%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN331+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 : n014.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 1.85s 1.30s
% Output : CNFRefutation 1.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 4 unt; 0 def)
% Number of atoms : 80 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 85 ( 23 ~; 22 |; 28 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% 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 : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 40 ( 0 sgn 32 !; 8 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0,X1] :
! [X2] :
( big_f(X0,X2)
=> ( big_f(X1,X2)
=> ( ( big_f(X0,X1)
<=> big_f(X2,X2) )
=> ( ( big_f(X2,X2)
| big_f(X1,X0) )
=> ( big_f(X2,X1)
| big_f(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_14_3) ).
fof(f2,negated_conjecture,
~ ? [X0,X1] :
! [X2] :
( big_f(X0,X2)
=> ( big_f(X1,X2)
=> ( ( big_f(X0,X1)
<=> big_f(X2,X2) )
=> ( ( big_f(X2,X2)
| big_f(X1,X0) )
=> ( big_f(X2,X1)
| big_f(X2,X0) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
! [X0,X1] :
? [X2] :
( big_f(X0,X2)
& big_f(X1,X2)
& ( big_f(X0,X1)
<=> big_f(X2,X2) )
& ( big_f(X2,X2)
| big_f(X1,X0) )
& ~ big_f(X2,X1)
& ~ big_f(X2,X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
! [X0,X1] :
? [X2] :
( big_f(X0,X2)
& big_f(X1,X2)
& ( big_f(X0,X1)
<=> big_f(X2,X2) )
& ( big_f(X2,X2)
| big_f(X1,X0) )
& ~ big_f(X2,X1)
& ~ big_f(X2,X0) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
! [X0,X1] :
? [X2] :
( big_f(X0,X2)
& big_f(X1,X2)
& ( ~ big_f(X0,X1)
| big_f(X2,X2) )
& ( ~ big_f(X2,X2)
| big_f(X0,X1) )
& ( big_f(X2,X2)
| big_f(X1,X0) )
& ~ big_f(X2,X1)
& ~ big_f(X2,X0) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
! [X0,X1] :
? [X2] :
( big_f(X0,X2)
& big_f(X1,X2)
& ( ~ big_f(X0,X1)
| big_f(X2,X2) )
& ( ~ big_f(X2,X2)
| big_f(X0,X1) )
& ( big_f(X2,X2)
| big_f(X1,X0) )
& ~ big_f(X2,X1)
& ~ big_f(X2,X0) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( big_f(X0,sK0(X0,X1))
& big_f(X1,sK0(X0,X1))
& ( ~ big_f(X0,X1)
| big_f(sK0(X0,X1),sK0(X0,X1)) )
& ( ~ big_f(sK0(X0,X1),sK0(X0,X1))
| big_f(X0,X1) )
& ( big_f(sK0(X0,X1),sK0(X0,X1))
| big_f(X1,X0) )
& ~ big_f(sK0(X0,X1),X1)
& ~ big_f(sK0(X0,X1),X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f6]) ).
fof(f11,plain,
! [X0,X1] :
( ~ big_f(sK0(X0,X1),sK0(X0,X1))
| big_f(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X0,X1] :
( big_f(sK0(X0,X1),sK0(X0,X1))
| big_f(X1,X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
! [X0,X1] : ~ big_f(sK0(X0,X1),X0),
inference(cnf_transformation,[],[f7]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i] : ~ big_f(sK0(X0,X1),X0),
inference(cnf_transformation,[],[f14]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X1,X0)
| big_f(sK0(X0,X1),sK0(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X0,X1)
| ~ big_f(sK0(X0,X1),sK0(X0,X1)) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( big_f(X1,X0)
| big_f(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_51,c_52]) ).
tcf(c_104,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X0,X1)
| ~ big_f(sK0(X0,X1),sK0(X0,X1)) ),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( big_f(sK0(X0,X1),X0)
| ~ big_f(sK0(sK0(X0,X1),X0),sK0(sK0(X0,X1),X0)) ),
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i] : big_f(sK0(sK0(X0,X1),X0),sK0(sK0(X0,X1),X0)),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_116,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_113,c_107,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN331+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n014.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % 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 00:51:33 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
% 0.11/0.45 % Proving...
% 1.85/1.30 % SZS status Started for theBenchmark.p
% 1.85/1.30 % SZS status Theorem for theBenchmark.p
% 1.85/1.30
% 1.85/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.85/1.30
% 1.85/1.30 % ------ iProver source info
% 1.85/1.30
% 1.85/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 1.85/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.85/1.30 % git: non_committed_changes: false
% 1.85/1.30
% 1.85/1.30 % ------ Parsing...
% 1.85/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.85/1.30
% 1.85/1.30 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.85/1.30
% 1.85/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.85/1.30 % ------ Proving...
% 1.85/1.30 % ------ Problem Properties
% 1.85/1.30
% 1.85/1.30 %
% 1.85/1.30 % clauses 7
% 1.85/1.30 % conjectures 6
% 1.85/1.30 % EPR 1
% 1.85/1.30 % Horn 6
% 1.85/1.30 % unary 4
% 1.85/1.30 % binary 3
% 1.85/1.30 % lits 10
% 1.85/1.30 % lits eq 0
% 1.85/1.30 % fd_pure 0
% 1.85/1.30 % fd_pseudo 0
% 1.85/1.30 % fd_cond 0
% 1.85/1.30 % fd_pseudo_cond 0
% 1.85/1.30 % AC symbols 0
% 1.85/1.30
% 1.85/1.30 % ------ Schedule dynamic 5 is on
% 1.85/1.30
% 1.85/1.30 % ------ no equalities: superposition off
% 1.85/1.30
% 1.85/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.85/1.30
% 1.85/1.30
% 1.85/1.30 % ------
% 1.85/1.30 % Current options:
% 1.85/1.30 % ------
% 1.85/1.30
% 1.85/1.30
% 1.85/1.30 %
% 1.85/1.30
% 1.85/1.30 % ------ Proving...
% 1.85/1.30 %
% 1.85/1.30
% 1.85/1.30 % SZS status Theorem for theBenchmark.p
% 1.85/1.30
% 1.85/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.85/1.30
% 1.85/1.30
%------------------------------------------------------------------------------