%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET595+3 : 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 : n006.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 02:47:29 PM UTC 2026
% Result : Theorem 4.14s 1.64s
% Output : CNFRefutation 4.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 60 ( 5 unt; 0 def)
% Number of atoms : 174 ( 16 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 185 ( 71 ~; 85 |; 19 &)
% ( 5 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 104 !; 6 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
<=> member(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_equal) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f3,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f9,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> X1 = union(X0,difference(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th54) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> X1 = union(X0,difference(X1,X0)) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
? [X0,X1] :
( subset(X0,X1)
& union(X0,difference(X1,X0)) != X1 ),
inference(ennf_transformation,[],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( ? [X2] :
( member(X2,X0)
<~> member(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f1]) ).
fof(f13,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f14,plain,
( subset(sK0,sK1)
& sK1 != union(sK0,difference(sK1,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f11]) ).
fof(f20,plain,
! [X0,X1] :
( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f12]) ).
fof(f21,plain,
! [X0,X1] :
( ( ( member(sK3(X0,X1),X0)
| member(sK3(X0,X1),X1) )
& ( ~ member(sK3(X0,X1),X0)
| ~ member(sK3(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) )
& ( ( ~ member(X2,X1)
& ~ member(X2,X0) )
| member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) )
& ( ( ~ member(X2,X1)
& ~ member(X2,X0) )
| member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( ~ member(X2,difference(X0,X1))
| ( ~ member(X2,X1)
& member(X2,X0) ) )
& ( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( ~ member(X2,difference(X0,X1))
| ( ~ member(X2,X1)
& member(X2,X0) ) )
& ( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f24]) ).
fof(f26,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,[],[f13]) ).
fof(f27,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,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK4(X0,X1),X0)
& ~ member(sK4(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f27]) ).
fof(f29,plain,
subset(sK0,sK1),
inference(cnf_transformation,[],[f14]) ).
fof(f30,plain,
sK1 != union(sK0,difference(sK1,sK0)),
inference(cnf_transformation,[],[f14]) ).
fof(f38,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| member(sK3(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
! [X0,X1] :
( ~ member(sK3(X0,X1),X0)
| ~ member(sK3(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f25]) ).
fof(f48,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f49,plain,
! [X0,X1] :
( member(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f50,plain,
! [X0,X1] :
( ~ member(sK4(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_49,negated_conjecture,
union(sK0,difference(sK1,sK0)) != sK1,
inference(cnf_transformation,[],[f30]) ).
tcf(c_50,negated_conjecture,
subset(sK0,sK1),
inference(cnf_transformation,[],[f29]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(sK3(X0,X1),X1)
| ~ member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( member(sK3(X0,X1),X1)
| member(sK3(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_879,plain,
( ( union(sK0,difference(sK1,sK0)) = sK1 )
| ~ member(sK3(union(sK0,difference(sK1,sK0)),sK1),sK1)
| ~ member(sK3(union(sK0,difference(sK1,sK0)),sK1),union(sK0,difference(sK1,sK0))) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_880,plain,
( member(sK3(union(sK0,difference(sK1,sK0)),sK1),sK1)
| member(sK3(union(sK0,difference(sK1,sK0)),sK1),union(sK0,difference(sK1,sK0)))
| ( union(sK0,difference(sK1,sK0)) = sK1 ) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_1085,plain,
( member(sK3(union(sK0,difference(sK1,sK0)),sK1),sK0)
| member(sK3(union(sK0,difference(sK1,sK0)),sK1),difference(sK1,sK0))
| ~ member(sK3(union(sK0,difference(sK1,sK0)),sK1),union(sK0,difference(sK1,sK0))) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_1166,plain,
( subset(sK1,union(sK0,difference(sK1,sK0)))
| member(sK4(sK1,union(sK0,difference(sK1,sK0))),sK1) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_1167,plain,
( subset(sK1,union(sK0,difference(sK1,sK0)))
| ~ member(sK4(sK1,union(sK0,difference(sK1,sK0))),union(sK0,difference(sK1,sK0))) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_1292,plain,
! [X0: $i] :
( member(sK3(union(sK0,difference(sK1,sK0)),sK1),X0)
| ~ subset(sK1,X0)
| ~ member(sK3(union(sK0,difference(sK1,sK0)),sK1),sK1) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_1506,plain,
! [X0: $i] :
( member(sK4(sK1,union(sK0,difference(sK1,sK0))),X0)
| member(sK4(sK1,union(sK0,difference(sK1,sK0))),difference(sK1,X0))
| ~ member(sK4(sK1,union(sK0,difference(sK1,sK0))),sK1) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_1511,plain,
( member(sK4(sK1,union(sK0,difference(sK1,sK0))),sK0)
| member(sK4(sK1,union(sK0,difference(sK1,sK0))),difference(sK1,sK0))
| ~ member(sK4(sK1,union(sK0,difference(sK1,sK0))),sK1) ),
inference(instantiation,[status(thm)],[c_1506]) ).
