%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM436+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 : n015.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 02:24:27 PM UTC 2026
% Result : Theorem 6.07s 2.20s
% Output : CNFRefutation 6.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 69 ( 23 unt; 0 def)
% Number of atoms : 225 ( 57 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 266 ( 110 ~; 110 |; 37 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 65 !; 5 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> aInteger0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
fof(f12,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f18,axiom,
! [X0] :
( aInteger0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
fof(f19,axiom,
! [X0,X1,X2] :
( ( X2 != sz00
& aInteger0(X2)
& aInteger0(X1)
& aInteger0(X0) )
=> ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquMod) ).
fof(f23,axiom,
( xq != sz00
& aInteger0(xq)
& xp != sz00
& aInteger0(xp)
& aInteger0(xb)
& aInteger0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__979) ).
fof(f25,axiom,
( sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1032) ).
fof(f26,axiom,
( sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm))
& sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1071) ).
fof(f27,conjecture,
( sdteqdtlpzmzozddtrp0(xa,xb,xq)
& sdteqdtlpzmzozddtrp0(xa,xb,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f28,negated_conjecture,
~ ( sdteqdtlpzmzozddtrp0(xa,xb,xq)
& sdteqdtlpzmzozddtrp0(xa,xb,xp) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f33,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f34,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f33]) ).
fof(f43,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f44,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f43]) ).
fof(f52,plain,
! [X0] :
( ~ aInteger0(X0)
| ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f53,plain,
! [X0,X1,X2] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f54,plain,
! [X0,X1,X2] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
inference(flattening,[],[f53]) ).
fof(f61,plain,
( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xp) ),
inference(ennf_transformation,[],[f28]) ).
fof(f62,plain,
! [X0] :
( ~ aInteger0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) ) )
& ( ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f63,plain,
! [X0] :
( ~ aInteger0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) ) )
& ( ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0] :
( ~ aInteger0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( ? [X3] :
( sdtasdt0(X1,X3) = X0
& aInteger0(X3) )
& X1 != sz00
& aInteger0(X1) ) )
& ( ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(rectify,[],[f63]) ).
fof(f65,plain,
! [X0] :
( ~ aInteger0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( sdtasdt0(X1,sK0(X0,X1)) = X0
& aInteger0(sK0(X0,X1))
& X1 != sz00
& aInteger0(X1) ) )
& ( ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f64]) ).
fof(f66,plain,
! [X0,X1,X2] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( ( ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
& ( ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f71,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f79,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f93,plain,
! [X2,X0,X1] :
( ~ aInteger0(X0)
| sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2)
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f95,plain,
! [X2,X0,X1] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X0,X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f99,plain,
sz00 != xq,
inference(cnf_transformation,[],[f23]) ).
fof(f100,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f23]) ).
fof(f101,plain,
sz00 != xp,
inference(cnf_transformation,[],[f23]) ).
fof(f102,plain,
aInteger0(xp),
inference(cnf_transformation,[],[f23]) ).
fof(f103,plain,
aInteger0(xb),
inference(cnf_transformation,[],[f23]) ).
fof(f104,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f23]) ).
fof(f107,plain,
aInteger0(xm),
inference(cnf_transformation,[],[f25]) ).
fof(f108,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f26]) ).
fof(f109,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xp,sdtasdt0(xq,xm)),
inference(cnf_transformation,[],[f26]) ).
fof(f110,plain,
( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xp) ),
inference(cnf_transformation,[],[f61]) ).
fof(f111,plain,
! [X2,X1] :
( ~ aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X2)
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,sdtasdt0(X1,X2)) ),
inference(equality_resolution,[],[f93]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( aDivisorOf0(X0,sdtasdt0(X0,X1))
| ( X0 = sz00 )
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aInteger0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdteqdtlpzmzozddtrp0(X1,X2,X0)
| ( X0 = sz00 )
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(X2))) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_81,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f104]) ).
tcf(c_82,plain,
aInteger0(xb),
inference(cnf_transformation,[],[f103]) ).
tcf(c_83,plain,
aInteger0(xp),
inference(cnf_transformation,[],[f102]) ).
tcf(c_84,plain,
sz00 != xp,
inference(cnf_transformation,[],[f101]) ).
tcf(c_85,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f100]) ).
tcf(c_86,plain,
sz00 != xq,
inference(cnf_transformation,[],[f99]) ).
tcf(c_88,plain,
aInteger0(xm),
inference(cnf_transformation,[],[f107]) ).
tcf(c_90,plain,
sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)),
inference(cnf_transformation,[],[f109]) ).
tcf(c_91,plain,
sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtpldt0(xa,smndt0(xb)),
inference(cnf_transformation,[],[f108]) ).
tcf(c_92,negated_conjecture,
( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xp) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] :
( aDivisorOf0(X0,sdtasdt0(X0,X1))
| ( X0 = sz00 )
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_71,c_53,c_71]) ).
tcf(c_1891,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xp) = sdtasdt0(xp,X0) )
| ~ aInteger0(X0) ),
inference(superposition,[status(thm)],[c_83,c_61]) ).
tcf(c_1892,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xq) = sdtasdt0(xq,X0) )
| ~ aInteger0(X0) ),
inference(superposition,[status(thm)],[c_85,c_61]) ).
