%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL816-1 : 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 : n007.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 11:56:43 AM UTC 2026
% Result : Unsatisfiable 5.14s 1.51s
% Output : Refutation 5.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 5
% Syntax : Number of formulae : 10 ( 8 unt; 0 def)
% Number of atoms : 14 ( 1 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 13 con; 0-5 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f541,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(f554,axiom,
! [X2,X3,X0,X1,X4] :
( c_Type_Otyping(X0,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| ~ c_Type_Otypings(X0,X2,X4)
| ~ c_Type_Otyping(X0,X1,c_List_Ofoldr(c_Type_Otype_OFun,X4,X3,tc_Type_Otype,tc_Type_Otype)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).
fof(f586,axiom,
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_CHAINED_0) ).
fof(f587,axiom,
c_Type_Otyping(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_Lambda_OdB_OVar(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)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f588,negated_conjecture,
~ c_Type_Otyping(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_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),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),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f620,plain,
~ c_Type_Otyping(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_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),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),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(definition_unfolding,[],[f588,f541]) ).
fof(f621,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(definition_unfolding,[],[f586,f541]) ).
fof(f624,plain,
c_Type_Otyping(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_Lambda_OdB_OVar(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)),
inference(definition_unfolding,[],[f587,f541,f541]) ).
fof(f628,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Type_Otyping(X0,X1,c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),X3,c_List_Orev(X4,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otypings(X0,X2,X4)
| c_Type_Otyping(X0,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
inference(definition_unfolding,[],[f554,f541]) ).
fof(f646,plain,
$false,
inference(unit_resulting_resolution,[],[f628,f624,f621,f620]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL816-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n007.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 16:52:55 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 5.14/1.51 % (1646709)Input is clausal, will run a generic CNF schedule.
% 5.14/1.51 % (1646719)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1618216739:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.14/1.51 % (1646714)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=2158542397:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.14/1.51 % (1646720)dis-21_1_sil=8000:lcm=predicate:random_seed=135850436: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)
% 5.14/1.51 % (1646716)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=308455741:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.14/1.51 % (1646717)lrs+10_1_sil=8000:sp=occurrence:random_seed=2380501023:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.14/1.51 % (1646715)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1383304733:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.14/1.51 % (1646718)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1996770290:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.14/1.51 % (1646719)Instruction limit reached!
% 5.14/1.51 % (1646719)------------------------------
% 5.14/1.51 % (1646719)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.14/1.51 % (1646719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.14/1.51 % (1646719)CaDiCaL version: 2.1.3
% 5.14/1.51 % (1646719)Termination reason: Instruction limit
% 5.14/1.51 % (1646719)Termination phase: Saturation
% 5.14/1.51 % (1646719)Time elapsed: 0.064 s
% 5.14/1.51 % (1646719)Peak memory usage: 90 MB
% 5.14/1.51 % (1646719)Instructions burned: 183 (million)
% 5.14/1.51 % (1646717)Instruction limit reached!
% 5.14/1.51 % (1646717)------------------------------
% 5.14/1.51 % (1646717)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.14/1.51 % (1646717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.14/1.51 % (1646717)CaDiCaL version: 2.1.3
% 5.14/1.51 % (1646717)Termination reason: Instruction limit
% 5.14/1.51 % (1646717)Termination phase: Saturation
% 5.14/1.51 % (1646717)Time elapsed: 0.065 s
% 5.14/1.51 % (1646717)Peak memory usage: 88 MB
% 5.14/1.51 % (1646717)Instructions burned: 107 (million)
% 5.14/1.51 % (1646720)Instruction limit reached!
% 5.14/1.51 % (1646720)------------------------------
% 5.14/1.51 % (1646720)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.14/1.51 % (1646720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.14/1.51 % (1646720)CaDiCaL version: 2.1.3
% 5.14/1.51 % (1646720)Termination reason: Instruction limit
% 5.14/1.51 % (1646720)Termination phase: Saturation
% 5.14/1.51 % (1646720)Time elapsed: 0.068 s
% 5.14/1.51 % (1646720)Peak memory usage: 89 MB
% 5.14/1.51 % (1646720)Instructions burned: 117 (million)
% 5.14/1.51 % (1646718)Instruction limit reached!
