%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET766+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 02:48:31 PM UTC 2026
% Result : Theorem 2.89s 1.28s
% Output : CNFRefutation 2.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 7 unt; 0 def)
% Number of atoms : 130 ( 2 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 150 ( 50 ~; 44 |; 35 &)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 85 ( 0 sgn 79 !; 6 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X2,X3,X4] :
( ( member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X2,X3) )
=> apply(X1,X2,X4) ) )
& ! [X2,X3] :
( ( member(X3,X0)
& member(X2,X0) )
=> ( apply(X1,X2,X3)
=> apply(X1,X3,X2) ) )
& ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax',equivalence) ).
fof(f15,axiom,
! [X0,X1,X2,X3] :
( member(X3,equivalence_class(X2,X1,X0))
<=> ( apply(X0,X2,X3)
& member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax',equivalence_class) ).
fof(f17,conjecture,
! [X0,X1,X2] :
( ( member(X2,X0)
& equivalence(X1,X0) )
=> member(X2,equivalence_class(X2,X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIII02) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( ( member(X2,X0)
& equivalence(X1,X0) )
=> member(X2,equivalence_class(X2,X0,X1)) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X5,X6,X7] :
( ( member(X7,X0)
& member(X6,X0)
& member(X5,X0) )
=> ( ( apply(X1,X6,X7)
& apply(X1,X5,X6) )
=> apply(X1,X5,X7) ) )
& ! [X3,X4] :
( ( member(X4,X0)
& member(X3,X0) )
=> ( apply(X1,X3,X4)
=> apply(X1,X4,X3) ) )
& ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) ) ) ),
inference(rectify,[],[f14]) ).
fof(f22,plain,
! [X0,X1] :
( equivalence(X1,X0)
=> ( ! [X5,X6,X7] :
( ( member(X7,X0)
& member(X6,X0)
& member(X5,X0) )
=> ( ( apply(X1,X6,X7)
& apply(X1,X5,X6) )
=> apply(X1,X5,X7) ) )
& ! [X3,X4] :
( ( member(X4,X0)
& member(X3,X0) )
=> ( apply(X1,X3,X4)
=> apply(X1,X4,X3) ) )
& ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) ) ) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f25,plain,
! [X0,X1] :
( ~ equivalence(X1,X0)
| ( ! [X5,X6,X7] :
( ~ member(X7,X0)
| ~ member(X6,X0)
| ~ member(X5,X0)
| ~ apply(X1,X6,X7)
| ~ apply(X1,X5,X6)
| apply(X1,X5,X7) )
& ! [X3,X4] :
( ~ member(X4,X0)
| ~ member(X3,X0)
| ~ apply(X1,X3,X4)
| apply(X1,X4,X3) )
& ! [X2] :
( ~ member(X2,X0)
| apply(X1,X2,X2) ) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f26,plain,
! [X0,X1] :
( ~ equivalence(X1,X0)
| ( ! [X5,X6,X7] :
( ~ member(X7,X0)
| ~ member(X6,X0)
| ~ member(X5,X0)
| ~ apply(X1,X6,X7)
| ~ apply(X1,X5,X6)
| apply(X1,X5,X7) )
& ! [X3,X4] :
( ~ member(X4,X0)
| ~ member(X3,X0)
| ~ apply(X1,X3,X4)
| apply(X1,X4,X3) )
& ! [X2] :
( ~ member(X2,X0)
| apply(X1,X2,X2) ) ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
? [X0,X1,X2] :
( member(X2,X0)
& equivalence(X1,X0)
& ~ member(X2,equivalence_class(X2,X0,X1)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f28,plain,
? [X0,X1,X2] :
( member(X2,X0)
& equivalence(X1,X0)
& ~ member(X2,equivalence_class(X2,X0,X1)) ),
inference(flattening,[],[f27]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( ( ~ member(X3,equivalence_class(X2,X1,X0))
| ( apply(X0,X2,X3)
& member(X3,X1) ) )
& ( ~ apply(X0,X2,X3)
| ~ member(X3,X1)
| member(X3,equivalence_class(X2,X1,X0)) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f49,plain,
! [X0,X1,X2,X3] :
( ( ~ member(X3,equivalence_class(X2,X1,X0))
| ( apply(X0,X2,X3)
& member(X3,X1) ) )
& ( ~ apply(X0,X2,X3)
| ~ member(X3,X1)
| member(X3,equivalence_class(X2,X1,X0)) ) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
( member(sK5,sK3)
& equivalence(sK4,sK3)
& ~ member(sK5,equivalence_class(sK5,sK3,sK4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f28]) ).
