%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN351+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 1.56s 1.28s
% Output : CNFRefutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 7 unt; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 99 ( 26 ~; 22 |; 33 &)
% ( 6 <=>; 10 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 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; 0-4 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 27 !; 16 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
? [X2,X3] :
! [X4] :
( big_f(X0,X3,X0,X4)
=> ( ( big_f(X0,X2,X0,X3)
<=> big_f(X2,X1,X2,X3) )
=> ( big_f(X0,X2,X0,X3)
=> ( ( big_f(X0,X4,X2,X4)
=> ( big_f(X0,X2,X0,X3)
<=> big_f(X0,X3,X2,X3) ) )
& ( big_f(X0,X3,X2,X3)
=> big_f(X0,X4,X2,X4) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_18_3) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
? [X2,X3] :
! [X4] :
( big_f(X0,X3,X0,X4)
=> ( ( big_f(X0,X2,X0,X3)
<=> big_f(X2,X1,X2,X3) )
=> ( big_f(X0,X2,X0,X3)
=> ( ( big_f(X0,X4,X2,X4)
=> ( big_f(X0,X2,X0,X3)
<=> big_f(X0,X3,X2,X3) ) )
& ( big_f(X0,X3,X2,X3)
=> big_f(X0,X4,X2,X4) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( big_f(X0,X3,X0,X4)
& ( big_f(X0,X2,X0,X3)
<=> big_f(X2,X1,X2,X3) )
& big_f(X0,X2,X0,X3)
& ( ( big_f(X0,X4,X2,X4)
& ( big_f(X0,X2,X0,X3)
<~> big_f(X0,X3,X2,X3) ) )
| ( big_f(X0,X3,X2,X3)
& ~ big_f(X0,X4,X2,X4) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( big_f(X0,X3,X0,X4)
& ( big_f(X0,X2,X0,X3)
<=> big_f(X2,X1,X2,X3) )
& big_f(X0,X2,X0,X3)
& ( ( big_f(X0,X4,X2,X4)
& ( big_f(X0,X2,X0,X3)
<~> big_f(X0,X3,X2,X3) ) )
| ( big_f(X0,X3,X2,X3)
& ~ big_f(X0,X4,X2,X4) ) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( big_f(X0,X3,X0,X4)
& ( ~ big_f(X0,X2,X0,X3)
| big_f(X2,X1,X2,X3) )
& ( ~ big_f(X2,X1,X2,X3)
| big_f(X0,X2,X0,X3) )
& big_f(X0,X2,X0,X3)
& ( ( big_f(X0,X4,X2,X4)
& ( big_f(X0,X2,X0,X3)
| big_f(X0,X3,X2,X3) )
& ( ~ big_f(X0,X2,X0,X3)
| ~ big_f(X0,X3,X2,X3) ) )
| ( big_f(X0,X3,X2,X3)
& ~ big_f(X0,X4,X2,X4) ) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( big_f(X0,X3,X0,X4)
& ( ~ big_f(X0,X2,X0,X3)
| big_f(X2,X1,X2,X3) )
& ( ~ big_f(X2,X1,X2,X3)
| big_f(X0,X2,X0,X3) )
& big_f(X0,X2,X0,X3)
& ( ( big_f(X0,X4,X2,X4)
& ( big_f(X0,X2,X0,X3)
| big_f(X0,X3,X2,X3) )
& ( ~ big_f(X0,X2,X0,X3)
| ~ big_f(X0,X3,X2,X3) ) )
| ( big_f(X0,X3,X2,X3)
& ~ big_f(X0,X4,X2,X4) ) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X2,X3] :
( big_f(sK0,X3,sK0,sK2(X2,X3))
& ( ~ big_f(sK0,X2,sK0,X3)
| big_f(X2,sK1,X2,X3) )
& ( ~ big_f(X2,sK1,X2,X3)
| big_f(sK0,X2,sK0,X3) )
& big_f(sK0,X2,sK0,X3)
& ( ( big_f(sK0,sK2(X2,X3),X2,sK2(X2,X3))
& ( big_f(sK0,X2,sK0,X3)
| big_f(sK0,X3,X2,X3) )
& ( ~ big_f(sK0,X2,sK0,X3)
| ~ big_f(sK0,X3,X2,X3) ) )
| ( big_f(sK0,X3,X2,X3)
& ~ big_f(sK0,sK2(X2,X3),X2,sK2(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(sK0,X2,sK0,X3),
inference(cnf_transformation,[],[f7]) ).
