%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN332+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 : n026.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 03:39:44 PM UTC 2026
% Result : Theorem 1.75s 1.29s
% Output : CNFRefutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 44 ( 5 unt; 0 def)
% Number of atoms : 220 ( 0 equ)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 255 ( 79 ~; 91 |; 51 &)
% ( 18 <=>; 10 =>; 0 <=; 6 <~>)
% Maximal formula depth : 16 ( 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 : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 90 ( 0 sgn 82 !; 8 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0,X1] :
! [X2] :
( ( ( big_f(X1,X0)
& big_f(X0,X1) )
<~> big_f(X0,X2) )
=> ( ( big_f(X0,X2)
<=> big_f(X2,X0) )
=> ( ( big_f(X0,X2)
<=> big_f(X1,X2) )
=> ( ( ( big_f(X1,X0)
=> big_f(X0,X1) )
<=> big_f(X2,X2) )
=> ( ( big_f(X0,X1)
<=> big_f(X1,X0) )
<=> big_f(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_14_4) ).
fof(f2,negated_conjecture,
~ ? [X0,X1] :
! [X2] :
( ( ( big_f(X1,X0)
& big_f(X0,X1) )
<~> big_f(X0,X2) )
=> ( ( big_f(X0,X2)
<=> big_f(X2,X0) )
=> ( ( big_f(X0,X2)
<=> big_f(X1,X2) )
=> ( ( ( big_f(X1,X0)
=> big_f(X0,X1) )
<=> big_f(X2,X2) )
=> ( ( big_f(X0,X1)
<=> big_f(X1,X0) )
<=> big_f(X2,X1) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
! [X0,X1] :
? [X2] :
( ( ( big_f(X1,X0)
& big_f(X0,X1) )
<~> big_f(X0,X2) )
& ( big_f(X0,X2)
<=> big_f(X2,X0) )
& ( big_f(X0,X2)
<=> big_f(X1,X2) )
& ( ( ~ big_f(X1,X0)
| big_f(X0,X1) )
<=> big_f(X2,X2) )
& ( ( big_f(X0,X1)
<=> big_f(X1,X0) )
<~> big_f(X2,X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
! [X0,X1] :
? [X2] :
( ( ( big_f(X1,X0)
& big_f(X0,X1) )
<~> big_f(X0,X2) )
& ( big_f(X0,X2)
<=> big_f(X2,X0) )
& ( big_f(X0,X2)
<=> big_f(X1,X2) )
& ( ( ~ big_f(X1,X0)
| big_f(X0,X1) )
<=> big_f(X2,X2) )
& ( ( big_f(X0,X1)
<=> big_f(X1,X0) )
<~> big_f(X2,X1) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
! [X0,X1] :
? [X2] :
( ( ( big_f(X1,X0)
& big_f(X0,X1) )
| big_f(X0,X2) )
& ( ~ big_f(X1,X0)
| ~ big_f(X0,X1)
| ~ big_f(X0,X2) )
& ( ~ big_f(X0,X2)
| big_f(X2,X0) )
& ( ~ big_f(X2,X0)
| big_f(X0,X2) )
& ( ~ big_f(X0,X2)
| big_f(X1,X2) )
& ( ~ big_f(X1,X2)
| big_f(X0,X2) )
& ( ( big_f(X1,X0)
& ~ big_f(X0,X1) )
| big_f(X2,X2) )
& ( ~ big_f(X2,X2)
| ~ big_f(X1,X0)
| big_f(X0,X1) )
& ( ( ( ~ big_f(X0,X1)
| big_f(X1,X0) )
& ( ~ big_f(X1,X0)
| big_f(X0,X1) ) )
| big_f(X2,X1) )
& ( ( ( big_f(X0,X1)
| big_f(X1,X0) )
& ( ~ big_f(X0,X1)
| ~ big_f(X1,X0) ) )
| ~ big_f(X2,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
! [X0,X1] :
? [X2] :
( ( ( big_f(X1,X0)
& big_f(X0,X1) )
| big_f(X0,X2) )
& ( ~ big_f(X1,X0)
| ~ big_f(X0,X1)
| ~ big_f(X0,X2) )
& ( ~ big_f(X0,X2)
| big_f(X2,X0) )
& ( ~ big_f(X2,X0)
| big_f(X0,X2) )
& ( ~ big_f(X0,X2)
| big_f(X1,X2) )
& ( ~ big_f(X1,X2)
| big_f(X0,X2) )
& ( ( big_f(X1,X0)
& ~ big_f(X0,X1) )
| big_f(X2,X2) )
& ( ~ big_f(X2,X2)
| ~ big_f(X1,X0)
| big_f(X0,X1) )
& ( ( ( ~ big_f(X0,X1)
| big_f(X1,X0) )
& ( ~ big_f(X1,X0)
| big_f(X0,X1) ) )
| big_f(X2,X1) )
& ( ( ( big_f(X0,X1)
| big_f(X1,X0) )
& ( ~ big_f(X0,X1)
| ~ big_f(X1,X0) ) )
| ~ big_f(X2,X1) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( ( ( big_f(X1,X0)
& big_f(X0,X1) )
| big_f(X0,sK0(X0,X1)) )
& ( ~ big_f(X1,X0)
