%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN413+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n017.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 03:40:00 PM UTC 2026
% Result : Theorem 1.40s 11.18s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 76 ( 31 ~; 24 |; 16 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 52 ( 0 sgn 40 !; 12 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
? [X1] :
! [X2] :
( f(X2,X1)
<=> ( ~ f(X2,X2)
& f(X2,X0) ) )
=> ~ ? [X3] :
! [X4] : f(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kalish256) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
? [X1] :
! [X2] :
( f(X2,X1)
<=> ( ~ f(X2,X2)
& f(X2,X0) ) )
=> ~ ? [X3] :
! [X4] : f(X4,X3) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X0] :
? [X1] :
! [X2] :
( f(X2,X1)
<=> ( ~ f(X2,X2)
& f(X2,X0) ) )
& ? [X3] :
! [X4] : f(X4,X3) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ! [X0] :
? [X1] :
! [X2] :
( ( ~ f(X2,X1)
| ( ~ f(X2,X2)
& f(X2,X0) ) )
& ( f(X2,X2)
| ~ f(X2,X0)
| f(X2,X1) ) )
& ? [X3] :
! [X4] : f(X4,X3) ),
inference(nnf_transformation,[],[f3]) ).
fof(f5,plain,
( ! [X0] :
? [X1] :
! [X2] :
( ( ~ f(X2,X1)
| ( ~ f(X2,X2)
& f(X2,X0) ) )
& ( f(X2,X2)
| ~ f(X2,X0)
| f(X2,X1) ) )
& ? [X3] :
! [X4] : f(X4,X3) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
( ! [X2] :
? [X3] :
! [X4] :
( ( ~ f(X4,X3)
| ( ~ f(X4,X4)
& f(X4,X2) ) )
& ( f(X4,X4)
| ~ f(X4,X2)
| f(X4,X3) ) )
& ? [X0] :
! [X1] : f(X1,X0) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ! [X2,X4] :
( ( ~ f(X4,sK1(X2))
| ( ~ f(X4,X4)
& f(X4,X2) ) )
& ( f(X4,X4)
| ~ f(X4,X2)
| f(X4,sK1(X2)) ) )
& ! [X1] : f(X1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X3,sK1(X2))],[f6]) ).
fof(f8,plain,
! [X2,X4] :
( ~ f(X4,sK1(X2))
| ~ f(X4,X4) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X2,X4] :
( f(X4,X4)
| ~ f(X4,X2)
| f(X4,sK1(X2)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X1] : f(X1,sK0),
inference(cnf_transformation,[],[f7]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] : f(X0,sK0),
inference(cnf_transformation,[],[f11]) ).
tcf(c_50,negated_conjecture,
! [X0: $i,X1: $i] :
( f(X0,X0)
| f(X0,sK1(X1))
| ~ f(X0,X1) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ f(X0,X0)
| ~ f(X0,sK1(X1)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_71,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ f(X0,X0)
| ~ f(X0,sK1(X1)) ),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_73,negated_conjecture,
! [X0: $i,X1: $i] :
( f(X0,X0)
| f(X0,sK1(X1))
| ~ f(X0,X1) ),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_74,negated_conjecture,
! [X0: $i] : f(X0,sK0),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( f(sK1(X0),sK1(X1))
| f(sK1(X0),sK1(X0))
| ~ f(sK1(X0),X1) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_78,plain,
! [X0: $i] : ~ f(sK1(X0),sK1(X0)),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_79,plain,
( f(sK1(sK0),sK1(sK0))
| ~ f(sK1(sK0),sK0) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_80,plain,
~ f(sK1(sK0),sK1(sK0)),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_87,plain,
! [X0: $i] : f(sK1(X0),sK0),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_88,plain,
f(sK1(sK0),sK0),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_89,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_88,c_80,c_79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN413+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/10.38 % Computer : n017.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Fri Sep 25 01:01:58 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/10.42 Running first-order theorem proving
% 0.13/10.42 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
% 0.13/10.43
% 0.13/10.43 % ======== iProver multi-core TPTP/SMT =========
% 0.13/10.43
% 0.13/10.43 % Detected problem language: tptp
% 0.13/10.44 % Proving...
% 1.40/11.18 % SZS status Started for theBenchmark.p
% 1.40/11.18 % SZS status Theorem for theBenchmark.p
% 1.40/11.18
% 1.40/11.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.40/11.18
% 1.40/11.18 % ------ iProver source info
% 1.40/11.18
% 1.40/11.18 % git: date: 2026-07-19 20:42:38 +0200
% 1.40/11.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.40/11.18 % git: non_committed_changes: false
% 1.40/11.18
% 1.40/11.18 % ------ Parsing...
% 1.40/11.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.40/11.18
% 1.40/11.18 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.40/11.18
% 1.40/11.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.40/11.18 % ------ Proving...
% 1.40/11.18 % ------ Problem Properties
% 1.40/11.18
% 1.40/11.18 %
% 1.40/11.18 % clauses 4
% 1.40/11.18 % conjectures 4
% 1.40/11.18 % EPR 1
% 1.40/11.18 % Horn 3
% 1.40/11.18 % unary 1
% 1.40/11.18 % binary 2
% 1.40/11.18 % lits 8
% 1.40/11.18 % lits eq 0
% 1.40/11.18 % fd_pure 0
% 1.40/11.18 % fd_pseudo 0
% 1.40/11.18 % fd_cond 0
% 1.40/11.18 % fd_pseudo_cond 0
% 1.40/11.18 % AC symbols 0
% 1.40/11.18
% 1.40/11.18 % ------ Schedule dynamic 5 is on
% 1.40/11.18
% 1.40/11.18 % ------ no equalities: superposition off
% 1.40/11.18
% 1.40/11.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.40/11.18
% 1.40/11.18
% 1.40/11.18 % ------
% 1.40/11.18 % Current options:
% 1.40/11.18 % ------
% 1.40/11.18
% 1.40/11.18
% 1.40/11.18 %
% 1.40/11.18
% 1.40/11.18 % ------ Proving...
% 1.40/11.18 %
% 1.40/11.18
% 1.40/11.18 % SZS status Theorem for theBenchmark.p
% 1.40/11.18
% 1.40/11.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.40/11.18
% 1.40/11.18
%------------------------------------------------------------------------------