%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM460+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n013.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 02:24:32 PM UTC 2026
% Result : Theorem 1.05s 1.74s
% Output : CNFRefutation 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 23 unt; 0 def)
% Number of atoms : 160 ( 51 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 162 ( 57 ~; 47 |; 52 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 49 !; 15 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(f22,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__773) ).
fof(f23,conjecture,
( ( sdtlseqdt0(xn,xl)
& ? [X0] :
( sdtpldt0(xn,X0) = xl
& aNaturalNumber0(X0) )
& sdtlseqdt0(xm,xn)
& ? [X0] :
( sdtpldt0(xm,X0) = xn
& aNaturalNumber0(X0) ) )
=> ( sdtlseqdt0(xm,xl)
| ? [X0] :
( sdtpldt0(xm,X0) = xl
& aNaturalNumber0(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f24,negated_conjecture,
~ ( ( sdtlseqdt0(xn,xl)
& ? [X0] :
( sdtpldt0(xn,X0) = xl
& aNaturalNumber0(X0) )
& sdtlseqdt0(xm,xn)
& ? [X0] :
( sdtpldt0(xm,X0) = xn
& aNaturalNumber0(X0) ) )
=> ( sdtlseqdt0(xm,xl)
| ? [X0] :
( sdtpldt0(xm,X0) = xl
& aNaturalNumber0(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f26,plain,
~ ( ( sdtlseqdt0(xn,xl)
& ? [X1] :
( xl = sdtpldt0(xn,X1)
& aNaturalNumber0(X1) )
& sdtlseqdt0(xm,xn)
& ? [X0] :
( sdtpldt0(xm,X0) = xn
& aNaturalNumber0(X0) ) )
=> ( sdtlseqdt0(xm,xl)
| ? [X2] :
( xl = sdtpldt0(xm,X2)
& aNaturalNumber0(X2) ) ) ),
inference(rectify,[],[f24]) ).
fof(f27,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f28,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f27]) ).
fof(f31,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f32,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
inference(flattening,[],[f33]) ).
fof(f59,plain,
( sdtlseqdt0(xn,xl)
& ? [X1] :
( xl = sdtpldt0(xn,X1)
& aNaturalNumber0(X1) )
& sdtlseqdt0(xm,xn)
& ? [X0] :
( sdtpldt0(xm,X0) = xn
& aNaturalNumber0(X0) )
& ~ sdtlseqdt0(xm,xl)
& ! [X2] :
( xl != sdtpldt0(xm,X2)
| ~ aNaturalNumber0(X2) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f60,plain,
( sdtlseqdt0(xn,xl)
& ? [X1] :
( xl = sdtpldt0(xn,X1)
& aNaturalNumber0(X1) )
& sdtlseqdt0(xm,xn)
& ? [X0] :
( sdtpldt0(xm,X0) = xn
& aNaturalNumber0(X0) )
& ~ sdtlseqdt0(xm,xl)
& ! [X2] :
( xl != sdtpldt0(xm,X2)
| ~ aNaturalNumber0(X2) ) ),
inference(flattening,[],[f59]) ).
fof(f66,plain,
( sdtlseqdt0(xn,xl)
& ? [X2] :
( xl = sdtpldt0(xn,X2)
& aNaturalNumber0(X2) )
& sdtlseqdt0(xm,xn)
& ? [X1] :
( xn = sdtpldt0(xm,X1)
& aNaturalNumber0(X1) )
& ~ sdtlseqdt0(xm,xl)
& ! [X0] :
( xl != sdtpldt0(xm,X0)
| ~ aNaturalNumber0(X0) ) ),
inference(rectify,[],[f60]) ).
fof(f67,plain,
( sdtlseqdt0(xn,xl)
& xl = sdtpldt0(xn,sK2)
& aNaturalNumber0(sK2)
& sdtlseqdt0(xm,xn)
& xn = sdtpldt0(xm,sK1)
& aNaturalNumber0(sK1)
& ~ sdtlseqdt0(xm,xl)
& ! [X0] :
( xl != sdtpldt0(xm,X0)
| ~ aNaturalNumber0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1),skolemize(X2,sK2)],[f66]) ).
fof(f71,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f73,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f74,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f101,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f22]) ).
fof(f102,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f22]) ).
fof(f104,plain,
xl = sdtpldt0(xn,sK2),
inference(cnf_transformation,[],[f67]) ).
fof(f105,plain,
aNaturalNumber0(sK2),
inference(cnf_transformation,[],[f67]) ).
fof(f107,plain,
xn = sdtpldt0(xm,sK1),
inference(cnf_transformation,[],[f67]) ).
fof(f108,plain,
aNaturalNumber0(sK1),
inference(cnf_transformation,[],[f67]) ).
fof(f110,plain,
! [X0] :
( xl != sdtpldt0(xm,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_81,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f102]) ).
tcf(c_82,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f101]) ).
tcf(c_84,negated_conjecture,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ( sdtpldt0(xm,X0) != xl ) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_86,negated_conjecture,
aNaturalNumber0(sK1),
inference(cnf_transformation,[],[f108]) ).
tcf(c_87,negated_conjecture,
sdtpldt0(xm,sK1) = xn,
inference(cnf_transformation,[],[f107]) ).
tcf(c_89,negated_conjecture,
aNaturalNumber0(sK2),
inference(cnf_transformation,[],[f105]) ).
tcf(c_90,negated_conjecture,
sdtpldt0(xn,sK2) = xl,
inference(cnf_transformation,[],[f104]) ).
