%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN334+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n019.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 03:39:45 PM UTC 2026
% Result : Theorem 0.42s 1.19s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 41 ( 3 unt; 0 def)
% Number of atoms : 154 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 189 ( 76 ~; 71 |; 22 &)
% ( 10 <=>; 8 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 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 : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 80 ( 0 sgn 72 !; 8 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0,X1] :
! [X2] :
( ( big_f(X0,X1)
=> ( big_f(X0,X2)
<=> big_g(X1,X2) ) )
=> ( ( big_f(X0,X1)
<=> ( big_f(X2,X2)
=> big_g(X2,X2) ) )
=> ( big_g(X0,X1)
<=> big_g(X2,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_14_6) ).
fof(f2,negated_conjecture,
~ ? [X0,X1] :
! [X2] :
( ( big_f(X0,X1)
=> ( big_f(X0,X2)
<=> big_g(X1,X2) ) )
=> ( ( big_f(X0,X1)
<=> ( big_f(X2,X2)
=> big_g(X2,X2) ) )
=> ( big_g(X0,X1)
<=> big_g(X2,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
! [X0,X1] :
? [X2] :
( ( ~ big_f(X0,X1)
| ( big_f(X0,X2)
<=> big_g(X1,X2) ) )
& ( big_f(X0,X1)
<=> ( ~ big_f(X2,X2)
| big_g(X2,X2) ) )
& ( big_g(X0,X1)
<~> big_g(X2,X2) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
! [X0,X1] :
? [X2] :
( ( ~ big_f(X0,X1)
| ( big_f(X0,X2)
<=> big_g(X1,X2) ) )
& ( big_f(X0,X1)
<=> ( ~ big_f(X2,X2)
| big_g(X2,X2) ) )
& ( big_g(X0,X1)
<~> big_g(X2,X2) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
! [X0,X1] :
? [X2] :
( ( ~ big_f(X0,X1)
| ( ( ~ big_f(X0,X2)
| big_g(X1,X2) )
& ( ~ big_g(X1,X2)
| big_f(X0,X2) ) ) )
& ( ~ big_f(X0,X1)
| ~ big_f(X2,X2)
| big_g(X2,X2) )
& ( ( big_f(X2,X2)
& ~ big_g(X2,X2) )
| big_f(X0,X1) )
& ( big_g(X0,X1)
| big_g(X2,X2) )
& ( ~ big_g(X0,X1)
| ~ big_g(X2,X2) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
! [X0,X1] :
? [X2] :
( ( ~ big_f(X0,X1)
| ( ( ~ big_f(X0,X2)
| big_g(X1,X2) )
& ( ~ big_g(X1,X2)
| big_f(X0,X2) ) ) )
& ( ~ big_f(X0,X1)
| ~ big_f(X2,X2)
| big_g(X2,X2) )
& ( ( big_f(X2,X2)
& ~ big_g(X2,X2) )
| big_f(X0,X1) )
& ( big_g(X0,X1)
| big_g(X2,X2) )
& ( ~ big_g(X0,X1)
| ~ big_g(X2,X2) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( ( ~ big_f(X0,X1)
| ( ( ~ big_f(X0,sK0(X0,X1))
| big_g(X1,sK0(X0,X1)) )
& ( ~ big_g(X1,sK0(X0,X1))
| big_f(X0,sK0(X0,X1)) ) ) )
& ( ~ big_f(X0,X1)
| ~ big_f(sK0(X0,X1),sK0(X0,X1))
| big_g(sK0(X0,X1),sK0(X0,X1)) )
& ( ( big_f(sK0(X0,X1),sK0(X0,X1))
& ~ big_g(sK0(X0,X1),sK0(X0,X1)) )
| big_f(X0,X1) )
& ( big_g(X0,X1)
| big_g(sK0(X0,X1),sK0(X0,X1)) )
& ( ~ big_g(X0,X1)
| ~ big_g(sK0(X0,X1),sK0(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( ~ big_f(X0,X1)
| ~ big_f(X0,sK0(X0,X1))
| big_g(X1,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( ~ big_f(X0,X1)
| ~ big_g(X1,sK0(X0,X1))
| big_f(X0,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X0,X1] :
( ~ big_f(X0,X1)
| ~ big_f(sK0(X0,X1),sK0(X0,X1))
| big_g(sK0(X0,X1),sK0(X0,X1)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X0,X1] :