| ~ big_f(X0,X1)
| ~ big_f(X0,sK0(X0,X1)) )
& ( ~ big_f(X0,sK0(X0,X1))
| big_f(sK0(X0,X1),X0) )
& ( ~ big_f(sK0(X0,X1),X0)
| big_f(X0,sK0(X0,X1)) )
& ( ~ big_f(X0,sK0(X0,X1))
| big_f(X1,sK0(X0,X1)) )
& ( ~ big_f(X1,sK0(X0,X1))
| big_f(X0,sK0(X0,X1)) )
& ( ( big_f(X1,X0)
& ~ big_f(X0,X1) )
| big_f(sK0(X0,X1),sK0(X0,X1)) )
& ( ~ big_f(sK0(X0,X1),sK0(X0,X1))
| ~ big_f(X1,X0)
| big_f(X0,X1) )
& ( ( ( ~ big_f(X0,X1)
| big_f(X1,X0) )
& ( ~ big_f(X1,X0)
| big_f(X0,X1) ) )
| big_f(sK0(X0,X1),X1) )
& ( ( ( big_f(X0,X1)
| big_f(X1,X0) )
& ( ~ big_f(X0,X1)
| ~ big_f(X1,X0) ) )
| ~ big_f(sK0(X0,X1),X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( big_f(X1,X0)
| big_f(X0,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( big_f(X0,X1)
| big_f(X0,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X0,X1] :
( ~ big_f(X0,sK0(X0,X1))
| big_f(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X0,X1] :
( ~ big_f(sK0(X0,X1),X0)
| big_f(X0,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X0,X1] :
( ~ big_f(X0,sK0(X0,X1))
| big_f(X1,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f17,plain,
! [X0,X1] :
( ~ big_f(sK0(X0,X1),sK0(X0,X1))
| ~ big_f(X1,X0)
| big_f(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f20,plain,
! [X0,X1] :
( big_f(X0,X1)
| big_f(X1,X0)
| ~ big_f(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f21,plain,
! [X0,X1] :
( ~ big_f(X0,X1)
| ~ big_f(X1,X0)
| ~ big_f(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ big_f(X1,X0)
| ~ big_f(X0,X1)
| ~ big_f(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_50,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X1,X0)
| big_f(X0,X1)
| ~ big_f(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X0,X1)
| ~ big_f(X1,X0)
| ~ big_f(sK0(X0,X1),sK0(X0,X1)) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_57,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X1,sK0(X0,X1))
| ~ big_f(X0,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_58,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X0,sK0(X0,X1))
| ~ big_f(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_59,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(sK0(X0,X1),X0)
| ~ big_f(X0,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_61,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X0,X1)
| big_f(X0,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_62,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X1,X0)
| big_f(X0,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( big_f(sK0(X0,X1),X0)
| big_f(X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_62,c_59]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( big_f(X1,X0)
| big_f(sK0(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_77]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( big_f(sK0(X0,X1),X0)
| big_f(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_61,c_59]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( big_f(X0,X1)
| big_f(sK0(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_81]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( ~ big_f(sK0(X0,X1),X0)
| big_f(X1,sK0(X0,X1)) ),
inference(prop_impl_just,[status(thm)],[c_58,c_57]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] :
( big_f(X1,sK0(X0,X1))
| ~ big_f(sK0(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_87]) ).
