%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL830-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 : Sun Sep 27 07:59:52 AM UTC 2026
% Result : Unsatisfiable 2.05s 0.75s
% Output : CNFRefutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 4 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-5 aty)
% Number of variables : 22 ( 3 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_ATP__Linkup_OCOMBC__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(c_COMBC(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4),VAR_5) = hAPP(hAPP(VAR_0,VAR_5),VAR_1),
file('theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
cnf(c_166,plain,
hAPP(c_COMBC(A,B,C,D,E),F) = hAPP(hAPP(A,F),B),
inference(clausify,[status(thm)],[cls_ATP__Linkup_OCOMBC__def_0]) ).
fof(cls_conjecture_0,axiom,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_180,plain,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_181,plain,
c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
fof(cls_map_Osimps_I2_J_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : c_List_Omap(VAR_0,c_List_Olist_OCons(VAR_1,VAR_2,VAR_3),VAR_3,VAR_4) = c_List_Olist_OCons(hAPP(VAR_0,VAR_1),c_List_Omap(VAR_0,VAR_2,VAR_3,VAR_4),VAR_4),
file('theBenchmark.p',cls_map_Osimps_I2_J_0) ).
cnf(c_185,plain,
c_List_Omap(A,c_List_Olist_OCons(B,C,D),D,E) = c_List_Olist_OCons(hAPP(A,B),c_List_Omap(A,C,D,E),E),
inference(clausify,[status(thm)],[cls_map_Osimps_I2_J_0]) ).
cnf(c_820,plain,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_a____),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
inference(paramod,[status(thm)],[c_185,c_180]) ).
cnf(c_821,plain,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_a____),v_i____),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
inference(paramod,[status(thm)],[c_166,c_820]) ).
cnf(c_822,plain,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
inference(paramod,[status(thm)],[c_166,c_821]) ).
cnf(c_819,plain,
$false,
inference(resolve,[status(thm)],[c_181,c_822]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL830-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n026.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 23:42:39 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 3750585 was started by sandbox2 on n026,
% 0.17/0.43 % Fri Sep 25 23:42:39 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 2.05/0.75
% 2.05/0.75 % SZS status Unsatisfiable for theBenchmark
% 2.05/0.75
% 2.05/0.75 % Proof 1 at 0.23 (+ 0.03) seconds.
% 2.05/0.75 % Length of proof is 5.
% 2.05/0.75 % Level of proof is 1.
% 2.05/0.75 % Maximum clause weight is 63.000.
% 2.05/0.75 % Given clauses 108.
% 2.05/0.75
% 2.05/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------