%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN082+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 : n004.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 12:27:05 PM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 69 ( 41 unt; 1 def)
% Number of atoms : 130 ( 40 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 111 ( 50 ~; 31 |; 29 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 1 con; 0-2 aty)
% Number of variables : 129 ( 0 sgn 102 !; 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(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(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] :
( r4(X0,X2,X1)
& ? [X3] :
( r1(X3)
& r2(X3,X2) ) )
& ? [X4] :
( r1(X4)
& X1 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xtimesoneeqzero) ).
fof(f13,negated_conjecture,
~ ? [X0,X1] :
( ? [X2] :
( r4(X0,X2,X1)
& ? [X3] :
( r1(X3)
& r2(X3,X2) ) )
& ? [X4] :
( r1(X4)
& X1 = X4 ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ! [X2] :
( ~ r4(X0,X2,X1)
| ! [X3] :
( ~ r1(X3)
| ~ r2(X3,X2) ) )
| ! [X4] :
( ~ r1(X4)
| X1 != X4 ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
! [X1] :
( r1(X1)
| sK0 != X1 ),
inference(cnf_transformation,[],[f1]) ).
fof(f16,plain,
! [X1] :
( ~ r1(X1)
| sK0 = 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(f20,plain,
! [X3,X0,X1] :
( ~ r3(X0,X1,X3)
| sK2(X0,X1) = X3 ),
inference(cnf_transformation,[],[f3]) ).
fof(f22,plain,
! [X3,X0,X1] :
( ~ r4(X0,X1,X3)
| sK3(X0,X1) = X3 ),
inference(cnf_transformation,[],[f4]) ).
fof(f26,plain,
! [X0,X1] : r3(X0,X1,sK5(X0,X1)),
inference(cnf_transformation,[],[f5]) ).
fof(f28,plain,
! [X0,X1] : r4(X0,sK11(X0,X1),sK10(X0,X1)),
inference(cnf_transformation,[],[f6]) ).
fof(f29,plain,
! [X0,X1] : r2(X1,sK11(X0,X1)),
inference(cnf_transformation,[],[f6]) ).
fof(f30,plain,
! [X0,X1] : sK8(X0,X1) = sK10(X0,X1),
inference(cnf_transformation,[],[f6]) ).
fof(f31,plain,
! [X0,X1] : r4(X0,X1,sK9(X0,X1)),
inference(cnf_transformation,[],[f6]) ).
fof(f32,plain,
! [X0,X1] : r3(sK9(X0,X1),X0,sK8(X0,X1)),
inference(cnf_transformation,[],[f6]) ).
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(f37,plain,
! [X0] : r4(X0,sK16(X0),sK14(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f38,plain,
! [X0] : r1(sK16(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f39,plain,
! [X0] : sK14(X0) = sK15(X0),
inference(cnf_transformation,[],[f9]) ).
fof(f40,plain,
! [X0] : r1(sK15(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f46,plain,
! [X2,X3,X0,X1,X4] :
( X1 != X4
| ~ r1(X4)
| ~ r2(X3,X2)
| ~ r1(X3)
| ~ r4(X0,X2,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f48,plain,
! [X0,X1] : r3(sK9(X0,X1),X0,sK10(X0,X1)),
inference(definition_unfolding,[],[f32,f30]) ).
fof(f49,plain,
! [X0] : r4(X0,sK16(X0),sK15(X0)),
inference(definition_unfolding,[],[f37,f39]) ).
fof(f50,plain,
r1(sK0),
inference(equality_resolution,[],[f15]) ).
fof(f51,plain,
! [X0] : r2(X0,sK1(X0)),
inference(equality_resolution,[],[f17]) ).
fof(f56,plain,
! [X2,X3,X0,X4] :
( ~ r4(X0,X2,X4)
| ~ r2(X3,X2)
| ~ r1(X3)
| ~ r1(X4) ),
inference(equality_resolution,[],[f46]) ).
fof(f58,plain,
! [X0] : sK0 = sK13(X0),
inference(resolution,[],[f16,f35]) ).
fof(f59,plain,
! [X0] : sK0 = sK15(X0),
inference(resolution,[],[f16,f40]) ).
fof(f60,plain,
! [X0] : sK0 = sK16(X0),
inference(resolution,[],[f16,f38]) ).
fof(f73,plain,
! [X0] : r3(X0,sK13(X0),X0),
inference(superposition,[],[f34,f36]) ).
fof(f74,plain,
! [X0] : r3(X0,sK0,X0),
inference(forward_demodulation,[],[f73,f58]) ).
fof(f98,plain,
! [X0,X1] : sK1(X0) = sK11(X1,X0),
inference(resolution,[],[f18,f29]) ).
fof(f104,plain,
! [X2,X0,X1] :
( ~ r2(X0,sK11(X1,X2))
| ~ r1(X0)
| ~ r1(sK10(X1,X2)) ),
inference(resolution,[],[f28,f56]) ).
fof(f105,plain,
! [X2,X0,X1] :
( ~ r1(X0)
| ~ r1(sK10(X1,X2))
| ~ r2(X0,sK1(X2)) ),
inference(forward_demodulation,[],[f104,f98]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ r1(sK10(X1,X2))
| ~ r2(sK16(X0),sK1(X2)) ),
inference(resolution,[],[f105,f38]) ).
