%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN077+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 : n015.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 03:39:07 PM UTC 2026
% Result : Theorem 1.89s 1.28s
% Output : CNFRefutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of formulae : 43 ( 6 unt; 0 def)
% Number of atoms : 144 ( 10 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 176 ( 75 ~; 72 |; 21 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% 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 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 100 ( 0 sgn 79 !; 21 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
? [X1] :
! [X2] :
( big_f(X2,X1)
<=> X2 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel54_1) ).
fof(f2,conjecture,
~ ? [X0] :
! [X1] :
( big_f(X1,X0)
<=> ! [X2] :
( big_f(X1,X2)
=> ? [X3] :
( ~ ? [X4] :
( big_f(X4,X3)
& big_f(X4,X2) )
& big_f(X3,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel54) ).
fof(f3,negated_conjecture,
~ ~ ? [X0] :
! [X1] :
( big_f(X1,X0)
<=> ! [X2] :
( big_f(X1,X2)
=> ? [X3] :
( ~ ? [X4] :
( big_f(X4,X3)
& big_f(X4,X2) )
& big_f(X3,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
? [X0] :
! [X1] :
( big_f(X1,X0)
<=> ! [X2] :
( big_f(X1,X2)
=> ? [X3] :
( ~ ? [X4] :
( big_f(X4,X3)
& big_f(X4,X2) )
& big_f(X3,X2) ) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
? [X0] :
! [X1] :
( big_f(X1,X0)
<=> ! [X2] :
( ~ big_f(X1,X2)
| ? [X3] :
( ! [X4] :
( ~ big_f(X4,X3)
| ~ big_f(X4,X2) )
& big_f(X3,X2) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f6,plain,
! [X0] :
? [X1] :
! [X2] :
( ( ~ big_f(X2,X1)
| X2 = X0 )
& ( X0 != X2
| big_f(X2,X1) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f7,plain,
! [X0,X2] :
( ( ~ big_f(X2,sK0(X0))
| X2 = X0 )
& ( X0 != X2
| big_f(X2,sK0(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f6]) ).
fof(f8,plain,
? [X0] :
! [X1] :
( ( ~ big_f(X1,X0)
| ! [X2] :
( ~ big_f(X1,X2)
| ? [X3] :
( ! [X4] :
( ~ big_f(X4,X3)
| ~ big_f(X4,X2) )
& big_f(X3,X2) ) ) )
& ( ? [X2] :
( big_f(X1,X2)
& ! [X3] :
( ? [X4] :
( big_f(X4,X3)
& big_f(X4,X2) )
| ~ big_f(X3,X2) ) )
| big_f(X1,X0) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f9,plain,
? [X0] :
! [X1] :
( ( ~ big_f(X1,X0)
| ! [X5] :
( ~ big_f(X1,X5)
| ? [X6] :
( ! [X7] :
( ~ big_f(X7,X6)
| ~ big_f(X7,X5) )
& big_f(X6,X5) ) ) )
& ( ? [X2] :
( big_f(X1,X2)
& ! [X3] :
( ? [X4] :
( big_f(X4,X3)
& big_f(X4,X2) )
| ~ big_f(X3,X2) ) )
| big_f(X1,X0) ) ),
inference(rectify,[],[f8]) ).
fof(f10,plain,
! [X1] :
( ( ~ big_f(X1,sK1)
| ! [X5] :
( ~ big_f(X1,X5)
| ( ! [X7] :
( ~ big_f(X7,sK4(X5))
| ~ big_f(X7,X5) )
& big_f(sK4(X5),X5) ) ) )
& ( ( big_f(X1,sK2(X1))
& ! [X3] :
( ( big_f(sK3(X1,X3),X3)
& big_f(sK3(X1,X3),sK2(X1)) )
| ~ big_f(X3,sK2(X1)) ) )
| big_f(X1,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X2,sK2(X1)),skolemize(X4,sK3(X1,X3)),skolemize(X6,sK4(X5))],[f9]) ).
fof(f11,plain,
! [X2,X0] :
( ~ big_f(X2,sK0(X0))
| X0 = X2 ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X2,X0] :
( X0 != X2
| big_f(X2,sK0(X0)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X1,X7,X5] :
( ~ big_f(X1,sK1)
| ~ big_f(X1,X5)
| ~ big_f(X7,sK4(X5))
| ~ big_f(X7,X5) ),
inference(cnf_transformation,[],[f10]) ).
fof(f14,plain,
! [X1,X5] :
( ~ big_f(X1,sK1)
| ~ big_f(X1,X5)
| big_f(sK4(X5),X5) ),
inference(cnf_transformation,[],[f10]) ).
fof(f15,plain,
! [X1] :
( big_f(X1,sK2(X1))
| big_f(X1,sK1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f16,plain,
! [X3,X1] :
( big_f(sK3(X1,X3),X3)
| ~ big_f(X3,sK2(X1))
| big_f(X1,sK1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f17,plain,
! [X3,X1] :
( big_f(sK3(X1,X3),sK2(X1))
| ~ big_f(X3,sK2(X1))
| big_f(X1,sK1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f18,plain,
! [X2] : big_f(X2,sK0(X2)),
inference(equality_resolution,[],[f12]) ).