( ~ big_g(sK0(X0,X1),sK0(X0,X1))
| big_f(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X0,X1] :
( big_g(X0,X1)
| big_g(sK0(X0,X1),sK0(X0,X1)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
! [X0,X1] :
( ~ big_g(X0,X1)
| ~ big_g(sK0(X0,X1),sK0(X0,X1)) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ big_g(X0,X1)
| ~ big_g(sK0(X0,X1),sK0(X0,X1)) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_50,negated_conjecture,
! [X0: $i,X1: $i] :
( big_g(X0,X1)
| big_g(sK0(X0,X1),sK0(X0,X1)) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X0,X1)
| ~ big_g(sK0(X0,X1),sK0(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i] :
( big_g(sK0(X0,X1),sK0(X0,X1))
| ~ big_f(X0,X1)
| ~ big_f(sK0(X0,X1),sK0(X0,X1)) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_54,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X1,sK0(X1,X0))
| ~ big_f(X1,X0)
| ~ big_g(X0,sK0(X1,X0)) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_55,negated_conjecture,
! [X0: $i,X1: $i] :
( big_g(X1,sK0(X0,X1))
| ~ big_f(X0,X1)
| ~ big_f(X0,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( ~ big_g(sK0(X0,X1),sK0(X0,X1))
| ~ big_g(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_49]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ~ big_g(X0,X1)
| ~ big_g(sK0(X0,X1),sK0(X0,X1)) ),
inference(renaming,[status(thm)],[c_63]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( big_f(X0,X1)
| big_g(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_50,c_51]) ).
tcf(c_90,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ big_f(X0,X1)
| ~ big_g(X0,X1)
| ~ big_f(sK0(X0,X1),sK0(X0,X1)) ),
inference(bin_hyper_res,[status(thm)],[c_53,c_64]) ).
tcf(c_127,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ big_f(X0,X1)
| ~ big_g(X0,X1)
| ~ big_f(sK0(X0,X1),sK0(X0,X1)) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_128,negated_conjecture,
! [X0: $i,X1: $i] :
( big_g(X1,sK0(X0,X1))
| ~ big_f(X0,X1)
| ~ big_f(X0,sK0(X0,X1)) ),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_129,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X1,sK0(X1,X0))
| ~ big_f(X1,X0)
| ~ big_g(X0,sK0(X1,X0)) ),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_131,negated_conjecture,
! [X0: $i,X1: $i] :
( big_g(X0,X1)
| big_g(sK0(X0,X1),sK0(X0,X1)) ),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_132,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ big_g(X0,X1)
| ~ big_g(sK0(X0,X1),sK0(X0,X1)) ),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i] :
( big_f(sK0(X0,X1),sK0(X0,X1))
| big_g(sK0(X0,X1),sK0(X0,X1)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_256,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ big_f(X0,X1)
| ~ big_g(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_127,c_49,c_53,c_149]) ).
tcf(c_343,plain,
! [X0: $i,X1: $i] :
( big_f(X1,sK0(X0,X1))
| big_f(X0,sK0(X0,X1))
| ~ big_f(X0,X1) ),
inference(superposition,[status(thm)],[c_67,c_129]) ).
tcf(c_355,plain,
! [X0: $i,X1: $i] :
( big_f(sK0(X0,X1),sK0(X0,X1))
| ~ big_g(X0,X1) ),
inference(superposition,[status(thm)],[c_67,c_132]) ).