tcf(c_15301,plain,
( aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| ( sz00 = xp )
| ~ aInteger0(xp)
| ~ aInteger0(sdtasdt0(xq,xm)) ),
inference(superposition,[status(thm)],[c_90,c_115]) ).
tcf(c_15302,plain,
( aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ( sz00 = xq )
| ~ aInteger0(xq)
| ~ aInteger0(sdtasdt0(xp,xm)) ),
inference(superposition,[status(thm)],[c_91,c_115]) ).
tcf(c_15389,plain,
( aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtasdt0(xp,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15302,c_86,c_85]) ).
tcf(c_15392,plain,
( aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtasdt0(xq,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15301,c_84,c_83]) ).
tcf(c_16583,plain,
( sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ( sz00 = xq )
| ~ aInteger0(xq)
| ~ aInteger0(xb)
| ~ aInteger0(xa)
| ~ aInteger0(sdtasdt0(xp,xm)) ),
inference(superposition,[status(thm)],[c_15389,c_76]) ).
tcf(c_16584,plain,
( sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ aInteger0(sdtasdt0(xp,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16583,c_86,c_85,c_82,c_81]) ).
tcf(c_16596,plain,
( sdteqdtlpzmzozddtrp0(xa,xb,xp)
| ( sz00 = xp )
| ~ aInteger0(xp)
| ~ aInteger0(xb)
| ~ aInteger0(xa)
| ~ aInteger0(sdtasdt0(xq,xm)) ),
inference(superposition,[status(thm)],[c_15392,c_76]) ).
tcf(c_16597,plain,
( sdteqdtlpzmzozddtrp0(xa,xb,xp)
| ~ aInteger0(sdtasdt0(xq,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16596,c_84,c_83,c_82,c_81]) ).
tcf(c_20634,plain,
sdtasdt0(xp,xm) = sdtasdt0(xm,xp),
inference(superposition,[status(thm)],[c_88,c_1891]) ).
tcf(c_21102,plain,
( aInteger0(sdtasdt0(xp,xm))
| ~ aInteger0(xm)
| ~ aInteger0(xp) ),
inference(superposition,[status(thm)],[c_20634,c_53]) ).
tcf(c_21103,plain,
aInteger0(sdtasdt0(xp,xm)),
inference(forward_subsumption_resolution,[status(thm)],[c_21102,c_88,c_83]) ).
tcf(c_22728,plain,
sdtasdt0(xq,xm) = sdtasdt0(xm,xq),
inference(superposition,[status(thm)],[c_88,c_1892]) ).
tcf(c_23037,plain,
( aInteger0(sdtasdt0(xq,xm))
| ~ aInteger0(xm)
| ~ aInteger0(xq) ),
inference(superposition,[status(thm)],[c_22728,c_53]) ).
tcf(c_23038,plain,
aInteger0(sdtasdt0(xq,xm)),
inference(forward_subsumption_resolution,[status(thm)],[c_23037,c_88,c_85]) ).
tcf(c_23045,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_23038,c_21103,c_16597,c_16584,c_92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM436+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 04:01:25 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 0.15/0.43
% 0.15/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.43
% 0.15/0.43 % Detected problem language: tptp
% 0.15/0.44 % Proving...
% 6.07/2.20 % SZS status Started for theBenchmark.p
% 6.07/2.20 % SZS status Theorem for theBenchmark.p
% 6.07/2.20
% 6.07/2.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.07/2.20
% 6.07/2.20 % ------ iProver source info
% 6.07/2.20
% 6.07/2.20 % git: date: 2026-07-19 20:42:38 +0200
% 6.07/2.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.07/2.20 % git: non_committed_changes: false
% 6.07/2.20
% 6.07/2.20 % ------ Parsing...
% 6.07/2.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.07/2.20
% 6.07/2.20 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 6.07/2.20
% 6.07/2.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.07/2.20
% 6.07/2.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.07/2.20 % ------ Proving...
% 6.07/2.20 % ------ Problem Properties
% 6.07/2.20
% 6.07/2.20 %
% 6.07/2.20 % clauses 44
% 6.07/2.20 % conjectures 1
% 6.07/2.20 % EPR 15
% 6.07/2.20 % Horn 37
% 6.07/2.20 % unary 13
% 6.07/2.20 % binary 13
% 6.07/2.20 % lits 115
% 6.07/2.20 % lits eq 31
% 6.07/2.20 % fd_pure 0
% 6.07/2.20 % fd_pseudo 0
% 6.07/2.20 % fd_cond 7
% 6.07/2.20 % fd_pseudo_cond 0
% 6.07/2.20 % AC symbols 0
% 6.07/2.20
% 6.07/2.20 % ------ Schedule dynamic 5 is on
% 6.07/2.20
% 6.07/2.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.07/2.20
% 6.07/2.20
% 6.07/2.20 % ------
% 6.07/2.20 % Current options:
% 6.07/2.20 % ------
% 6.07/2.20
% 6.07/2.20
% 6.07/2.20 %
% 6.07/2.20
% 6.07/2.20 % ------ Proving...
% 6.07/2.20 %
% 6.07/2.20
% 6.07/2.20 % SZS status Theorem for theBenchmark.p
% 6.07/2.20
% 6.07/2.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.07/2.20
% 6.07/2.20
%------------------------------------------------------------------------------