%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN076+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 12:27:04 PM UTC 2026
% Result : Theorem 0.07s 0.37s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 12 unt; 0 def)
% Number of atoms : 120 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 149 ( 67 ~; 50 |; 32 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 96 ( 73 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( id(X1,X0)
& r1(X1) )
| ( ~ r1(X1)
& ~ id(X1,X0) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_2) ).
fof(f5,axiom,
! [X0] : id(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(f8,axiom,
! [X0,X1] :
( ~ id(X0,X1)
| ( ~ r1(X0)
& ~ r1(X1) )
| ( r1(X0)
& r1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_8) ).
fof(f15,axiom,
! [X0] :
? [X1] :
( id(X1,X0)
& ? [X2] :
( r1(X2)
& r3(X0,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_4a) ).
fof(f16,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r4(X0,X2,X1) )
& ? [X3] :
( id(X1,X3)
& r1(X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5a) ).
fof(f19,conjecture,
? [X0,X1,X2] :
( ? [X3] :
( id(X3,X0)
& ? [X4] :
( r4(X4,X1,X3)
& ? [X5] :
( r2(X5,X4)
& ? [X6] :
( r1(X6)
& r2(X6,X5) ) ) ) )
& ? [X7] :
( id(X7,X0)
& r3(X1,X2,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thereexistsanevennumberid) ).
fof(f20,negated_conjecture,
~ ? [X0,X1,X2] :
( ? [X3] :
( id(X3,X0)
& ? [X4] :
( r4(X4,X1,X3)
& ? [X5] :
( r2(X5,X4)
& ? [X6] :
( r1(X6)
& r2(X6,X5) ) ) ) )
& ? [X7] :
( id(X7,X0)
& r3(X1,X2,X7) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ! [X3] :
( ~ id(X3,X0)
| ! [X4] :
( ~ r4(X4,X1,X3)
| ! [X5] :
( ~ r2(X5,X4)
| ! [X6] :
( ~ r1(X6)
| ~ r2(X6,X5) ) ) ) )
| ! [X7] :
( ~ id(X7,X0)
| ~ r3(X1,X2,X7) ) ),
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(f28,plain,
! [X0] :
( id(sK12(X0),X0)
& r1(sK13(X0))
& r3(X0,sK13(X0),sK12(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X1,sK12(X0)),skolemize(X2,sK13(X0))],[f15]) ).
fof(f29,plain,
! [X0] :
( r1(sK15(X0))
& r4(X0,sK15(X0),sK14(X0))
& id(sK14(X0),sK16(X0))
& r1(sK16(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X1,sK14(X0)),skolemize(X2,sK15(X0)),skolemize(X3,sK16(X0))],[f16]) ).
fof(f34,plain,
! [X1] :
( id(X1,sK0)
| ~ r1(X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
! [X2,X0] :
( ~ id(X2,sK1(X0))
| r2(X0,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f47,plain,
! [X0] : id(X0,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f51,plain,
! [X0,X1] :
( ~ id(X0,X1)
| ~ r1(X1)
| r1(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f77,plain,
! [X0] : r3(X0,sK13(X0),sK12(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f79,plain,
! [X0] : id(sK12(X0),X0),
inference(cnf_transformation,[],[f28]) ).
fof(f80,plain,
! [X0] : r1(sK16(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f81,plain,
! [X0] : id(sK14(X0),sK16(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f82,plain,
! [X0] : r4(X0,sK15(X0),sK14(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f83,plain,
! [X0] : r1(sK15(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f89,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ r4(X4,X1,X3)
| ~ id(X3,X0)
| ~ r2(X5,X4)
| ~ r1(X6)
| ~ r2(X6,X5)
| ~ id(X7,X0)
| ~ r3(X1,X2,X7) ),
inference(cnf_transformation,[],[f21]) ).
fof(f107,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r3(sK15(X0),X5,X4)
| ~ r2(X2,X0)
| ~ r1(X3)
| ~ r2(X3,X2)
| ~ id(X4,X1)
| ~ id(sK14(X0),X1) ),
inference(resolution,[],[f82,f89]) ).
fof(f108,plain,
! [X0] : r2(X0,sK1(X0)),
inference(resolution,[],[f35,f47]) ).
fof(f115,plain,
! [X0] :
( r1(sK12(X0))
| ~ r1(X0) ),
inference(resolution,[],[f51,f79]) ).
fof(f120,plain,
! [X0] :
( ~ r1(sK16(X0))
| r1(sK14(X0)) ),
inference(resolution,[],[f51,f81]) ).
