%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL855-1 : 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 : n006.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 02:08:35 PM UTC 2026
% Result : Unsatisfiable 4.40s 16.62s
% Output : CNFRefutation 4.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 13 ( 13 unt; 0 def)
% Number of atoms : 13 ( 7 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 21 ( 0 sgn 21 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f416,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(f438,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(f443,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(f461,axiom,
c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f462,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tcf(c_433,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____)),
inference(cnf_transformation,[],[f462]) ).
tcf(c_438,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,[],[f443]) ).
tcf(c_439,plain,
c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))),
inference(cnf_transformation,[],[f461]) ).
tcf(c_451,plain,
! [X0: $i,X1: $i] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,X0) = X1,
inference(cnf_transformation,[],[f438]) ).
tcf(c_514,plain,
! [X0: $i,X1: $i,X2: $i] : c_Lambda_Osubst(c_Lambda_Olift(X0,X1),X2,X1) = X0,
inference(cnf_transformation,[],[f416]) ).
tcf(c_5485,plain,
! [X0: $i,X1: $i,X2: $i] : c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(X0),X1),X2,X0) = c_Lambda_OdB_OApp(X2,c_Lambda_Osubst(X1,X2,X0)),
inference(superposition,[status(thm)],[c_451,c_438]) ).
tcf(c_6703,plain,
c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____)),
inference(demodulation,[status(thm)],[c_439,c_514,c_5485]) ).
tcf(c_6704,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6703,c_433]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL855-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/15.63 % Computer : n006.cluster.edu
% 0.15/15.63 % Model : x86_64 x86_64
% 0.15/15.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/15.63 % Memory : 8046.5625MB
% 0.15/15.63 % OS : Linux 6.8.0-71-generic
% 0.15/15.63 % CPULimit : 300
% 0.15/15.63 % WCLimit : 300
% 0.15/15.63 % DateTime : Thu Sep 24 00:36:00 UTC 2026
% 0.15/15.64 % CPUTime :
% 0.15/15.64 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/15.69 Running first-order theorem proving
% 0.15/15.69 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
% 0.19/15.71
% 0.19/15.71 % ======== iProver multi-core TPTP/SMT =========
% 0.19/15.71
% 0.19/15.71 % Detected problem language: tptp
% 0.19/15.73 % Proving...
% 4.40/16.62 % SZS status Started for theBenchmark.p
% 4.40/16.62 % SZS status Unsatisfiable for theBenchmark.p
% 4.40/16.62
% 4.40/16.62 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.40/16.62
% 4.40/16.62 % ------ iProver source info
% 4.40/16.62
% 4.40/16.62 % git: date: 2026-07-19 20:42:38 +0200
% 4.40/16.62 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.40/16.62 % git: non_committed_changes: false
% 4.40/16.62
% 4.40/16.62 % ------ Parsing...% successful
% 4.40/16.62
% 4.40/16.62
% 4.40/16.62 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.40/16.62
% 4.40/16.62 % ------ Preprocessing... sup_sim: 9 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 %
% 4.40/16.62
% 4.40/16.62 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.40/16.62
% 4.40/16.62 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.40/16.62 % ------ Proving...
% 4.40/16.62 % ------ Problem Properties
% 4.40/16.62
% 4.40/16.62 %
% 4.40/16.62 % clauses 140
% 4.40/16.62 % conjectures 1
% 4.40/16.62 % EPR 5
% 4.40/16.62 % Horn 123
% 4.40/16.62 % unary 59
% 4.40/16.62 % binary 55
% 4.40/16.62 % lits 247
% 4.40/16.62 % lits eq 114
% 4.40/16.62 % fd_pure 0
% 4.40/16.62 % fd_pseudo 0
% 4.40/16.62 % fd_cond 12
% 4.40/16.62 % fd_pseudo_cond 17
% 4.40/16.62 % AC symbols 0
% 4.40/16.62
% 4.40/16.62 % ------ Schedule dynamic 5 is on
% 4.40/16.62
% 4.40/16.62 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.40/16.62
% 4.40/16.62
% 4.40/16.62 % ------
% 4.40/16.62 % Current options:
% 4.40/16.62 % ------
% 4.40/16.62
% 4.40/16.62
% 4.40/16.62 %
% 4.40/16.62
% 4.40/16.62 % ------ Proving...
% 4.40/16.62 %
% 4.40/16.62
% 4.40/16.62 % SZS status Unsatisfiable for theBenchmark.p
% 4.40/16.62
% 4.40/16.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.40/16.62
% 4.40/16.62
%------------------------------------------------------------------------------