%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET610+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 : n012.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 02:47:33 PM UTC 2026
% Result : Theorem 2.67s 0.97s
% Output : CNFRefutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 59 ( 19 unt; 3 def)
% Number of atoms : 212 ( 26 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 135 ( 54 ~; 65 |; 11 &)
% ( 3 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 84 !; 4 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
<=> member(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f5,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f9,conjecture,
! [X0,X1] : difference(union(X0,X1),X1) = difference(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th83) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] : difference(union(X0,X1),X1) = difference(X0,X1),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ? [X2] :
( member(X2,X0)
<~> member(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f1]) ).
fof(f13,plain,
? [X0,X1] : difference(X0,X1) != difference(union(X0,X1),X1),
inference(ennf_transformation,[],[f10]) ).
fof(f14,plain,
! [X0,X1] :
( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f11]) ).
fof(f15,plain,
! [X0,X1] :
( ( ( member(sK0(X0,X1),X0)
| member(sK0(X0,X1),X1) )
& ( ~ member(sK0(X0,X1),X0)
| ~ member(sK0(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f14]) ).
fof(f16,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(f17,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,[],[f16]) ).
fof(f18,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(f19,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,[],[f18]) ).
fof(f28,plain,
difference(sK3,sK4) != difference(union(sK3,sK4),sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f13]) ).
fof(f29,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| member(sK0(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X0)
| ~ member(sK0(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f36,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f40,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f49,plain,
difference(sK3,sK4) != difference(union(sK3,sK4),sK4),
inference(cnf_transformation,[],[f28]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(sK0(X0,X1),X1)
| ~ member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X1)
| member(sK0(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f40]) ).
tcf(c_67,negated_conjecture,
difference(union(sK3,sK4),sK4) != difference(sK3,sK4),
inference(cnf_transformation,[],[f49]) ).
tcf(c_179,plain,
difference(union(sK4,sK3),sK4) != difference(sK3,sK4),
inference(demodulation,[status(thm)],[c_67,c_60]) ).
tcf(c_388,definition,
iPr_def_10 = union(sK4,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_389,definition,
iPr_def_11 = difference(iPr_def_10,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_390,definition,
iPr_def_12 = difference(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_391,plain,
iPr_def_11 != iPr_def_12,
inference(demodulation,[status(thm)],[c_179,c_390,c_388,c_389]) ).
tcf(c_645,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_388,c_52]) ).
tcf(c_654,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_390,c_55]) ).
tcf(c_655,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_389,c_55]) ).
tcf(c_682,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_12)
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_390,c_56]) ).
tcf(c_683,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_11)
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_389,c_56]) ).
tcf(c_792,plain,
( ( iPr_def_11 = iPr_def_12 )
| ~ member(sK0(iPr_def_11,iPr_def_12),iPr_def_12)
| ~ member(sK0(iPr_def_11,iPr_def_12),iPr_def_11) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_804,plain,
! [X0: $i] :
( member(X0,sK4)
| member(X0,sK3)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_388,c_53]) ).
tcf(c_813,plain,
( member(sK0(iPr_def_11,iPr_def_12),iPr_def_12)
| member(sK0(iPr_def_11,iPr_def_12),iPr_def_11)
| ( iPr_def_11 = iPr_def_12 ) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_820,plain,
! [X0: $i] :
( member(X0,iPr_def_12)
| member(X0,sK4)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_390,c_54]) ).
tcf(c_821,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| member(X0,sK4)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_389,c_54]) ).
tcf(c_889,plain,
! [X0: $i] :
( member(sK0(X0,iPr_def_12),sK3)
| member(sK0(X0,iPr_def_12),X0)
| ( X0 = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_50,c_654]) ).
tcf(c_8246,plain,
( member(sK0(iPr_def_11,iPr_def_12),iPr_def_10)
| member(sK0(iPr_def_11,iPr_def_12),sK3)
| ( iPr_def_11 = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_889,c_655]) ).
tcf(c_8251,plain,
( member(sK0(iPr_def_11,iPr_def_12),iPr_def_10)
| member(sK0(iPr_def_11,iPr_def_12),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8246,c_391]) ).