tcf(c_193,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X0,X1)
| ~ big_f(X1,X0)
| ~ big_f(sK0(X0,X1),sK0(X0,X1)) ),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_196,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X1,X0)
| big_f(X0,X1)
| ~ big_f(sK0(X0,X1),X1) ),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_197,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ big_f(X1,X0)
| ~ big_f(X0,X1)
| ~ big_f(sK0(X0,X1),X1) ),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_493,plain,
! [X0: $i] : big_f(X0,X0),
inference(superposition,[status(thm)],[c_78,c_196]) ).
tcf(c_502,plain,
! [X0: $i] : big_f(X0,X0),
inference(superposition,[status(thm)],[c_78,c_196]) ).
tcf(c_536,plain,
! [X0: $i,X1: $i] :
( big_f(X1,X0)
| ~ big_f(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_193,c_493]) ).
tcf(c_539,plain,
! [X0: $i,X1: $i] :
( big_f(X1,X0)
| ~ big_f(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_193,c_502]) ).
tcf(c_546,plain,
! [X0: $i,X1: $i] :
( big_f(X1,X0)
| ~ big_f(sK0(X0,X1),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_196,c_536]) ).
tcf(c_559,plain,
! [X0: $i,X1: $i] :
( ~ big_f(X0,X1)
| ~ big_f(sK0(X0,X1),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_197,c_539]) ).
tcf(c_648,plain,
! [X0: $i,X1: $i] :
( big_f(X1,X0)
| big_f(X0,sK0(X1,X0)) ),
inference(superposition,[status(thm)],[c_82,c_88]) ).
tcf(c_658,plain,
! [X0: $i,X1: $i] :
( big_f(X1,X0)
| big_f(X0,sK0(X1,X0)) ),
inference(superposition,[status(thm)],[c_82,c_88]) ).
tcf(c_668,plain,
! [X0: $i,X1: $i] :
( big_f(X0,X1)
| big_f(sK0(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_648,c_536]) ).
tcf(c_672,plain,
! [X0: $i,X1: $i] : big_f(X1,X0),
inference(global_subsumption_just,[status(thm)],[c_658,c_536,c_546,c_668]) ).
tcf(c_673,plain,
! [X0: $i,X1: $i] : big_f(X0,X1),
inference(renaming,[status(thm)],[c_672]) ).
tcf(c_674,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_559,c_673]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN332+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 00:54:40 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 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...
% 1.75/1.29 % SZS status Started for theBenchmark.p
% 1.75/1.29 % SZS status Theorem for theBenchmark.p
% 1.75/1.29
% 1.75/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.75/1.29
% 1.75/1.29 % ------ iProver source info
% 1.75/1.29
% 1.75/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.75/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.75/1.29 % git: non_committed_changes: false
% 1.75/1.29
% 1.75/1.29 % ------ Parsing...
% 1.75/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.75/1.29
% 1.75/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.75/1.29
% 1.75/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.75/1.29 % ------ Proving...
% 1.75/1.29 % ------ Problem Properties
% 1.75/1.29
% 1.75/1.29 %
% 1.75/1.29 % clauses 14
% 1.75/1.29 % conjectures 11
% 1.75/1.29 % EPR 0
% 1.75/1.29 % Horn 8
% 1.75/1.29 % unary 0
% 1.75/1.29 % binary 8
% 1.75/1.29 % lits 34
% 1.75/1.29 % lits eq 0
% 1.75/1.29 % fd_pure 0
% 1.75/1.29 % fd_pseudo 0
% 1.75/1.29 % fd_cond 0
% 1.75/1.29 % fd_pseudo_cond 0
% 1.75/1.29 % AC symbols 0
% 1.75/1.29
% 1.75/1.29 % ------ Schedule dynamic 5 is on
% 1.75/1.29
% 1.75/1.29 % ------ no equalities: superposition off
% 1.75/1.29
% 1.75/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.75/1.29
% 1.75/1.29
% 1.75/1.29 % ------
% 1.75/1.29 % Current options:
% 1.75/1.29 % ------
% 1.75/1.29
% 1.75/1.29
% 1.75/1.29 %
% 1.75/1.29
% 1.75/1.29 % ------ Proving...
% 1.75/1.29 %
% 1.75/1.29
% 1.75/1.29 % SZS status Theorem for theBenchmark.p
% 1.75/1.29
% 1.75/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.75/1.29
% 1.75/1.29
%------------------------------------------------------------------------------