% 5.14/1.51 % (1646718)------------------------------
% 5.14/1.51 % (1646718)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.14/1.51 % (1646718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.14/1.51 % (1646718)CaDiCaL version: 2.1.3
% 5.14/1.51 % (1646718)Termination reason: Instruction limit
% 5.14/1.51 % (1646718)Termination phase: Saturation
% 5.14/1.51 % (1646718)Time elapsed: 0.071 s
% 5.14/1.51 % (1646718)Peak memory usage: 89 MB
% 5.14/1.51 % (1646718)Instructions burned: 115 (million)
% 5.14/1.51 % (1646728)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=2469841998:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.14/1.51 % (1646728)Refutation not found, incomplete strategy
% 5.14/1.51 % (1646728)------------------------------
% 5.14/1.51 % (1646728)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.14/1.51 % (1646728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.14/1.51 % (1646728)CaDiCaL version: 2.1.3
% 5.14/1.51 % (1646728)Termination reason: Refutation not found, incomplete strategy
% 5.14/1.51 % (1646728)Time elapsed: 0.006 s
% 5.14/1.51 % (1646728)Peak memory usage: 88 MB
% 5.14/1.51 % (1646728)Instructions burned: 17 (million)
% 5.14/1.51 % (1646731)lrs+10_64_to=lpo:sil=8000:random_seed=3404345558:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 5.14/1.51 % (1646730)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2914665832:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.14/1.51 % (1646729)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2528740426: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)
% 5.14/1.51 % (1646729)First to succeed.
% 5.14/1.51 % (1646729)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1646709"
% 5.14/1.51 % (1646731)Instruction limit reached!
% 5.14/1.51 % (1646731)------------------------------
% 5.14/1.51 % (1646731)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.14/1.51 % (1646731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.14/1.51 % (1646731)CaDiCaL version: 2.1.3
% 5.14/1.51 % (1646731)Termination reason: Instruction limit
% 5.14/1.51 % (1646731)Termination phase: Saturation
% 5.14/1.51 % (1646731)Time elapsed: 0.077 s
% 5.14/1.51 % (1646731)Peak memory usage: 88 MB
% 5.14/1.51 % (1646731)Instructions burned: 127 (million)
% 5.14/1.51 % (1646728)------------------------------
% 5.14/1.51 % (1646728)------------------------------
% 5.14/1.51 % (1646730)Instruction limit reached!
% 5.14/1.51 % (1646730)------------------------------
% 5.14/1.51 % (1646730)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.14/1.51 % (1646730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.14/1.51 % (1646730)CaDiCaL version: 2.1.3
% 5.14/1.51 % (1646730)Termination reason: Instruction limit
% 5.14/1.51 % (1646730)Termination phase: Saturation
% 5.14/1.51 % (1646730)Time elapsed: 0.114 s
% 5.14/1.51 % (1646730)Peak memory usage: 89 MB
% 5.14/1.51 % (1646730)Instructions burned: 223 (million)
% 5.14/1.51 % (1646737)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=4007299936:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 5.14/1.51 % (1646736)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1511378044:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 5.14/1.51 % (1646738)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=1042423571:i=3394:sd=4:ss=included:sgt=64_2994 on theBenchmark for (2994ds/3394Mi)
% 5.14/1.51 % (1646729)Refutation found. Thanks to Tanya!
% 5.14/1.51 % SZS status Unsatisfiable for theBenchmark
% 5.14/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 5.14/1.51 % (1646729)------------------------------
% 5.14/1.51 % (1646729)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.14/1.51 % (1646729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.14/1.51 % (1646729)CaDiCaL version: 2.1.3
% 5.14/1.51 % (1646729)Termination reason: Refutation
% 5.14/1.51 % (1646729)Time elapsed: 0.022 s
% 5.14/1.51 % (1646729)Peak memory usage: 89 MB
% 5.14/1.51 % (1646729)Instructions burned: 38 (million)
% 5.14/1.51 % (1646729)------------------------------
% 5.14/1.51 % (1646729)------------------------------
% 5.14/1.51 % (1646709)Success in time 0.668 s
% 5.14/1.51 % Vampire exiting
%------------------------------------------------------------------------------