%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN349+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 03:39:48 PM UTC 2026
% Result : Theorem 0.54s 1.29s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 37 ( 1 unt; 0 def)
% Number of atoms : 237 ( 0 equ)
% Maximal formula atoms : 26 ( 6 avg)
% Number of connectives : 238 ( 86 ~; 110 |; 28 &)
% ( 11 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 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 : 3 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-2 aty)
% Number of variables : 64 ( 0 sgn 54 !; 10 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0] :
! [X1] :
? [X2] :
! [X3] :
( ( big_f(X0,X3)
<=> big_f(X1,X3) )
=> ( ( ( big_f(X0,X3)
<=> big_f(X3,X2) )
<=> big_f(X2,X3) )
<=> big_f(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_17_5) ).
fof(f2,negated_conjecture,
~ ? [X0] :
! [X1] :
? [X2] :
! [X3] :
( ( big_f(X0,X3)
<=> big_f(X1,X3) )
=> ( ( ( big_f(X0,X3)
<=> big_f(X3,X2) )
<=> big_f(X2,X3) )
<=> big_f(X3,X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
! [X0] :
? [X1] :
! [X2] :
? [X3] :
( ( big_f(X0,X3)
<=> big_f(X1,X3) )
& ( ( ( big_f(X0,X3)
<=> big_f(X3,X2) )
<=> big_f(X2,X3) )
<~> big_f(X3,X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
! [X0] :
? [X1] :
! [X2] :
? [X3] :
( ( ~ big_f(X0,X3)
| big_f(X1,X3) )
& ( ~ big_f(X1,X3)
| big_f(X0,X3) )
& ( ( ( ( ( big_f(X0,X3)
| big_f(X3,X2) )
& ( ~ big_f(X0,X3)
| ~ big_f(X3,X2) ) )
| big_f(X2,X3) )
& ( ~ big_f(X2,X3)
| ( ( ~ big_f(X0,X3)
| big_f(X3,X2) )
& ( ~ big_f(X3,X2)
| big_f(X0,X3) ) ) ) )
| big_f(X3,X1) )
& ( ( ( ( ( ~ big_f(X0,X3)
| big_f(X3,X2) )
& ( ~ big_f(X3,X2)
| big_f(X0,X3) ) )
| big_f(X2,X3) )
& ( ( ( big_f(X0,X3)
| big_f(X3,X2) )
& ( ~ big_f(X0,X3)
| ~ big_f(X3,X2) ) )
| ~ big_f(X2,X3) ) )
| ~ big_f(X3,X1) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f5,plain,
! [X0] :
? [X1] :
! [X2] :
? [X3] :
( ( ~ big_f(X0,X3)
| big_f(X1,X3) )
& ( ~ big_f(X1,X3)
| big_f(X0,X3) )
& ( ( ( ( ( big_f(X0,X3)
| big_f(X3,X2) )
& ( ~ big_f(X0,X3)
| ~ big_f(X3,X2) ) )
| big_f(X2,X3) )
& ( ~ big_f(X2,X3)
| ( ( ~ big_f(X0,X3)
| big_f(X3,X2) )
& ( ~ big_f(X3,X2)
| big_f(X0,X3) ) ) ) )
| big_f(X3,X1) )
& ( ( ( ( ( ~ big_f(X0,X3)
| big_f(X3,X2) )
& ( ~ big_f(X3,X2)
| big_f(X0,X3) ) )
| big_f(X2,X3) )
& ( ( ( big_f(X0,X3)
| big_f(X3,X2) )
& ( ~ big_f(X0,X3)
| ~ big_f(X3,X2) ) )
| ~ big_f(X2,X3) ) )
| ~ big_f(X3,X1) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
! [X0,X2] :
( ( ~ big_f(X0,sK1(X0,X2))
| big_f(sK0(X0),sK1(X0,X2)) )
& ( ~ big_f(sK0(X0),sK1(X0,X2))
| big_f(X0,sK1(X0,X2)) )
& ( ( ( ( ( big_f(X0,sK1(X0,X2))
| big_f(sK1(X0,X2),X2) )
& ( ~ big_f(X0,sK1(X0,X2))
| ~ big_f(sK1(X0,X2),X2) ) )
| big_f(X2,sK1(X0,X2)) )
& ( ~ big_f(X2,sK1(X0,X2))
| ( ( ~ big_f(X0,sK1(X0,X2))
| big_f(sK1(X0,X2),X2) )
& ( ~ big_f(sK1(X0,X2),X2)
| big_f(X0,sK1(X0,X2)) ) ) ) )
| big_f(sK1(X0,X2),sK0(X0)) )
& ( ( ( ( ( ~ big_f(X0,sK1(X0,X2))
| big_f(sK1(X0,X2),X2) )
& ( ~ big_f(sK1(X0,X2),X2)
| big_f(X0,sK1(X0,X2)) ) )
| big_f(X2,sK1(X0,X2)) )
& ( ( ( big_f(X0,sK1(X0,X2))
| big_f(sK1(X0,X2),X2) )
& ( ~ big_f(X0,sK1(X0,X2))
| ~ big_f(sK1(X0,X2),X2) ) )
| ~ big_f(X2,sK1(X0,X2)) ) )
| ~ big_f(sK1(X0,X2),sK0(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0(X0)),skolemize(X3,sK1(X0,X2))],[f5]) ).
