%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL794-1 : 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 : n011.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 11:56:37 AM UTC 2026
% Result : Unsatisfiable 3.64s 1.43s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 16 ( 10 unt; 0 def)
% Number of atoms : 23 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 13 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-5 aty)
% Number of variables : 29 ( 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f438,axiom,
! [X2,X3,X0,X1,X4,X5] : c_List_Ofoldr(X0,c_List_Olist_OCons(X1,X2,X3),X4,X3,X5) = hAPP(hAPP(X0,X1),c_List_Ofoldr(X0,X2,X4,X3,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
fof(f482,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uT_0) ).
fof(f484,axiom,
v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_T_0) ).
fof(f485,axiom,
! [X2,X3,X0,X1,X4] :
( c_Type_Otyping(c_Type_Oshift(X0,X1,X2,tc_Type_Otype),c_Lambda_Olift(X3,X1),X4)
| ~ c_Type_Otyping(X0,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__type_0) ).
fof(f489,axiom,
! [X2,X3,X0,X1,X4] :
( c_Type_Otyping(X0,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3)
| ~ c_Type_Otyping(X0,X2,X4)
| ~ c_Type_Otyping(X0,X1,hAPP(hAPP(c_Type_Otype_OFun,X4),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App_0) ).
fof(f494,axiom,
! [X2,X3,X0,X1] : hAPP(c_Type_Oshift(X0,X1,X2,X3),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__eq_0) ).
fof(f497,axiom,
! [X0,X1] : c_Type_Otyping(X0,c_Lambda_OdB_OVar(X1),hAPP(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
fof(f499,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))),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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f532,plain,
! [X2,X3,X0,X1] : c_Type_Otyping(c_Type_Oshift(X1,X2,X0,X3),c_Lambda_OdB_OVar(X2),X0),
inference(superposition,[],[f497,f494]) ).
fof(f927,plain,
v_T____ = c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype),
inference(superposition,[],[f438,f484]) ).
fof(f969,plain,
! [X0] :
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0)
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_Type_Otype_OFun,X0),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ),
inference(resolution,[],[f489,f499]) ).
fof(f976,plain,
! [X0] :
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(X0,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0) ),
inference(forward_demodulation,[],[f969,f438]) ).
fof(f977,plain,
! [X0] :
( ~ c_Type_Otyping(v_e____,v_u____,c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(X0,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0) ),
inference(resolution,[],[f976,f485]) ).
fof(f1436,plain,
( ~ c_Type_Otyping(v_e____,v_u____,v_T____)
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),v_T_H_H____) ),
inference(superposition,[],[f977,f927]) ).
fof(f1441,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),v_T_H_H____),
inference(forward_subsumption_resolution,[],[f1436,f482]) ).
fof(f1442,plain,
$false,
inference(forward_subsumption_resolution,[],[f1441,f532]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL794-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 % Computer : n011.cluster.edu
% 0.13/0.43 % Model : x86_64 x86_64
% 0.13/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.43 % Memory : 8046.5625MB
% 0.13/0.43 % OS : Linux 6.8.0-71-generic
% 0.13/0.43 % CPULimit : 300
% 0.13/0.43 % WCLimit : 300
% 0.13/0.43 % DateTime : Sun Sep 27 16:51:16 UTC 2026
% 0.13/0.43 % CPUTime :
% 0.13/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.49 Running first-order theorem proving
% 0.17/0.49 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
% 3.64/1.43 % (2616484)Input is clausal, will run a generic CNF schedule.
% 3.64/1.43 % (2616496)dis-21_1_sil=8000:lcm=predicate:random_seed=2725329915: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)
% 3.64/1.43 % (2616493)lrs+10_1_sil=8000:sp=occurrence:random_seed=3690852948:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.64/1.43 % (2616491)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=565933918:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.64/1.43 % (2616490)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=3015777589:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.64/1.43 % (2616495)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=396442968:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.64/1.43 % (2616494)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=476039850:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.64/1.43 % (2616492)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=775510079:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.64/1.43 % (2616496)Instruction limit reached!
