%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW297+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 01:30:03 PM UTC 2026
% Result : Theorem 4.22s 1.63s
% Output : Refutation 4.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 5 unt; 0 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 58 ( 20 ~; 13 |; 9 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 52 ( 46 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2,X3] :
( c_Natural_Oevaln(X3,X2,X1,X0)
=> c_Natural_Oevaln(X3,X2,hAPP(c_Nat_OSuc,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__Suc) ).
fof(f5225,conjecture,
( ! [X0,X1] :
( v_fun1(X0,X1)
=> ! [X2] :
( c_Natural_Oevaln(v_com,X1,hAPP(c_Nat_OSuc,v_n),X2)
=> v_fun2(X0,X2) ) )
=> ! [X0,X1] :
( v_fun1(X0,X1)
=> ! [X2] :
( c_Natural_Oevaln(v_com,X1,v_n,X2)
=> v_fun2(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f5226,negated_conjecture,
~ ( ! [X0,X1] :
( v_fun1(X0,X1)
=> ! [X2] :
( c_Natural_Oevaln(v_com,X1,hAPP(c_Nat_OSuc,v_n),X2)
=> v_fun2(X0,X2) ) )
=> ! [X0,X1] :
( v_fun1(X0,X1)
=> ! [X2] :
( c_Natural_Oevaln(v_com,X1,v_n,X2)
=> v_fun2(X0,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f5225]) ).
fof(f5227,plain,
~ ( ! [X0,X1] :
( v_fun1(X0,X1)
=> ! [X2] :
( c_Natural_Oevaln(v_com,X1,hAPP(c_Nat_OSuc,v_n),X2)
=> v_fun2(X0,X2) ) )
=> ! [X3,X4] :
( v_fun1(X3,X4)
=> ! [X5] :
( c_Natural_Oevaln(v_com,X4,v_n,X5)
=> v_fun2(X3,X5) ) ) ),
inference(rectify,[],[f5226]) ).
fof(f5230,plain,
( ? [X3,X4] :
( ? [X5] :
( ~ v_fun2(X3,X5)
& c_Natural_Oevaln(v_com,X4,v_n,X5) )
& v_fun1(X3,X4) )
& ! [X0,X1] :
( ! [X2] :
( v_fun2(X0,X2)
| ~ c_Natural_Oevaln(v_com,X1,hAPP(c_Nat_OSuc,v_n),X2) )
| ~ v_fun1(X0,X1) ) ),
inference(ennf_transformation,[],[f5227]) ).
fof(f5233,plain,
! [X0,X1,X2,X3] :
( c_Natural_Oevaln(X3,X2,hAPP(c_Nat_OSuc,X1),X0)
| ~ c_Natural_Oevaln(X3,X2,X1,X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f5474,plain,
( ? [X0,X1] :
( ? [X2] :
( ~ v_fun2(X0,X2)
& c_Natural_Oevaln(v_com,X1,v_n,X2) )
& v_fun1(X0,X1) )
& ! [X3,X4] :
( ! [X5] :
( v_fun2(X3,X5)
| ~ c_Natural_Oevaln(v_com,X4,hAPP(c_Nat_OSuc,v_n),X5) )
| ~ v_fun1(X3,X4) ) ),
inference(rectify,[],[f5230]) ).
fof(f5475,plain,
( ~ v_fun2(sK0,sK2)
& c_Natural_Oevaln(v_com,sK1,v_n,sK2)
& v_fun1(sK0,sK1)
& ! [X3,X4] :
( ! [X5] :
( v_fun2(X3,X5)
| ~ c_Natural_Oevaln(v_com,X4,hAPP(c_Nat_OSuc,v_n),X5) )
| ~ v_fun1(X3,X4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f5474]) ).
fof(f5628,plain,
! [X3,X4,X5] :
( ~ c_Natural_Oevaln(v_com,X4,hAPP(c_Nat_OSuc,v_n),X5)
| v_fun2(X3,X5)
| ~ v_fun1(X3,X4) ),
inference(cnf_transformation,[],[f5475]) ).
fof(f5629,plain,
v_fun1(sK0,sK1),
inference(cnf_transformation,[],[f5475]) ).
fof(f5630,plain,
c_Natural_Oevaln(v_com,sK1,v_n,sK2),
inference(cnf_transformation,[],[f5475]) ).
fof(f5631,plain,
~ v_fun2(sK0,sK2),
inference(cnf_transformation,[],[f5475]) ).
fof(f5633,plain,
! [X2,X3,X0,X1] :
( c_Natural_Oevaln(X3,X2,hAPP(c_Nat_OSuc,X1),X0)
| ~ c_Natural_Oevaln(X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f5233]) ).
fof(f6294,plain,
! [X2,X0,X1] :
( ~ c_Natural_Oevaln(v_com,X0,v_n,X1)
| v_fun2(X2,X1)
| ~ v_fun1(X2,X0) ),
inference(resolution,[],[f5633,f5628]) ).
fof(f6298,plain,
! [X0] :
( v_fun2(X0,sK2)
| ~ v_fun1(X0,sK1) ),
inference(resolution,[],[f6294,f5630]) ).
fof(f6299,plain,
~ v_fun1(sK0,sK1),
inference(resolution,[],[f6298,f5631]) ).
fof(f6300,plain,
$false,
inference(forward_subsumption_resolution,[],[f6299,f5629]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW297+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n002.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 13:33:52 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 4.22/1.63 % (353183)Detected formulas, will run a generic FOF schedule.
