%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET595+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 : n016.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 3.76s 21.42s
% Output : CNFRefutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 58 ( 5 unt; 0 def)
% Number of atoms : 160 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 171 ( 69 ~; 74 |; 19 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% 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 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 105 ( 0 sgn 101 !; 4 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(f5,axiom,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X2)
| member(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',union) ).
fof(f7,axiom,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( ~ member(X0,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',difference) ).
fof(f12,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> equal_set(union(difference(X1,X0),X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI27) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> equal_set(union(difference(X1,X0),X0),X1) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f15,plain,
? [X0,X1] :
( subset(X0,X1)
& ~ equal_set(union(difference(X1,X0),X0),X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f17,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f18,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
( subset(sK0,sK1)
& ~ equal_set(union(difference(sK1,sK0),sK0),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15]) ).
fof(f20,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,[],[f16]) ).
fof(f21,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,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK2(X0,X1),X0)
& ~ member(sK2(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) )
& ( ( ~ member(X0,X2)
& ~ member(X0,X1) )
| member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) )
& ( ( ~ member(X0,X2)
& ~ member(X0,X1) )
| member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( ~ member(X0,difference(X2,X1))
| ( ~ member(X0,X1)
& member(X0,X2) ) )
& ( member(X0,X1)
| ~ member(X0,X2)
| member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( ~ member(X0,difference(X2,X1))
| ( ~ member(X0,X1)
& member(X0,X2) ) )
& ( member(X0,X1)
| ~ member(X0,X2)
| member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
subset(sK0,sK1),
inference(cnf_transformation,[],[f19]) ).
fof(f28,plain,
~ equal_set(union(difference(sK1,sK0),sK0),sK1),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f30,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f31,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f35,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| member(X0,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f38,plain,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,X2)
| member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_49,negated_conjecture,
~ equal_set(union(difference(sK1,sK0),sK0),sK1),
inference(cnf_transformation,[],[f28]) ).
tcf(c_50,negated_conjecture,
subset(sK0,sK1),
inference(cnf_transformation,[],[f27]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_120,plain,
( ~ subset(sK1,union(difference(sK1,sK0),sK0))
| ~ subset(union(difference(sK1,sK0),sK0),sK1) ),
inference(resolution,[status(thm)],[c_49,c_57]) ).
tcf(c_177,plain,
( subset(union(difference(sK1,sK0),sK0),sK1)
| ~ member(sK2(union(difference(sK1,sK0),sK0),sK1),sK1) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_178,plain,
( subset(union(difference(sK1,sK0),sK0),sK1)
| member(sK2(union(difference(sK1,sK0),sK0),sK1),union(difference(sK1,sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_179,plain,
( subset(sK1,union(difference(sK1,sK0),sK0))
| member(sK2(sK1,union(difference(sK1,sK0),sK0)),sK1) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_180,plain,
( subset(sK1,union(difference(sK1,sK0),sK0))
| ~ member(sK2(sK1,union(difference(sK1,sK0),sK0)),union(difference(sK1,sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_183,plain,
! [X0: $i] :
( member(sK2(sK1,union(difference(sK1,sK0),sK0)),X0)
| member(sK2(sK1,union(difference(sK1,sK0),sK0)),difference(sK1,X0))
| ~ member(sK2(sK1,union(difference(sK1,sK0),sK0)),sK1) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_188,plain,
( member(sK2(sK1,union(difference(sK1,sK0),sK0)),sK0)
| member(sK2(sK1,union(difference(sK1,sK0),sK0)),difference(sK1,sK0))
| ~ member(sK2(sK1,union(difference(sK1,sK0),sK0)),sK1) ),
inference(instantiation,[status(thm)],[c_183]) ).
tcf(c_201,plain,
( member(sK2(union(difference(sK1,sK0),sK0),sK1),sK0)
| member(sK2(union(difference(sK1,sK0),sK0),sK1),difference(sK1,sK0))
| ~ member(sK2(union(difference(sK1,sK0),sK0),sK1),union(difference(sK1,sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_232,plain,
! [X0: $i,X1: $i] :
( member(sK2(sK1,union(difference(sK1,sK0),sK0)),union(X1,X0))
| ~ member(sK2(sK1,union(difference(sK1,sK0),sK0)),X0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i] :
( member(sK2(sK1,union(difference(sK1,sK0),sK0)),union(X0,X1))
| ~ member(sK2(sK1,union(difference(sK1,sK0),sK0)),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_301,plain,
! [X0: $i] :
( member(sK2(union(difference(sK1,sK0),sK0),sK1),X0)
| ~ subset(sK0,X0)
| ~ member(sK2(union(difference(sK1,sK0),sK0),sK1),sK0) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_424,plain,
( member(sK2(union(difference(sK1,sK0),sK0),sK1),sK1)
| ~ member(sK2(union(difference(sK1,sK0),sK0),sK1),difference(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_528,plain,
! [X0: $i,X1: $i] :
( member(sK2(sK1,union(difference(sK1,sK0),sK0)),union(difference(sK1,X0),X1))
| ~ member(sK2(sK1,union(difference(sK1,sK0),sK0)),difference(sK1,X0)) ),
inference(instantiation,[status(thm)],[c_233]) ).
