%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL834-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.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 02:08:31 PM UTC 2026
% Result : Unsatisfiable 3.57s 1.08s
% Output : CNFRefutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 9 unt; 0 def)
% Number of atoms : 15 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 7 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 13 ( 13 usr; 8 con; 0-5 aty)
% Number of variables : 26 ( 0 sgn 26 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f497,axiom,
! [X2,X3,X0,X1,X4,X5] : c_List_Ofoldl(X0,X1,c_List_Olist_OCons(X2,X3,X4),X5,X4) = c_List_Ofoldl(X0,hAPP(hAPP(X0,X1),X2),X3,X5,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
fof(f572,axiom,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),X1)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X1),c_HOL_Ozero__class_Ozero(tc_nat)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta_0) ).
fof(f573,axiom,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X2))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
fof(f583,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tcf(c_881,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_List_Ofoldl(X0,hAPP(hAPP(X0,X1),X2),X3,X4,X5) = c_List_Ofoldl(X0,X1,c_List_Olist_OCons(X2,X3,X5),X4,X5),
inference(cnf_transformation,[],[f497]) ).
tcf(c_936,plain,
! [X0: $i,X1: $i] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),X1)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X1),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(cnf_transformation,[],[f572]) ).
tcf(c_937,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X1)) ),
inference(cnf_transformation,[],[f573]) ).
tcf(c_945,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
inference(cnf_transformation,[],[f583]) ).
tcf(c_1153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,c_List_Olist_OCons(X1,X3,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1)),X2)) ),
inference(superposition,[status(thm)],[c_881,c_937]) ).
tcf(c_1170,plain,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____),c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
inference(demodulation,[status(thm)],[c_945,c_881]) ).
tcf(c_1493,plain,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____)),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(superposition,[status(thm)],[c_1153,c_1170]) ).
tcf(c_2732,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1493,c_936]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL834-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 00:34:54 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 3.57/1.08 % SZS status Started for theBenchmark.p
% 3.57/1.08 % SZS status Unsatisfiable for theBenchmark.p
% 3.57/1.08
% 3.57/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.57/1.08
% 3.57/1.08 % ------ iProver source info
% 3.57/1.08
% 3.57/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 3.57/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.57/1.08 % git: non_committed_changes: false
% 3.57/1.08
% 3.57/1.08 % ------ Parsing...% successful
% 3.57/1.08
% 3.57/1.08
% 3.57/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.57/1.08 % ------ Proving...
% 3.57/1.08 % ------ Problem Properties
% 3.57/1.08
% 3.57/1.08 %
% 3.57/1.08 % clauses 453
% 3.57/1.08 % conjectures 1
% 3.57/1.08 % EPR 43
% 3.57/1.08 % Horn 387
% 3.57/1.08 % unary 161
% 3.57/1.08 % binary 179
% 3.57/1.08 % lits 914
% 3.57/1.08 % lits eq 396
% 3.57/1.08 % fd_pure 0
% 3.57/1.08 % fd_pseudo 0
% 3.57/1.08 % fd_cond 12
% 3.57/1.08 % fd_pseudo_cond 72
% 3.57/1.08 % AC symbols 0
% 3.57/1.08
% 3.57/1.08 % ------ Input Options Time Limit: Unbounded
% 3.57/1.08
% 3.57/1.08
% 3.57/1.08 % ------
% 3.57/1.08 % Current options:
% 3.57/1.08 % ------
% 3.57/1.08
% 3.57/1.08
% 3.57/1.08 %
% 3.57/1.08
% 3.57/1.08 % ------ Proving...
% 3.57/1.08 %
% 3.57/1.08
% 3.57/1.08 % SZS status Unsatisfiable for theBenchmark.p
% 3.57/1.08
% 3.57/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.57/1.08
% 3.57/1.08
%------------------------------------------------------------------------------