fof(f122,plain,
! [X0] : r1(sK14(X0)),
inference(forward_subsumption_resolution,[],[f120,f80]) ).
fof(f157,plain,
! [X2,X3,X0,X1] :
( ~ id(sK12(sK15(X1)),X3)
| ~ r1(X2)
| ~ r2(X2,X0)
| ~ r2(X0,X1)
| ~ id(sK14(X1),X3) ),
inference(resolution,[],[f107,f77]) ).
fof(f165,plain,
! [X2,X0,X1] :
( ~ r1(sK12(sK15(X2)))
| ~ r2(X0,X1)
| ~ r2(X1,X2)
| ~ id(sK14(X2),sK0)
| ~ r1(X0) ),
inference(resolution,[],[f157,f34]) ).
fof(f273,plain,
! [X2,X0,X1] :
( ~ r1(sK15(X0))
| ~ r2(X1,X2)
| ~ r2(X2,X0)
| ~ id(sK14(X0),sK0)
| ~ r1(X1) ),
inference(resolution,[],[f115,f165]) ).
fof(f274,plain,
! [X2,X0,X1] :
( ~ id(sK14(X0),sK0)
| ~ r2(X2,X0)
| ~ r2(X1,X2)
| ~ r1(X1) ),
inference(forward_subsumption_resolution,[],[f273,f83]) ).
fof(f275,plain,
! [X2,X0,X1] :
( ~ r2(X0,X1)
| ~ r2(X2,X0)
| ~ r1(X2)
| ~ r1(sK14(X1)) ),
inference(resolution,[],[f274,f34]) ).
fof(f276,plain,
! [X2,X0,X1] :
( ~ r2(X2,X0)
| ~ r2(X0,X1)
| ~ r1(X2) ),
inference(forward_subsumption_resolution,[],[f275,f122]) ).
fof(f279,plain,
! [X0,X1] :
( ~ r2(sK1(X0),X1)
| ~ r1(X0) ),
inference(resolution,[],[f276,f108]) ).
fof(f291,plain,
! [X0] : ~ r1(X0),
inference(resolution,[],[f279,f108]) ).
fof(f304,plain,
$false,
inference(resolution,[],[f291,f80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUN076+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.05/0.32 % Computer : n012.cluster.edu
% 0.05/0.32 % Model : x86_64 x86_64
% 0.05/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.32 % Memory : 8046.5625MB
% 0.05/0.32 % OS : Linux 6.8.0-71-generic
% 0.05/0.32 % CPULimit : 300
% 0.05/0.32 % WCLimit : 300
% 0.05/0.32 % DateTime : Sun Sep 27 21:56:50 UTC 2026
% 0.05/0.32 % CPUTime :
% 0.05/0.32 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.34 Running first-order model finding
% 0.07/0.34 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.37 % (2792290)Will run a generic schedule for satisfiability detection.
% 0.07/0.37 % (2792296)% WARNING: option uhcvi not known.
% 0.07/0.37 % (2792297)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1464206563:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.37 % (2792295)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=780713695_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.37 % (2792300)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=773744610:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.37 % (2792296)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2158653259:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.37 % (2792298)dis+10_1_sil=32000:sp=arity:random_seed=4237376263:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.37 % (2792299)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3607677103:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.37 % (2792301)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2961805204:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.37 % TRYING [1]
% 0.07/0.37 % TRYING [2]
% 0.07/0.37 % TRYING [3]
% 0.07/0.37 % (2792298) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2792290-2792298"...
% 0.07/0.37 % (2792297) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2792290-2792297"...
% 0.07/0.37 % TRYING [4]
% 0.07/0.37 % (2792298)...printing done.
% 0.07/0.37 % (2792297)...printing done.
% 0.07/0.37 % (2792298)Refutation found. Thanks to Tanya!
% 0.07/0.37 % SZS status Theorem for theBenchmark
% 0.07/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.37 % (2792298)------------------------------
% 0.07/0.37 % (2792298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.37 % (2792298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.37 % (2792298)CaDiCaL version: 2.1.3
% 0.07/0.37 % (2792298)Termination reason: Refutation
% 0.07/0.37 % (2792298)Time elapsed: 0.004 s
% 0.07/0.37 % (2792298)Peak memory usage: 11 MB
% 0.07/0.37 % (2792298)Instructions burned: 11 (million)
% 0.07/0.37 % (2792290)Success in time 0.028 s
% 0.07/0.37 % Vampire exiting
%------------------------------------------------------------------------------