%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN067+1 : 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 : n005.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 0.11s 0.46s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 7 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 68 ( 34 ~; 22 |; 12 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 44 ( 39 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( id(X1,X0)
& r1(X1) )
| ( ~ r1(X1)
& ~ id(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_1) ).
fof(f2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( id(X2,X1)
& r2(X0,X2) )
| ( ~ r2(X0,X2)
& ~ id(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_2) ).
fof(f6,axiom,
! [X0,X1] :
( ~ id(X0,X1)
| id(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_6) ).
fof(f8,axiom,
! [X0,X1] :
( ~ id(X0,X1)
| ( ~ r1(X0)
& ~ r1(X1) )
| ( r1(X0)
& r1(X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_8) ).
fof(f18,axiom,
! [X0,X1] :
( ! [X2] :
( ~ id(X2,X1)
| ~ r1(X2) )
| ~ r2(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_7a) ).
fof(f19,conjecture,
? [X0] :
! [X1] :
( ~ id(X0,X1)
| ~ r1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonzerosexistid) ).
fof(f20,negated_conjecture,
~ ? [X0] :
! [X1] :
( ~ id(X0,X1)
| ~ r1(X1) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0] :
? [X1] :
( id(X0,X1)
& r1(X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f22,plain,
! [X1] :
( ( id(X1,sK0)
& r1(X1) )
| ( ~ r1(X1)
& ~ id(X1,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f1]) ).
fof(f23,plain,
! [X0,X2] :
( ( id(X2,sK1(X0))
& r2(X0,X2) )
| ( ~ r2(X0,X2)
& ~ id(X2,sK1(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f2]) ).
fof(f31,plain,
! [X0] :
( id(X0,sK20(X0))
& r1(sK20(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X1,sK20(X0))],[f21]) ).
fof(f35,plain,
! [X1] :
( id(X1,sK0)
| ~ r1(X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
! [X2,X0] :
( ~ id(X2,sK1(X0))
| r2(X0,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f49,plain,
! [X0,X1] :
( ~ id(X0,X1)
| id(X1,X0) ),
inference(cnf_transformation,[],[f6]) ).
fof(f52,plain,
! [X0,X1] :
( ~ id(X0,X1)
| ~ r1(X1)
| r1(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f89,plain,
! [X2,X0,X1] :
( ~ id(X2,X1)
| ~ r1(X2)
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f90,plain,
! [X0] : r1(sK20(X0)),
inference(cnf_transformation,[],[f31]) ).
fof(f91,plain,
! [X0] : id(X0,sK20(X0)),
inference(cnf_transformation,[],[f31]) ).
fof(f95,plain,
! [X0] : id(sK20(X0),X0),
inference(resolution,[],[f49,f91]) ).
fof(f97,plain,
! [X0] :
( id(sK0,X0)
| ~ r1(X0) ),
inference(resolution,[],[f49,f35]) ).
fof(f107,plain,
! [X0] :
( r2(X0,sK0)
| ~ r1(sK1(X0)) ),
inference(resolution,[],[f36,f97]) ).
fof(f116,plain,
! [X0] :
( ~ r1(sK20(X0))
| r1(X0) ),
inference(resolution,[],[f52,f91]) ).
fof(f124,plain,
! [X0] : r1(X0),
inference(forward_subsumption_resolution,[],[f116,f90]) ).
fof(f129,plain,
! [X0] : r2(X0,sK0),
inference(forward_subsumption_resolution,[],[f107,f124]) ).
fof(f140,plain,
! [X2,X0,X1] :
( ~ r2(X0,X1)
| ~ id(X2,X1) ),
inference(forward_subsumption_resolution,[],[f89,f124]) ).
fof(f141,plain,
! [X0] : ~ id(X0,sK0),
inference(resolution,[],[f140,f129]) ).
fof(f153,plain,
$false,
inference(resolution,[],[f141,f95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN067+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n005.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 21:53:17 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.11/0.46 % (208002)Will run a generic schedule for satisfiability detection.
% 0.11/0.46 % (208007)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2677511633_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.46 % TRYING [1]
% 0.11/0.46 % TRYING [2]
% 0.11/0.46 % (208008)% WARNING: option uhcvi not known.
% 0.11/0.46 % TRYING [3]
% 0.11/0.46 % TRYING [4]
% 0.11/0.46 % (208011)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4162847591:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.46 % (208008)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=105022953:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.46 % (208009)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3649515315:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.46 % (208010)dis+10_1_sil=32000:sp=arity:random_seed=1015833199:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.46 % (208013)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1487732711:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.46 % (208012)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3219195151:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.46 % (208010) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-208002-208010"...
% 0.11/0.46 % (208008) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-208002-208008"...
% 0.11/0.46 % (208009) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-208002-208009"...
% 0.11/0.46 % TRYING [5]
% 0.11/0.46 % (208013) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-208002-208013"...
% 0.11/0.46 % (208012) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-208002-208012"...
% 0.11/0.46 % (208010)...printing done.
% 0.11/0.46 % (208008)...printing done.
% 0.11/0.46 % (208011) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-208002-208011"...
% 0.11/0.46 % (208009)...printing done.
% 0.11/0.46 % (208013)...printing done.
% 0.11/0.46 % (208010)Refutation found. Thanks to Tanya!
% 0.11/0.46 % SZS status Theorem for theBenchmark
% 0.11/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.46 % (208010)------------------------------
% 0.11/0.46 % (208010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.46 % (208010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.46 % (208010)CaDiCaL version: 2.1.3
% 0.11/0.46 % (208010)Termination reason: Refutation
% 0.11/0.46 % (208010)Time elapsed: 0.003 s
% 0.11/0.46 % (208010)Peak memory usage: 11 MB
% 0.11/0.46 % (208010)Instructions burned: 3 (million)
% 0.11/0.46 % (208002)Success in time 0.037 s
% 0.11/0.46 % Vampire exiting
%------------------------------------------------------------------------------