%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM213_1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 09:39:48 AM UTC 2026
% Result : Theorem 0.20s 1.13s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 17 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 34 ( 14 ~; 12 |; 5 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 7 con; 0-3 aty)
% Number of variables : 18 ( 15 !; 3 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
vTerm: $tType ).
tff(type_def_6,type,
vOptTerm: $tType ).
tff(type_def_7,type,
vTy: $tType ).
tff(func_def_0,type,
vNat: vTy ).
tff(func_def_1,type,
vSucc: vTerm > vTerm ).
tff(func_def_2,type,
vPred: vTerm > vTerm ).
tff(func_def_3,type,
vsomeTerm: vTerm > vOptTerm ).
tff(func_def_4,type,
vZero: vTerm ).
tff(func_def_5,type,
vIszero: vTerm > vTerm ).
tff(func_def_6,type,
vTrue: vTerm ).
tff(func_def_7,type,
vFalse: vTerm ).
tff(func_def_8,type,
vnoTerm: vOptTerm ).
tff(func_def_9,type,
vPlus: ( vTerm * vTerm ) > vTerm ).
tff(func_def_10,type,
vB: vTy ).
tff(func_def_11,type,
vIfelse: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_12,type,
vt1: vTerm ).
tff(func_def_13,type,
vreduce: vTerm > vOptTerm ).
tff(func_def_14,type,
vplusop: ( vTerm * vTerm ) > vTerm ).
tff(func_def_15,type,
vgetTerm: vOptTerm > vTerm ).
tff(func_def_16,type,
sK0: vTerm > vTerm ).
tff(func_def_17,type,
sK1: vTerm > vTerm ).
tff(func_def_18,type,
sK2: vTerm > vTerm ).
tff(func_def_19,type,
sK3: vTerm > vTerm ).
tff(pred_def_1,type,
visValue: vTerm > $o ).
tff(pred_def_2,type,
visNV: vTerm > $o ).
tff(pred_def_3,type,
visSomeTerm: vOptTerm > $o ).
tff(pred_def_4,type,
vptchecksimple: ( vTerm * vTy ) > $o ).
tff(f26,axiom,
! [X0: vTerm] : ( vZero != vPred(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-Zero-Pred') ).
tff(f29,axiom,
! [X0: vTerm,X1: vTerm] : ( vSucc(X0) != vPred(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-Succ-Pred') ).
tff(f44,axiom,
! [X0: vTerm] :
( visNV(X0)
=> ( ( X0 = vZero )
| ? [X1: vTerm] :
( ( X0 = vSucc(X1) )
& visNV(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','isNV-true-INV') ).
tff(f106,conjecture,
( visNV(vPred(vt1))
=> vptchecksimple(vPred(vt1),vNat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','isNVisNat-Pred') ).
tff(f107,negated_conjecture,
~ ( visNV(vPred(vt1))
=> vptchecksimple(vPred(vt1),vNat) ),
inference(negated_conjecture,[status(cth)],[f106]) ).
tff(f108,plain,
( ~ vptchecksimple(vPred(vt1),vNat)
& visNV(vPred(vt1)) ),
inference(ennf_transformation,[],[f107]) ).
tff(f123,plain,
! [X0: vTerm] :
( ( X0 = vZero )
| ? [X1: vTerm] :
( ( X0 = vSucc(X1) )
& visNV(X1) )
| ~ visNV(X0) ),
inference(ennf_transformation,[],[f44]) ).
tff(f124,plain,
! [X0: vTerm] :
( ( X0 = vZero )
| ? [X1: vTerm] :
( ( X0 = vSucc(X1) )
& visNV(X1) )
| ~ visNV(X0) ),
inference(flattening,[],[f123]) ).
tff(f135,plain,
! [X0: vTerm] :
( ( X0 = vZero )
| ( ( vSucc(sK2(X0)) = X0 )
& visNV(sK2(X0)) )
| ~ visNV(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f124]) ).
tff(f138,plain,
visNV(vPred(vt1)),
inference(cnf_transformation,[],[f108]) ).
