%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM240_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 09:39:51 AM UTC 2026
% Result : Theorem 2.74s 1.17s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 12 unt; 0 typ; 1 def)
% Number of atoms : 32 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 26 ( 11 ~; 0 |; 13 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 8 con; 0-3 aty)
% Number of variables : 7 ( 5 !; 2 ?; 7 :)
% 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,
sK1: vTy ).
tff(func_def_17,type,
sK2: vTerm > vTerm ).
tff(func_def_18,type,
sK3: vTerm > vTerm ).
tff(func_def_19,type,
sK4: vTerm > vTerm ).
tff(func_def_20,type,
sK5: vTerm > vTerm ).
tff(func_def_21,type,
sK6: vTerm > vTerm ).
tff(func_def_22,type,
sK7: vTerm > vTerm ).
tff(func_def_23,type,
sK8: vTerm > vTerm ).
tff(func_def_24,type,
sK9: vTerm > vTerm ).
tff(func_def_25,type,
sK10: vTerm > vTerm ).
tff(func_def_26,type,
sK11: vTerm > vTerm ).
tff(func_def_27,type,
sK12: vTerm > vTerm ).
tff(func_def_28,type,
sK13: vTerm > vTerm ).
tff(func_def_29,type,
sK14: vTerm > vTerm ).
tff(func_def_30,type,
sK15: vTerm > vTerm ).
tff(func_def_31,type,
sK16: vTerm > vTerm ).
tff(func_def_32,type,
sK17: vTerm > vTerm ).
tff(func_def_33,type,
sK18: vTerm > vTerm ).
tff(func_def_34,type,
sK19: vTerm > vTerm ).
tff(func_def_35,type,
sK20: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_36,type,
sK21: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_37,type,
sK22: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_38,type,
sK23: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_39,type,
sK24: vOptTerm > 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(pred_def_5,type,
sP0: ( vTerm * vTerm * vTerm ) > $o ).
tff(pred_def_6,type,
sP25: vTerm > $o ).
tff(pred_def_7,type,
sP26: vTerm > $o ).
tff(pred_def_8,type,
sP27: vTerm > $o ).
tff(pred_def_9,type,
sP28: vTerm > $o ).
tff(pred_def_10,type,
sP29: vTerm > $o ).
tff(pred_def_11,type,
sP30: vTerm > $o ).
tff(pred_def_12,type,
sP31: vOptTerm > $o ).
tff(pred_def_13,type,
sP32: vOptTerm > $o ).
tff(f37,axiom,
! [X0: vTerm] : ( vnoTerm != vsomeTerm(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-noTerm-someTerm') ).
tff(f65,axiom,
vreduce(vPred(vZero)) = vsomeTerm(vZero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reduce-6') ).
tff(f106,conjecture,
! [X0: vTy] :
( ( ( vt1 = vZero )
& vptchecksimple(vPred(vt1),X0)
& ~ visValue(vPred(vt1)) )
=> ( vreduce(vPred(vt1)) != vnoTerm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Progress-Pred-Zero') ).
tff(f107,negated_conjecture,
~ ! [X0: vTy] :
( ( ( vt1 = vZero )
& vptchecksimple(vPred(vt1),X0)
& ~ visValue(vPred(vt1)) )
=> ( vreduce(vPred(vt1)) != vnoTerm ) ),
inference(negated_conjecture,[status(cth)],[f106]) ).
tff(f109,plain,
? [X0: vTy] :
( ( vnoTerm = vreduce(vPred(vt1)) )
& ( vt1 = vZero )
& vptchecksimple(vPred(vt1),X0)
& ~ visValue(vPred(vt1)) ),
inference(ennf_transformation,[],[f107]) ).
tff(f110,plain,
? [X0: vTy] :
( ( vnoTerm = vreduce(vPred(vt1)) )
& ( vt1 = vZero )
& vptchecksimple(vPred(vt1),X0)
& ~ visValue(vPred(vt1)) ),
inference(flattening,[],[f109]) ).
