%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM513+3 : 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 : n004.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 02:25:47 PM UTC 2026
% Result : Theorem 4.34s 1.30s
% Output : CNFRefutation 4.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 60 ( 30 unt; 0 def)
% Number of atoms : 192 ( 83 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 198 ( 66 ~; 57 |; 65 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 40 !; 7 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f36,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& X0 != sz00 )
=> ! [X2] :
( aNaturalNumber0(X2)
=> sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivAsso) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f45,axiom,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(f48,axiom,
( isPrime0(xr)
& ! [X0] :
( ( ( doDivides0(X0,xr)
| ? [X1] :
( xr = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xr
| X0 = sz10 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(f52,axiom,
( doDivides0(xr,xn)
& ? [X0] :
( xn = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2487) ).
fof(f55,conjecture,
( ( xk = sdtasdt0(xr,sdtsldt0(xk,xr))
& aNaturalNumber0(sdtsldt0(xk,xr)) )
=> ( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) )
=> sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f56,negated_conjecture,
~ ( ( xk = sdtasdt0(xr,sdtsldt0(xk,xr))
& aNaturalNumber0(sdtsldt0(xk,xr)) )
=> ( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) )
=> sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) ) ),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f62,plain,
( isPrime0(xr)
& ! [X1] :
( ( ( doDivides0(X1,xr)
| ? [X2] :
( sdtasdt0(X1,X2) = xr
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( xr = X1
| sz10 = X1 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ),
inference(rectify,[],[f48]) ).
fof(f74,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f75,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f74]) ).
fof(f123,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f124,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0) ) ),
inference(flattening,[],[f123]) ).
fof(f136,plain,
( isPrime0(xr)
& ! [X1] :
( ( ~ doDivides0(X1,xr)
& ! [X2] :
( sdtasdt0(X1,X2) != xr
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| xr = X1
| sz10 = X1 )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ),
inference(ennf_transformation,[],[f62]) ).
fof(f137,plain,
( isPrime0(xr)
& ! [X1] :
( ( ~ doDivides0(X1,xr)
& ! [X2] :
( sdtasdt0(X1,X2) != xr
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| xr = X1
| sz10 = X1 )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ),
inference(flattening,[],[f136]) ).
fof(f140,plain,
( xk = sdtasdt0(xr,sdtsldt0(xk,xr))
& aNaturalNumber0(sdtsldt0(xk,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,sdtsldt0(xk,xr)) ),
inference(ennf_transformation,[],[f56]) ).
fof(f141,plain,
( xk = sdtasdt0(xr,sdtsldt0(xk,xr))
& aNaturalNumber0(sdtsldt0(xk,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,sdtsldt0(xk,xr)) ),
inference(flattening,[],[f140]) ).
fof(f172,plain,
( isPrime0(xr)
& ! [X1] :
( ( ~ doDivides0(X1,xr)
& ! [X2] :
( sdtasdt0(X1,X2) != xr
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| xr = X1
| sz10 = X1 )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& xk = sdtasdt0(xr,sK14)
& aNaturalNumber0(sK14)
& aNaturalNumber0(xr) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f137]) ).
fof(f179,plain,
( doDivides0(xr,xn)
& xn = sdtasdt0(xr,sK20)
& aNaturalNumber0(sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X0,sK20)],[f52]) ).
fof(f190,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f238,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f249,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f250,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f251,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f289,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f45]) ).
fof(f290,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f45]) ).
fof(f299,plain,
sz00 != xr,
inference(cnf_transformation,[],[f172]) ).
fof(f300,plain,
doDivides0(xr,xk),
inference(cnf_transformation,[],[f172]) ).
fof(f303,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f172]) ).
fof(f319,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f179]) ).
fof(f339,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(cnf_transformation,[],[f141]) ).
fof(f340,plain,
sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,sdtsldt0(xk,xr)),
inference(cnf_transformation,[],[f141]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sz00 )
| ( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f238]) ).
tcf(c_116,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f251]) ).
tcf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f250]) ).
tcf(c_118,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f249]) ).
tcf(c_155,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f290]) ).
tcf(c_156,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f289]) ).
tcf(c_162,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f303]) ).
tcf(c_165,plain,
doDivides0(xr,xk),
inference(cnf_transformation,[],[f300]) ).
tcf(c_166,plain,
sz00 != xr,
inference(cnf_transformation,[],[f299]) ).
tcf(c_188,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f319]) ).
