%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL777-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n014.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 02:08:21 PM UTC 2026
% Result : Unsatisfiable 3.73s 1.27s
% Output : CNFRefutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 13 unt; 0 def)
% Number of atoms : 19 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-5 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f392,axiom,
! [X2,X0,X1] : c_List_Orotate1(c_List_Olist_OCons(X0,X1,X2),X2) = c_List_Oappend(X1,c_List_Olist_OCons(X0,c_List_Olist_ONil(X2),X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_1) ).
fof(f417,axiom,
! [X2,X0,X1] :
( hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,X2,c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_3) ).
fof(f418,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,X2,c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| c_List_Olist_ONil(tc_Lambda_OdB) = c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(reorient_equations,[],[f417]) ).
fof(f427,axiom,
! [X2,X0,X1] : hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2) = c_List_Ofoldl(c_Lambda_OdB_OApp,X0,c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__last_0) ).
fof(f492,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f495,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
tcf(c_723,plain,
! [X0: $i,X1: $i,X2: $i] : c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2) = c_List_Orotate1(c_List_Olist_OCons(X1,X0,X2),X2),
inference(cnf_transformation,[],[f392]) ).
tcf(c_741,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) = c_List_Olist_ONil(tc_Lambda_OdB) )
| ( c_List_Ofoldl(c_Lambda_OdB_OApp,X0,c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2) ) ),
inference(cnf_transformation,[],[f418]) ).
tcf(c_748,plain,
! [X0: $i,X1: $i,X2: $i] : c_List_Ofoldl(c_Lambda_OdB_OApp,X0,c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2),
inference(cnf_transformation,[],[f427]) ).
tcf(c_797,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
inference(cnf_transformation,[],[f492]) ).
tcf(c_800,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(cnf_transformation,[],[f495]) ).
tcf(c_1083,plain,
! [X0: $i,X1: $i,X2: $i] : c_List_Ofoldl(c_Lambda_OdB_OApp,X0,c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2),
inference(global_subsumption_just,[status(thm)],[c_741,c_748]) ).
tcf(c_3666,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Orotate1(c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),v_ss,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(demodulation,[status(thm)],[c_800,c_723]) ).
tcf(c_3760,plain,
! [X0: $i,X1: $i,X2: $i] : c_List_Ofoldl(c_Lambda_OdB_OApp,X0,c_List_Orotate1(c_List_Olist_OCons(X1,X2,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X1),
inference(demodulation,[status(thm)],[c_1083,c_723]) ).
tcf(c_3761,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
inference(demodulation,[status(thm)],[c_3666,c_3760]) ).
tcf(c_3762,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3761,c_797]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL777-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 00:28:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 3.73/1.27 % SZS status Started for theBenchmark.p
% 3.73/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 3.73/1.27
% 3.73/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.73/1.27
% 3.73/1.27 % ------ iProver source info
% 3.73/1.27
% 3.73/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.73/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.73/1.27 % git: non_committed_changes: false
% 3.73/1.27
% 3.73/1.27 % ------ Parsing...% successful
% 3.73/1.27
% 3.73/1.27
% 3.73/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.73/1.27
% 3.73/1.27 % ------ Preprocessing...%
% 3.73/1.27
% 3.73/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 3.73/1.27
% 3.73/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.73/1.27
% 3.73/1.27
%------------------------------------------------------------------------------