tcf(c_142,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sK2) = sdtpldt0(sK2,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_54]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(xm,X0),X1) = sdtpldt0(xm,sdtpldt0(X0,X1)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_81,c_55]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(sK2,X0),X1) = sdtpldt0(sK2,sdtpldt0(X0,X1)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_55]) ).
tcf(c_262,plain,
sdtpldt0(xm,sK2) = sdtpldt0(sK2,xm),
inference(superposition,[status(thm)],[c_81,c_142]) ).
tcf(c_263,plain,
sdtpldt0(xn,sK2) = sdtpldt0(sK2,xn),
inference(superposition,[status(thm)],[c_82,c_142]) ).
tcf(c_265,plain,
sdtpldt0(sK1,sK2) = sdtpldt0(sK2,sK1),
inference(superposition,[status(thm)],[c_86,c_142]) ).
tcf(c_398,plain,
! [X0: $i] :
( ( sdtpldt0(sdtpldt0(sK2,xm),X0) = sdtpldt0(sK2,sdtpldt0(xm,X0)) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_81,c_187]) ).
tcf(c_516,plain,
! [X0: $i] :
( ( sdtpldt0(sdtpldt0(xm,sK2),X0) = sdtpldt0(xm,sdtpldt0(sK2,X0)) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_183]) ).
tcf(c_619,plain,
( aNaturalNumber0(sdtpldt0(sK1,sK2))
| ~ aNaturalNumber0(sK2)
| ~ aNaturalNumber0(sK1) ),
inference(superposition,[status(thm)],[c_265,c_52]) ).
tcf(c_658,plain,
sdtpldt0(sK2,xn) = xl,
inference(light_normalisation,[status(thm)],[c_263,c_90]) ).
tcf(c_1159,plain,
! [X0: $i] :
( ( sdtpldt0(sdtpldt0(xm,sK2),X0) = sdtpldt0(sK2,sdtpldt0(xm,X0)) )
| ~ aNaturalNumber0(X0) ),
inference(light_normalisation,[status(thm)],[c_398,c_262]) ).
tcf(c_1168,plain,
sdtpldt0(sdtpldt0(xm,sK2),sK1) = sdtpldt0(sK2,sdtpldt0(xm,sK1)),
inference(superposition,[status(thm)],[c_86,c_1159]) ).
tcf(c_1549,plain,
sdtpldt0(sdtpldt0(xm,sK2),sK1) = sdtpldt0(xm,sdtpldt0(sK2,sK1)),
inference(superposition,[status(thm)],[c_86,c_516]) ).
tcf(c_1819,plain,
aNaturalNumber0(sdtpldt0(sK1,sK2)),
inference(global_subsumption_just,[status(thm)],[c_619,c_89,c_86,c_619]) ).
tcf(c_5844,plain,
sdtpldt0(sdtpldt0(xm,sK2),sK1) = xl,
inference(light_normalisation,[status(thm)],[c_1168,c_87,c_658]) ).
tcf(c_8834,plain,
sdtpldt0(xm,sdtpldt0(sK1,sK2)) = xl,
inference(light_normalisation,[status(thm)],[c_1549,c_265,c_5844]) ).
tcf(c_8843,plain,
~ aNaturalNumber0(sdtpldt0(sK1,sK2)),
inference(superposition,[status(thm)],[c_8834,c_84]) ).
tcf(c_8844,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_1819,c_8843]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM460+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n013.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 04:04:36 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.42
% 0.14/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.42
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 1.05/1.74 % SZS status Started for theBenchmark.p
% 1.05/1.74 % SZS status Theorem for theBenchmark.p
% 1.05/1.74
% 1.05/1.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.05/1.74
% 1.05/1.74 % ------ iProver source info
% 1.05/1.74
% 1.05/1.74 % git: date: 2026-07-19 20:42:38 +0200
% 1.05/1.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.05/1.74 % git: non_committed_changes: false
% 1.05/1.74
% 1.05/1.74 % ------ Parsing...
% 1.05/1.74 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.05/1.74 % ------ Proving...
% 1.05/1.74 % ------ Problem Properties
% 1.05/1.74
% 1.05/1.74 %
% 1.05/1.74 % clauses 43
% 1.05/1.74 % conjectures 8
% 1.05/1.74 % EPR 13
% 1.05/1.74 % Horn 40
% 1.05/1.74 % unary 13
% 1.05/1.74 % binary 8
% 1.05/1.74 % lits 122
% 1.05/1.74 % lits eq 37
% 1.05/1.74 % fd_pure 0
% 1.05/1.74 % fd_pseudo 0
% 1.05/1.74 % fd_cond 3
% 1.05/1.74 % fd_pseudo_cond 5
% 1.05/1.74 % AC symbols 0
% 1.05/1.74
% 1.05/1.74 % ------ Input Options Time Limit: Unbounded
% 1.05/1.74
% 1.05/1.74
% 1.05/1.74 % ------
% 1.05/1.74 % Current options:
% 1.05/1.74 % ------
% 1.05/1.74
% 1.05/1.74
% 1.05/1.74 %
% 1.05/1.74
% 1.05/1.74 % ------ Proving...
% 1.05/1.74 %
% 1.05/1.74
% 1.05/1.74 % SZS status Theorem for theBenchmark.p
% 1.05/1.74
% 1.05/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.05/1.74
% 1.05/1.74
%------------------------------------------------------------------------------