%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN986+1.003 : 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 : 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 03:45:35 PM UTC 2026
% Result : Theorem 1.61s 6.28s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 40 ( 15 unt; 0 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 110 ( 55 ~; 47 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 17 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 72 ( 0 sgn 64 !; 8 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : r(X0,zero,succ(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN002+0.ax',hyp1) ).
fof(f2,axiom,
! [X0,X1,X2,X3] :
( r(X0,X1,X2)
=> ( r(X2,X1,X3)
=> r(X0,succ(X1),X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN002+0.ax',hyp2) ).
fof(f3,conjecture,
? [X0,X1,X2,X3] :
( r(zero,X2,X3)
& r(zero,X1,X2)
& r(zero,X0,X1)
& r(zero,zero,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ck) ).
fof(f4,negated_conjecture,
~ ? [X0,X1,X2,X3] :
( r(zero,X2,X3)
& r(zero,X1,X2)
& r(zero,X0,X1)
& r(zero,zero,X0) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [X0,X1,X2,X3] :
( ~ r(X0,X1,X2)
| ~ r(X2,X1,X3)
| r(X0,succ(X1),X3) ),
inference(ennf_transformation,[],[f2]) ).
fof(f6,plain,
! [X0,X1,X2,X3] :
( ~ r(X0,X1,X2)
| ~ r(X2,X1,X3)
| r(X0,succ(X1),X3) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X0,X1,X2,X3] :
( ~ r(zero,X2,X3)
| ~ r(zero,X1,X2)
| ~ r(zero,X0,X1)
| ~ r(zero,zero,X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f8,plain,
! [X0] : r(X0,zero,succ(X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f9,plain,
! [X2,X3,X0,X1] :
( ~ r(X0,X1,X2)
| ~ r(X2,X1,X3)
| r(X0,succ(X1),X3) ),
inference(cnf_transformation,[],[f6]) ).
fof(f10,plain,
! [X2,X3,X0,X1] :
( ~ r(zero,X2,X3)
| ~ r(zero,X1,X2)
| ~ r(zero,X0,X1)
| ~ r(zero,zero,X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_49,plain,
! [X0: $i] : r(X0,zero,succ(X0)),
inference(cnf_transformation,[],[f8]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r(X0,succ(X1),X3)
| ~ r(X2,X1,X3)
| ~ r(X0,X1,X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ r(zero,zero,X0)
| ~ r(zero,X2,X3)
| ~ r(zero,X1,X2)
| ~ r(zero,X0,X1) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_52,plain,
r(zero,zero,succ(zero)),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_71,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ r(zero,zero,X0)
| ~ r(zero,X2,X3)
| ~ r(zero,X1,X2)
| ~ r(zero,X0,X1) ),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ r(zero,X1,X2)
| ~ r(zero,X0,X1)
| ~ r(zero,zero,succ(zero))
| ~ r(zero,succ(zero),X0) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( r(X0,succ(zero),X1)
| ~ r(X0,zero,succ(X0))
| ~ r(succ(X0),zero,X1) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_78,plain,
! [X0: $i] :
( r(X0,succ(zero),succ(succ(X0)))
| ~ r(X0,zero,succ(X0))
| ~ r(succ(X0),zero,succ(succ(X0))) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_79,plain,
! [X0: $i] : r(succ(X0),zero,succ(succ(X0))),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_80,plain,
( r(zero,succ(zero),succ(succ(zero)))
| ~ r(zero,zero,succ(zero))
| ~ r(succ(zero),zero,succ(succ(zero))) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_81,plain,
r(succ(zero),zero,succ(succ(zero))),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( r(X0,succ(succ(zero)),X1)
| ~ r(X0,succ(zero),succ(succ(X0)))
| ~ r(succ(succ(X0)),succ(zero),X1) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( ~ r(zero,X0,X1)
| ~ r(zero,zero,succ(zero))
| ~ r(zero,succ(succ(zero)),X0)
| ~ r(zero,succ(zero),succ(succ(zero))) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_98,plain,
! [X0: $i] :
( r(zero,succ(succ(zero)),X0)
| ~ r(zero,succ(zero),succ(succ(zero)))
| ~ r(succ(succ(zero)),succ(zero),X0) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_116,plain,
( r(zero,succ(succ(zero)),succ(succ(succ(succ(zero)))))
| ~ r(zero,succ(zero),succ(succ(zero)))
| ~ r(succ(succ(zero)),succ(zero),succ(succ(succ(succ(zero))))) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_117,plain,
( r(succ(succ(zero)),succ(zero),succ(succ(succ(succ(zero)))))
| ~ r(succ(succ(zero)),zero,succ(succ(succ(zero))))
| ~ r(succ(succ(succ(zero))),zero,succ(succ(succ(succ(zero))))) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( r(X0,succ(zero),X1)
| ~ r(succ(X0),zero,X1) ),
inference(superposition,[status(thm)],[c_49,c_50]) ).