tff(f139,plain,
( ( vnoTerm = vreduce(vPred(vt1)) )
& ( vt1 = vZero )
& vptchecksimple(vPred(vt1),sK1)
& ~ visValue(vPred(vt1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f110]) ).
tff(f153,plain,
vZero = vt1,
inference(cnf_transformation,[],[f139]) ).
tff(f154,plain,
vnoTerm = vreduce(vPred(vt1)),
inference(cnf_transformation,[],[f139]) ).
tff(f167,plain,
vreduce(vPred(vZero)) = vsomeTerm(vZero),
inference(cnf_transformation,[],[f65]) ).
tff(f188,plain,
! [X0: vTerm] : ( vnoTerm != vsomeTerm(X0) ),
inference(cnf_transformation,[],[f37]) ).
tff(f191,plain,
vreduce(vPred(vt1)) = vsomeTerm(vt1),
inference(definition_unfolding,[],[f167,f153,f153]) ).
tff(f209,definition,
~ sP31(vnoTerm),
introduced(definition,[new_symbols(definition,[sP31])],[inequality_splitting_name_introduction]) ).
tff(f210,plain,
! [X0: vTerm] : sP31(vsomeTerm(X0)),
inference(inequality_splitting,[],[f188,f209]) ).
tff(f213,plain,
sP31(vreduce(vPred(vt1))),
inference(superposition,[],[f210,f191]) ).
tff(f214,plain,
sP31(vnoTerm),
inference(forward_demodulation,[],[f213,f154]) ).
tff(f215,plain,
$false,
inference(forward_subsumption_resolution,[],[f214,f209]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM240_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 % Computer : n014.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Mon Sep 28 22:02:46 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running first-order theorem proving
% 0.07/0.24 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
% 2.74/1.17 % (2229579)Detected formulas, will run a generic FOF schedule.
% 2.74/1.17 % (2229587)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2572295815:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.74/1.17 % (2229587)First to succeed.
% 2.74/1.17 % (2229587)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2229579"
% 2.74/1.17 % (2229584)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=2607343227:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.74/1.17 % (2229590)dis-21_1_sil=8000:lcm=predicate:random_seed=1855262868: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)
% 2.74/1.17 % (2229588)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=575379604:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.74/1.17 % (2229586)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=112433471:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.74/1.17 % (2229585)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=2841950504:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.74/1.17 % (2229589)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3472748852:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.74/1.17 % (2229588)Also succeeded, but the first one will report.
% 2.74/1.17 % (2229589)Also succeeded, but the first one will report.
% 2.74/1.17 % (2229590)Instruction limit reached!
% 2.74/1.17 % (2229590)------------------------------
% 2.74/1.17 % (2229590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.17 % (2229590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.17 % (2229590)CaDiCaL version: 2.1.3
% 2.74/1.17 % (2229590)Termination reason: Instruction limit
% 2.74/1.17 % (2229590)Termination phase: Saturation
% 2.74/1.17 % (2229590)Time elapsed: 0.076 s
% 2.74/1.17 % (2229590)Peak memory usage: 90 MB
% 2.74/1.17 % (2229590)Instructions burned: 129 (million)
% 2.74/1.17 % (2229587)Refutation found. Thanks to Tanya!
% 2.74/1.17 % SZS status Theorem for theBenchmark
% 2.74/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.74/1.17 % (2229587)------------------------------
% 2.74/1.17 % (2229587)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.17 % (2229587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.17 % (2229587)CaDiCaL version: 2.1.3
% 2.74/1.17 % (2229587)Termination reason: Refutation
% 2.74/1.17 % (2229587)Time elapsed: 0.002 s
% 2.74/1.17 % (2229587)Peak memory usage: 89 MB
% 2.74/1.17 % (2229587)Instructions burned: 4 (million)
% 2.74/1.17 % (2229587)------------------------------
% 2.74/1.17 % (2229587)------------------------------
% 2.74/1.17 % (2229579)Success in time 0.299 s
% 2.74/1.17 % Vampire exiting
%------------------------------------------------------------------------------