X1,X3)
| sK2(X0,X1) = X3 ),
inference(cnf_transformation,[],[f3]) ).
fof(f23,plain,
! [X0,X1] : r3(X0,sK7(X0,X1),sK6(X0,X1)),
inference(cnf_transformation,[],[f5]) ).
fof(f24,plain,
! [X0,X1] : r2(X1,sK7(X0,X1)),
inference(cnf_transformation,[],[f5]) ).
fof(f25,plain,
! [X0,X1] : sK4(X0,X1) = sK6(X0,X1),
inference(cnf_transformation,[],[f5]) ).
fof(f26,plain,
! [X0,X1] : r3(X0,X1,sK5(X0,X1)),
inference(cnf_transformation,[],[f5]) ).
fof(f27,plain,
! [X0,X1] : r2(sK5(X0,X1),sK4(X0,X1)),
inference(cnf_transformation,[],[f5]) ).
fof(f34,plain,
! [X0] : r3(X0,sK13(X0),sK12(X0)),
inference(cnf_transformation,[],[f8]) ).
fof(f35,plain,
! [X0] : r1(sK13(X0)),
inference(cnf_transformation,[],[f8]) ).
fof(f36,plain,
! [X0] : sK12(X0) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f46,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ r2(X8,X7)
| ~ r1(X8)
| ~ r2(X7,X6)
| ~ r3(X6,X6,X0)
| ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f47,plain,
! [X0,X1] : r2(sK5(X0,X1),sK6(X0,X1)),
inference(definition_unfolding,[],[f27,f25]) ).
fof(f50,plain,
r1(sK0),
inference(equality_resolution,[],[f15]) ).
fof(f51,plain,
! [X0] : r2(X0,sK1(X0)),
inference(equality_resolution,[],[f17]) ).
fof(f52,plain,
! [X0,X1] : r3(X0,X1,sK2(X0,X1)),
inference(equality_resolution,[],[f19]) ).
fof(f56,plain,
! [X2,X3,X1,X8,X6,X7,X4,X5] :
( ~ r2(X8,X7)
| ~ r1(X8)
| ~ r2(X7,X6)
| ~ r3(X6,X6,X1)
| ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X1) ),
inference(equality_resolution,[],[f46]) ).
fof(f57,plain,
! [X1] :
( r1(X1)
| sK0 = X1 ),
inference(consistent_polarity_flipping,[],[f16]) ).
fof(f58,plain,
~ r1(sK0),
inference(consistent_polarity_flipping,[],[f50]) ).
fof(f63,plain,
! [X0] : ~ r1(sK13(X0)),
inference(consistent_polarity_flipping,[],[f35]) ).
fof(f70,plain,
! [X2,X3,X1,X8,X6,X7,X4,X5] :
( ~ r3(X6,X6,X1)
| r1(X8)
| ~ r2(X7,X6)
| ~ r2(X8,X7)
| ~ r2(X5,X4)
| r1(X5)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X1) ),
inference(consistent_polarity_flipping,[],[f56]) ).
fof(f72,plain,
! [X0] : sK0 = sK13(X0),
inference(resolution,[],[f57,f63]) ).
fof(f79,plain,
! [X0] : r3(X0,sK13(X0),X0),
inference(forward_demodulation,[],[f34,f36]) ).
fof(f82,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ r2(X6,sK2(X2,X2))
| ~ r2(X1,X2)
| ~ r2(X0,X1)
| ~ r2(X3,X4)
| r1(X3)
| ~ r2(X4,X5)
| ~ r2(X5,X6)
| r1(X0) ),
inference(resolution,[],[f52,f70]) ).
fof(f84,plain,
! [X0,X1] : sK1(X0) = sK7(X1,X0),
inference(resolution,[],[f18,f24]) ).
fof(f98,plain,
! [X0,X1] : sK2(X0,X1) = sK5(X0,X1),
inference(resolution,[],[f20,f26]) ).
fof(f100,plain,
! [X0] : sK2(X0,sK13(X0)) = X0,
inference(resolution,[],[f20,f79]) ).
fof(f101,plain,
! [X0,X1] : sK6(X0,X1) = sK2(X0,sK7(X0,X1)),
inference(resolution,[],[f20,f23]) ).
fof(f103,plain,
! [X0] : sK2(X0,sK0) = X0,
inference(forward_demodulation,[],[f100,f72]) ).
fof(f146,plain,
! [X0,X1] : r2(sK2(X0,X1),sK6(X0,X1)),
inference(superposition,[],[f47,f98]) ).
fof(f175,plain,
! [X0,X1] : sK6(X0,X1) = sK2(X0,sK1(X1)),
inference(forward_demodulation,[],[f101,f84]) ).