tcf(c_8650,plain,
member(sK0(iPr_def_11,iPr_def_12),iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_8251,c_645]) ).
tcf(c_8652,plain,
( member(sK0(iPr_def_11,iPr_def_12),iPr_def_11)
| member(sK0(iPr_def_11,iPr_def_12),sK4) ),
inference(superposition,[status(thm)],[c_8650,c_821]) ).
tcf(c_8653,plain,
( member(sK0(iPr_def_11,iPr_def_12),sK4)
| member(sK0(iPr_def_11,iPr_def_12),sK3) ),
inference(superposition,[status(thm)],[c_8650,c_804]) ).
tcf(c_8817,plain,
( member(sK0(iPr_def_11,iPr_def_12),iPr_def_12)
| member(sK0(iPr_def_11,iPr_def_12),sK4) ),
inference(superposition,[status(thm)],[c_8653,c_820]) ).
tcf(c_9662,plain,
member(sK0(iPr_def_11,iPr_def_12),sK4),
inference(global_subsumption_just,[status(thm)],[c_8817,c_391,c_792,c_8652,c_8817]) ).
tcf(c_9666,plain,
~ member(sK0(iPr_def_11,iPr_def_12),iPr_def_11),
inference(superposition,[status(thm)],[c_9662,c_683]) ).
tcf(c_9667,plain,
~ member(sK0(iPr_def_11,iPr_def_12),iPr_def_12),
inference(superposition,[status(thm)],[c_9662,c_682]) ).
tcf(c_9671,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9666,c_9667,c_813,c_391]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET610+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Thu Sep 24 11:26:37 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 0.07/0.33
% 0.07/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.33
% 0.07/0.33 % Detected problem language: tptp
% 0.07/0.33 % Proving...
% 2.67/0.97 % SZS status Started for theBenchmark.p
% 2.67/0.97 % SZS status Theorem for theBenchmark.p
% 2.67/0.97
% 2.67/0.97 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.67/0.97
% 2.67/0.97 % ------ iProver source info
% 2.67/0.97
% 2.67/0.97 % git: date: 2026-07-19 20:42:38 +0200
% 2.67/0.97 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.67/0.97 % git: non_committed_changes: false
% 2.67/0.97
% 2.67/0.97 % ------ Parsing...
% 2.67/0.97 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.67/0.97
% 2.67/0.97 % ------ 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 %
% 2.67/0.97
% 2.67/0.97 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.67/0.97
% 2.67/0.97 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.67/0.97 % ------ Proving...
% 2.67/0.97 % ------ Problem Properties
% 2.67/0.97
% 2.67/0.97 %
% 2.67/0.97 % clauses 20
% 2.67/0.97 % conjectures 0
% 2.67/0.97 % EPR 4
% 2.67/0.97 % Horn 15
% 2.67/0.97 % unary 6
% 2.67/0.97 % binary 6
% 2.67/0.97 % lits 42
% 2.67/0.97 % lits eq 10
% 2.67/0.97 % fd_pure 0
% 2.67/0.97 % fd_pseudo 0
% 2.67/0.97 % fd_cond 0
% 2.67/0.97 % fd_pseudo_cond 5
% 2.67/0.97 % AC symbols 0
% 2.67/0.97
% 2.67/0.97 % ------ Schedule dynamic 5 is on
% 2.67/0.97
% 2.67/0.97 % ------ no conjectures: strip conj schedule
% 2.67/0.97
% 2.67/0.97 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.67/0.97
% 2.67/0.97
% 2.67/0.97 % ------
% 2.67/0.97 % Current options:
% 2.67/0.97 % ------
% 2.67/0.97
% 2.67/0.97
% 2.67/0.97 %
% 2.67/0.97
% 2.67/0.97 % ------ Proving...
% 2.67/0.97 %
% 2.67/0.97
% 2.67/0.97 % SZS status Theorem for theBenchmark.p
% 2.67/0.97
% 2.67/0.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.67/0.97
% 2.67/0.97
%------------------------------------------------------------------------------