% 3.64/1.43 % (2616496)------------------------------
% 3.64/1.43 % (2616496)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.43 % (2616496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.43 % (2616496)CaDiCaL version: 2.1.3
% 3.64/1.43 % (2616496)Termination reason: Instruction limit
% 3.64/1.43 % (2616496)Termination phase: Saturation
% 3.64/1.43 % (2616496)Time elapsed: 0.040 s
% 3.64/1.43 % (2616496)Peak memory usage: 89 MB
% 3.64/1.43 % (2616496)Instructions burned: 121 (million)
% 3.64/1.43 % (2616494)Instruction limit reached!
% 3.64/1.43 % (2616494)------------------------------
% 3.64/1.43 % (2616494)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.43 % (2616494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.43 % (2616494)CaDiCaL version: 2.1.3
% 3.64/1.43 % (2616494)Termination reason: Instruction limit
% 3.64/1.43 % (2616494)Termination phase: Saturation
% 3.64/1.43 % (2616494)Time elapsed: 0.049 s
% 3.64/1.43 % (2616494)Peak memory usage: 88 MB
% 3.64/1.43 % (2616494)Instructions burned: 115 (million)
% 3.64/1.43 % (2616495)First to succeed.
% 3.64/1.43 % (2616495)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2616484"
% 3.64/1.43 % (2616493)Instruction limit reached!
% 3.64/1.43 % (2616493)------------------------------
% 3.64/1.43 % (2616493)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.43 % (2616493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.43 % (2616493)CaDiCaL version: 2.1.3
% 3.64/1.43 % (2616493)Termination reason: Instruction limit
% 3.64/1.43 % (2616493)Termination phase: Saturation
% 3.64/1.43 % (2616493)Time elapsed: 0.071 s
% 3.64/1.43 % (2616493)Peak memory usage: 89 MB
% 3.64/1.43 % (2616493)Instructions burned: 108 (million)
% 3.64/1.43 % (2616505)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=512741607:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.64/1.43 % (2616505)Refutation not found, incomplete strategy
% 3.64/1.43 % (2616505)------------------------------
% 3.64/1.43 % (2616505)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.43 % (2616505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.43 % (2616505)CaDiCaL version: 2.1.3
% 3.64/1.43 % (2616505)Termination reason: Refutation not found, incomplete strategy
% 3.64/1.43 % (2616505)Time elapsed: 0.004 s
% 3.64/1.43 % (2616505)Peak memory usage: 88 MB
% 3.64/1.43 % (2616505)Instructions burned: 11 (million)
% 3.64/1.43 % (2616506)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=13255346:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2998 on theBenchmark for (2998ds/189Mi)
% 3.64/1.43 % (2616506)Also succeeded, but the first one will report.
% 3.64/1.43 % (2616507)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=557701600:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.64/1.43 % (2616495)Refutation found. Thanks to Tanya!
% 3.64/1.43 % SZS status Unsatisfiable for theBenchmark
% 3.64/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 3.64/1.43 % (2616495)------------------------------
% 3.64/1.43 % (2616495)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.43 % (2616495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.43 % (2616495)CaDiCaL version: 2.1.3
% 3.64/1.43 % (2616495)Termination reason: Refutation
% 3.64/1.43 % (2616495)Time elapsed: 0.053 s
% 3.64/1.43 % (2616495)Peak memory usage: 89 MB
% 3.64/1.43 % (2616495)Instructions burned: 75 (million)
% 3.64/1.43 % (2616495)------------------------------
% 3.64/1.43 % (2616495)------------------------------
% 3.64/1.43 % (2616484)Success in time 0.448 s
% 3.64/1.43 % Vampire exiting
%------------------------------------------------------------------------------