% 4.22/1.63 % (353188)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=943345154:i=141193_2995 on theBenchmark for (2995ds/141193Mi)
% 4.22/1.63 % (353192)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2298763457:i=119:av=off:ss=axioms_2995 on theBenchmark for (2995ds/119Mi)
% 4.22/1.63 % (353190)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=3920213715:i=141695:sd=1:nm=32:gsp=on:ss=included_2995 on theBenchmark for (2995ds/141695Mi)
% 4.22/1.63 % (353193)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=308020047:s2a=on:i=139:gtg=position_2995 on theBenchmark for (2995ds/139Mi)
% 4.22/1.63 % (353191)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2755482887:i=109:sd=1:ins=1:gsp=on:ss=axioms_2995 on theBenchmark for (2995ds/109Mi)
% 4.22/1.63 % (353194)dis-21_1_sil=8000:lcm=predicate:random_seed=407199590:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2995 on theBenchmark for (2995ds/129Mi)
% 4.22/1.63 % (353189)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=541749679:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2995 on theBenchmark for (2995ds/134677Mi)
% 4.22/1.63 % (353191)Refutation not found, incomplete strategy
% 4.22/1.63 % (353191)------------------------------
% 4.22/1.63 % (353191)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.22/1.63 % (353191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.22/1.63 % (353191)CaDiCaL version: 2.1.3
% 4.22/1.63 % (353191)Termination reason: Refutation not found, incomplete strategy
% 4.22/1.63 % (353191)Time elapsed: 0.032 s
% 4.22/1.63 % (353191)Peak memory usage: 94 MB
% 4.22/1.63 % (353191)Instructions burned: 45 (million)
% 4.22/1.63 % (353192)First to succeed.
% 4.22/1.63 % (353192)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-353183"
% 4.22/1.63 % (353193)Instruction limit reached!
% 4.22/1.63 % (353193)------------------------------
% 4.22/1.63 % (353193)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.22/1.63 % (353193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.22/1.63 % (353193)CaDiCaL version: 2.1.3
% 4.22/1.63 % (353193)Termination reason: Instruction limit
% 4.22/1.63 % (353193)Termination phase: SInE selection
% 4.22/1.63 % (353193)Time elapsed: 0.058 s
% 4.22/1.63 % (353193)Peak memory usage: 90 MB
% 4.22/1.63 % (353193)Instructions burned: 140 (million)
% 4.22/1.63 % (353194)Instruction limit reached!
% 4.22/1.63 % (353194)------------------------------
% 4.22/1.63 % (353194)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.22/1.63 % (353194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.22/1.63 % (353194)CaDiCaL version: 2.1.3
% 4.22/1.63 % (353194)Termination reason: Instruction limit
% 4.22/1.63 % (353194)Termination phase: Preprocessing 3
% 4.22/1.63 % (353194)Time elapsed: 0.084 s
% 4.22/1.63 % (353194)Peak memory usage: 93 MB
% 4.22/1.63 % (353194)Instructions burned: 129 (million)
% 4.22/1.63 % (353202)lrs+10_1_sil=8000:sp=occurrence:random_seed=1337763019:i=285:sd=3:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/285Mi)
% 4.22/1.63 % (353203)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3714202941:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/157Mi)
% 4.22/1.63 % (353202)Also succeeded, but the first one will report.
% 4.22/1.63 % (353191)------------------------------
% 4.22/1.63 % (353191)------------------------------
% 4.22/1.63 % (353203)Instruction limit reached!
% 4.22/1.63 % (353203)------------------------------
% 4.22/1.63 % (353203)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.22/1.63 % (353203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.22/1.63 % (353203)CaDiCaL version: 2.1.3
% 4.22/1.63 % (353203)Termination reason: Instruction limit
% 4.22/1.63 % (353203)Termination phase: Saturation
% 4.22/1.63 % (353203)Time elapsed: 0.073 s
% 4.22/1.63 % (353203)Peak memory usage: 92 MB
% 4.22/1.63 % (353203)Instructions burned: 159 (million)
% 4.22/1.63 % (353192)Refutation found. Thanks to Tanya!
% 4.22/1.63 % SZS status Theorem for theBenchmark
% 4.22/1.63 % SZS output start Proof for theBenchmark
% See solution above
% 4.22/1.63 % (353192)------------------------------
% 4.22/1.63 % (353192)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.22/1.63 % (353192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.22/1.63 % (353192)CaDiCaL version: 2.1.3
% 4.22/1.63 % (353192)Termination reason: Refutation
% 4.22/1.63 % (353192)Time elapsed: 0.044 s
% 4.22/1.63 % (353192)Peak memory usage: 94 MB
% 4.22/1.63 % (353192)Instructions burned: 71 (million)
% 4.22/1.63 % (353192)------------------------------
% 4.22/1.63 % (353192)------------------------------
% 4.22/1.63 % (353183)Success in time 0.862 s
% 4.22/1.63 % Vampire exiting
%------------------------------------------------------------------------------