fof(f79,plain,
! [X2,X0,X1] :
( ~ equivalence(X1,X0)
| ~ member(X2,X0)
| apply(X1,X2,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f82,plain,
! [X2,X3,X0,X1] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1)
| member(X3,equivalence_class(X2,X1,X0)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f83,plain,
member(sK5,sK3),
inference(cnf_transformation,[],[f50]) ).
fof(f84,plain,
equivalence(sK4,sK3),
inference(cnf_transformation,[],[f50]) ).
fof(f85,plain,
~ member(sK5,equivalence_class(sK5,sK3,sK4)),
inference(cnf_transformation,[],[f50]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X2,X0,X0)
| ~ equivalence(X2,X1)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X2,equivalence_class(X1,X3,X0))
| ~ member(X2,X3)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_81,negated_conjecture,
~ member(sK5,equivalence_class(sK5,sK3,sK4)),
inference(cnf_transformation,[],[f85]) ).
tcf(c_82,negated_conjecture,
equivalence(sK4,sK3),
inference(cnf_transformation,[],[f84]) ).
tcf(c_83,negated_conjecture,
member(sK5,sK3),
inference(cnf_transformation,[],[f83]) ).
tcf(c_540,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X1,X2,X2)
| ~ member(X2,X0)
| ( X1 != sK4 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_75,c_82]) ).
tcf(c_541,plain,
! [X0: $i] :
( apply(sK4,X0,X0)
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_540]) ).
tcf(c_725,plain,
! [X0: $i] :
( apply(sK4,X0,X0)
| ~ member(X0,sK3) ),
inference(prop_impl_just,[status(thm)],[c_541]) ).
tcf(c_2010,plain,
( apply(sK4,sK5,sK5)
| ~ member(sK5,sK3) ),
inference(instantiation,[status(thm)],[c_725]) ).
tcf(c_2837,plain,
! [X0: $i,X1: $i] :
( member(X0,equivalence_class(X0,X1,sK4))
| ~ member(X0,X1)
| ~ apply(sK4,X0,X0) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_8975,plain,
( member(sK5,equivalence_class(sK5,sK3,sK4))
| ~ member(sK5,sK3)
| ~ apply(sK4,sK5,sK5) ),
inference(instantiation,[status(thm)],[c_2837]) ).
tcf(c_8976,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_8975,c_2010,c_81,c_83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET766+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 11:53:59 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 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...
% 2.89/1.28 % SZS status Started for theBenchmark.p
% 2.89/1.28 % SZS status Theorem for theBenchmark.p
% 2.89/1.28
% 2.89/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.89/1.28
% 2.89/1.28 % ------ iProver source info
% 2.89/1.28
% 2.89/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.89/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.89/1.28 % git: non_committed_changes: false
% 2.89/1.28
% 2.89/1.28 % ------ Parsing...
% 2.89/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.89/1.28
% 2.89/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.89/1.28
% 2.89/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.89/1.28
% 2.89/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.89/1.28 % ------ Proving...
% 2.89/1.28 % ------ Problem Properties
% 2.89/1.28
% 2.89/1.28 %
% 2.89/1.28 % clauses 35
% 2.89/1.28 % conjectures 2
% 2.89/1.28 % EPR 7
% 2.89/1.28 % Horn 30
% 2.89/1.28 % unary 7
% 2.89/1.28 % binary 18
% 2.89/1.28 % lits 77
% 2.89/1.28 % lits eq 4
% 2.89/1.28 % fd_pure 0
% 2.89/1.28 % fd_pseudo 0
% 2.89/1.28 % fd_cond 0
% 2.89/1.28 % fd_pseudo_cond 2
% 2.89/1.28 % AC symbols 0
% 2.89/1.28
% 2.89/1.28 % ------ Schedule dynamic 5 is on
% 2.89/1.28
% 2.89/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.89/1.28
% 2.89/1.28
% 2.89/1.28 % ------
% 2.89/1.28 % Current options:
% 2.89/1.28 % ------
% 2.89/1.28
% 2.89/1.28
% 2.89/1.28 %
% 2.89/1.28
% 2.89/1.28 % ------ Proving...
% 2.89/1.28 %
% 2.89/1.28
% 2.89/1.28 % SZS status Theorem for theBenchmark.p
% 2.89/1.28
% 2.89/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.89/1.28
% 2.89/1.28
%------------------------------------------------------------------------------