%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM436+3 : 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 : n003.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 3.74s 1.27s
% Output : CNFRefutation 3.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 17 unt; 3 def)
% Number of atoms : 129 ( 33 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 141 ( 63 ~; 48 |; 29 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 8 ( 6 usr; 4 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 24 !; 6 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> aInteger0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
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)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ? [X0] :
( sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(X0) ) )
& ( sdteqdtlpzmzozddtrp0(xa,xb,xp)
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| ? [X0] :
( sdtasdt0(xp,X0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f28,negated_conjecture,
~ ( ( sdteqdtlpzmzozddtrp0(xa,xb,xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ? [X0] :
( sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(X0) ) )
& ( sdteqdtlpzmzozddtrp0(xa,xb,xp)
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| ? [X0] :
( sdtasdt0(xp,X0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f30,plain,
~ ( ( sdteqdtlpzmzozddtrp0(xa,xb,xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ? [X1] :
( sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,X1)
& aInteger0(X1) ) )
& ( sdteqdtlpzmzozddtrp0(xa,xb,xp)
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| ? [X0] :
( sdtasdt0(xp,X0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(X0) ) ) ),
inference(rectify,[],[f28]) ).
fof(f34,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f35,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f34]) ).
fof(f62,plain,
( ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& ! [X1] :
( sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,X1)
| ~ aInteger0(X1) ) )
| ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xp)
& ~ aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
& ! [X0] :
( sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xp,X0)
| ~ aInteger0(X0) ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f77,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f106,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f23]) ).
fof(f108,plain,
aInteger0(xp),
inference(cnf_transformation,[],[f23]) ).
fof(f117,plain,
aInteger0(xm),
inference(cnf_transformation,[],[f25]) ).
fof(f118,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f26]) ).
fof(f119,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xp,sdtasdt0(xq,xm)),
inference(cnf_transformation,[],[f26]) ).
fof(f125,plain,
! [X0] :
( sP0
| sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xp,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_83,plain,
aInteger0(xp),
inference(cnf_transformation,[],[f108]) ).
tcf(c_85,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f106]) ).
tcf(c_92,plain,
aInteger0(xm),
inference(cnf_transformation,[],[f117]) ).
tcf(c_94,plain,
sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)),
inference(cnf_transformation,[],[f119]) ).
tcf(c_95,plain,
sdtasdt0(xq,sdtasdt0(xp,xm)) = sdtpldt0(xa,smndt0(xb)),
inference(cnf_transformation,[],[f118]) ).
tcf(c_99,negated_conjecture,
! [X0: $i] :
( sP0
| ~ aInteger0(X0)
| ( sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xp,X0) ) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_1072,definition,
iPr_def_10 = smndt0(xb),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1073,definition,
iPr_def_11 = sdtpldt0(xa,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1076,negated_conjecture,
! [X0: $i] :
( sP0
| ~ aInteger0(X0)
| ( iPr_def_11 != sdtasdt0(xp,X0) ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_2295,plain,
sdtasdt0(xp,sdtasdt0(xq,xm)) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_94,c_1072,c_1073]) ).
tcf(c_2297,plain,
( sP0
| ~ aInteger0(sdtasdt0(xq,xm)) ),
inference(superposition,[status(thm)],[c_2295,c_1076]) ).
tcf(c_2300,plain,
sdtasdt0(xq,sdtasdt0(xp,xm)) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_95,c_1072,c_1073]) ).
tcf(c_2493,plain,
( sP0
| ~ aInteger0(xm)
| ~ aInteger0(xq) ),
inference(superposition,[status(thm)],[c_53,c_2297]) ).
tcf(c_2494,plain,
sP0,
inference(forward_subsumption_resolution,[status(thm)],[c_2493,c_92,c_85]) ).
fof(f63,definition,
( ~ sP0
| ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& ! [X1] :
( sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,X1)
| ~ aInteger0(X1) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f64,plain,
( sP0
| ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xp)
& ~ aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
& ! [X0] :
( sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xp,X0)
| ~ aInteger0(X0) ) ) ),
inference(definition_folding,[],[f62,f63]) ).
fof(f71,plain,
( ~ sP0
| ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& ! [X1] :
( sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,X1)
| ~ aInteger0(X1) ) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f72,plain,
( ~ sP0
| ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& ! [X0] :
( sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,X0)
| ~ aInteger0(X0) ) ) ),
inference(rectify,[],[f71]) ).
fof(f122,plain,
! [X0] :
( ~ sP0
| sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_96,plain,
! [X0: $i] :
( ~ sP0
| ~ aInteger0(X0)
| ( sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,X0) ) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_2571,plain,
! [X0: $i] :
( ( sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,X0) )
| ~ aInteger0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_96,c_96,c_2494]) ).
tcf(c_2572,plain,
! [X0: $i] :
( ~ aInteger0(X0)
| ( sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,X0) ) ),
inference(renaming,[status(thm)],[c_2571]) ).
tcf(c_2574,plain,
! [X0: $i] :
( ~ aInteger0(X0)
| ( sdtasdt0(xq,X0) != iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_2572,c_1072,c_1073]) ).
tcf(c_2581,plain,
~ aInteger0(sdtasdt0(xp,xm)),
inference(superposition,[status(thm)],[c_2300,c_2574]) ).
tcf(c_2794,plain,
( ~ aInteger0(xm)
| ~ aInteger0(xp) ),
inference(superposition,[status(thm)],[c_53,c_2581]) ).
tcf(c_2795,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2794,c_92,c_83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM436+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n003.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 03:59:50 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 3.74/1.27 % SZS status Started for theBenchmark.p
% 3.74/1.27 % SZS status Theorem for theBenchmark.p
% 3.74/1.27
% 3.74/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.74/1.27
% 3.74/1.27 % ------ iProver source info
% 3.74/1.27
% 3.74/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.74/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.74/1.27 % git: non_committed_changes: false
% 3.74/1.27
% 3.74/1.27 % ------ Parsing...
% 3.74/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.74/1.27
% 3.74/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.74/1.27
% 3.74/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.74/1.27
% 3.74/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.74/1.27 % ------ Proving...
% 3.74/1.27 % ------ Problem Properties
% 3.74/1.27
% 3.74/1.27 %
% 3.74/1.27 % clauses 55
% 3.74/1.27 % conjectures 3
% 3.74/1.27 % EPR 18
% 3.74/1.27 % Horn 48
% 3.74/1.27 % unary 19
% 3.74/1.27 % binary 16
% 3.74/1.27 % lits 133
% 3.74/1.27 % lits eq 37
% 3.74/1.27 % fd_pure 0
% 3.74/1.27 % fd_pseudo 0
% 3.74/1.27 % fd_cond 7
% 3.74/1.27 % fd_pseudo_cond 0
% 3.74/1.27 % AC symbols 0
% 3.74/1.27
% 3.74/1.27 % ------ Schedule dynamic 5 is on
% 3.74/1.27
% 3.74/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.74/1.27
% 3.74/1.27
% 3.74/1.27 % ------
% 3.74/1.27 % Current options:
% 3.74/1.27 % ------
% 3.74/1.27
% 3.74/1.27
% 3.74/1.27 %
% 3.74/1.27
% 3.74/1.27 % ------ Proving...
% 3.74/1.27 %
% 3.74/1.27
% 3.74/1.27 % SZS status Theorem for theBenchmark.p
% 3.74/1.27
% 3.74/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.74/1.27
% 3.74/1.27
%------------------------------------------------------------------------------