%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW343+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 01:30:09 PM UTC 2026
% Result : Theorem 3.45s 1.08s
% Output : Refutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 11 unt; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 13 ~; 8 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 20 ( 20 usr; 16 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2,X3] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X3),X2,hAPP(c_Nat_OSuc,X1),X0)
<=> c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X3)),X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I9_J) ).
fof(f5206,axiom,
! [X0,X1] :
( v_P(X0,X1)
=> ! [X2] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),X1,hAPP(c_Nat_OSuc,v_na),X2)
=> v_Q(X0,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X2),hAPP(c_Natural_Ogetlocs,v_s_H))),v_X),hAPP(hAPP(c_Natural_Ogetlocs,X2),c_Com_ORes))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f5207,axiom,
v_P(v_Z,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s_H),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),v_a(v_s_H))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
fof(f5208,axiom,
c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s_H),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),v_a(v_s_H)),v_na,v_s1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
fof(f5209,conjecture,
v_Q(v_Z,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s1),hAPP(c_Natural_Ogetlocs,v_s_H))),v_X),hAPP(hAPP(c_Natural_Ogetlocs,v_s1),c_Com_ORes))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
fof(f5210,negated_conjecture,
~ v_Q(v_Z,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s1),hAPP(c_Natural_Ogetlocs,v_s_H))),v_X),hAPP(hAPP(c_Natural_Ogetlocs,v_s1),c_Com_ORes))),
inference(negated_conjecture,[status(cth)],[f5209]) ).
fof(f5211,plain,
~ v_Q(v_Z,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s1),hAPP(c_Natural_Ogetlocs,v_s_H))),v_X),hAPP(hAPP(c_Natural_Ogetlocs,v_s1),c_Com_ORes))),
inference(flattening,[],[f5210]) ).
fof(f5214,plain,
! [X0,X1] :
( ! [X2] :
( v_Q(X0,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X2),hAPP(c_Natural_Ogetlocs,v_s_H))),v_X),hAPP(hAPP(c_Natural_Ogetlocs,X2),c_Com_ORes)))
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),X1,hAPP(c_Nat_OSuc,v_na),X2) )
| ~ v_P(X0,X1) ),
inference(ennf_transformation,[],[f5206]) ).
fof(f5359,plain,
! [X0,X1,X2,X3] :
( ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X3),X2,hAPP(c_Nat_OSuc,X1),X0)
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X3)),X2,X1,X0) )
& ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X3)),X2,X1,X0)
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X3),X2,hAPP(c_Nat_OSuc,X1),X0) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f5365,plain,
! [X2,X0,X1] :
( v_Q(X0,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X2),hAPP(c_Natural_Ogetlocs,v_s_H))),v_X),hAPP(hAPP(c_Natural_Ogetlocs,X2),c_Com_ORes)))
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),X1,hAPP(c_Nat_OSuc,v_na),X2)
| ~ v_P(X0,X1) ),
inference(cnf_transformation,[],[f5214]) ).
fof(f5366,plain,
v_P(v_Z,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s_H),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),v_a(v_s_H))),
inference(cnf_transformation,[],[f5207]) ).
fof(f5367,plain,
c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s_H),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),v_a(v_s_H)),v_na,v_s1),
inference(cnf_transformation,[],[f5208]) ).
fof(f5368,plain,
~ v_Q(v_Z,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s1),hAPP(c_Natural_Ogetlocs,v_s_H))),v_X),hAPP(hAPP(c_Natural_Ogetlocs,v_s1),c_Com_ORes))),
inference(cnf_transformation,[],[f5211]) ).
fof(f5560,plain,
! [X2,X3,X0,X1] :
( ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X3)),X2,X1,X0)
| c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X3),X2,hAPP(c_Nat_OSuc,X1),X0) ),
inference(cnf_transformation,[],[f5359]) ).
fof(f5650,plain,
c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s_H),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),v_a(v_s_H)),hAPP(c_Nat_OSuc,v_na),v_s1),
inference(resolution,[],[f5367,f5560]) ).
fof(f5651,plain,
! [X0] :
( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),X0,hAPP(c_Nat_OSuc,v_na),v_s1)
| ~ v_P(v_Z,X0) ),
inference(resolution,[],[f5365,f5368]) ).
fof(f5664,plain,
~ v_P(v_Z,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s_H),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),v_a(v_s_H))),
inference(resolution,[],[f5650,f5651]) ).
fof(f5665,plain,
$false,
inference(forward_subsumption_resolution,[],[f5664,f5366]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW343+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n010.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 13:39:19 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 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
% 3.45/1.08 % (1927977)Detected formulas, will run a generic FOF schedule.
