%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN076+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 12:26:45 PM UTC 2026
% Result : Theorem 3.42s 1.38s
% Output : Refutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 10 unt; 0 def)
% Number of atoms : 136 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 173 ( 77 ~; 60 |; 36 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 113 ( 87 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( id(X1,X0)
& r1(X1) )
| ( ~ r1(X1)
& ~ id(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f6,axiom,
! [X0,X1] :
( ~ id(X0,X1)
| id(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ~ id(X0,X1)
| id(X0,X2)
| ~ id(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
fof(f8,axiom,
! [X0,X1] :
( ~ id(X0,X1)
| ( ~ r1(X0)
& ~ r1(X1) )
| ( r1(X0)
& r1(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
fof(f12,axiom,
! [X0,X1] :
? [X2] :
( ? [X3] :
( id(X3,X2)
& ? [X4] :
( r2(X1,X4)
& r3(X0,X4,X3) ) )
& ? [X5] :
( r2(X5,X2)
& r3(X0,X1,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1a) ).
fof(f15,axiom,
! [X0] :
? [X1] :
( id(X1,X0)
& ? [X2] :
( r1(X2)
& r3(X0,X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4a) ).
fof(f16,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r4(X0,X2,X1) )
& ? [X3] :
( id(X1,X3)
& r1(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/sandbox/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(f23,plain,
! [X1] :
( ( id(X1,sK3)
& r1(X1) )
| ( ~ r1(X1)
& ~ id(X1,sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f1]) ).
fof(f25,plain,
! [X0] :
( id(sK5(X0),X0)
& r1(sK6(X0))
& r3(X0,sK6(X0),sK5(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X1,sK5(X0)),skolemize(X2,sK6(X0))],[f15]) ).
fof(f26,plain,
! [X0,X1] :
( id(sK8(X0,X1),sK7(X0,X1))
& r2(X1,sK9(X0,X1))
& r3(X0,sK9(X0,X1),sK8(X0,X1))
& r2(sK10(X0,X1),sK7(X0,X1))
& r3(X0,X1,sK10(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10]),skolemize(X2,sK7(X0,X1)),skolemize(X3,sK8(X0,X1)),skolemize(X4,sK9(X0,X1)),skolemize(X5,sK10(X0,X1))],[f12]) ).
fof(f28,plain,
! [X0] :
( r1(sK13(X0))
& r4(X0,sK13(X0),sK12(X0))
& id(sK12(X0),sK14(X0))
& r1(sK14(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X1,sK12(X0)),skolemize(X2,sK13(X0)),skolemize(X3,sK14(X0))],[f16]) ).
fof(f31,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(f32,plain,
! [X2,X0,X1] :
( id(X0,X2)
| ~ id(X0,X1)
| ~ id(X1,X2) ),
inference(cnf_transformation,[],[f7]) ).
fof(f33,plain,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f41,plain,
! [X0,X1] :
( ~ id(X0,X1)
| ~ r1(X1)
| r1(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f47,plain,
! [X1] :
( id(X1,sK3)
| ~ r1(X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f57,plain,
! [X0] : r3(X0,sK6(X0),sK5(X0)),
inference(cnf_transformation,[],[f25]) ).
fof(f59,plain,
! [X0] : id(sK5(X0),X0),
inference(cnf_transformation,[],[f25]) ).
fof(f63,plain,
! [X0,X1] : r2(X1,sK9(X0,X1)),
inference(cnf_transformation,[],[f26]) ).
fof(f73,plain,
! [X0] : r1(sK14(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f74,plain,
! [X0] : id(sK12(X0),sK14(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f75,plain,
! [X0] : r4(X0,sK13(X0),sK12(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f76,plain,
! [X0] : r1(sK13(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f97,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r3(sK13(X0),X5,X4)
| ~ r2(X2,X0)
| ~ r1(X3)
| ~ r2(X3,X2)
| ~ id(X4,X1)
| ~ id(sK12(X0),X1) ),
inference(resolution,[],[f75,f31]) ).
fof(f99,plain,
! [X2,X3,X0,X1] :
( ~ id(sK5(sK13(X1)),X3)
| ~ r1(X2)
| ~ r2(X2,X0)
| ~ r2(X0,X1)
| ~ id(sK12(X1),X3) ),
inference(resolution,[],[f97,f57]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ id(sK12(X2),sK13(X2))
| ~ r2(X0,X1)
| ~ r2(X1,X2)
| ~ r1(X0) ),
inference(resolution,[],[f99,f59]) ).
fof(f113,plain,
! [X0] :
( ~ r1(sK14(X0))
| r1(sK12(X0)) ),
inference(resolution,[],[f41,f74]) ).
fof(f114,plain,
! [X0] : r1(sK12(X0)),
inference(forward_subsumption_resolution,[],[f113,f73]) ).
fof(f193,plain,
! [X2,X3,X0,X1] :
( ~ id(sK12(X0),X1)
| ~ id(X1,sK13(X0))
| ~ r2(X2,X3)
| ~ r2(X3,X0)
| ~ r1(X2) ),
inference(resolution,[],[f32,f101]) ).
fof(f203,plain,
! [X2,X0,X1] :
( ~ id(sK3,sK13(X0))
| ~ r2(X1,X2)
| ~ r2(X2,X0)
| ~ r1(X1)
| ~ r1(sK12(X0)) ),
inference(resolution,[],[f193,f47]) ).
