%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN352+1 : TPTP v9.3.1. Released v2.0.0.
% 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 03:39:49 PM UTC 2026
% Result : Theorem 1.55s 1.17s
% Output : CNFRefutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 24 ( 1 unt; 0 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 154 ( 46 ~; 60 |; 28 &)
% ( 4 <=>; 12 =>; 0 <=; 4 <~>)
% Maximal formula depth : 13 ( 7 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 : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 40 !; 16 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
? [X2,X3] :
! [X4] :
( big_f(X0,X1)
=> ( ( big_f(X2,X3)
=> ( big_f(X3,X4)
| big_f(X1,X4) ) )
=> ( ( ( big_f(X2,X3)
=> ( big_f(X1,X4)
<=> big_f(X2,X4) ) )
=> big_f(X4,X4) )
=> ( ( big_f(X2,X4)
<=> big_f(X3,X4) )
& big_f(X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_18_4) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
? [X2,X3] :
! [X4] :
( big_f(X0,X1)
=> ( ( big_f(X2,X3)
=> ( big_f(X3,X4)
| big_f(X1,X4) ) )
=> ( ( ( big_f(X2,X3)
=> ( big_f(X1,X4)
<=> big_f(X2,X4) ) )
=> big_f(X4,X4) )
=> ( ( big_f(X2,X4)
<=> big_f(X3,X4) )
& big_f(X2,X3) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( big_f(X0,X1)
& ( ~ big_f(X2,X3)
| big_f(X3,X4)
| big_f(X1,X4) )
& ( ( big_f(X2,X3)
& ( big_f(X1,X4)
<~> big_f(X2,X4) ) )
| big_f(X4,X4) )
& ( ( big_f(X2,X4)
<~> big_f(X3,X4) )
| ~ big_f(X2,X3) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( big_f(X0,X1)
& ( ~ big_f(X2,X3)
| big_f(X3,X4)
| big_f(X1,X4) )
& ( ( big_f(X2,X3)
& ( big_f(X1,X4)
<~> big_f(X2,X4) ) )
| big_f(X4,X4) )
& ( ( big_f(X2,X4)
<~> big_f(X3,X4) )
| ~ big_f(X2,X3) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( big_f(X0,X1)
& ( ~ big_f(X2,X3)
| big_f(X3,X4)
| big_f(X1,X4) )
& ( ( big_f(X2,X3)
& ( big_f(X1,X4)
| big_f(X2,X4) )
& ( ~ big_f(X1,X4)
| ~ big_f(X2,X4) ) )
| big_f(X4,X4) )
& ( ( ( big_f(X2,X4)
| big_f(X3,X4) )
& ( ~ big_f(X2,X4)
| ~ big_f(X3,X4) ) )
| ~ big_f(X2,X3) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( big_f(X0,X1)
& ( ~ big_f(X2,X3)
| big_f(X3,X4)
| big_f(X1,X4) )
& ( ( big_f(X2,X3)
& ( big_f(X1,X4)
| big_f(X2,X4) )
& ( ~ big_f(X1,X4)
| ~ big_f(X2,X4) ) )
| big_f(X4,X4) )
& ( ( ( big_f(X2,X4)
| big_f(X3,X4) )
& ( ~ big_f(X2,X4)
| ~ big_f(X3,X4) ) )
| ~ big_f(X2,X3) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X2,X3] :
( big_f(sK0,sK1)
& ( ~ big_f(X2,X3)
| big_f(X3,sK2(X2,X3))
| big_f(sK1,sK2(X2,X3)) )
& ( ( big_f(X2,X3)
& ( big_f(sK1,sK2(X2,X3))
| big_f(X2,sK2(X2,X3)) )
& ( ~ big_f(sK1,sK2(X2,X3))
| ~ big_f(X2,sK2(X2,X3)) ) )
| big_f(sK2(X2,X3),sK2(X2,X3)) )
& ( ( ( big_f(X2,sK2(X2,X3))
| big_f(X3,sK2(X2,X3)) )
& ( ~ big_f(X2,sK2(X2,X3))
| ~ big_f(X3,sK2(X2,X3)) ) )
| ~ big_f(X2,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X4,sK2(X2,X3))],[f6]) ).
