%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET159+3 : 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 : 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 02:46:47 PM UTC 2026
% Result : Theorem 12.61s 7.73s
% Output : CNFRefutation 12.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 55 ( 14 unt; 0 def)
% Number of atoms : 144 ( 24 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 152 ( 63 ~; 73 |; 13 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 70 !; 5 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f3,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f7,conjecture,
! [X0,X1,X2] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_union) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f10,plain,
? [X0,X1,X2] : union(union(X0,X1),X2) != union(X0,union(X1,X2)),
inference(ennf_transformation,[],[f8]) ).
fof(f11,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,[],[f1]) ).
fof(f12,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,[],[f11]) ).
fof(f18,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X2] :
( ( ~ member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X1)
| member(X2,X0) ) ) )
& ( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f19,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X1) )
& ( ~ member(X3,X1)
| member(X3,X0) ) ) )
& ( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ) ),
inference(rectify,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X1) )
& ( ~ member(X3,X1)
| member(X3,X0) ) ) )
& ( ( ( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1) )
& ( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1) ) )
| X0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f19]) ).
fof(f21,plain,
union(union(sK2,sK3),sK4) != union(sK2,union(sK3,sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f10]) ).
fof(f22,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f23,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f28,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f35,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
union(union(sK2,sK3),sK4) != union(sK2,union(sK3,sK4)),
inference(cnf_transformation,[],[f21]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f28]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_62,negated_conjecture,
union(union(sK2,sK3),sK4) != union(sK2,union(sK3,sK4)),
inference(cnf_transformation,[],[f37]) ).
tcf(c_122,plain,
union(sK2,union(sK3,sK4)) != union(sK4,union(sK2,sK3)),
inference(demodulation,[status(thm)],[c_62,c_55]) ).
tcf(c_342,plain,
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK4,union(sK2,sK3)))
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,union(sK3,sK4)))
| ( union(sK2,union(sK3,sK4)) = union(sK4,union(sK2,sK3)) ) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_343,plain,
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK4,union(sK2,sK3)))
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,union(sK3,sK4)))
| ( union(sK2,union(sK3,sK4)) = union(sK4,union(sK2,sK3)) ) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_344,plain,
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK4,union(sK2,sK3)))
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,union(sK3,sK4))) ),
inference(global_subsumption_just,[status(thm)],[c_343,c_122,c_342]) ).
tcf(c_352,plain,
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK2)
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK3,sK4))
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,union(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_353,plain,
( ( union(sK2,union(sK3,sK4)) = union(sK4,union(sK2,sK3)) )
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK4,union(sK2,sK3)))
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,union(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_354,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,union(sK3,sK4)))
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK4,union(sK2,sK3))) ),
inference(global_subsumption_just,[status(thm)],[c_353,c_122,c_353]) ).
tcf(c_355,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK4,union(sK2,sK3)))
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,union(sK3,sK4))) ),
inference(renaming,[status(thm)],[c_354]) ).
tcf(c_368,plain,
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK4)
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,sK3))
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK4,union(sK2,sK3))) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_387,plain,
! [X0: $i,X1: $i] :
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(X0,X1))
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),X0) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i] :
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(X1,X0))
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),X0) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_434,plain,
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK4)
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK3)
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_450,plain,
! [X0: $i] :
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(X0,union(sK3,sK4)))
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_388]) ).
tcf(c_451,plain,
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,union(sK3,sK4)))
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_450]) ).
tcf(c_624,plain,
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK4,union(sK2,sK3)))
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK4) ),
inference(instantiation,[status(thm)],[c_387]) ).
tcf(c_625,plain,
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK3,sK4))
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK3) ),
inference(instantiation,[status(thm)],[c_387]) ).
tcf(c_631,plain,
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,union(sK3,sK4)))
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK2) ),
inference(instantiation,[status(thm)],[c_387]) ).
tcf(c_633,plain,
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK4,union(sK2,sK3)))
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_388]) ).
