%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL763-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 : Fri Sep 25 02:02:53 PM UTC 2026
% Result : Unsatisfiable 40.90s 5.79s
% Output : Proof 40.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 15 unt; 0 def)
% Number of atoms : 23 ( 4 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 9 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-5 aty)
% Number of variables : 33 ( 9 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f385,axiom,
( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
fof(f385_nnf,plain,
! [V_n,V_rs] :
( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(nnf_transformation,[status(thm)],[f385]) ).
fof(f385_sk,plain,
! [V_n,V_rs] :
( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(skolemisation,[status(esa)],[f385_nnf]) ).
cnf(c385,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0),X1,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(cnf_transformation,[status(esa)],[f385_sk]) ).
cnf(f197,axiom,
c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
fof(f197_nnf,plain,
! [V_A,T_a] : c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a),
inference(nnf_transformation,[status(thm)],[f197]) ).
fof(f197_sk,plain,
! [V_A,T_a] : c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a),
inference(skolemisation,[status(esa)],[f197_nnf]) ).
cnf(c197,plain,
c_List_Olistsp(X0,c_List_Olist_ONil(X1),X1),
inference(cnf_transformation,[status(esa)],[f197_sk]) ).
cnf(p1143,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X0))),
inference(resolution,[status(thm)],[c385,c197]) ).
cnf(f395,axiom,
c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
fof(f395_nnf,plain,
! [V_f,V_a,T_b,T_a] : c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a,
inference(nnf_transformation,[status(thm)],[f395]) ).
fof(f395_sk,plain,
! [V_f,V_a,T_b,T_a] : c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a,
inference(skolemisation,[status(esa)],[f395_nnf]) ).
cnf(c395,plain,
c_List_Ofoldl(X0,X1,c_List_Olist_ONil(X2),X3,X2) = X1,
inference(cnf_transformation,[status(esa)],[f395_sk]) ).
cnf(f400,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f400_nnf,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(nnf_transformation,[status(thm)],[f400]) ).
fof(f400_sk,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(skolemisation,[status(esa)],[f400_nnf]) ).
cnf(c400,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(cnf_transformation,[status(esa)],[f400_sk]) ).
cnf(p469,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_n))),
inference(superposition,[status(thm)],[c395,c400]) ).
cnf(p1145,plain,
$false,
inference(resolution,[status(thm)],[p1143,p469]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL763-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.37 % Computer : n005.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Thu Sep 24 00:26:33 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 40.90/5.79 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 40.90/5.79 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------