%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU328+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n002.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 02:56:56 PM UTC 2026
% Result : Theorem 6.41s 6.97s
% Output : CNFRefutation 6.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 21 unt; 0 def)
% Number of atoms : 111 ( 52 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 97 ( 44 ~; 35 |; 7 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 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 : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 78 ( 0 sgn 74 !; 4 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0] : cast_to_subset(X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
fof(f18,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,X1) = set_difference(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f22,axiom,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(f23,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f27,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(meet_of_subsets(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
fof(f39,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f46,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(f48,conjecture,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( X1 != empty_set
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_complement(X0,meet_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_tops_2) ).
fof(f49,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( X1 != empty_set
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_complement(X0,meet_of_subsets(X0,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f54,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( X1 != empty_set
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_setfam_1) ).
fof(f61,plain,
? [X0,X1] :
( element(X1,powerset(powerset(X0)))
& X1 != empty_set
& union_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_complement(X0,meet_of_subsets(X0,X1)) ),
inference(ennf_transformation,[],[f49]) ).
fof(f62,plain,
? [X0,X1] :
( element(X1,powerset(powerset(X0)))
& X1 != empty_set
& union_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_complement(X0,meet_of_subsets(X0,X1)) ),
inference(flattening,[],[f61]) ).
fof(f64,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(ennf_transformation,[],[f39]) ).
fof(f65,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(ennf_transformation,[],[f23]) ).
fof(f66,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,X1) = set_difference(X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f67,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set = X1
| union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ),
inference(ennf_transformation,[],[f54]) ).
fof(f68,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set = X1
| union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ),
inference(flattening,[],[f67]) ).
fof(f70,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(meet_of_subsets(X0,X1),powerset(X0)) ),
inference(ennf_transformation,[],[f27]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
inference(ennf_transformation,[],[f46]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
inference(flattening,[],[f80]) ).
fof(f94,plain,
( element(sK1,powerset(powerset(sK0)))
& empty_set != sK1
& union_of_subsets(sK0,complements_of_subsets(sK0,sK1)) != subset_complement(sK0,meet_of_subsets(sK0,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f62]) ).
fof(f99,plain,
element(sK1,powerset(powerset(sK0))),
inference(cnf_transformation,[],[f94]) ).
fof(f100,plain,
empty_set != sK1,
inference(cnf_transformation,[],[f94]) ).
fof(f101,plain,
union_of_subsets(sK0,complements_of_subsets(sK0,sK1)) != subset_complement(sK0,meet_of_subsets(sK0,sK1)),
inference(cnf_transformation,[],[f94]) ).
fof(f103,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f64]) ).
fof(f104,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f105,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,X1) = set_difference(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f107,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set = X1
| union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ),
inference(cnf_transformation,[],[f68]) ).
fof(f109,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(meet_of_subsets(X0,X1),powerset(X0)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f141,plain,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f142,plain,
! [X0] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f17]) ).
fof(f143,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_49,negated_conjecture,
union_of_subsets(sK0,complements_of_subsets(sK0,sK1)) != subset_complement(sK0,meet_of_subsets(sK0,sK1)),
inference(cnf_transformation,[],[f101]) ).
tcf(c_50,negated_conjecture,
sK1 != empty_set,
inference(cnf_transformation,[],[f100]) ).
tcf(c_51,negated_conjecture,
element(sK1,powerset(powerset(sK0))),
inference(cnf_transformation,[],[f99]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,subset_complement(X1,X0)) = X0 )
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,X0) = set_difference(X1,X0) )
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X0)) = union_of_subsets(X1,complements_of_subsets(X1,X0)) )
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( element(meet_of_subsets(X1,X0),powerset(X1))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_91,plain,
! [X0: $i] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f141]) ).
tcf(c_92,plain,
! [X0: $i] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f142]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_difference(X1,X0,X2) = set_difference(X0,X2) )
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_488,plain,
! [X0: $i] : element(X0,powerset(X0)),
inference(light_normalisation,[status(thm)],[c_91,c_92]) ).
tcf(c_697,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( subset_difference(X1,X1,meet_of_subsets(X1,X0)) = union_of_subsets(X1,complements_of_subsets(X1,X0)) )
| ~ element(X0,powerset(powerset(X1))) ),
inference(demodulation,[status(thm)],[c_57,c_92]) ).
tcf(c_1255,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,subset_complement(X1,meet_of_subsets(X1,X0))) = meet_of_subsets(X1,X0) )
| ~ element(X0,powerset(powerset(X1))) ),
inference(superposition,[status(thm)],[c_59,c_53]) ).
tcf(c_1404,plain,
! [X0: $i,X1: $i] :
( ( subset_difference(X1,X1,X0) = set_difference(X1,X0) )
| ~ element(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_488,c_93]) ).
tcf(c_1459,plain,
( ( sK1 = empty_set )
| ( subset_difference(sK0,sK0,meet_of_subsets(sK0,sK1)) = union_of_subsets(sK0,complements_of_subsets(sK0,sK1)) ) ),
inference(superposition,[status(thm)],[c_51,c_697]) ).
