%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM457+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 : n026.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 2.91s 1.28s
% Output : CNFRefutation 2.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 22 unt; 1 def)
% Number of atoms : 115 ( 59 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 104 ( 47 ~; 40 |; 10 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 25 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 != sz00
=> ! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtasdt0(X1,X0) = sdtasdt0(X2,X0)
| sdtasdt0(X0,X1) = sdtasdt0(X0,X2) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(f17,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__624) ).
fof(f18,conjecture,
( sdtasdt0(xm,xn) = sz00
=> ( xn = sz00
| xm = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f19,negated_conjecture,
~ ( sdtasdt0(xm,xn) = sz00
=> ( xn = sz00
| xm = sz00 ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f35,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f40,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ! [X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| X1 = X2 ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f41,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ! [X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| X1 = X2 ) ),
inference(flattening,[],[f40]) ).
fof(f44,plain,
( sdtasdt0(xm,xn) = sz00
& sz00 != xn
& sz00 != xm ),
inference(ennf_transformation,[],[f19]) ).
fof(f45,plain,
( sdtasdt0(xm,xn) = sz00
& sz00 != xn
& sz00 != xm ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f60,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f35]) ).
fof(f66,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f69,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f17]) ).
fof(f70,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f17]) ).
fof(f71,plain,
sz00 = sdtasdt0(xm,xn),
inference(cnf_transformation,[],[f45]) ).
fof(f72,plain,
sz00 != xn,
inference(cnf_transformation,[],[f45]) ).
fof(f73,plain,
sz00 != xm,
inference(cnf_transformation,[],[f45]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f46]) ).
tcf(c_62,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz00) = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_72,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f70]) ).
tcf(c_73,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f69]) ).
tcf(c_74,negated_conjecture,
sz00 != xm,
inference(cnf_transformation,[],[f73]) ).
tcf(c_75,negated_conjecture,
sz00 != xn,
inference(cnf_transformation,[],[f72]) ).
tcf(c_76,negated_conjecture,
sdtasdt0(xm,xn) = sz00,
inference(cnf_transformation,[],[f71]) ).
tcf(c_392,definition,
iPr_def_10 = sdtasdt0(xm,xn),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_393,negated_conjecture,
iPr_def_10 = sz00,
inference(demodulation,[status(thm)],[c_76,c_392]) ).
tcf(c_394,negated_conjecture,
sz00 != xn,
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_395,negated_conjecture,
sz00 != xm,
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_776,plain,
xn != iPr_def_10,
inference(light_normalisation,[status(thm)],[c_394,c_393]) ).
tcf(c_777,plain,
xm != iPr_def_10,
inference(light_normalisation,[status(thm)],[c_395,c_393]) ).
tcf(c_778,plain,
aNaturalNumber0(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_49,c_393]) ).
tcf(c_814,plain,
! [X0: $i] :
( ( sdtasdt0(X0,iPr_def_10) = iPr_def_10 )
| ~ aNaturalNumber0(X0) ),
inference(light_normalisation,[status(thm)],[c_62,c_393]) ).
tcf(c_822,plain,
sdtasdt0(xm,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_72,c_814]) ).
tcf(c_2026,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = iPr_def_10 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ),
inference(light_normalisation,[status(thm)],[c_68,c_393]) ).
tcf(c_2072,plain,
! [X0: $i] :
( ( xm = iPr_def_10 )
| ( X0 = iPr_def_10 )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(xm,X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_822,c_2026]) ).
tcf(c_2092,plain,
! [X0: $i] :
( ( X0 = iPr_def_10 )
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(xm,X0) != iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2072,c_777,c_778,c_72]) ).
tcf(c_2782,plain,
( ( xn = iPr_def_10 )
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_392,c_2092]) ).
tcf(c_2785,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2782,c_776,c_73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM457+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 04:07:09 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 2.91/1.28 % SZS status Started for theBenchmark.p
% 2.91/1.28 % SZS status Theorem for theBenchmark.p
% 2.91/1.28
% 2.91/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.91/1.28
% 2.91/1.28 % ------ iProver source info
% 2.91/1.28
% 2.91/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.91/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.91/1.28 % git: non_committed_changes: false
% 2.91/1.28
% 2.91/1.28 % ------ Parsing...
% 2.91/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.91/1.28
% 2.91/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.91/1.28
% 2.91/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.91/1.28
% 2.91/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.91/1.28 % ------ Proving...
% 2.91/1.28 % ------ Problem Properties
% 2.91/1.28
% 2.91/1.28 %
% 2.91/1.28 % clauses 29
% 2.91/1.28 % conjectures 3
% 2.91/1.28 % EPR 8
% 2.91/1.28 % Horn 27
% 2.91/1.28 % unary 9
% 2.91/1.28 % binary 6
% 2.91/1.28 % lits 79
% 2.91/1.28 % lits eq 31
% 2.91/1.28 % fd_pure 0
% 2.91/1.28 % fd_pseudo 0
% 2.91/1.28 % fd_cond 2
% 2.91/1.28 % fd_pseudo_cond 4
% 2.91/1.28 % AC symbols 0
% 2.91/1.28
% 2.91/1.28 % ------ Schedule dynamic 5 is on
% 2.91/1.28
% 2.91/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.91/1.28
% 2.91/1.28
% 2.91/1.28 % ------
% 2.91/1.28 % Current options:
% 2.91/1.28 % ------
% 2.91/1.28
% 2.91/1.28
% 2.91/1.28 %
% 2.91/1.28
% 2.91/1.28 % ------ Proving...
% 2.91/1.28 %
% 2.91/1.28
% 2.91/1.28 % SZS status Theorem for theBenchmark.p
% 2.91/1.28
% 2.91/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.91/1.28
% 2.91/1.28
%------------------------------------------------------------------------------