fof(f17,plain,
! [X2,X3] :
( ~ big_f(sK0,X2,sK0,X3)
| ~ big_f(sK0,X3,X2,X3)
| ~ big_f(sK0,sK2(X2,X3),X2,sK2(X2,X3)) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ big_f(sK0,X0,sK0,X1)
| ~ big_f(sK0,X1,X0,X1)
| ~ big_f(sK0,sK2(X0,X1),X0,sK2(X0,X1)) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i] : big_f(sK0,X0,sK0,X1),
inference(cnf_transformation,[],[f11]) ).
tcf(c_57,plain,
big_f(sK0,sK0,sK0,sK0),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_60,plain,
( ~ big_f(sK0,sK0,sK0,sK0)
| ~ big_f(sK0,sK2(sK0,sK0),sK0,sK2(sK0,sK0)) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_126,negated_conjecture,
! [X0: $i,X1: $i] : big_f(sK0,X0,sK0,X1),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_131,plain,
! [X0: $i] : big_f(sK0,sK2(sK0,X0),sK0,sK2(sK0,X0)),
inference(instantiation,[status(thm)],[c_126]) ).
tcf(c_132,plain,
big_f(sK0,sK2(sK0,sK0),sK0,sK2(sK0,sK0)),
inference(instantiation,[status(thm)],[c_131]) ).
tcf(c_133,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_132,c_60,c_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN351+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
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 00:58:37 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...
% 1.56/1.28 % SZS status Started for theBenchmark.p
% 1.56/1.28 % SZS status Theorem for theBenchmark.p
% 1.56/1.28
% 1.56/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.56/1.28
% 1.56/1.28 % ------ iProver source info
% 1.56/1.28
% 1.56/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.56/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.56/1.28 % git: non_committed_changes: false
% 1.56/1.28
% 1.56/1.28 % ------ Parsing...
% 1.56/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.56/1.28
% 1.56/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.56/1.28
% 1.56/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.56/1.28 % ------ Proving...
% 1.56/1.28 % ------ Problem Properties
% 1.56/1.28
% 1.56/1.28 %
% 1.56/1.28 % clauses 4
% 1.56/1.28 % conjectures 3
% 1.56/1.28 % EPR 2
% 1.56/1.28 % Horn 3
% 1.56/1.28 % unary 2
% 1.56/1.28 % binary 2
% 1.56/1.28 % lits 6
% 1.56/1.28 % lits eq 0
% 1.56/1.28 % fd_pure 0
% 1.56/1.28 % fd_pseudo 0
% 1.56/1.28 % fd_cond 0
% 1.56/1.28 % fd_pseudo_cond 0
% 1.56/1.28 % AC symbols 0
% 1.56/1.28
% 1.56/1.28 % ------ Schedule dynamic 5 is on
% 1.56/1.28
% 1.56/1.28 % ------ no equalities: superposition off
% 1.56/1.28
% 1.56/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.56/1.28
% 1.56/1.28
% 1.56/1.28 % ------
% 1.56/1.28 % Current options:
% 1.56/1.28 % ------
% 1.56/1.28
% 1.56/1.28
% 1.56/1.28 %
% 1.56/1.28
% 1.56/1.28 % ------ Proving...
% 1.56/1.28 %
% 1.56/1.28
% 1.56/1.28 % SZS status Theorem for theBenchmark.p
% 1.56/1.28
% 1.56/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.56/1.28
% 1.56/1.28
%------------------------------------------------------------------------------