fof(f11,plain,
! [X2,X3] :
( big_f(sK1,sK2(X2,X3))
| big_f(X2,sK2(X2,X3))
| big_f(sK2(X2,X3),sK2(X2,X3)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X2,X3] :
( ~ big_f(sK1,sK2(X2,X3))
| ~ big_f(X2,sK2(X2,X3))
| big_f(sK2(X2,X3),sK2(X2,X3)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X2,X3] :
( big_f(X2,sK2(X2,X3))
| big_f(X3,sK2(X2,X3))
| ~ big_f(X2,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
! [X2,X3] :
( ~ big_f(X2,sK2(X2,X3))
| ~ big_f(X3,sK2(X2,X3))
| ~ big_f(X2,X3) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ big_f(X0,X1)
| ~ big_f(X1,sK2(X0,X1))
| ~ big_f(X0,sK2(X0,X1)) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_50,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X1,sK2(X0,X1))
| big_f(X0,sK2(X0,X1))
| ~ big_f(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(sK2(X0,X1),sK2(X0,X1))
| ~ big_f(sK1,sK2(X0,X1))
| ~ big_f(X0,sK2(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(sK1,sK2(X0,X1))
| big_f(X0,sK2(X0,X1))
| big_f(sK2(X0,X1),sK2(X0,X1)) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_59,plain,
( big_f(sK1,sK2(sK1,sK1))
| big_f(sK2(sK1,sK1),sK2(sK1,sK1)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_60,plain,
( big_f(sK2(sK1,sK1),sK2(sK1,sK1))
| ~ big_f(sK1,sK2(sK1,sK1)) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_102,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X1,sK2(X0,X1))
| big_f(X0,sK2(X0,X1))
| ~ big_f(X0,X1) ),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_103,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ big_f(X0,X1)
| ~ big_f(X1,sK2(X0,X1))
| ~ big_f(X0,sK2(X0,X1)) ),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( big_f(sK2(X0,X1),sK2(sK2(X0,X1),sK2(X0,X1)))
| ~ big_f(sK2(X0,X1),sK2(X0,X1)) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_108,plain,
( big_f(sK2(sK1,sK1),sK2(sK2(sK1,sK1),sK2(sK1,sK1)))
| ~ big_f(sK2(sK1,sK1),sK2(sK1,sK1)) ),
inference(instantiation,[status(thm)],[c_107]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( ~ big_f(sK2(X0,X1),sK2(X0,X1))
| ~ big_f(sK2(X0,X1),sK2(sK2(X0,X1),sK2(X0,X1))) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_111,plain,
( ~ big_f(sK2(sK1,sK1),sK2(sK1,sK1))
| ~ big_f(sK2(sK1,sK1),sK2(sK2(sK1,sK1),sK2(sK1,sK1))) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_116,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_111,c_108,c_60,c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN352+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 00:58:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 1.55/1.17 % SZS status Started for theBenchmark.p
% 1.55/1.17 % SZS status Theorem for theBenchmark.p
% 1.55/1.17
% 1.55/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.55/1.17
% 1.55/1.17 % ------ iProver source info
% 1.55/1.17
% 1.55/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 1.55/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.55/1.17 % git: non_committed_changes: false
% 1.55/1.17
% 1.55/1.17 % ------ Parsing...
% 1.55/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.55/1.17
% 1.55/1.17 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.55/1.17
% 1.55/1.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.55/1.17 % ------ Proving...
% 1.55/1.17 % ------ Problem Properties
% 1.55/1.17
% 1.55/1.17 %
% 1.55/1.17 % clauses 7
% 1.55/1.17 % conjectures 7
% 1.55/1.17 % EPR 1
% 1.55/1.17 % Horn 3
% 1.55/1.17 % unary 1
% 1.55/1.17 % binary 3
% 1.55/1.17 % lits 16
% 1.55/1.17 % lits eq 0
% 1.55/1.17 % fd_pure 0
% 1.55/1.17 % fd_pseudo 0
% 1.55/1.17 % fd_cond 0
% 1.55/1.17 % fd_pseudo_cond 0
% 1.55/1.17 % AC symbols 0
% 1.55/1.17
% 1.55/1.17 % ------ Schedule dynamic 5 is on
% 1.55/1.17
% 1.55/1.17 % ------ no equalities: superposition off
% 1.55/1.17
% 1.55/1.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.55/1.17
% 1.55/1.17
% 1.55/1.17 % ------
% 1.55/1.17 % Current options:
% 1.55/1.17 % ------
% 1.55/1.17
% 1.55/1.17
% 1.55/1.17 %
% 1.55/1.17
% 1.55/1.17 % ------ Proving...
% 1.55/1.17 %
% 1.55/1.17
% 1.55/1.17 % SZS status Theorem for theBenchmark.p
% 1.55/1.17
% 1.55/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.55/1.17
% 1.55/1.17
%------------------------------------------------------------------------------