tcf(c_153,plain,
r(succ(succ(zero)),zero,succ(succ(succ(zero)))),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_156,plain,
! [X0: $i] : r(succ(succ(X0)),zero,succ(succ(succ(X0)))),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_163,plain,
r(succ(succ(succ(zero))),zero,succ(succ(succ(succ(zero))))),
inference(instantiation,[status(thm)],[c_156]) ).
tcf(c_180,plain,
! [X0: $i] : r(X0,succ(zero),succ(succ(X0))),
inference(superposition,[status(thm)],[c_49,c_138]) ).
tcf(c_199,plain,
! [X0: $i,X1: $i] :
( r(X0,succ(succ(zero)),X1)
| ~ r(succ(succ(X0)),succ(zero),X1) ),
inference(superposition,[status(thm)],[c_180,c_50]) ).
tcf(c_268,plain,
! [X0: $i] : r(X0,succ(succ(zero)),succ(succ(succ(succ(X0))))),
inference(superposition,[status(thm)],[c_180,c_199]) ).
tcf(c_323,plain,
! [X0: $i,X1: $i] :
( r(X0,succ(succ(succ(zero))),X1)
| ~ r(succ(succ(succ(succ(X0)))),succ(succ(zero)),X1) ),
inference(superposition,[status(thm)],[c_268,c_50]) ).
tcf(c_344,plain,
( ~ r(zero,zero,succ(zero))
| ~ r(zero,succ(zero),succ(succ(zero)))
| ~ r(zero,succ(succ(zero)),succ(succ(succ(succ(zero)))))
| ~ r(zero,succ(succ(succ(succ(zero)))),succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(zero))))))))))))))))) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_377,plain,
! [X0: $i] : r(X0,succ(succ(succ(zero))),succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))),
inference(superposition,[status(thm)],[c_268,c_323]) ).
tcf(c_427,plain,
! [X0: $i,X1: $i] :
( r(X0,succ(succ(succ(succ(zero)))),X1)
| ~ r(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))),succ(succ(succ(zero))),X1) ),
inference(superposition,[status(thm)],[c_377,c_50]) ).
tcf(c_488,plain,
! [X0: $i] : r(X0,succ(succ(succ(succ(zero)))),succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))))))),
inference(superposition,[status(thm)],[c_377,c_427]) ).
tcf(c_489,plain,
r(zero,succ(succ(succ(succ(zero)))),succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(zero))))))))))))))))),
inference(instantiation,[status(thm)],[c_488]) ).
tcf(c_490,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_489,c_344,c_163,c_153,c_117,c_116,c_81,c_80,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN986+1.003 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.37 % Computer : n004.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Fri Sep 25 02:44:00 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 1.61/6.28 % SZS status Started for theBenchmark.p
% 1.61/6.28 % SZS status Theorem for theBenchmark.p
% 1.61/6.28
% 1.61/6.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.61/6.28
% 1.61/6.28 % ------ iProver source info
% 1.61/6.28
% 1.61/6.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.61/6.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.61/6.28 % git: non_committed_changes: false
% 1.61/6.28
% 1.61/6.28 % ------ Parsing...
% 1.61/6.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.61/6.28
% 1.61/6.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.61/6.28
% 1.61/6.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.61/6.28 % ------ Proving...
% 1.61/6.28 % ------ Problem Properties
% 1.61/6.28
% 1.61/6.28 %
% 1.61/6.28 % clauses 3
% 1.61/6.28 % conjectures 1
% 1.61/6.28 % EPR 1
% 1.61/6.28 % Horn 3
% 1.61/6.28 % unary 1
% 1.61/6.28 % binary 0
% 1.61/6.28 % lits 8
% 1.61/6.28 % lits eq 0
% 1.61/6.28 % fd_pure 0
% 1.61/6.28 % fd_pseudo 0
% 1.61/6.28 % fd_cond 0
% 1.61/6.28 % fd_pseudo_cond 0
% 1.61/6.28 % AC symbols 0
% 1.61/6.28
% 1.61/6.28 % ------ Schedule dynamic 5 is on
% 1.61/6.28
% 1.61/6.28 % ------ no equalities: superposition off
% 1.61/6.28
% 1.61/6.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.61/6.28
% 1.61/6.28
% 1.61/6.28 % ------
% 1.61/6.28 % Current options:
% 1.61/6.28 % ------
% 1.61/6.28
% 1.61/6.28
% 1.61/6.28 %
% 1.61/6.28
% 1.61/6.28 % ------ Proving...
% 1.61/6.28 %
% 1.61/6.28
% 1.61/6.28 % SZS status Theorem for theBenchmark.p
% 1.61/6.28
% 1.61/6.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.61/6.28
% 1.61/6.28
%------------------------------------------------------------------------------