%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM458+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n019.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 02:24:31 PM UTC 2026
% Result : Theorem 3.35s 1.31s
% Output : CNFRefutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 13 unt; 0 def)
% Number of atoms : 103 ( 21 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 124 ( 56 ~; 49 |; 13 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 41 !; 5 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(f20,axiom,
aNaturalNumber0(xm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__718) ).
fof(f21,conjecture,
sdtlseqdt0(xm,xm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f22,negated_conjecture,
~ sdtlseqdt0(xm,xm),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f24,plain,
~ sdtlseqdt0(xm,xm),
inference(flattening,[],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f26,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f25]) ).
fof(f33,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f50,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f51,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f50]) ).
fof(f54,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f55,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(rectify,[],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ( sdtpldt0(X0,sK0(X0,X1)) = X1
& aNaturalNumber0(sK0(X0,X1)) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f55]) ).
fof(f59,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f62,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f67,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f33]) ).
fof(f85,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f89,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f20]) ).
fof(f90,plain,
~ sdtlseqdt0(xm,xm),
inference(cnf_transformation,[],[f24]) ).
fof(f91,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f85]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f59]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_56,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_79,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f89]) ).
tcf(c_80,negated_conjecture,
~ sdtlseqdt0(xm,xm),
inference(cnf_transformation,[],[f90]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).
tcf(c_573,plain,
! [X0: $i,X1: $i] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( X0 != xm )
| ( sdtpldt0(X0,X1) != xm ) ),
inference(resolution_lifted,[status(thm)],[c_103,c_80]) ).
tcf(c_574,plain,
! [X0: $i] :
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xm,X0) != xm ) ),
inference(unflattening,[status(thm)],[c_573]) ).
tcf(c_575,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00)
| ( sdtpldt0(xm,sz00) != xm ) ),
inference(instantiation,[status(thm)],[c_574]) ).
tcf(c_1458,plain,
sdtpldt0(xm,sz00) = xm,
inference(superposition,[status(thm)],[c_79,c_56]) ).
tcf(c_1459,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1458,c_575,c_49,c_79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM458+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n019.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 04:04:34 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 3.35/1.31 % SZS status Started for theBenchmark.p
% 3.35/1.31 % SZS status Theorem for theBenchmark.p
% 3.35/1.31
% 3.35/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.35/1.31
% 3.35/1.31 % ------ iProver source info
% 3.35/1.31
% 3.35/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 3.35/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.35/1.31 % git: non_committed_changes: false
% 3.35/1.31
% 3.35/1.31 % ------ Parsing...
% 3.35/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.35/1.31
% 3.35/1.31 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.35/1.31
% 3.35/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.35/1.31
% 3.35/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.35/1.31 % ------ Proving...
% 3.35/1.31 % ------ Problem Properties
% 3.35/1.31
% 3.35/1.31 %
% 3.35/1.31 % clauses 31
% 3.35/1.31 % conjectures 0
% 3.35/1.31 % EPR 4
% 3.35/1.31 % Horn 28
% 3.35/1.31 % unary 4
% 3.35/1.31 % binary 7
% 3.35/1.31 % lits 96
% 3.35/1.31 % lits eq 34
% 3.35/1.31 % fd_pure 0
% 3.35/1.31 % fd_pseudo 0
% 3.35/1.31 % fd_cond 3
% 3.35/1.31 % fd_pseudo_cond 4
% 3.35/1.31 % AC symbols 0
% 3.35/1.31
% 3.35/1.31 % ------ Schedule dynamic 5 is on
% 3.35/1.31
% 3.35/1.31 % ------ no conjectures: strip conj schedule
% 3.35/1.31
% 3.35/1.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.35/1.31
% 3.35/1.31
% 3.35/1.31 % ------
% 3.35/1.31 % Current options:
% 3.35/1.31 % ------
% 3.35/1.31
% 3.35/1.31
% 3.35/1.31 %
% 3.35/1.31
% 3.35/1.31 % ------ Proving...
% 3.35/1.31 %
% 3.35/1.31
% 3.35/1.31 % SZS status Theorem for theBenchmark.p
% 3.35/1.31
% 3.35/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.35/1.31
% 3.35/1.31
%------------------------------------------------------------------------------