%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL815-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 11:56:42 AM UTC 2026
% Result : Unsatisfiable 5.36s 1.78s
% Output : Refutation 5.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 7 ( 6 unt; 0 def)
% Number of atoms : 8 ( 1 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 4 ~; 1 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 12 con; 0-5 aty)
% Number of variables : 10 ( 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f907,axiom,
! [X2,X3,X0,X1,X4] : c_List_Ofoldr(X0,X1,X2,X3,X4) = c_List_Ofoldl(c_COMBC(X0,X3,X4,X4),X2,c_List_Orev(X1,X3),X4,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__foldl_0) ).
fof(f962,axiom,
! [X2,X3,X0,X1,X4] :
( c_Type_Otypings(c_Type_Oshift(X0,X1,X2,tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otypings(X0,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__types_0) ).
fof(f964,axiom,
c_Type_Otypings(v_e____,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f965,negated_conjecture,
~ c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f998,plain,
~ c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(v_Ts____,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
inference(forward_demodulation,[],[f965,f907]) ).
fof(f999,plain,
~ c_Type_Otypings(v_e____,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
inference(resolution,[],[f998,f962]) ).
fof(f1000,plain,
$false,
inference(forward_subsumption_resolution,[],[f999,f964]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL815-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n008.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 16:55:24 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 5.36/1.78 % (1450938)Input is clausal, will run a generic CNF schedule.
% 5.36/1.78 % (1450943)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=1092657526:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.36/1.78 % (1450948)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=920511945:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.36/1.78 % (1450947)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3170661320:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.36/1.78 % (1450944)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3942065773:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.36/1.78 % (1450945)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3456914456:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.36/1.78 % (1450946)lrs+10_1_sil=8000:sp=occurrence:random_seed=2195638460:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.36/1.78 % (1450949)dis-21_1_sil=8000:lcm=predicate:random_seed=1338674547: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)
% 5.36/1.78 % (1450949)Instruction limit reached!
% 5.36/1.78 % (1450949)------------------------------
% 5.36/1.78 % (1450949)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/1.78 % (1450949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.78 % (1450949)CaDiCaL version: 2.1.3
% 5.36/1.78 % (1450949)Termination reason: Instruction limit
% 5.36/1.78 % (1450949)Termination phase: Saturation
% 5.36/1.78 % (1450949)Time elapsed: 0.065 s
% 5.36/1.78 % (1450949)Peak memory usage: 89 MB
% 5.36/1.78 % (1450949)Instructions burned: 117 (million)
% 5.36/1.78 % (1450946)Instruction limit reached!
% 5.36/1.78 % (1450946)------------------------------
% 5.36/1.78 % (1450946)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/1.78 % (1450946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.78 % (1450946)CaDiCaL version: 2.1.3
% 5.36/1.78 % (1450946)Termination reason: Instruction limit
% 5.36/1.78 % (1450946)Termination phase: Saturation
% 5.36/1.78 % (1450946)Time elapsed: 0.067 s
% 5.36/1.78 % (1450946)Peak memory usage: 88 MB
% 5.36/1.78 % (1450946)Instructions burned: 108 (million)
% 5.36/1.78 % (1450947)Instruction limit reached!
% 5.36/1.78 % (1450947)------------------------------
% 5.36/1.78 % (1450947)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/1.78 % (1450947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.78 % (1450947)CaDiCaL version: 2.1.3
% 5.36/1.78 % (1450947)Termination reason: Instruction limit
% 5.36/1.78 % (1450947)Termination phase: Saturation
% 5.36/1.78 % (1450947)Time elapsed: 0.072 s
% 5.36/1.78 % (1450947)Peak memory usage: 89 MB
% 5.36/1.78 % (1450947)Instructions burned: 115 (million)
% 5.36/1.78 % (1450948)Instruction limit reached!
% 5.36/1.78 % (1450948)------------------------------
% 5.36/1.78 % (1450948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/1.78 % (1450948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.78 % (1450948)CaDiCaL version: 2.1.3
% 5.36/1.78 % (1450948)Termination reason: Instruction limit
% 5.36/1.78 % (1450948)Termination phase: Saturation
% 5.36/1.78 % (1450948)Time elapsed: 0.120 s
% 5.36/1.78 % (1450948)Peak memory usage: 90 MB
% 5.36/1.78 % (1450948)Instructions burned: 181 (million)
% 5.36/1.78 % (1450957)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=3169328553:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.36/1.78 % (1450958)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3511546443: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)
% 5.36/1.78 % (1450959)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=921759446:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.36/1.78 % (1450957)Refutation not found, incomplete strategy
% 5.36/1.78 % (1450957)------------------------------
% 5.36/1.78 % (1450957)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/1.78 % (1450957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.78 % (1450957)CaDiCaL version: 2.1.3
% 5.36/1.78 % (1450957)Termination reason: Refutation not found, incomplete strategy
% 5.36/1.78 % (1450957)Time elapsed: 0.015 s
% 5.36/1.78 % (1450957)Peak memory usage: 88 MB
% 5.36/1.78 % (1450957)Instructions burned: 22 (million)
% 5.36/1.78 % (1450959)First to succeed.
% 5.36/1.78 % (1450959)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1450938"
% 5.36/1.78 % (1450958)Also succeeded, but the first one will report.
% 5.36/1.78 % (1450960)lrs+10_64_to=lpo:sil=8000:random_seed=1597666517:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 5.36/1.78 % (1450960)Instruction limit reached!
% 5.36/1.78 % (1450960)------------------------------
% 5.36/1.78 % (1450960)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/1.78 % (1450960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.78 % (1450960)CaDiCaL version: 2.1.3
% 5.36/1.78 % (1450960)Termination reason: Instruction limit
% 5.36/1.78 % (1450960)Termination phase: Saturation
% 5.36/1.78 % (1450960)Time elapsed: 0.083 s
% 5.36/1.78 % (1450960)Peak memory usage: 90 MB
% 5.36/1.78 % (1450960)Instructions burned: 127 (million)
% 5.36/1.78 % (1450943)Also succeeded, but the first one will report.
% 5.36/1.78 % (1450957)------------------------------
% 5.36/1.78 % (1450957)------------------------------
% 5.36/1.78 % (1450959)Refutation found. Thanks to Tanya!
% 5.36/1.78 % SZS status Unsatisfiable for theBenchmark
% 5.36/1.78 % SZS output start Proof for theBenchmark
% See solution above
% 5.36/1.78 % (1450959)------------------------------
% 5.36/1.78 % (1450959)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/1.78 % (1450959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.78 % (1450959)CaDiCaL version: 2.1.3
% 5.36/1.78 % (1450959)Termination reason: Refutation
% 5.36/1.78 % (1450959)Time elapsed: 0.020 s
% 5.36/1.78 % (1450959)Peak memory usage: 89 MB
% 5.36/1.78 % (1450959)Instructions burned: 32 (million)
% 5.36/1.78 % (1450959)------------------------------
% 5.36/1.78 % (1450959)------------------------------
% 5.36/1.78 % (1450938)Success in time 0.709 s
% 5.36/1.78 % Vampire exiting
%------------------------------------------------------------------------------