tcf(c_1470,plain,
subset_difference(sK0,sK0,meet_of_subsets(sK0,sK1)) = union_of_subsets(sK0,complements_of_subsets(sK0,sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_1459,c_50]) ).
tcf(c_1554,plain,
( element(meet_of_subsets(sK0,sK1),powerset(sK0))
| ~ element(sK1,powerset(powerset(sK0))) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_10080,plain,
subset_complement(sK0,subset_complement(sK0,meet_of_subsets(sK0,sK1))) = meet_of_subsets(sK0,sK1),
inference(superposition,[status(thm)],[c_51,c_1255]) ).
tcf(c_10265,plain,
( element(meet_of_subsets(sK0,sK1),powerset(sK0))
| ~ element(subset_complement(sK0,meet_of_subsets(sK0,sK1)),powerset(sK0)) ),
inference(superposition,[status(thm)],[c_10080,c_54]) ).
tcf(c_10272,plain,
element(meet_of_subsets(sK0,sK1),powerset(sK0)),
inference(global_subsumption_just,[status(thm)],[c_10265,c_51,c_1554]) ).
tcf(c_10278,plain,
subset_difference(sK0,sK0,meet_of_subsets(sK0,sK1)) = set_difference(sK0,meet_of_subsets(sK0,sK1)),
inference(superposition,[status(thm)],[c_10272,c_1404]) ).
tcf(c_10281,plain,
subset_complement(sK0,meet_of_subsets(sK0,sK1)) = set_difference(sK0,meet_of_subsets(sK0,sK1)),
inference(superposition,[status(thm)],[c_10272,c_55]) ).
tcf(c_10290,plain,
union_of_subsets(sK0,complements_of_subsets(sK0,sK1)) != set_difference(sK0,meet_of_subsets(sK0,sK1)),
inference(demodulation,[status(thm)],[c_49,c_10281]) ).
tcf(c_10291,plain,
union_of_subsets(sK0,complements_of_subsets(sK0,sK1)) = set_difference(sK0,meet_of_subsets(sK0,sK1)),
inference(demodulation,[status(thm)],[c_1470,c_10278]) ).
tcf(c_10292,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_10291,c_10290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU328+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.63 % Computer : n002.cluster.edu
% 0.15/5.63 % Model : x86_64 x86_64
% 0.15/5.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.63 % Memory : 8046.5625MB
% 0.15/5.63 % OS : Linux 6.8.0-71-generic
% 0.15/5.63 % CPULimit : 300
% 0.15/5.63 % WCLimit : 300
% 0.15/5.63 % DateTime : Thu Sep 24 13:45:40 UTC 2026
% 0.15/5.64 % CPUTime :
% 0.15/5.64 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.67 Running first-order theorem proving
% 0.15/5.67 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
% 0.15/5.69
% 0.15/5.69 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.69
% 0.15/5.69 % Detected problem language: tptp
% 0.19/5.70 % Proving...
% 6.41/6.97 % SZS status Started for theBenchmark.p
% 6.41/6.97 % SZS status Theorem for theBenchmark.p
% 6.41/6.97
% 6.41/6.97 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.41/6.97
% 6.41/6.97 % ------ iProver source info
% 6.41/6.97
% 6.41/6.97 % git: date: 2026-07-19 20:42:38 +0200
% 6.41/6.97 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.41/6.97 % git: non_committed_changes: false
% 6.41/6.97
% 6.41/6.97 % ------ Parsing...
% 6.41/6.97 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.41/6.97
% 6.41/6.97 % ------ Preprocessing... sup_sim: 2 sf_s rm: 55 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe_e %
% 6.41/6.97
% 6.41/6.97 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.41/6.97
% 6.41/6.97 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.41/6.97 % ------ Proving...
% 6.41/6.97 % ------ Problem Properties
% 6.41/6.97
% 6.41/6.97 %
% 6.41/6.97 % clauses 27
% 6.41/6.97 % conjectures 3
% 6.41/6.97 % EPR 5
% 6.41/6.97 % Horn 25
% 6.41/6.97 % unary 13
% 6.41/6.97 % binary 10
% 6.41/6.97 % lits 45
% 6.41/6.98 % lits eq 13
% 6.41/6.98 % fd_pure 0
% 6.41/6.98 % fd_pseudo 0
% 6.41/6.98 % fd_cond 2
% 6.41/6.98 % fd_pseudo_cond 1
% 6.41/6.98 % AC symbols 0
% 6.41/6.98
% 6.41/6.98 % ------ Schedule dynamic 5 is on
% 6.41/6.98
% 6.41/6.98 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.41/6.98
% 6.41/6.98
% 6.41/6.98 % ------
% 6.41/6.98 % Current options:
% 6.41/6.98 % ------
% 6.41/6.98
% 6.41/6.98
% 6.41/6.98 %
% 6.41/6.98
% 6.41/6.98 % ------ Proving...
% 6.41/6.98 %
% 6.41/6.98
% 6.41/6.98 % SZS status Theorem for theBenchmark.p
% 6.41/6.98
% 6.41/6.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.41/6.98
% 6.41/6.98
%------------------------------------------------------------------------------