tcf(c_531,plain,
( member(sK2(sK1,union(difference(sK1,sK0),sK0)),union(difference(sK1,sK0),sK0))
| ~ member(sK2(sK1,union(difference(sK1,sK0),sK0)),difference(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_528]) ).
tcf(c_897,plain,
( member(sK2(union(difference(sK1,sK0),sK0),sK1),sK1)
| ~ subset(sK0,sK1)
| ~ member(sK2(union(difference(sK1,sK0),sK0),sK1),sK0) ),
inference(instantiation,[status(thm)],[c_301]) ).
tcf(c_1779,plain,
( member(sK2(sK1,union(difference(sK1,sK0),sK0)),union(difference(sK1,sK0),sK0))
| ~ member(sK2(sK1,union(difference(sK1,sK0),sK0)),sK0) ),
inference(instantiation,[status(thm)],[c_232]) ).
tcf(c_1780,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1779,c_897,c_531,c_424,c_201,c_188,c_179,c_180,c_178,c_177,c_120,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET595+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/20.59 % Computer : n016.cluster.edu
% 0.09/20.59 % Model : x86_64 x86_64
% 0.09/20.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/20.59 % Memory : 8046.5625MB
% 0.09/20.59 % OS : Linux 6.8.0-71-generic
% 0.09/20.59 % CPULimit : 300
% 0.09/20.59 % WCLimit : 300
% 0.09/20.59 % DateTime : Thu Sep 24 11:28:18 UTC 2026
% 0.09/20.59 % CPUTime :
% 0.09/20.59 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/20.63 Running first-order theorem proving
% 0.13/20.63 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
% 0.13/20.64
% 0.13/20.64 % ======== iProver multi-core TPTP/SMT =========
% 0.13/20.64
% 0.13/20.65 % Detected problem language: tptp
% 0.13/20.66 % Proving...
% 3.76/21.42 % SZS status Started for theBenchmark.p
% 3.76/21.42 % SZS status Theorem for theBenchmark.p
% 3.76/21.42
% 3.76/21.42 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.76/21.42
% 3.76/21.42 % ------ iProver source info
% 3.76/21.42
% 3.76/21.42 % git: date: 2026-07-19 20:42:38 +0200
% 3.76/21.42 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.76/21.42 % git: non_committed_changes: false
% 3.76/21.42
% 3.76/21.42 % ------ Parsing...
% 3.76/21.42 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.76/21.42
% 3.76/21.42 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.76/21.42
% 3.76/21.42 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.76/21.42 % ------ Proving...
% 3.76/21.42 % ------ Problem Properties
% 3.76/21.42
% 3.76/21.42 %
% 3.76/21.42 % clauses 11
% 3.76/21.42 % conjectures 1
% 3.76/21.42 % EPR 2
% 3.76/21.42 % Horn 8
% 3.76/21.42 % unary 1
% 3.76/21.42 % binary 7
% 3.76/21.42 % lits 24
% 3.76/21.42 % lits eq 0
% 3.76/21.42 % fd_pure 0
% 3.76/21.42 % fd_pseudo 0
% 3.76/21.42 % fd_cond 0
% 3.76/21.42 % fd_pseudo_cond 0
% 3.76/21.42 % AC symbols 0
% 3.76/21.42
% 3.76/21.42 % ------ Schedule dynamic 5 is on
% 3.76/21.42
% 3.76/21.42 % ------ no equalities: superposition off
% 3.76/21.42
% 3.76/21.42 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.76/21.42
% 3.76/21.42
% 3.76/21.42 % ------
% 3.76/21.42 % Current options:
% 3.76/21.42 % ------
% 3.76/21.42
% 3.76/21.42
% 3.76/21.42 %
% 3.76/21.42
% 3.76/21.42 % ------ Proving...
% 3.76/21.42 %
% 3.76/21.42
% 3.76/21.42 % SZS status Theorem for theBenchmark.p
% 3.76/21.42
% 3.76/21.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.76/21.42
%------------------------------------------------------------------------------