%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV254-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n003.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 03:16:48 PM UTC 2026
% Result : Unsatisfiable 10.27s 2.19s
% Output : CNFRefutation 10.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 14 unt; 0 def)
% Number of atoms : 26 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 9 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2349,axiom,
! [X0] : c_0 != c_Suc(X0),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Nat_OZero__not__Suc_0) ).
fof(f2350,axiom,
! [X0] : c_plus(X0,c_0,tc_nat) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Nat_Oadd__0__right_0) ).
fof(f2374,axiom,
! [X0] :
( X0 = c_0
| ~ c_lessequals(X0,c_0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Nat_Ole__0__eq_0) ).
fof(f2375,plain,
! [X0] :
( c_0 = X0
| ~ c_lessequals(X0,c_0,tc_nat) ),
inference(reorient_equations,[],[f2374]) ).
fof(f2426,axiom,
! [X2,X0,X1] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_plus(X0,X1,tc_nat),c_plus(X0,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Nat_Onat__add__left__cancel__le_0) ).
fof(f3054,axiom,
! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_Suc(X0),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_SetInterval_Ocard__atMost_0) ).
fof(f3055,plain,
! [X0] : c_Suc(X0) = c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),
inference(reorient_equations,[],[f3054]) ).
fof(f3391,negated_conjecture,
! [X0] : c_lessequals(X0,v_x(X0),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f3392,negated_conjecture,
! [X0] : v_x(X0) = v_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3519,plain,
! [X0] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f2349,f3055]) ).
fof(f3616,plain,
! [X0] : c_lessequals(X0,v_nat,tc_nat),
inference(definition_unfolding,[],[f3391,f3392]) ).
tcf(c_4374,plain,
! [X0: $i] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) != c_0,
inference(cnf_transformation,[],[f3519]) ).
tcf(c_4375,plain,
! [X0: $i] : c_plus(X0,c_0,tc_nat) = X0,
inference(cnf_transformation,[],[f2350]) ).
tcf(c_4391,plain,
! [X0: $i] :
( ( X0 = c_0 )
| ~ c_lessequals(X0,c_0,tc_nat) ),
inference(cnf_transformation,[],[f2375]) ).
tcf(c_4431,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_plus(X0,X1,tc_nat),c_plus(X0,X2,tc_nat),tc_nat) ),
inference(cnf_transformation,[],[f2426]) ).
tcf(c_5031,negated_conjecture,
! [X0: $i] : c_lessequals(X0,v_nat,tc_nat),
inference(cnf_transformation,[],[f3616]) ).
tcf(c_6320,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X1,c_0,tc_nat)
| ~ c_lessequals(c_plus(X0,X1,tc_nat),X0,tc_nat) ),
inference(superposition,[status(thm)],[c_4375,c_4431]) ).
tcf(c_11463,plain,
! [X0: $i] : c_lessequals(X0,c_0,tc_nat),
inference(superposition,[status(thm)],[c_5031,c_6320]) ).
tcf(c_11473,plain,
! [X0: $i] : X0 = c_0,
inference(backward_subsumption_resolution,[status(thm)],[c_4391,c_11463]) ).
tcf(c_11474,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_4374,c_11473]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV254-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 18:55:37 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 10.27/2.19 % SZS status Started for theBenchmark.p
% 10.27/2.19 % SZS status Unsatisfiable for theBenchmark.p
% 10.27/2.19
% 10.27/2.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.27/2.19
% 10.27/2.19 % ------ iProver source info
% 10.27/2.19
% 10.27/2.19 % git: date: 2026-07-19 20:42:38 +0200
% 10.27/2.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.27/2.19 % git: non_committed_changes: false
% 10.27/2.19
% 10.27/2.19 % ------ Parsing...% successful
% 10.27/2.19
% 10.27/2.19
% 10.27/2.19 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 10.27/2.19 % ------ Proving...
% 10.27/2.19 % ------ Problem Properties
% 10.27/2.19
% 10.27/2.19 %
% 10.27/2.19 % clauses 2194
% 10.27/2.19 % conjectures 1
% 10.27/2.19 % EPR 669
% 10.27/2.19 % Horn 2006
% 10.27/2.19 % unary 650
% 10.27/2.19 % binary 1100
% 10.27/2.19 % lits 4410
% 10.27/2.19 % lits eq 1220
% 10.27/2.19 % fd_pure 0
% 10.27/2.19 % fd_pseudo 0
% 10.27/2.19 % fd_cond 118
% 10.27/2.19 % fd_pseudo_cond 77
% 10.27/2.19 % AC symbols 0
% 10.27/2.19
% 10.27/2.19 % ------ Input Options Time Limit: Unbounded
% 10.27/2.19
% 10.27/2.19
% 10.27/2.19 % ------
% 10.27/2.19 % Current options:
% 10.27/2.19 % ------
% 10.27/2.19
% 10.27/2.19
% 10.27/2.19 %
% 10.27/2.19
% 10.27/2.19 % ------ Proving...
% 10.27/2.19 %
% 10.27/2.19
% 10.27/2.19 % ------ Proving...
% 10.27/2.19 %
% 10.27/2.19
% 10.27/2.19 % ------ Proving...
% 10.27/2.19 %
% 10.27/2.19
% 10.27/2.19 % ------ Proving...
% 10.27/2.19 %
% 10.27/2.19
% 10.27/2.19 % SZS status Unsatisfiable for theBenchmark.p
% 10.27/2.19
% 10.27/2.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.27/2.19
% 10.27/2.19
%------------------------------------------------------------------------------