tcf(c_49,plain,
! [X0: $i] : big_f(X0,sK0(X0)),
inference(cnf_transformation,[],[f18]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ big_f(X0,sK0(X1)) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X1,sK1)
| big_f(sK3(X1,X0),sK2(X1))
| ~ big_f(X0,sK2(X1)) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X1,sK1)
| big_f(sK3(X1,X0),X0)
| ~ big_f(X0,sK2(X1)) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_53,negated_conjecture,
! [X0: $i] :
( big_f(X0,sK1)
| big_f(X0,sK2(X0)) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_54,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(sK4(X1),X1)
| ~ big_f(X0,sK1)
| ~ big_f(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_55,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ big_f(X2,sK1)
| ~ big_f(X2,X1)
| ~ big_f(X0,X1)
| ~ big_f(X0,sK4(X1)) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_56,plain,
big_f(sK1,sK0(sK1)),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_135,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ big_f(X2,sK1)
| ~ big_f(X2,X1)
| ~ big_f(X0,X1)
| ~ big_f(X0,sK4(X1)) ),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_136,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(sK4(X1),X1)
| ~ big_f(X0,sK1)
| ~ big_f(X0,X1) ),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_137,negated_conjecture,
! [X0: $i] :
( big_f(X0,sK1)
| big_f(X0,sK2(X0)) ),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_138,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X1,sK1)
| big_f(sK3(X1,X0),X0)
| ~ big_f(X0,sK2(X1)) ),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_139,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(X1,sK1)
| big_f(sK3(X1,X0),sK2(X1))
| ~ big_f(X0,sK2(X1)) ),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_293,plain,
! [X0: $i,X1: $i,X2: $i] :
( big_f(X0,sK1)
| ~ big_f(X2,sK1)
| ~ big_f(X2,X1)
| ~ big_f(sK4(X1),sK2(X0))
| ~ big_f(sK3(X0,sK4(X1)),X1) ),
inference(superposition,[status(thm)],[c_138,c_135]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i] :
( big_f(X0,sK1)
| ~ big_f(X1,sK1)
| ~ big_f(X1,sK2(X0))
| ~ big_f(sK4(sK2(X0)),sK2(X0)) ),
inference(superposition,[status(thm)],[c_139,c_293]) ).
tcf(c_343,plain,
! [X0: $i] :
( big_f(sK4(sK0(X0)),sK0(X0))
| ~ big_f(X0,sK1) ),
inference(superposition,[status(thm)],[c_49,c_136]) ).
tcf(c_361,plain,
! [X0: $i] :
( ( sK4(sK0(X0)) = X0 )
| ~ big_f(X0,sK1) ),
inference(superposition,[status(thm)],[c_343,c_50]) ).
tcf(c_450,plain,
! [X0: $i,X1: $i] :
( big_f(X1,sK1)
| ~ big_f(X0,sK1)
| ~ big_f(X0,sK2(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_338,c_136]) ).
tcf(c_460,plain,
! [X0: $i,X1: $i] :
( big_f(X0,sK1)
| ~ big_f(X1,sK2(X0))
| ~ big_f(sK3(X0,X1),sK1) ),
inference(superposition,[status(thm)],[c_139,c_450]) ).
tcf(c_491,plain,
! [X0: $i] :
( big_f(X0,sK1)
| ~ big_f(sK1,sK2(X0)) ),
inference(superposition,[status(thm)],[c_138,c_460]) ).
tcf(c_499,plain,
big_f(sK1,sK1),
inference(superposition,[status(thm)],[c_137,c_491]) ).
tcf(c_500,plain,
sK4(sK0(sK1)) = sK1,
inference(superposition,[status(thm)],[c_499,c_361]) ).
tcf(c_548,plain,
! [X0: $i,X1: $i] :
( ~ big_f(X1,sK1)
| ~ big_f(X0,sK1)
| ~ big_f(X1,sK0(sK1))
| ~ big_f(X0,sK0(sK1)) ),
inference(superposition,[status(thm)],[c_500,c_135]) ).
tcf(c_560,plain,
( ~ big_f(sK1,sK1)
| ~ big_f(sK1,sK0(sK1)) ),
inference(instantiation,[status(thm)],[c_548]) ).
tcf(c_561,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_560,c_499,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN077+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 : n015.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
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 00:09:12 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 1.89/1.28 % SZS status Started for theBenchmark.p
% 1.89/1.28 % SZS status Theorem for theBenchmark.p
% 1.89/1.28
% 1.89/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.89/1.28
% 1.89/1.28 % ------ iProver source info
% 1.89/1.28
% 1.89/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.89/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.89/1.28 % git: non_committed_changes: false
% 1.89/1.28
% 1.89/1.28 % ------ Parsing...
% 1.89/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.89/1.28
% 1.89/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.89/1.28
% 1.89/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.89/1.28
% 1.89/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.89/1.28 % ------ Proving...
% 1.89/1.28 % ------ Problem Properties
% 1.89/1.28
% 1.89/1.28 %
% 1.89/1.28 % clauses 7
% 1.89/1.28 % conjectures 5
% 1.89/1.28 % EPR 0
% 1.89/1.28 % Horn 4
% 1.89/1.28 % unary 1
% 1.89/1.28 % binary 2
% 1.89/1.28 % lits 18
% 1.89/1.28 % lits eq 1
% 1.89/1.28 % fd_pure 0
% 1.89/1.28 % fd_pseudo 0
% 1.89/1.28 % fd_cond 0
% 1.89/1.28 % fd_pseudo_cond 1
% 1.89/1.28 % AC symbols 0
% 1.89/1.28
% 1.89/1.28 % ------ Schedule dynamic 5 is on
% 1.89/1.28
% 1.89/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.89/1.28
% 1.89/1.28
% 1.89/1.28 % ------
% 1.89/1.28 % Current options:
% 1.89/1.28 % ------
% 1.89/1.28
% 1.89/1.28
% 1.89/1.28 %
% 1.89/1.28
% 1.89/1.28 % ------ Proving...
% 1.89/1.28 %
% 1.89/1.28
% 1.89/1.28 % SZS status Theorem for theBenchmark.p
% 1.89/1.28
% 1.89/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.89/1.28
% 1.89/1.28
%------------------------------------------------------------------------------