tff(f159,plain,
! [X0: vTerm] :
( ( vSucc(sK2(X0)) = X0 )
| ( vZero = X0 )
| ~ visNV(X0) ),
inference(cnf_transformation,[],[f135]) ).
tff(f166,plain,
! [X0: vTerm,X1: vTerm] : ( vPred(X1) != vSucc(X0) ),
inference(cnf_transformation,[],[f29]) ).
tff(f167,plain,
! [X0: vTerm] : ( vZero != vPred(X0) ),
inference(cnf_transformation,[],[f26]) ).
tff(f208,plain,
! [X0: vTerm,X1: vTerm] :
( ( vPred(X1) != X0 )
| ( vZero = X0 )
| ~ visNV(X0) ),
inference(superposition,[],[f166,f159]) ).
tff(f234,plain,
! [X0: vTerm] :
( ( vZero = vPred(X0) )
| ~ visNV(vPred(X0)) ),
inference(equality_resolution,[],[f208]) ).
tff(f235,plain,
! [X0: vTerm] : ~ visNV(vPred(X0)),
inference(forward_subsumption_resolution,[],[f234,f167]) ).
tff(f237,plain,
$false,
inference(resolution,[],[f235,f138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM213_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.19 % Computer : n014.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Mon Sep 28 22:01:46 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.23 Running first-order theorem proving
% 0.12/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/1.13 % (2226720)Detected formulas, will run a generic FOF schedule.
% 0.20/1.13 % (2226850)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3081284982:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.20/1.13 % (2226850)First to succeed.
% 0.20/1.13 % (2226850)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2226720"
% 0.20/1.13 % (2226852)dis-21_1_sil=8000:lcm=predicate:random_seed=1743729808: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)
% 0.20/1.13 % (2226846)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=278613843:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.20/1.13 % (2226849)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=139289626:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.20/1.13 % (2226851)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=416970938:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.20/1.13 % (2226848)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=185331193:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.20/1.13 % (2226847)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=3754628603:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.20/1.13 % (2226849)Refutation not found, incomplete strategy
% 0.20/1.13 % (2226849)------------------------------
% 0.20/1.13 % (2226849)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.13 % (2226849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.13 % (2226849)CaDiCaL version: 2.1.3
% 0.20/1.13 % (2226849)Termination reason: Refutation not found, incomplete strategy
% 0.20/1.13 % (2226849)Time elapsed: 0.002 s
% 0.20/1.13 % (2226849)Peak memory usage: 88 MB
% 0.20/1.13 % (2226849)Instructions burned: 2 (million)
% 0.20/1.13 % (2226851)Also succeeded, but the first one will report.
% 0.20/1.13 % (2226852)Instruction limit reached!
% 0.20/1.13 % (2226852)------------------------------
% 0.20/1.13 % (2226852)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.13 % (2226852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.13 % (2226852)CaDiCaL version: 2.1.3
% 0.20/1.13 % (2226852)Termination reason: Instruction limit
% 0.20/1.13 % (2226852)Termination phase: Saturation
% 0.20/1.13 % (2226852)Time elapsed: 0.074 s
% 0.20/1.13 % (2226852)Peak memory usage: 90 MB
% 0.20/1.13 % (2226852)Instructions burned: 130 (million)
% 0.20/1.13 % (2226850)Refutation found. Thanks to Tanya!
% 0.20/1.13 % SZS status Theorem for theBenchmark
% 0.20/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.13 % (2226850)------------------------------
% 0.20/1.13 % (2226850)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.13 % (2226850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.13 % (2226850)CaDiCaL version: 2.1.3
% 0.20/1.13 % (2226850)Termination reason: Refutation
% 0.20/1.13 % (2226850)Time elapsed: 0.002 s
% 0.20/1.13 % (2226850)Peak memory usage: 88 MB
% 0.20/1.13 % (2226850)Instructions burned: 5 (million)
% 0.20/1.13 % (2226850)------------------------------
% 0.20/1.13 % (2226850)------------------------------
% 0.20/1.13 % (2226720)Success in time 0.263 s
% 0.20/1.13 % Vampire exiting
%------------------------------------------------------------------------------