%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL800-1 : 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 02:08:25 PM UTC 2026
% Result : Unsatisfiable 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 17 ( 17 unt; 2 def)
% Number of atoms : 23 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 22 ( 0 sgn 22 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
fof(f444,axiom,
! [X2,X3,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,X1),X2,X3) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X0,X2,X3),c_Lambda_Osubst(X1,X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__App_0) ).
fof(f447,axiom,
! [X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,X0) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__eq_0) ).
fof(f463,axiom,
! [X2,X0,X1] : c_Lambda_Osubst(c_Lambda_Olift(X0,X1),X2,X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lift_0) ).
fof(f468,axiom,
c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f469,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tcf(c_705,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lambda_OdB_OApp(c_Lambda_Osubst(X0,X1,X2),c_Lambda_Osubst(X3,X1,X2)) = c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,X3),X1,X2),
inference(cnf_transformation,[],[f444]) ).
tcf(c_708,plain,
! [X0: $i,X1: $i] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,X0) = X1,
inference(cnf_transformation,[],[f447]) ).
tcf(c_723,plain,
! [X0: $i,X1: $i,X2: $i] : c_Lambda_Osubst(c_Lambda_Olift(X0,X1),X2,X1) = X0,
inference(cnf_transformation,[],[f463]) ).
tcf(c_728,plain,
c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(cnf_transformation,[],[f468]) ).
tcf(c_729,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____))),
inference(cnf_transformation,[],[f469]) ).
tcf(c_6608,definition,
iPr_def_10 = c_Lambda_Osubst(v_a____,v_u____,v_i____),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_6609,definition,
iPr_def_11 = c_Lambda_OdB_OApp(v_u____,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_6610,negated_conjecture,
~ c_InductTermi_OIT(iPr_def_11),
inference(demodulation,[status(thm)],[c_729,c_6608,c_6609]) ).
tcf(c_9052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(X0,X1),X2),X3,X1) = c_Lambda_OdB_OApp(X0,c_Lambda_Osubst(X2,X3,X1)),
inference(superposition,[status(thm)],[c_723,c_705]) ).
tcf(c_19537,plain,
c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),iPr_def_10,c_HOL_Ozero__class_Ozero(tc_nat))),
inference(light_normalisation,[status(thm)],[c_728,c_6608]) ).
tcf(c_19538,plain,
c_InductTermi_OIT(iPr_def_11),
inference(demodulation,[status(thm)],[c_19537,c_708,c_6609,c_9052]) ).
tcf(c_19539,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_19538,c_6610]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL800-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 00:31:54 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.26/1.72 % SZS status Started for theBenchmark.p
% 1.26/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.72
% 1.26/1.72 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.26/1.72
% 1.26/1.72 % ------ iProver source info
% 1.26/1.72
% 1.26/1.72 % git: date: 2026-07-19 20:42:38 +0200
% 1.26/1.72 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.26/1.72 % git: non_committed_changes: false
% 1.26/1.72
% 1.26/1.72 % ------ Parsing...% successful
% 1.26/1.72
% 1.26/1.72
% 1.26/1.72 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.26/1.72
% 1.26/1.72 % ------ Preprocessing... sup_sim: 9 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e sup_sim: 5 sf_s rm: 23 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 23 0s sf_e pe_s pe_e %
% 1.26/1.72
% 1.26/1.72 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.26/1.72
% 1.26/1.72 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.26/1.72 % ------ Proving...
% 1.26/1.72 % ------ Problem Properties
% 1.26/1.72
% 1.26/1.72 %
% 1.26/1.72 % clauses 164
% 1.26/1.72 % conjectures 1
% 1.26/1.72 % EPR 7
% 1.26/1.72 % Horn 145
% 1.26/1.72 % unary 68
% 1.26/1.72 % binary 67
% 1.26/1.72 % lits 289
% 1.26/1.72 % lits eq 135
% 1.26/1.72 % fd_pure 0
% 1.26/1.72 % fd_pseudo 0
% 1.26/1.72 % fd_cond 13
% 1.26/1.72 % fd_pseudo_cond 20
% 1.26/1.72 % AC symbols 0
% 1.26/1.72
% 1.26/1.72 % ------ Schedule dynamic 5 is on
% 1.26/1.72
% 1.26/1.72 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.26/1.72
% 1.26/1.72
% 1.26/1.72 % ------
% 1.26/1.72 % Current options:
% 1.26/1.72 % ------
% 1.26/1.72
% 1.26/1.72
% 1.26/1.72 %
% 1.26/1.72
% 1.26/1.72 % ------ Proving...
% 1.26/1.72 %
% 1.26/1.72
% 1.26/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.72
% 1.26/1.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.26/1.72
% 1.26/1.72
%------------------------------------------------------------------------------