tcf(c_203,negated_conjecture,
sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,sdtsldt0(xk,xr)),
inference(cnf_transformation,[],[f340]) ).
tcf(c_204,negated_conjecture,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(cnf_transformation,[],[f339]) ).
tcf(c_268,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xm) = sdtasdt0(xm,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_117,c_58]) ).
tcf(c_375,plain,
! [X0: $i] :
( ( sz00 = xr )
| ( sdtasdt0(X0,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(X0,xk),xr) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_165,c_105]) ).
tcf(c_377,plain,
! [X0: $i] :
( ( sz00 = xr )
| ( sdtasdt0(X0,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(X0,xn),xr) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_188,c_105]) ).
tcf(c_547,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(superposition,[status(thm)],[c_116,c_268]) ).
tcf(c_552,plain,
sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xm,sdtsldt0(xn,xr)),
inference(superposition,[status(thm)],[c_204,c_268]) ).
tcf(c_557,plain,
sdtasdt0(xm,sdtsldt0(xn,xr)) != sdtasdt0(xp,sdtsldt0(xk,xr)),
inference(demodulation,[status(thm)],[c_203,c_552]) ).
tcf(c_1132,plain,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(X0,xn),xr) ) ),
inference(global_subsumption_just,[status(thm)],[c_377,c_162,c_116,c_166,c_377]) ).
tcf(c_1133,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(X0,xn),xr) )
| ~ aNaturalNumber0(X0) ),
inference(renaming,[status(thm)],[c_1132]) ).
tcf(c_1142,plain,
sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(xm,xn),xr),
inference(superposition,[status(thm)],[c_117,c_1133]) ).
tcf(c_1169,plain,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(X0,xk),xr) ) ),
inference(global_subsumption_just,[status(thm)],[c_375,c_162,c_155,c_166,c_375]) ).
tcf(c_1170,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(X0,xk),xr) )
| ~ aNaturalNumber0(X0) ),
inference(renaming,[status(thm)],[c_1169]) ).
tcf(c_1180,plain,
sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(xp,xk),xr),
inference(superposition,[status(thm)],[c_118,c_1170]) ).
tcf(c_5223,plain,
sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(xn,xm),xr),
inference(light_normalisation,[status(thm)],[c_1142,c_547]) ).
tcf(c_5553,plain,
sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtasdt0(xp,sdtsldt0(xk,xr)),
inference(light_normalisation,[status(thm)],[c_1180,c_156,c_5223]) ).
tcf(c_5554,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5553,c_557]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM513+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n004.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 04:22:50 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 4.34/1.30 % SZS status Started for theBenchmark.p
% 4.34/1.30 % SZS status Theorem for theBenchmark.p
% 4.34/1.30
% 4.34/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.34/1.30
% 4.34/1.30 % ------ iProver source info
% 4.34/1.30
% 4.34/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 4.34/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.34/1.30 % git: non_committed_changes: false
% 4.34/1.30
% 4.34/1.30 % ------ Parsing...
% 4.34/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.34/1.30 % ------ Proving...
% 4.34/1.30 % ------ Problem Properties
% 4.34/1.30
% 4.34/1.30 %
% 4.34/1.30 % clauses 159
% 4.34/1.30 % conjectures 5
% 4.34/1.30 % EPR 57
% 4.34/1.30 % Horn 114
% 4.34/1.30 % unary 67
% 4.34/1.30 % binary 22
% 4.34/1.30 % lits 467
% 4.34/1.30 % lits eq 148
% 4.34/1.30 % fd_pure 0
% 4.34/1.30 % fd_pseudo 0
% 4.34/1.30 % fd_cond 24
% 4.34/1.30 % fd_pseudo_cond 15
% 4.34/1.30 % AC symbols 0
% 4.34/1.30
% 4.34/1.30 % ------ Input Options Time Limit: Unbounded
% 4.34/1.30
% 4.34/1.30
% 4.34/1.30 % ------
% 4.34/1.30 % Current options:
% 4.34/1.30 % ------
% 4.34/1.30
% 4.34/1.30
% 4.34/1.30 %
% 4.34/1.30
% 4.34/1.30 % ------ Proving...
% 4.34/1.30 %
% 4.34/1.30
% 4.34/1.30 % SZS status Theorem for theBenchmark.p
% 4.34/1.30
% 4.34/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.34/1.30
% 4.34/1.30
%------------------------------------------------------------------------------