tcf(c_2345,plain,
! [X0: $i] :
( member(sK3(union(sK0,difference(sK1,sK0)),sK1),X0)
| ~ subset(sK0,X0)
| ~ member(sK3(union(sK0,difference(sK1,sK0)),sK1),sK0) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_2617,plain,
! [X0: $i,X1: $i] :
( member(sK3(union(sK0,difference(sK1,sK0)),sK1),X0)
| ~ member(sK3(union(sK0,difference(sK1,sK0)),sK1),difference(X0,X1)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_3318,plain,
( member(sK3(union(sK0,difference(sK1,sK0)),sK1),union(sK0,difference(sK1,sK0)))
| ~ subset(sK1,union(sK0,difference(sK1,sK0)))
| ~ member(sK3(union(sK0,difference(sK1,sK0)),sK1),sK1) ),
inference(instantiation,[status(thm)],[c_1292]) ).
tcf(c_3820,plain,
( member(sK4(sK1,union(sK0,difference(sK1,sK0))),union(sK0,difference(sK1,sK0)))
| ~ member(sK4(sK1,union(sK0,difference(sK1,sK0))),sK0) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_4098,plain,
( member(sK4(sK1,union(sK0,difference(sK1,sK0))),union(sK0,difference(sK1,sK0)))
| ~ member(sK4(sK1,union(sK0,difference(sK1,sK0))),difference(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_6039,plain,
( member(sK3(union(sK0,difference(sK1,sK0)),sK1),sK1)
| ~ subset(sK0,sK1)
| ~ member(sK3(union(sK0,difference(sK1,sK0)),sK1),sK0) ),
inference(instantiation,[status(thm)],[c_2345]) ).
tcf(c_7468,plain,
! [X0: $i] :
( member(sK3(union(sK0,difference(sK1,sK0)),sK1),sK1)
| ~ member(sK3(union(sK0,difference(sK1,sK0)),sK1),difference(sK1,X0)) ),
inference(instantiation,[status(thm)],[c_2617]) ).
tcf(c_7469,plain,
( member(sK3(union(sK0,difference(sK1,sK0)),sK1),sK1)
| ~ member(sK3(union(sK0,difference(sK1,sK0)),sK1),difference(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_7468]) ).
tcf(c_7666,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_7469,c_6039,c_4098,c_3820,c_3318,c_1511,c_1166,c_1167,c_1085,c_880,c_879,c_49,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET595+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.74 % Computer : n006.cluster.edu
% 0.09/0.74 % Model : x86_64 x86_64
% 0.09/0.74 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.74 % Memory : 8046.5625MB
% 0.09/0.74 % OS : Linux 6.8.0-71-generic
% 0.09/0.74 % CPULimit : 300
% 0.09/0.74 % WCLimit : 300
% 0.09/0.74 % DateTime : Thu Sep 24 11:23:03 UTC 2026
% 0.09/0.74 % CPUTime :
% 0.09/0.74 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.77 Running first-order theorem proving
% 0.09/0.77 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
% 0.09/0.78
% 0.09/0.78 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.78
% 0.09/0.78 % Detected problem language: tptp
% 0.09/0.80 % Proving...
% 4.14/1.64 % SZS status Started for theBenchmark.p
% 4.14/1.64 % SZS status Theorem for theBenchmark.p
% 4.14/1.64
% 4.14/1.64 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.14/1.64
% 4.14/1.64 % ------ iProver source info
% 4.14/1.64
% 4.14/1.64 % git: date: 2026-07-19 20:42:38 +0200
% 4.14/1.64 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.14/1.64 % git: non_committed_changes: false
% 4.14/1.64
% 4.14/1.64 % ------ Parsing...
% 4.14/1.64 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.14/1.64
% 4.14/1.64 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.14/1.64
% 4.14/1.64 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.14/1.64
% 4.14/1.64 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.14/1.64 % ------ Proving...
% 4.14/1.64 % ------ Problem Properties
% 4.14/1.64
% 4.14/1.64 %
% 4.14/1.64 % clauses 18
% 4.14/1.64 % conjectures 2
% 4.14/1.64 % EPR 4
% 4.14/1.64 % Horn 13
% 4.14/1.64 % unary 4
% 4.14/1.64 % binary 6
% 4.14/1.64 % lits 40
% 4.14/1.64 % lits eq 7
% 4.14/1.64 % fd_pure 0
% 4.14/1.64 % fd_pseudo 0
% 4.14/1.64 % fd_cond 0
% 4.14/1.64 % fd_pseudo_cond 5
% 4.14/1.64 % AC symbols 0
% 4.14/1.64
% 4.14/1.64 % ------ Schedule dynamic 5 is on
% 4.14/1.64
% 4.14/1.64 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.14/1.64
% 4.14/1.64
% 4.14/1.64 % ------
% 4.14/1.64 % Current options:
% 4.14/1.64 % ------
% 4.14/1.64
% 4.14/1.64
% 4.14/1.64 %
% 4.14/1.64
% 4.14/1.64 % ------ Proving...
% 4.14/1.64 %
% 4.14/1.64
% 4.14/1.64 % SZS status Theorem for theBenchmark.p
% 4.14/1.64
% 4.14/1.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.14/1.65
% 4.14/1.65
%------------------------------------------------------------------------------