fof(f110,plain,
! [X2,X1] :
( ~ r1(sK10(X1,X2))
| ~ r2(sK0,sK1(X2)) ),
inference(forward_demodulation,[],[f108,f60]) ).
fof(f121,plain,
! [X0,X1] : sK2(X0,X1) = sK5(X0,X1),
inference(resolution,[],[f20,f26]) ).
fof(f122,plain,
! [X0] : sK2(X0,sK0) = X0,
inference(resolution,[],[f20,f74]) ).
fof(f125,plain,
! [X0,X1] : sK10(X0,X1) = sK2(sK9(X0,X1),X0),
inference(resolution,[],[f20,f48]) ).
fof(f130,plain,
! [X0,X1] : sK3(X0,X1) = sK9(X0,X1),
inference(resolution,[],[f22,f31]) ).
fof(f132,plain,
! [X0] : sK15(X0) = sK3(X0,sK16(X0)),
inference(resolution,[],[f22,f49]) ).
fof(f135,plain,
! [X0] : sK15(X0) = sK3(X0,sK0),
inference(forward_demodulation,[],[f132,f60]) ).
fof(f136,plain,
! [X0] : sK0 = sK3(X0,sK0),
inference(forward_demodulation,[],[f135,f59]) ).
fof(f186,plain,
! [X0] : sK5(X0,sK0) = X0,
inference(superposition,[],[f122,f121]) ).
fof(f287,plain,
! [X0,X1] : sK10(X0,X1) = sK5(sK9(X0,X1),X0),
inference(superposition,[],[f121,f125]) ).
fof(f288,plain,
! [X0,X1] : sK10(X0,X1) = sK5(sK3(X0,X1),X0),
inference(forward_demodulation,[],[f287,f130]) ).
fof(f452,plain,
! [X0] : sK10(X0,sK0) = sK5(sK0,X0),
inference(superposition,[],[f288,f136]) ).
fof(f962,plain,
! [X0] :
( ~ r1(sK5(sK0,X0))
| ~ r2(sK0,sK1(sK0)) ),
inference(superposition,[],[f110,f452]) ).
fof(f980,definition,
( spl20_8
<=> ! [X0] : ~ r1(sK5(sK0,X0)) ),
introduced(definition,[new_symbols(definition,[spl20_8])],[avatar_definition]) ).
fof(f981,plain,
( ! [X0] : ~ r1(sK5(sK0,X0))
| ~ spl20_8 ),
inference(avatar_component_clause,[],[f980]) ).
fof(f992,plain,
! [X0] : ~ r1(sK5(sK0,X0)),
inference(forward_subsumption_resolution,[],[f962,f51]) ).
fof(f1004,plain,
spl20_8,
inference(avatar_split_clause,[],[f992,f980]) ).
fof(f1008,plain,
( ~ r1(sK0)
| ~ spl20_8 ),
inference(superposition,[],[f981,f186]) ).
fof(f1009,plain,
( $false
| ~ spl20_8 ),
inference(forward_subsumption_resolution,[],[f1008,f50]) ).
fof(f1010,plain,
~ spl20_8,
inference(avatar_contradiction_clause,[],[f1009]) ).
cnf(s15,plain,
spl20_8,
inference(sat_conversion,[],[f1004]) ).
cnf(s16,plain,
~ spl20_8,
inference(sat_conversion,[],[f1010]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s15,s16]) ).
fof(f1011,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN082+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n004.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 21:58:22 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 Running first-order model finding
% 0.12/0.40 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
% 0.12/0.45 % (3916588)Will run a generic schedule for satisfiability detection.
% 0.12/0.45 % (3916597)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2006255789:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.45 % (3916594)% WARNING: option uhcvi not known.
% 0.12/0.45 % (3916593)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3353066159_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.45 % (3916599)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4046844248:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.45 % (3916596)dis+10_1_sil=32000:sp=arity:random_seed=2583295342:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.45 % (3916595)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3270445464:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.45 % (3916598)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=108949712:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.45 % TRYING [1]
% 0.12/0.45 % TRYING [2]
% 0.12/0.45 % TRYING [3]
% 0.12/0.45 % (3916594)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=989724837:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.45 % TRYING [4]
% 0.12/0.45 % (3916596) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3916588-3916596"...
% 0.12/0.45 % TRYING [5]
% 0.12/0.45 % (3916597) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3916588-3916597"...
% 0.12/0.45 % (3916597)...printing done.
% 0.12/0.45 % (3916596)...printing done.
% 0.12/0.45 % (3916595) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3916588-3916595"...
% 0.12/0.45 % (3916597)Refutation found. Thanks to Tanya!
% 0.12/0.45 % SZS status Theorem for theBenchmark
% 0.12/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.45 % (3916597)------------------------------
% 0.12/0.45 % (3916597)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.45 % (3916597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.45 % (3916597)CaDiCaL version: 2.1.3
% 0.12/0.45 % (3916597)Termination reason: Refutation
% 0.12/0.45 % (3916597)Time elapsed: 0.017 s
% 0.12/0.45 % (3916597)Peak memory usage: 13 MB
% 0.12/0.45 % (3916597)Instructions burned: 47 (million)
% 0.12/0.45 % (3916588)Success in time 0.042 s
% 0.12/0.45 % Vampire exiting
%------------------------------------------------------------------------------