tcf(c_357,plain,
! [X0: $i,X1: $i] :
( big_f(X1,sK0(X0,X1))
| big_f(X0,sK0(X0,X1))
| ~ big_f(X0,X1) ),
inference(superposition,[status(thm)],[c_67,c_129]) ).
tcf(c_402,plain,
! [X0: $i] :
( big_f(X0,sK0(X0,X0))
| ~ big_f(X0,X0) ),
inference(equality_factoring,[status(thm)],[c_343]) ).
tcf(c_420,plain,
! [X0: $i] :
( big_f(X0,sK0(X0,X0))
| ~ big_f(X0,X0) ),
inference(equality_factoring,[status(thm)],[c_357]) ).
tcf(c_517,plain,
! [X0: $i] :
( big_g(X0,sK0(X0,X0))
| ~ big_f(X0,X0) ),
inference(superposition,[status(thm)],[c_402,c_128]) ).
tcf(c_527,plain,
! [X0: $i] :
( big_g(X0,sK0(X0,X0))
| ~ big_f(X0,X0) ),
inference(superposition,[status(thm)],[c_420,c_128]) ).
tcf(c_534,plain,
! [X0: $i] :
( ~ big_f(X0,X0)
| ~ big_f(X0,sK0(X0,X0)) ),
inference(superposition,[status(thm)],[c_517,c_256]) ).
tcf(c_539,plain,
! [X0: $i] : ~ big_f(X0,X0),
inference(global_subsumption_just,[status(thm)],[c_527,c_402,c_534]) ).
tcf(c_542,plain,
! [X0: $i,X1: $i] : ~ big_g(X0,X1),
inference(backward_subsumption_resolution,[status(thm)],[c_355,c_539]) ).
tcf(c_544,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_131,c_542]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN334+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n019.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 00:52:21 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 0.42/1.19 % SZS status Started for theBenchmark.p
% 0.42/1.19 % SZS status Theorem for theBenchmark.p
% 0.42/1.19
% 0.42/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.42/1.19
% 0.42/1.19 % ------ iProver source info
% 0.42/1.19
% 0.42/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 0.42/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.42/1.19 % git: non_committed_changes: false
% 0.42/1.19
% 0.42/1.19 % ------ Parsing...
% 0.42/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.42/1.19
% 0.42/1.19 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.42/1.19
% 0.42/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.42/1.19 % ------ Proving...
% 0.42/1.19 % ------ Problem Properties
% 0.42/1.19
% 0.42/1.19 %
% 0.42/1.19 % clauses 7
% 0.42/1.19 % conjectures 6
% 0.42/1.19 % EPR 1
% 0.42/1.19 % Horn 4
% 0.42/1.19 % unary 0
% 0.42/1.19 % binary 4
% 0.42/1.19 % lits 17
% 0.42/1.19 % lits eq 0
% 0.42/1.19 % fd_pure 0
% 0.42/1.19 % fd_pseudo 0
% 0.42/1.19 % fd_cond 0
% 0.42/1.19 % fd_pseudo_cond 0
% 0.42/1.19 % AC symbols 0
% 0.42/1.19
% 0.42/1.19 % ------ Schedule dynamic 5 is on
% 0.42/1.19
% 0.42/1.19 % ------ no equalities: superposition off
% 0.42/1.19
% 0.42/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.42/1.19
% 0.42/1.19
% 0.42/1.19 % ------
% 0.42/1.19 % Current options:
% 0.42/1.19 % ------
% 0.42/1.19
% 0.42/1.19
% 0.42/1.19 %
% 0.42/1.19
% 0.42/1.19 % ------ Proving...
% 0.42/1.19 %
% 0.42/1.19
% 0.42/1.19 % SZS status Theorem for theBenchmark.p
% 0.42/1.19
% 0.42/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.42/1.19
% 0.42/1.19
%------------------------------------------------------------------------------