%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL759-1 : TPTP v9.3.1. Released v4.1.0.
% 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 11:56:29 AM UTC 2026
% Result : Unsatisfiable 4.19s 1.66s
% Output : Refutation 4.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 10 ( 7 unt; 0 def)
% Number of atoms : 15 ( 1 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 10 con; 0-5 aty)
% Number of variables : 14 ( 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f701,axiom,
! [X0,X1] : c_Lambda_Osubstn(X0,X1,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X1),c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn__subst__0_0) ).
fof(f755,axiom,
! [X2,X0,X1] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X1),c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Beta_0) ).
fof(f771,negated_conjecture,
! [X0,X1] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X0))),c_Suc(X1))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X0),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X1,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f773,negated_conjecture,
! [X0,X1] : hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f774,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f1052,plain,
! [X0,X1] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X0))),c_Suc(X1)),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X0),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X1,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(superposition,[],[f771,f701]) ).
fof(f2176,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X0,X1,c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(forward_demodulation,[],[f755,f701]) ).
fof(f2177,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja)),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja))) ),
inference(resolution,[],[f2176,f774]) ).
fof(f2183,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja))),
inference(forward_subsumption_resolution,[],[f2177,f1052]) ).
fof(f2184,plain,
$false,
inference(forward_subsumption_resolution,[],[f2183,f773]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL759-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n014.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 16:44:32 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 4.19/1.66 % (1003237)Input is clausal, will run a generic CNF schedule.
% 4.19/1.66 % (1003271)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=342255073:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.19/1.66 % (1003279)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3638080674:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.19/1.66 % (1003275)lrs+10_1_sil=8000:sp=occurrence:random_seed=1785190782:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.19/1.66 % (1003277)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=102483152:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.19/1.66 % (1003272)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=739285502:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.19/1.66 % (1003274)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=164868249:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.19/1.66 % (1003280)dis-21_1_sil=8000:lcm=predicate:random_seed=3482327247:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 4.19/1.66 % (1003280)Instruction limit reached!
% 4.19/1.66 % (1003280)------------------------------
% 4.19/1.66 % (1003280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.66 % (1003280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.66 % (1003280)CaDiCaL version: 2.1.3
% 4.19/1.66 % (1003280)Termination reason: Instruction limit
% 4.19/1.66 % (1003280)Termination phase: Saturation
% 4.19/1.66 % (1003280)Time elapsed: 0.065 s
% 4.19/1.66 % (1003280)Peak memory usage: 89 MB
% 4.19/1.66 % (1003280)Instructions burned: 118 (million)
% 4.19/1.66 % (1003275)Instruction limit reached!
% 4.19/1.66 % (1003275)------------------------------
% 4.19/1.66 % (1003275)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.66 % (1003275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.66 % (1003275)CaDiCaL version: 2.1.3
% 4.19/1.66 % (1003275)Termination reason: Instruction limit
% 4.19/1.66 % (1003275)Termination phase: Saturation
% 4.19/1.66 % (1003275)Time elapsed: 0.066 s
% 4.19/1.66 % (1003275)Peak memory usage: 89 MB
% 4.19/1.66 % (1003275)Instructions burned: 108 (million)
% 4.19/1.66 % (1003277)Instruction limit reached!
% 4.19/1.66 % (1003277)------------------------------
% 4.19/1.66 % (1003277)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.66 % (1003277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.66 % (1003277)CaDiCaL version: 2.1.3
% 4.19/1.66 % (1003277)Termination reason: Instruction limit
% 4.19/1.66 % (1003277)Termination phase: Saturation
% 4.19/1.66 % (1003277)Time elapsed: 0.072 s
% 4.19/1.66 % (1003277)Peak memory usage: 89 MB
% 4.19/1.66 % (1003277)Instructions burned: 114 (million)
% 4.19/1.66 % (1003279)First to succeed.
% 4.19/1.66 % (1003279)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1003237"
% 4.19/1.66 % (1003358)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1032999986:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.19/1.66 % (1003360)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=577587685:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 4.19/1.66 % (1003361)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=4132976060:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.19/1.66 % (1003358)Also succeeded, but the first one will report.
% 4.19/1.66 % (1003360)Also succeeded, but the first one will report.
% 4.19/1.66 % (1003361)Instruction limit reached!
% 4.19/1.66 % (1003361)------------------------------
% 4.19/1.66 % (1003361)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.66 % (1003361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.66 % (1003361)CaDiCaL version: 2.1.3
% 4.19/1.66 % (1003361)Termination reason: Instruction limit
% 4.19/1.66 % (1003361)Termination phase: Saturation
% 4.19/1.66 % (1003361)Time elapsed: 0.124 s
% 4.19/1.66 % (1003361)Peak memory usage: 90 MB
% 4.19/1.66 % (1003361)Instructions burned: 220 (million)
% 4.19/1.66 % (1003279)Refutation found. Thanks to Tanya!
% 4.19/1.66 % SZS status Unsatisfiable for theBenchmark
% 4.19/1.66 % SZS output start Proof for theBenchmark
% See solution above
% 4.19/1.66 % (1003279)------------------------------
% 4.19/1.66 % (1003279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.66 % (1003279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.66 % (1003279)CaDiCaL version: 2.1.3
% 4.19/1.66 % (1003279)Termination reason: Refutation
% 4.19/1.66 % (1003279)Time elapsed: 0.093 s
% 4.19/1.66 % (1003279)Peak memory usage: 90 MB
% 4.19/1.66 % (1003279)Instructions burned: 155 (million)
% 4.19/1.66 % (1003279)------------------------------
% 4.19/1.66 % (1003279)------------------------------
% 4.19/1.66 % (1003237)Success in time 0.511 s
% 4.19/1.66 % Vampire exiting
%------------------------------------------------------------------------------