% 3.45/1.08 % (1927985)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1788916791:i=109:sd=1:ins=1:gsp=on:ss=axioms_2998 on theBenchmark for (2998ds/109Mi)
% 3.45/1.08 % (1927988)dis-21_1_sil=8000:lcm=predicate:random_seed=1008351755:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2998 on theBenchmark for (2998ds/129Mi)
% 3.45/1.08 % (1927983)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=4013196343:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2998 on theBenchmark for (2998ds/134677Mi)
% 3.45/1.08 % (1927984)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=112791456:i=141695:sd=1:nm=32:gsp=on:ss=included_2998 on theBenchmark for (2998ds/141695Mi)
% 3.45/1.08 % (1927982)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=2545536716:i=141193_2998 on theBenchmark for (2998ds/141193Mi)
% 3.45/1.08 % (1927987)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1089266627:s2a=on:i=139:gtg=position_2998 on theBenchmark for (2998ds/139Mi)
% 3.45/1.08 % (1927986)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3577203501:i=119:av=off:ss=axioms_2998 on theBenchmark for (2998ds/119Mi)
% 3.45/1.08 % (1927985)First to succeed.
% 3.45/1.08 % (1927985)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1927977"
% 3.45/1.08 % (1927987)Instruction limit reached!
% 3.45/1.08 % (1927987)------------------------------
% 3.45/1.08 % (1927987)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.08 % (1927987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.08 % (1927987)CaDiCaL version: 2.1.3
% 3.45/1.08 % (1927987)Termination reason: Instruction limit
% 3.45/1.08 % (1927987)Termination phase: SInE selection
% 3.45/1.08 % (1927987)Time elapsed: 0.056 s
% 3.45/1.08 % (1927987)Peak memory usage: 90 MB
% 3.45/1.08 % (1927987)Instructions burned: 140 (million)
% 3.45/1.08 % (1927986)Instruction limit reached!
% 3.45/1.08 % (1927986)------------------------------
% 3.45/1.08 % (1927986)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.08 % (1927986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.08 % (1927986)CaDiCaL version: 2.1.3
% 3.45/1.08 % (1927986)Termination reason: Instruction limit
% 3.45/1.08 % (1927986)Termination phase: Property scanning
% 3.45/1.08 % (1927986)Time elapsed: 0.070 s
% 3.45/1.08 % (1927986)Peak memory usage: 93 MB
% 3.45/1.08 % (1927986)Instructions burned: 119 (million)
% 3.45/1.08 % (1927988)Instruction limit reached!
% 3.45/1.08 % (1927988)------------------------------
% 3.45/1.08 % (1927988)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.08 % (1927988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.08 % (1927988)CaDiCaL version: 2.1.3
% 3.45/1.08 % (1927988)Termination reason: Instruction limit
% 3.45/1.08 % (1927988)Termination phase: Preprocessing 3
% 3.45/1.08 % (1927988)Time elapsed: 0.080 s
% 3.45/1.08 % (1927988)Peak memory usage: 93 MB
% 3.45/1.08 % (1927988)Instructions burned: 129 (million)
% 3.45/1.08 % (1927996)lrs+10_1_sil=8000:sp=occurrence:random_seed=3412059846:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 3.45/1.08 % (1927997)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3538201467:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 3.45/1.08 % (1927998)lrs+1011_1_sil=32000:sp=occurrence:random_seed=619877964:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 3.45/1.08 % (1927997)Instruction limit reached!
% 3.45/1.08 % (1927997)------------------------------
% 3.45/1.08 % (1927997)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.08 % (1927997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.08 % (1927997)CaDiCaL version: 2.1.3
% 3.45/1.08 % (1927997)Termination reason: Instruction limit
% 3.45/1.08 % (1927997)Termination phase: Saturation
% 3.45/1.08 % (1927997)Time elapsed: 0.069 s
% 3.45/1.08 % (1927997)Peak memory usage: 92 MB
% 3.45/1.08 % (1927997)Instructions burned: 157 (million)
% 3.45/1.08 % (1927985)Refutation found. Thanks to Tanya!
% 3.45/1.08 % SZS status Theorem for theBenchmark
% 3.45/1.08 % SZS output start Proof for theBenchmark
% See solution above
% 3.45/1.08 % (1927985)------------------------------
% 3.45/1.08 % (1927985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.08 % (1927985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.08 % (1927985)CaDiCaL version: 2.1.3
% 3.45/1.08 % (1927985)Termination reason: Refutation
% 3.45/1.08 % (1927985)Time elapsed: 0.040 s
% 3.45/1.08 % (1927985)Peak memory usage: 95 MB
% 3.45/1.08 % (1927985)Instructions burned: 60 (million)
% 3.45/1.08 % (1927985)------------------------------
% 3.45/1.08 % (1927985)------------------------------
% 3.45/1.08 % (1927977)Success in time 0.59 s
% 3.45/1.08 % Vampire exiting
%------------------------------------------------------------------------------