tcf(c_634,plain,
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK3,sK4))
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK4) ),
inference(instantiation,[status(thm)],[c_388]) ).
tcf(c_635,plain,
~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK4),
inference(global_subsumption_just,[status(thm)],[c_634,c_355,c_451,c_624,c_634]) ).
tcf(c_694,plain,
! [X0: $i,X1: $i] :
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(X0,X1))
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),X0) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_695,plain,
! [X0: $i,X1: $i] :
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(X1,X0))
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),X0) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_732,plain,
! [X0: $i,X1: $i] :
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),X1)
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),X0)
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(X0,X1)) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_834,plain,
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,sK3))
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK2) ),
inference(instantiation,[status(thm)],[c_694]) ).
tcf(c_835,plain,
~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK2),
inference(global_subsumption_just,[status(thm)],[c_834,c_122,c_353,c_631,c_633,c_834]) ).
tcf(c_839,plain,
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,sK3))
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK3) ),
inference(instantiation,[status(thm)],[c_695]) ).
tcf(c_840,plain,
member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,sK3)),
inference(global_subsumption_just,[status(thm)],[c_839,c_344,c_352,c_368,c_434,c_635,c_835,c_839]) ).
tcf(c_1015,plain,
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK3)
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK2)
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_732]) ).
tcf(c_1016,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1015,c_840,c_835,c_633,c_625,c_451,c_355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET159+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/5.37 % Computer : n016.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Thu Sep 24 10:09:18 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.41 Running first-order theorem proving
% 0.13/5.41 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
% 0.13/5.42
% 0.13/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.42
% 0.13/5.42 % Detected problem language: tptp
% 0.13/5.43 % Proving...
% 12.61/7.73 % SZS status Started for theBenchmark.p
% 12.61/7.73 % SZS status Theorem for theBenchmark.p
% 12.61/7.73
% 12.61/7.73 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 12.61/7.73
% 12.61/7.73 % ------ iProver source info
% 12.61/7.73
% 12.61/7.73 % git: date: 2026-07-19 20:42:38 +0200
% 12.61/7.73 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 12.61/7.73 % git: non_committed_changes: false
% 12.61/7.73
% 12.61/7.73 % ------ Parsing...
% 12.61/7.73 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 12.61/7.73
% 12.61/7.73 % ------ Preprocessing... sup_sim: 1 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 %
% 12.61/7.73
% 12.61/7.73 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 12.61/7.73
% 12.61/7.73 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 12.61/7.73 % ------ Proving...
% 12.61/7.73 % ------ Problem Properties
% 12.61/7.73
% 12.61/7.73 %
% 12.61/7.73 % clauses 12
% 12.61/7.73 % conjectures 0
% 12.61/7.73 % EPR 3
% 12.61/7.73 % Horn 9
% 12.61/7.73 % unary 3
% 12.61/7.73 % binary 4
% 12.61/7.73 % lits 26
% 12.61/7.73 % lits eq 5
% 12.61/7.73 % fd_pure 0
% 12.61/7.73 % fd_pseudo 0
% 12.61/7.73 % fd_cond 0
% 12.61/7.73 % fd_pseudo_cond 3
% 12.61/7.73 % AC symbols 0
% 12.61/7.73
% 12.61/7.73 % ------ Input Options Time Limit: Unbounded
% 12.61/7.73
% 12.61/7.73
% 12.61/7.73 % ------
% 12.61/7.73 % Current options:
% 12.61/7.73 % ------
% 12.61/7.73
% 12.61/7.73
% 12.61/7.73 %
% 12.61/7.73
% 12.61/7.73 % ------ Proving...
% 12.61/7.73 %
% 12.61/7.73
% 12.61/7.73 % SZS status Theorem for theBenchmark.p
% 12.61/7.73
% 12.61/7.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 12.61/7.73
% 12.61/7.73
%------------------------------------------------------------------------------