fof(f7,plain,
! [X2,X0] :
( ~ big_f(X0,sK1(X0,X2))
| big_f(sK0(X0),sK1(X0,X2)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f8,plain,
! [X2,X0] :
( ~ big_f(sK0(X0),sK1(X0,X2))
| big_f(X0,sK1(X0,X2)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f9,plain,
! [X2,X0] :
( big_f(X0,sK1(X0,X2))
| big_f(sK1(X0,X2),X2)
| big_f(X2,sK1(X0,X2))
| big_f(sK1(X0,X2),sK0(X0)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f11,plain,
! [X2,X0] :
( ~ big_f(X2,sK1(X0,X2))
| ~ big_f(X0,sK1(X0,X2))
| big_f(sK1(X0,X2),X2)
| big_f(sK1(X0,X2),sK0(X0)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f14,plain,
! [X2,X0] :
( ~ big_f(sK1(X0,X2),X2)
| big_f(X0,sK1(X0,X2))
| big_f(X2,sK1(X0,X2))
| ~ big_f(sK1(X0,X2),sK0(X0)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f16,plain,
! [X2,X0] :
( ~ big_f(X0,sK1(X0,X2))
| ~ big_f(sK1(X0,X2),X2)
| ~ big_f(X2,sK1(X0,X2))
| ~ big_f(sK1(X0,X2),sK0(X0)) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ big_f(X1,sK1(X0,X1))
| ~ big_f(X0,sK1(X0,X1))
| ~ big_f(sK1(X0,X1),X1)
| ~ big_f(sK1(X0,X1),sK0(X0)) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X1,sK1(X0,X1))
| big_f(X0,sK1(X0,X1))
| ~ big_f(sK1(X0,X1),X1)
| ~ big_f(sK1(X0,X1),sK0(X0)) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_54,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(sK1(X0,X1),X1)
| big_f(sK1(X0,X1),sK0(X0))
| ~ big_f(X1,sK1(X0,X1))
| ~ big_f(X0,sK1(X0,X1)) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_56,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X1,sK1(X0,X1))
| big_f(X0,sK1(X0,X1))
| big_f(sK1(X0,X1),X1)
| big_f(sK1(X0,X1),sK0(X0)) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_57,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X0,sK1(X0,X1))
| ~ big_f(sK0(X0),sK1(X0,X1)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_58,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(sK0(X0),sK1(X0,X1))
| ~ big_f(X0,sK1(X0,X1)) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_153,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(sK0(X0),sK1(X0,X1))
| ~ big_f(X0,sK1(X0,X1)) ),
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_154,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X0,sK1(X0,X1))
| ~ big_f(sK0(X0),sK1(X0,X1)) ),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_155,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X1,sK1(X0,X1))
| big_f(X0,sK1(X0,X1))
| big_f(sK1(X0,X1),X1)
| big_f(sK1(X0,X1),sK0(X0)) ),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_157,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(sK1(X0,X1),X1)
| big_f(sK1(X0,X1),sK0(X0))
| ~ big_f(X1,sK1(X0,X1))
| ~ big_f(X0,sK1(X0,X1)) ),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_160,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X1,sK1(X0,X1))
| big_f(X0,sK1(X0,X1))
| ~ big_f(sK1(X0,X1),X1)
| ~ big_f(sK1(X0,X1),sK0(X0)) ),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_162,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ big_f(X1,sK1(X0,X1))
| ~ big_f(X0,sK1(X0,X1))
| ~ big_f(sK1(X0,X1),X1)
| ~ big_f(sK1(X0,X1),sK0(X0)) ),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_163,plain,
! [X0: $i] :
( ~ big_f(X0,sK1(X0,sK0(X0)))
| ~ big_f(sK0(X0),sK1(X0,sK0(X0)))
| ~ big_f(sK1(X0,sK0(X0)),sK0(X0)) ),
inference(instantiation,[status(thm)],[c_162]) ).
tcf(c_164,plain,
! [X0: $i] :
( big_f(sK1(X0,sK0(X0)),sK0(X0))
| ~ big_f(X0,sK1(X0,sK0(X0)))
| ~ big_f(sK0(X0),sK1(X0,sK0(X0))) ),
inference(instantiation,[status(thm)],[c_157]) ).
tcf(c_165,plain,
( ~ big_f(iProver_bot,sK1(iProver_bot,sK0(iProver_bot)))
| ~ big_f(sK0(iProver_bot),sK1(iProver_bot,sK0(iProver_bot)))
| ~ big_f(sK1(iProver_bot,sK0(iProver_bot)),sK0(iProver_bot)) ),
inference(instantiation,[status(thm)],[c_163]) ).
