%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN350+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 : n005.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 1.73s 6.30s
% Output : CNFRefutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 4 unt; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 98 ( 36 ~; 33 |; 19 &)
% ( 5 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 6 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 : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 32 !; 10 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
? [X1,X2] :
! [X3] :
( ( big_f(X0,X3)
<=> big_f(X3,X0) )
=> ( big_f(X0,X3)
<=> ( ( big_f(X1,X3)
=> big_f(X1,X2) )
& big_f(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_18_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
? [X1,X2] :
! [X3] :
( ( big_f(X0,X3)
<=> big_f(X3,X0) )
=> ( big_f(X0,X3)
<=> ( ( big_f(X1,X3)
=> big_f(X1,X2) )
& big_f(X2,X3) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0] :
! [X1,X2] :
? [X3] :
( ( big_f(X0,X3)
<=> big_f(X3,X0) )
& ( big_f(X0,X3)
<~> ( ( ~ big_f(X1,X3)
| big_f(X1,X2) )
& big_f(X2,X3) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
? [X0] :
! [X1,X2] :
? [X3] :
( ( ~ big_f(X0,X3)
| big_f(X3,X0) )
& ( ~ big_f(X3,X0)
| big_f(X0,X3) )
& ( big_f(X0,X3)
| ( ( ~ big_f(X1,X3)
| big_f(X1,X2) )
& big_f(X2,X3) ) )
& ( ~ big_f(X0,X3)
| ( big_f(X1,X3)
& ~ big_f(X1,X2) )
| ~ big_f(X2,X3) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f5,plain,
? [X0] :
! [X1,X2] :
? [X3] :
( ( ~ big_f(X0,X3)
| big_f(X3,X0) )
& ( ~ big_f(X3,X0)
| big_f(X0,X3) )
& ( big_f(X0,X3)
| ( ( ~ big_f(X1,X3)
| big_f(X1,X2) )
& big_f(X2,X3) ) )
& ( ~ big_f(X0,X3)
| ( big_f(X1,X3)
& ~ big_f(X1,X2) )
| ~ big_f(X2,X3) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
! [X1,X2] :
( ( ~ big_f(sK0,sK1(X1,X2))
| big_f(sK1(X1,X2),sK0) )
& ( ~ big_f(sK1(X1,X2),sK0)
| big_f(sK0,sK1(X1,X2)) )
& ( big_f(sK0,sK1(X1,X2))
| ( ( ~ big_f(X1,sK1(X1,X2))
| big_f(X1,X2) )
& big_f(X2,sK1(X1,X2)) ) )
& ( ~ big_f(sK0,sK1(X1,X2))
| ( big_f(X1,sK1(X1,X2))
& ~ big_f(X1,X2) )
| ~ big_f(X2,sK1(X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X3,sK1(X1,X2))],[f5]) ).
fof(f7,plain,
! [X2,X1] :
( ~ big_f(sK0,sK1(X1,X2))
| big_f(sK1(X1,X2),sK0) ),
inference(cnf_transformation,[],[f6]) ).
fof(f10,plain,
! [X2,X1] :
( big_f(sK0,sK1(X1,X2))
| big_f(X2,sK1(X1,X2)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f12,plain,
! [X2,X1] :
( ~ big_f(sK0,sK1(X1,X2))
| ~ big_f(X1,X2)
| ~ big_f(X2,sK1(X1,X2)) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ big_f(X1,X0)
| ~ big_f(sK0,sK1(X1,X0))
| ~ big_f(X0,sK1(X1,X0)) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(sK0,sK1(X1,X0))
| big_f(X0,sK1(X1,X0)) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_54,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(sK1(X0,X1),sK0)
| ~ big_f(sK0,sK1(X0,X1)) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_55,plain,
big_f(sK0,sK1(sK0,sK0)),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_56,plain,
( big_f(sK1(sK0,sK0),sK0)
| ~ big_f(sK0,sK1(sK0,sK0)) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_114,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(sK0,sK1(X1,X0))
| big_f(X0,sK1(X1,X0)) ),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ big_f(X1,X0)
| ~ big_f(sK0,sK1(X1,X0))
| ~ big_f(X0,sK1(X1,X0)) ),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i] :
( ~ big_f(sK1(X0,X1),sK0)
| ~ big_f(sK0,sK1(sK1(X0,X1),sK0)) ),
inference(instantiation,[status(thm)],[c_116]) ).
tcf(c_121,plain,
( ~ big_f(sK1(sK0,sK0),sK0)
| ~ big_f(sK0,sK1(sK1(sK0,sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_120]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i] : big_f(sK0,sK1(sK1(X0,X1),sK0)),
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_124,plain,
big_f(sK0,sK1(sK1(sK0,sK0),sK0)),
inference(instantiation,[status(thm)],[c_123]) ).
tcf(c_125,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_124,c_121,c_56,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN350+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.38 % Computer : n005.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Fri Sep 25 00:56:07 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.44
% 0.14/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.44
% 0.14/5.44 % Detected problem language: tptp
% 0.14/5.45 % Proving...
% 1.73/6.30 % SZS status Started for theBenchmark.p
% 1.73/6.30 % SZS status Theorem for theBenchmark.p
% 1.73/6.30
% 1.73/6.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.73/6.30
% 1.73/6.30 % ------ iProver source info
% 1.73/6.30
% 1.73/6.30 % git: date: 2026-07-19 20:42:38 +0200
% 1.73/6.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.73/6.30 % git: non_committed_changes: false
% 1.73/6.30
% 1.73/6.30 % ------ Parsing...
% 1.73/6.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.73/6.30
% 1.73/6.30 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.73/6.30
% 1.73/6.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.73/6.30 % ------ Proving...
% 1.73/6.30 % ------ Problem Properties
% 1.73/6.30
% 1.73/6.30 %
% 1.73/6.30 % clauses 6
% 1.73/6.30 % conjectures 6
% 1.73/6.30 % EPR 0
% 1.73/6.30 % Horn 4
% 1.73/6.30 % unary 0
% 1.73/6.30 % binary 3
% 1.73/6.30 % lits 15
% 1.73/6.30 % lits eq 0
% 1.73/6.30 % fd_pure 0
% 1.73/6.30 % fd_pseudo 0
% 1.73/6.30 % fd_cond 0
% 1.73/6.30 % fd_pseudo_cond 0
% 1.73/6.30 % AC symbols 0
% 1.73/6.30
% 1.73/6.30 % ------ Schedule dynamic 5 is on
% 1.73/6.30
% 1.73/6.30 % ------ no equalities: superposition off
% 1.73/6.30
% 1.73/6.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.73/6.30
% 1.73/6.30
% 1.73/6.30 % ------
% 1.73/6.30 % Current options:
% 1.73/6.30 % ------
% 1.73/6.30
% 1.73/6.30
% 1.73/6.30 %
% 1.73/6.30
% 1.73/6.30 % ------ Proving...
% 1.73/6.30 %
% 1.73/6.30
% 1.73/6.30 % SZS status Theorem for theBenchmark.p
% 1.73/6.30
% 1.73/6.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.73/6.30
% 1.73/6.30
%------------------------------------------------------------------------------