%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET767+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n026.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 1.80s 1.18s
% Output : CNFRefutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 5 unt; 1 def)
% Number of atoms : 81 ( 1 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 73 ( 28 ~; 26 |; 13 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 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 : 7 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 56 ( 0 sgn 51 !; 5 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f15,axiom,
! [X0,X1,X2,X3] :
( member(X3,equivalence_class(X2,X1,X0))
<=> ( apply(X0,X2,X3)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',equivalence_class) ).
fof(f17,conjecture,
! [X0,X1,X2] :
( equivalence(X1,X0)
=> subset(equivalence_class(X2,X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII03) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( equivalence(X1,X0)
=> subset(equivalence_class(X2,X0,X1),X0) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f27,plain,
? [X0,X1,X2] :
( equivalence(X1,X0)
& ~ subset(equivalence_class(X2,X0,X1),X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f28,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f29,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK0(X0,X1),X0)
& ~ member(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f29]) ).
fof(f47,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(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(flattening,[],[f47]) ).
fof(f49,plain,
( equivalence(sK4,sK3)
& ~ subset(equivalence_class(sK5,sK3,sK4),sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f27]) ).
fof(f51,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f52,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f80,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,equivalence_class(X2,X1,X0))
| member(X3,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f83,plain,
~ subset(equivalence_class(sK5,sK3,sK4),sK3),
inference(cnf_transformation,[],[f49]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ member(X0,equivalence_class(X1,X2,X3)) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_81,negated_conjecture,
~ subset(equivalence_class(sK5,sK3,sK4),sK3),
inference(cnf_transformation,[],[f83]) ).
tcf(c_1174,definition,
iPr_def_10 = equivalence_class(sK5,sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1177,negated_conjecture,
~ subset(iPr_def_10,sK3),
inference(demodulation,[status(thm)],[c_81,c_1174]) ).
tcf(c_2026,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1174,c_79]) ).
tcf(c_2052,plain,
( subset(iPr_def_10,sK3)
| ~ member(sK0(iPr_def_10,sK3),sK3) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_2078,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| member(sK0(iPr_def_10,X0),sK3) ),
inference(superposition,[status(thm)],[c_50,c_2026]) ).
tcf(c_2087,plain,
( subset(iPr_def_10,sK3)
| member(sK0(iPr_def_10,sK3),sK3) ),
inference(instantiation,[status(thm)],[c_2078]) ).
tcf(c_2088,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2087,c_2052,c_1177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET767+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 11:56:39 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 1.80/1.18 % SZS status Started for theBenchmark.p
% 1.80/1.18 % SZS status Theorem for theBenchmark.p
% 1.80/1.18
% 1.80/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.80/1.18
% 1.80/1.18 % ------ iProver source info
% 1.80/1.18
% 1.80/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 1.80/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.80/1.18 % git: non_committed_changes: false
% 1.80/1.18
% 1.80/1.18 % ------ Parsing...
% 1.80/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.80/1.18
% 1.80/1.18 % ------ 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 %
% 1.80/1.18
% 1.80/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.80/1.18
% 1.80/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.80/1.18 % ------ Proving...
% 1.80/1.18 % ------ Problem Properties
% 1.80/1.18
% 1.80/1.18 %
% 1.80/1.18 % clauses 34
% 1.80/1.18 % conjectures 1
% 1.80/1.18 % EPR 6
% 1.80/1.18 % Horn 29
% 1.80/1.18 % unary 6
% 1.80/1.18 % binary 18
% 1.80/1.18 % lits 76
% 1.80/1.18 % lits eq 4
% 1.80/1.18 % fd_pure 0
% 1.80/1.18 % fd_pseudo 0
% 1.80/1.18 % fd_cond 0
% 1.80/1.18 % fd_pseudo_cond 2
% 1.80/1.18 % AC symbols 0
% 1.80/1.18
% 1.80/1.18 % ------ Schedule dynamic 5 is on
% 1.80/1.18
% 1.80/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.80/1.18
% 1.80/1.18
% 1.80/1.18 % ------
% 1.80/1.18 % Current options:
% 1.80/1.18 % ------
% 1.80/1.18
% 1.80/1.18
% 1.80/1.18 %
% 1.80/1.18
% 1.80/1.18 % ------ Proving...
% 1.80/1.18 %
% 1.80/1.18
% 1.80/1.18 % SZS status Theorem for theBenchmark.p
% 1.80/1.18
% 1.80/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.80/1.18
% 1.80/1.18
%------------------------------------------------------------------------------