tcf(c_166,plain,
( big_f(sK1(iProver_bot,sK0(iProver_bot)),sK0(iProver_bot))
| ~ big_f(iProver_bot,sK1(iProver_bot,sK0(iProver_bot)))
| ~ big_f(sK0(iProver_bot),sK1(iProver_bot,sK0(iProver_bot))) ),
inference(instantiation,[status(thm)],[c_164]) ).
tcf(c_168,plain,
! [X0: $i] :
( big_f(X0,sK1(X0,sK0(X0)))
| big_f(sK0(X0),sK1(X0,sK0(X0)))
| ~ big_f(sK1(X0,sK0(X0)),sK0(X0)) ),
inference(instantiation,[status(thm)],[c_160]) ).
tcf(c_170,plain,
! [X0: $i] :
( big_f(X0,sK1(X0,sK0(X0)))
| big_f(sK0(X0),sK1(X0,sK0(X0)))
| big_f(sK1(X0,sK0(X0)),sK0(X0)) ),
inference(instantiation,[status(thm)],[c_155]) ).
tcf(c_171,plain,
! [X0: $i] :
( big_f(X0,sK1(X0,sK0(X0)))
| ~ big_f(sK0(X0),sK1(X0,sK0(X0))) ),
inference(instantiation,[status(thm)],[c_154]) ).
tcf(c_172,plain,
( big_f(iProver_bot,sK1(iProver_bot,sK0(iProver_bot)))
| ~ big_f(sK0(iProver_bot),sK1(iProver_bot,sK0(iProver_bot))) ),
inference(instantiation,[status(thm)],[c_171]) ).
tcf(c_173,plain,
( big_f(iProver_bot,sK1(iProver_bot,sK0(iProver_bot)))
| big_f(sK0(iProver_bot),sK1(iProver_bot,sK0(iProver_bot)))
| big_f(sK1(iProver_bot,sK0(iProver_bot)),sK0(iProver_bot)) ),
inference(instantiation,[status(thm)],[c_170]) ).
tcf(c_174,plain,
( big_f(iProver_bot,sK1(iProver_bot,sK0(iProver_bot)))
| big_f(sK0(iProver_bot),sK1(iProver_bot,sK0(iProver_bot)))
| ~ big_f(sK1(iProver_bot,sK0(iProver_bot)),sK0(iProver_bot)) ),
inference(instantiation,[status(thm)],[c_168]) ).
tcf(c_182,plain,
! [X0: $i] :
( big_f(sK0(X0),sK1(X0,sK0(X0)))
| ~ big_f(X0,sK1(X0,sK0(X0))) ),
inference(instantiation,[status(thm)],[c_153]) ).
tcf(c_183,plain,
( big_f(sK0(iProver_bot),sK1(iProver_bot,sK0(iProver_bot)))
| ~ big_f(iProver_bot,sK1(iProver_bot,sK0(iProver_bot))) ),
inference(instantiation,[status(thm)],[c_182]) ).
tcf(c_185,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_183,c_174,c_173,c_172,c_166,c_165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN349+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 00:56:17 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 0.54/1.29 % SZS status Started for theBenchmark.p
% 0.54/1.29 % SZS status Theorem for theBenchmark.p
% 0.54/1.29
% 0.54/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.54/1.29
% 0.54/1.29 % ------ iProver source info
% 0.54/1.29
% 0.54/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.54/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.54/1.29 % git: non_committed_changes: false
% 0.54/1.29
% 0.54/1.29 % ------ Parsing...
% 0.54/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.54/1.29
% 0.54/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.54/1.29
% 0.54/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.54/1.29 % ------ Proving...
% 0.54/1.29 % ------ Problem Properties
% 0.54/1.29
% 0.54/1.29 %
% 0.54/1.29 % clauses 10
% 0.54/1.29 % conjectures 10
% 0.54/1.29 % EPR 0
% 0.54/1.29 % Horn 3
% 0.54/1.29 % unary 0
% 0.54/1.29 % binary 2
% 0.54/1.29 % lits 36
% 0.54/1.29 % lits eq 0
% 0.54/1.29 % fd_pure 0
% 0.54/1.29 % fd_pseudo 0
% 0.54/1.29 % fd_cond 0
% 0.54/1.29 % fd_pseudo_cond 0
% 0.54/1.29 % AC symbols 0
% 0.54/1.29
% 0.54/1.29 % ------ Schedule dynamic 5 is on
% 0.54/1.29
% 0.54/1.29 % ------ no equalities: superposition off
% 0.54/1.29
% 0.54/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.54/1.29
% 0.54/1.29
% 0.54/1.29 % ------
% 0.54/1.29 % Current options:
% 0.54/1.29 % ------
% 0.54/1.29
% 0.54/1.29
% 0.54/1.29 %
% 0.54/1.29
% 0.54/1.29 % ------ Proving...
% 0.54/1.29 %
% 0.54/1.29
% 0.54/1.29 % SZS status Theorem for theBenchmark.p
% 0.54/1.29
% 0.54/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.54/1.29
% 0.54/1.29
%------------------------------------------------------------------------------