fof(f223,plain,
! [X2,X0,X1] :
( ~ id(sK13(X2),sK3)
| ~ r2(X1,X2)
| ~ r1(X0)
| ~ r1(sK12(X2))
| ~ r2(X0,X1) ),
inference(resolution,[],[f203,f33]) ).
fof(f224,plain,
! [X2,X0,X1] :
( ~ r2(X0,X1)
| ~ r1(X2)
| ~ r1(sK12(X1))
| ~ r2(X2,X0)
| ~ r1(sK13(X1)) ),
inference(resolution,[],[f223,f47]) ).
fof(f227,plain,
! [X2,X0,X1] :
( ~ r2(X2,X0)
| ~ r1(X2)
| ~ r1(sK12(X1))
| ~ r2(X0,X1) ),
inference(forward_subsumption_resolution,[],[f224,f76]) ).
fof(f232,plain,
! [X2,X0,X1] :
( ~ r2(sK9(X2,X0),X1)
| ~ r1(sK12(X1))
| ~ r1(X0) ),
inference(resolution,[],[f227,f63]) ).
fof(f246,plain,
! [X2,X0,X1] :
( ~ r1(sK12(sK9(X0,sK9(X1,X2))))
| ~ r1(X2) ),
inference(resolution,[],[f232,f63]) ).
fof(f341,plain,
! [X0] : ~ r1(X0),
inference(resolution,[],[f114,f246]) ).
fof(f352,plain,
$false,
inference(resolution,[],[f341,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN076+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n019.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 21:57:19 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.42/1.38 % (3448312)Detected formulas, will run a generic FOF schedule.
% 3.42/1.38 % (3448320)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2080348462:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.42/1.38 % (3448320)Instruction limit reached!
% 3.42/1.38 % (3448320)------------------------------
% 3.42/1.38 % (3448320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.38 % (3448320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.38 % (3448320)CaDiCaL version: 2.1.3
% 3.42/1.38 % (3448320)Termination reason: Instruction limit
% 3.42/1.38 % (3448320)Termination phase: Saturation
% 3.42/1.38 % (3448320)Time elapsed: 0.036 s
% 3.42/1.38 % (3448320)Peak memory usage: 89 MB
% 3.42/1.38 % (3448320)Instructions burned: 116 (million)
% 3.42/1.38 % (3448317)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3259824221:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.42/1.38 % (3448319)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=858799280:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.42/1.38 % (3448318)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3668555305:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.42/1.38 % (3448321)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=340356977:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.42/1.38 % (3448323)dis-21_1_sil=8000:lcm=predicate:random_seed=773354722:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.42/1.38 % (3448321)First to succeed.
% 3.42/1.38 % (3448321)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3448312"
% 3.42/1.38 % (3448322)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1742690884:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.42/1.38 % (3448323)Instruction limit reached!
% 3.42/1.38 % (3448323)------------------------------
% 3.42/1.38 % (3448323)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.38 % (3448323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.38 % (3448323)CaDiCaL version: 2.1.3
% 3.42/1.38 % (3448323)Termination reason: Instruction limit
% 3.42/1.38 % (3448323)Termination phase: Saturation
% 3.42/1.38 % (3448323)Time elapsed: 0.081 s
% 3.42/1.38 % (3448323)Peak memory usage: 89 MB
% 3.42/1.38 % (3448323)Instructions burned: 131 (million)
% 3.42/1.38 % (3448325)lrs+10_1_sil=8000:sp=occurrence:random_seed=314753332:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.42/1.38 % (3448325)Also succeeded, but the first one will report.
% 3.42/1.38 % (3448322)Instruction limit reached!
% 3.42/1.38 % (3448322)------------------------------
% 3.42/1.38 % (3448322)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.38 % (3448322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.38 % (3448322)CaDiCaL version: 2.1.3
% 3.42/1.38 % (3448322)Termination reason: Instruction limit
% 3.42/1.38 % (3448322)Termination phase: Saturation
% 3.42/1.38 % (3448322)Time elapsed: 0.091 s
% 3.42/1.38 % (3448322)Peak memory usage: 89 MB
% 3.42/1.38 % (3448322)Instructions burned: 140 (million)
% 3.42/1.38 % (3448333)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1523248590:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.42/1.38 % (3448334)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2979981181:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.42/1.38 % (3448321)Refutation found. Thanks to Tanya!
% 3.42/1.38 % SZS status Theorem for theBenchmark
% 3.42/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.42/1.38 % (3448321)------------------------------
% 3.42/1.38 % (3448321)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.38 % (3448321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.38 % (3448321)CaDiCaL version: 2.1.3
% 3.42/1.38 % (3448321)Termination reason: Refutation
% 3.42/1.38 % (3448321)Time elapsed: 0.009 s
% 3.42/1.38 % (3448321)Peak memory usage: 88 MB
% 3.42/1.38 % (3448321)Instructions burned: 12 (million)
% 3.42/1.38 % (3448321)------------------------------
% 3.42/1.38 % (3448321)------------------------------
% 3.42/1.38 % (3448312)Success in time 0.417 s
% 3.42/1.38 % Vampire exiting
%------------------------------------------------------------------------------