fof(f177,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ r2(X2,sK1(X0))
| ~ r2(X1,sK6(sK1(X0),X0))
| ~ r2(X3,X2)
| ~ r2(X4,X5)
| r1(X4)
| ~ r2(X5,X6)
| ~ r2(X6,X1)
| r1(X3) ),
inference(superposition,[],[f82,f175]) ).
fof(f180,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r2(X0,sK6(sK1(X1),X1))
| ~ r2(X2,X1)
| ~ r2(X3,X4)
| r1(X3)
| ~ r2(X4,X5)
| ~ r2(X5,X0)
| r1(X2) ),
inference(resolution,[],[f177,f51]) ).
fof(f184,plain,
! [X2,X3,X0,X1,X4] :
( ~ r2(X0,X1)
| ~ r2(X2,X3)
| r1(X2)
| ~ r2(X3,X4)
| ~ r2(X4,sK5(sK1(X1),X1))
| r1(X0) ),
inference(resolution,[],[f180,f47]) ).
fof(f186,plain,
! [X2,X3,X0,X1,X4] :
( ~ r2(X4,sK2(sK1(X1),X1))
| ~ r2(X0,X1)
| ~ r2(X2,X3)
| r1(X2)
| ~ r2(X3,X4)
| r1(X0) ),
inference(forward_demodulation,[],[f184,f98]) ).
fof(f209,plain,
! [X2,X3,X0,X1,X4] :
( ~ r2(X2,sK1(X0))
| ~ r2(X1,sK6(sK1(sK1(X0)),X0))
| ~ r2(X3,X4)
| r1(X3)
| ~ r2(X4,X1)
| r1(X2) ),
inference(superposition,[],[f186,f175]) ).
fof(f243,plain,
! [X2,X3,X0,X1] :
( ~ r2(X0,sK6(sK1(sK1(X1)),X1))
| ~ r2(X2,X3)
| r1(X2)
| ~ r2(X3,X0)
| r1(X1) ),
inference(resolution,[],[f209,f51]) ).
fof(f267,plain,
! [X2,X0,X1] :
( ~ r2(X1,sK2(sK1(sK1(X2)),X2))
| r1(X0)
| ~ r2(X0,X1)
| r1(X2) ),
inference(resolution,[],[f243,f146]) ).
fof(f291,plain,
! [X0,X1] :
( ~ r2(X0,sK1(sK1(sK0)))
| r1(X1)
| ~ r2(X1,X0)
| r1(sK0) ),
inference(superposition,[],[f267,f103]) ).
fof(f293,plain,
! [X0,X1] :
( ~ r2(X0,sK1(sK1(sK0)))
| r1(X1)
| ~ r2(X1,X0) ),
inference(forward_subsumption_resolution,[],[f291,f58]) ).
fof(f323,plain,
! [X0] :
( ~ r2(X0,sK1(sK0))
| r1(X0) ),
inference(resolution,[],[f293,f51]) ).
fof(f324,plain,
r1(sK0),
inference(resolution,[],[f323,f51]) ).
fof(f325,plain,
$false,
inference(forward_subsumption_resolution,[],[f324,f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN057+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n026.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 21:54:27 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.43 Running first-order model finding
% 0.11/0.43 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
% 0.17/0.49 % (3249266)Will run a generic schedule for satisfiability detection.
% 0.17/0.49 % (3249271)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=168400809_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.49 % TRYING [1]
% 0.17/0.49 % TRYING [2]
% 0.17/0.49 % TRYING [3]
% 0.17/0.49 % TRYING [4]
% 0.17/0.49 % (3249272)% WARNING: option uhcvi not known.
% 0.17/0.49 % TRYING [5]
% 0.17/0.49 % (3249272)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4279893131:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.49 % (3249273)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4179755874:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.49 % (3249276)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3448056776:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.49 % (3249274)dis+10_1_sil=32000:sp=arity:random_seed=1316519711:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.49 % (3249275)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2332129984:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.49 % (3249277)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1640834243:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.49 % TRYING [6]
% 0.17/0.49 % (3249272) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3249266-3249272"...
% 0.17/0.49 % TRYING [7]
% 0.17/0.49 % (3249272)...printing done.
% 0.17/0.49 % (3249272)Refutation found. Thanks to Tanya!
% 0.17/0.49 % SZS status Theorem for theBenchmark
% 0.17/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.49 % (3249272)------------------------------
% 0.17/0.49 % (3249272)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.49 % (3249272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.49 % (3249272)CaDiCaL version: 2.1.3
% 0.17/0.49 % (3249272)Termination reason: Refutation
% 0.17/0.49 % (3249272)Time elapsed: 0.012 s
% 0.17/0.49 % (3249272)Peak memory usage: 12 MB
% 0.17/0.49 % (3249272)Instructions burned: 15 (million)
% 0.17/0.49 % (3249266)Success in time 0.049 s
% 0.17/0.49 % Vampire exiting
%------------------------------------------------------------------------------