%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL754-1 : 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 02:08:17 PM UTC 2026
% Result : Unsatisfiable 10.36s 7.48s
% Output : CNFRefutation 10.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 18 unt; 0 def)
% Number of atoms : 46 ( 10 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 31 ( 17 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 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; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 52 ( 0 sgn 52 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
fof(f139,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_Suc(X0),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
fof(f186,axiom,
! [X0] : c_Suc(X0) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
fof(f456,axiom,
! [X0] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).
fof(f473,axiom,
! [X0,X1] :
( ~ c_lessequals(c_Suc(X1),X0,tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
fof(f509,axiom,
! [X0] : c_lessequals(X0,X0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
fof(f730,axiom,
! [X2,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,X2) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X0,c_Lambda_Olift(X1,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Abs_0) ).
fof(f739,axiom,
! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).
fof(f828,axiom,
! [X0] :
( ~ c_InductTermi_OIT(X0)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).
fof(f833,negated_conjecture,
! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X0),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f834,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(v_ia),v_ja)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f907,plain,
! [X0,X1] :
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) ),
inference(definition_unfolding,[],[f473,f186]) ).
fof(f938,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
inference(definition_unfolding,[],[f139,f186]) ).
tcf(c_768,negated_conjecture,
! [X0: $i,X1: $i] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X0),X1)),
inference(cnf_transformation,[],[f833]) ).
tcf(c_769,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(v_ia),v_ja)),
inference(cnf_transformation,[],[f834]) ).
tcf(c_770,plain,
! [X0: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X0))
| ~ c_InductTermi_OIT(X0) ),
inference(cnf_transformation,[],[f828]) ).
tcf(c_781,plain,
! [X0: $i,X1: $i,X2: $i] : c_Lambda_OdB_OAbs(c_Lambda_Osubst(X0,c_Lambda_Olift(X1,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) = c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,X2),
inference(cnf_transformation,[],[f730]) ).
tcf(c_792,plain,
! [X0: $i,X1: $i] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ( c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1) ) ),
inference(cnf_transformation,[],[f739]) ).
tcf(c_814,plain,
! [X0: $i] : c_lessequals(X0,X0,tc_nat),
inference(cnf_transformation,[],[f509]) ).
tcf(c_820,plain,
! [X0: $i] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),
inference(cnf_transformation,[],[f456]) ).
tcf(c_949,plain,
! [X0: $i,X1: $i] :
( ~ c_lessequals(X1,X0,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
inference(cnf_transformation,[],[f907]) ).
tcf(c_980,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ),
inference(cnf_transformation,[],[f938]) ).
tcf(c_1231,plain,
! [X0: $i,X1: $i] :
( ( c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1) )
| ~ c_lessequals(X1,X0,tc_nat) ),
inference(prop_impl_just,[status(thm)],[c_980,c_949,c_792]) ).
tcf(c_1232,plain,
! [X0: $i,X1: $i] :
( ( c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X0) )
| ~ c_lessequals(X0,X1,tc_nat) ),
inference(renaming,[status(thm)],[c_1231]) ).
tcf(c_4244,plain,
! [X0: $i,X1: $i] :
( ( c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X0) )
| ~ c_lessequals(X0,X1,tc_nat) ),
inference(prop_impl_just,[status(thm)],[c_1232]) ).
tcf(c_8035,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,X2))
| ~ c_InductTermi_OIT(c_Lambda_Osubst(X0,c_Lambda_Olift(X1,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ),
inference(superposition,[status(thm)],[c_781,c_770]) ).
tcf(c_15842,plain,
! [X0: $i] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),
inference(superposition,[status(thm)],[c_814,c_4244]) ).
tcf(c_15854,plain,
! [X0: $i] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(superposition,[status(thm)],[c_820,c_4244]) ).
tcf(c_18716,plain,
! [X0: $i,X1: $i] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),X1)),
inference(superposition,[status(thm)],[c_15842,c_768]) ).
tcf(c_19302,plain,
! [X0: $i,X1: $i] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X1)),
inference(superposition,[status(thm)],[c_15842,c_18716]) ).
tcf(c_19307,plain,
! [X0: $i,X1: $i] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),X1)),
inference(light_normalisation,[status(thm)],[c_19302,c_15854]) ).
tcf(c_19322,plain,
! [X0: $i,X1: $i] : c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(X0),X1)),
inference(superposition,[status(thm)],[c_19307,c_8035]) ).
tcf(c_19325,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_769,c_19322]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL754-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.55 % Computer : n008.cluster.edu
% 0.09/5.55 % Model : x86_64 x86_64
% 0.09/5.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.55 % Memory : 8046.5625MB
% 0.09/5.55 % OS : Linux 6.8.0-71-generic
% 0.09/5.55 % CPULimit : 300
% 0.09/5.55 % WCLimit : 300
% 0.09/5.55 % DateTime : Thu Sep 24 00:26:19 UTC 2026
% 0.09/5.56 % CPUTime :
% 0.09/5.56 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.60 Running first-order theorem proving
% 0.09/5.60 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
% 0.14/5.61
% 0.14/5.61 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.61
% 0.14/5.61 % Detected problem language: tptp
% 0.14/5.62 % Proving...
% 10.36/7.48 % SZS status Started for theBenchmark.p
% 10.36/7.48 % SZS status Unsatisfiable for theBenchmark.p
% 10.36/7.48
% 10.36/7.48 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.36/7.48
% 10.36/7.48 % ------ iProver source info
% 10.36/7.48
% 10.36/7.48 % git: date: 2026-07-19 20:42:38 +0200
% 10.36/7.48 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.36/7.48 % git: non_committed_changes: false
% 10.36/7.48
% 10.36/7.48 % ------ Parsing...% successful
% 10.36/7.48
% 10.36/7.48
% 10.36/7.48 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.36/7.48
% 10.36/7.48 % ------ Preprocessing... sup_sim: 19 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 sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 10.36/7.48
% 10.36/7.48 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.36/7.48
% 10.36/7.48 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.36/7.48 % ------ Proving...
% 10.36/7.48 % ------ Problem Properties
% 10.36/7.48
% 10.36/7.48 %
% 10.36/7.48 % clauses 146
% 10.36/7.48 % conjectures 3
% 10.36/7.48 % EPR 8
% 10.36/7.48 % Horn 120
% 10.36/7.48 % unary 48
% 10.36/7.48 % binary 75
% 10.36/7.48 % lits 269
% 10.36/7.48 % lits eq 90
% 10.36/7.48 % fd_pure 0
% 10.36/7.48 % fd_pseudo 0
% 10.36/7.48 % fd_cond 11
% 10.36/7.48 % fd_pseudo_cond 11
% 10.36/7.48 % AC symbols 0
% 10.36/7.48
% 10.36/7.48 % ------ Schedule dynamic 5 is on
% 10.36/7.48
% 10.36/7.48 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.36/7.48
% 10.36/7.48
% 10.36/7.48 % ------
% 10.36/7.48 % Current options:
% 10.36/7.48 % ------
% 10.36/7.48
% 10.36/7.48
% 10.36/7.48 %
% 10.36/7.48
% 10.36/7.48 % ------ Proving...
% 10.36/7.48 %
% 10.36/7.48
% 10.36/7.48 % SZS status Unsatisfiable for theBenchmark.p
% 10.36/7.48
% 10.36/7.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.36/7.48
% 10.36/7.48
%------------------------------------------------------------------------------