%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL784-1 : 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 : 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 02:08:22 PM UTC 2026
% Result : Unsatisfiable 4.35s 1.29s
% Output : CNFRefutation 4.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 17 unt; 0 def)
% Number of atoms : 17 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 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 : 12 ( 12 usr; 8 con; 0-5 aty)
% Number of variables : 15 ( 0 sgn 15 !; 0 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
fof(f272,axiom,
! [X0,X1] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X0)),X1),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
fof(f300,axiom,
! [X2,X3,X0,X1] : c_List_Ofoldl(X0,X1,c_List_Olist_ONil(X2),X3,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
fof(f337,axiom,
v_rs____ = c_List_Olist_ONil(tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil_0) ).
fof(f338,plain,
c_List_Olist_ONil(tc_Lambda_OdB) = v_rs____,
inference(reorient_equations,[],[f337]) ).
fof(f349,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uIT_0) ).
fof(f364,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f366,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f387,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
inference(definition_unfolding,[],[f366,f364]) ).
tcf(c_366,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
inference(cnf_transformation,[],[f387]) ).
tcf(c_376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_List_Ofoldl(X0,X1,c_List_Olist_ONil(X2),X3,X2) = X1,
inference(cnf_transformation,[],[f300]) ).
tcf(c_392,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X0)),X1),X0) = X1,
inference(cnf_transformation,[],[f272]) ).
tcf(c_402,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(cnf_transformation,[],[f349]) ).
tcf(c_404,plain,
c_List_Olist_ONil(tc_Lambda_OdB) = v_rs____,
inference(cnf_transformation,[],[f338]) ).
tcf(c_3563,plain,
! [X0: $i,X1: $i,X2: $i] : c_List_Ofoldl(X0,X1,v_rs____,X2,tc_Lambda_OdB) = X1,
inference(superposition,[status(thm)],[c_404,c_376]) ).
tcf(c_3569,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____),v_i____))),
inference(demodulation,[status(thm)],[c_366,c_3563]) ).
tcf(c_3572,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(demodulation,[status(thm)],[c_3569,c_392]) ).
tcf(c_3573,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3572,c_402]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL784-1 : 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 : n008.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 00:30:40 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 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...
% 4.35/1.29 % SZS status Started for theBenchmark.p
% 4.35/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 4.35/1.29
% 4.35/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.35/1.29
% 4.35/1.29 % ------ iProver source info
% 4.35/1.29
% 4.35/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 4.35/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.35/1.29 % git: non_committed_changes: false
% 4.35/1.29
% 4.35/1.29 % ------ Parsing...% successful
% 4.35/1.29
% 4.35/1.29
% 4.35/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.35/1.29
% 4.35/1.29 % ------ Preprocessing... sup_sim: 4 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.35/1.29
% 4.35/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.35/1.29
% 4.35/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.35/1.29 % ------ Proving...
% 4.35/1.29 % ------ Problem Properties
% 4.35/1.29
% 4.35/1.29 %
% 4.35/1.29 % clauses 95
% 4.35/1.29 % conjectures 1
% 4.35/1.29 % EPR 2
% 4.35/1.29 % Horn 84
% 4.35/1.29 % unary 29
% 4.35/1.29 % binary 48
% 4.35/1.29 % lits 179
% 4.35/1.29 % lits eq 81
% 4.35/1.29 % fd_pure 0
% 4.35/1.29 % fd_pseudo 0
% 4.35/1.29 % fd_cond 3
% 4.35/1.29 % fd_pseudo_cond 32
% 4.35/1.29 % AC symbols 0
% 4.35/1.29
% 4.35/1.29 % ------ Schedule dynamic 5 is on
% 4.35/1.29
% 4.35/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.35/1.29
% 4.35/1.29
% 4.35/1.29 % ------
% 4.35/1.29 % Current options:
% 4.35/1.29 % ------
% 4.35/1.29
% 4.35/1.29
% 4.35/1.29 %
% 4.35/1.29
% 4.35/1.29 % ------ Proving...
% 4.35/1.29 %
% 4.35/1.29
% 4.35/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 4.35/1.29
% 4.35/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.35/1.29
% 4.35/1.29
%------------------------------------------------------------------------------