%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN321+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 : 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 03:39:42 PM UTC 2026
% Result : Theorem 1.56s 1.43s
% Output : CNFRefutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 23 ( 5 unt; 0 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 95 ( 33 ~; 29 |; 16 &)
% ( 3 <=>; 12 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 6 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 : 4 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 81 ( 0 sgn 69 !; 12 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0,X1] :
( ( ? [X2] : big_f(X0,X2)
=> ! [X2] : big_g(X0,X2) )
=> ( ! [X2] :
( big_g(X2,X2)
=> big_f(X2,X1) )
=> ( big_f(X0,X1)
<=> ! [X2] : big_g(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_3_2) ).
fof(f2,negated_conjecture,
~ ? [X0,X1] :
( ( ? [X2] : big_f(X0,X2)
=> ! [X2] : big_g(X0,X2) )
=> ( ! [X2] :
( big_g(X2,X2)
=> big_f(X2,X1) )
=> ( big_f(X0,X1)
<=> ! [X2] : big_g(X0,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ? [X0,X1] :
( ( ? [X2] : big_f(X0,X2)
=> ! [X3] : big_g(X0,X3) )
=> ( ! [X4] :
( big_g(X4,X4)
=> big_f(X4,X1) )
=> ( big_f(X0,X1)
<=> ! [X5] : big_g(X0,X5) ) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
! [X0,X1] :
( ( ! [X2] : ~ big_f(X0,X2)
| ! [X3] : big_g(X0,X3) )
& ! [X4] :
( ~ big_g(X4,X4)
| big_f(X4,X1) )
& ( big_f(X0,X1)
<~> ! [X5] : big_g(X0,X5) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
! [X0,X1] :
( ( ! [X2] : ~ big_f(X0,X2)
| ! [X3] : big_g(X0,X3) )
& ! [X4] :
( ~ big_g(X4,X4)
| big_f(X4,X1) )
& ( big_f(X0,X1)
<~> ! [X5] : big_g(X0,X5) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
! [X0,X1] :
( ( ! [X2] : ~ big_f(X0,X2)
| ! [X3] : big_g(X0,X3) )
& ! [X4] :
( ~ big_g(X4,X4)
| big_f(X4,X1) )
& ( big_f(X0,X1)
| ! [X5] : big_g(X0,X5) )
& ( ~ big_f(X0,X1)
| ? [X5] : ~ big_g(X0,X5) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( ( ! [X2] : ~ big_f(X0,X2)
| ! [X3] : big_g(X0,X3) )
& ! [X4] :
( ~ big_g(X4,X4)
| big_f(X4,X1) )
& ( big_f(X0,X1)
| ! [X5] : big_g(X0,X5) )
& ( ~ big_f(X0,X1)
| ? [X5] : ~ big_g(X0,X5) ) ),
inference(flattening,[],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( ( ! [X6] : ~ big_f(X0,X6)
| ! [X5] : big_g(X0,X5) )
& ! [X4] :
( ~ big_g(X4,X4)
| big_f(X4,X1) )
& ( big_f(X0,X1)
| ! [X3] : big_g(X0,X3) )
& ( ~ big_f(X0,X1)
| ? [X2] : ~ big_g(X0,X2) ) ),
inference(rectify,[],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( ( ! [X6] : ~ big_f(X0,X6)
| ! [X5] : big_g(X0,X5) )
& ! [X4] :
( ~ big_g(X4,X4)
| big_f(X4,X1) )
& ( big_f(X0,X1)
| ! [X3] : big_g(X0,X3) )
& ( ~ big_f(X0,X1)
| ~ big_g(X0,sK0(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0))],[f8]) ).
fof(f10,plain,
! [X0,X6,X5] :
( ~ big_f(X0,X6)
| big_g(X0,X5) ),
inference(cnf_transformation,[],[f9]) ).
fof(f11,plain,
! [X1,X4] :
( ~ big_g(X4,X4)
| big_f(X4,X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f12,plain,
! [X3,X0,X1] :
( big_f(X0,X1)
| big_g(X0,X3) ),
inference(cnf_transformation,[],[f9]) ).
fof(f13,plain,
! [X0,X1] :
( ~ big_f(X0,X1)
| ~ big_g(X0,sK0(X0)) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ big_f(X0,X1)
| ~ big_g(X0,sK0(X0)) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_50,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X0,X2)
| big_g(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X0,X1)
| ~ big_g(X0,X0) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_g(X0,X2)
| ~ big_f(X0,X1) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_55,plain,
( big_f(iProver_bot,iProver_bot)
| ~ big_g(iProver_bot,iProver_bot) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : big_g(X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[c_50,c_52]) ).
tcf(c_60,plain,
big_g(iProver_bot,iProver_bot),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] : ~ big_f(X0,X1),
inference(backward_subsumption_resolution,[status(thm)],[c_49,c_59]) ).
tcf(c_66,plain,
~ big_f(iProver_bot,iProver_bot),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_67,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_66,c_60,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN321+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n015.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 00:52:42 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 0.14/0.44
% 0.14/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.44
% 0.14/0.44 % Detected problem language: tptp
% 0.14/0.46 % Proving...
% 1.56/1.43 % SZS status Started for theBenchmark.p
% 1.56/1.43 % SZS status Theorem for theBenchmark.p
% 1.56/1.43
% 1.56/1.43 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.56/1.43
% 1.56/1.43 % ------ iProver source info
% 1.56/1.43
% 1.56/1.43 % git: date: 2026-07-19 20:42:38 +0200
% 1.56/1.43 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.56/1.43 % git: non_committed_changes: false
% 1.56/1.43
% 1.56/1.43 % ------ Parsing...
% 1.56/1.43 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.56/1.43
% 1.56/1.43 % ------ Preprocessing...%
% 1.56/1.43
% 1.56/1.43 % SZS status Theorem for theBenchmark.p
% 1.56/1.43
% 1.56/1.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.56/1.43
% 1.56/1.43
%------------------------------------------------------------------------------