%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET580+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 : n020.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 02:47:26 PM UTC 2026
% Result : Theorem 0.89s 1.19s
% Output : CNFRefutation 0.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 63 ( 6 unt; 3 def)
% Number of atoms : 218 ( 5 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 206 ( 86 ~; 97 |; 15 &)
% ( 6 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 5 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 73 !; 6 ?; 27 :)
% 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(f2,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(f3,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f7,conjecture,
! [X0,X1,X2] :
( member(X0,symmetric_difference(X1,X2))
<=> ~ ( member(X0,X1)
<=> member(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th23) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2] :
( member(X0,symmetric_difference(X1,X2))
<=> ~ ( member(X0,X1)
<=> member(X0,X2) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
? [X0,X1,X2] :
( member(X0,symmetric_difference(X1,X2))
<~> ( member(X0,X1)
<~> member(X0,X2) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f10,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(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(flattening,[],[f10]) ).
fof(f12,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,[],[f2]) ).
fof(f13,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,[],[f12]) ).
fof(f17,plain,
? [X0,X1,X2] :
( ( member(X0,symmetric_difference(X1,X2))
| ( ( member(X0,X1)
| member(X0,X2) )
& ( ~ member(X0,X1)
| ~ member(X0,X2) ) ) )
& ( ~ member(X0,symmetric_difference(X1,X2))
| ( ( ~ member(X0,X1)
| member(X0,X2) )
& ( ~ member(X0,X2)
| member(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f18,plain,
( ( member(sK1,symmetric_difference(sK2,sK3))
| ( ( member(sK1,sK2)
| member(sK1,sK3) )
& ( ~ member(sK1,sK2)
| ~ member(sK1,sK3) ) ) )
& ( ~ member(sK1,symmetric_difference(sK2,sK3))
| ( ( ~ member(sK1,sK2)
| member(sK1,sK3) )
& ( ~ member(sK1,sK3)
| member(sK1,sK2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f17]) ).
fof(f19,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f20,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f21,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f22,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f24,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f25,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f3]) ).
fof(f32,plain,
( member(sK1,symmetric_difference(sK2,sK3))
| member(sK1,sK2)
| member(sK1,sK3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
( member(sK1,symmetric_difference(sK2,sK3))
| ~ member(sK1,sK2)
| ~ member(sK1,sK3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
( ~ member(sK1,symmetric_difference(sK2,sK3))
| ~ member(sK1,sK2)
| member(sK1,sK3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
( ~ member(sK1,symmetric_difference(sK2,sK3))
| ~ member(sK1,sK3)
| member(sK1,sK2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f37,plain,
( ~ member(sK1,union(difference(sK2,sK3),difference(sK3,sK2)))
| ~ member(sK1,sK3)
| member(sK1,sK2) ),
inference(definition_unfolding,[],[f35,f25]) ).
fof(f38,plain,
( ~ member(sK1,union(difference(sK2,sK3),difference(sK3,sK2)))
| ~ member(sK1,sK2)
| member(sK1,sK3) ),
inference(definition_unfolding,[],[f34,f25]) ).
fof(f39,plain,
( member(sK1,union(difference(sK2,sK3),difference(sK3,sK2)))
| ~ member(sK1,sK2)
| ~ member(sK1,sK3) ),
inference(definition_unfolding,[],[f33,f25]) ).
fof(f40,plain,
( member(sK1,union(difference(sK2,sK3),difference(sK3,sK2)))
| member(sK1,sK2)
| member(sK1,sK3) ),
inference(definition_unfolding,[],[f32,f25]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_59,negated_conjecture,
( member(sK1,sK2)
| ~ member(sK1,sK3)
| ~ member(sK1,union(difference(sK2,sK3),difference(sK3,sK2))) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_60,negated_conjecture,
( member(sK1,sK3)
| ~ member(sK1,sK2)
| ~ member(sK1,union(difference(sK2,sK3),difference(sK3,sK2))) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_61,negated_conjecture,
( member(sK1,union(difference(sK2,sK3),difference(sK3,sK2)))
| ~ member(sK1,sK3)
| ~ member(sK1,sK2) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_62,negated_conjecture,
( member(sK1,sK3)
| member(sK1,sK2)
| member(sK1,union(difference(sK2,sK3),difference(sK3,sK2))) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_339,definition,
iPr_def_10 = difference(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_340,definition,
iPr_def_11 = difference(sK3,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_341,definition,
iPr_def_12 = union(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_342,negated_conjecture,
( member(sK1,iPr_def_12)
| member(sK1,sK3)
| member(sK1,sK2) ),
inference(demodulation,[status(thm)],[c_62,c_340,c_339,c_341]) ).
tcf(c_343,negated_conjecture,
( member(sK1,iPr_def_12)
| ~ member(sK1,sK3)
| ~ member(sK1,sK2) ),
inference(demodulation,[status(thm)],[c_61]) ).
tcf(c_344,negated_conjecture,
( member(sK1,sK3)
| ~ member(sK1,iPr_def_12)
| ~ member(sK1,sK2) ),
inference(demodulation,[status(thm)],[c_60]) ).
tcf(c_345,negated_conjecture,
( member(sK1,sK2)
| ~ member(sK1,iPr_def_12)
| ~ member(sK1,sK3) ),
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_586,plain,
! [X0: $i] :
( member(X0,iPr_def_12)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_341,c_49]) ).
tcf(c_589,plain,
( member(sK1,iPr_def_12)
| ~ member(sK1,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_586]) ).
tcf(c_596,plain,
! [X0: $i] :
( member(X0,iPr_def_12)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_341,c_50]) ).
tcf(c_599,plain,
( member(sK1,iPr_def_12)
| ~ member(sK1,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_596]) ).
tcf(c_604,plain,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_339,c_53]) ).
tcf(c_605,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_340,c_53]) ).
tcf(c_610,plain,
( member(sK1,sK3)
| ~ member(sK1,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_605]) ).
tcf(c_611,plain,
( member(sK1,sK2)
| ~ member(sK1,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_604]) ).
tcf(c_616,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_10)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_339,c_54]) ).
tcf(c_617,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_11)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_340,c_54]) ).
tcf(c_622,plain,
( ~ member(sK1,iPr_def_11)
| ~ member(sK1,sK2) ),
inference(instantiation,[status(thm)],[c_617]) ).
tcf(c_623,plain,
( ~ member(sK1,iPr_def_10)
| ~ member(sK1,sK3) ),
inference(instantiation,[status(thm)],[c_616]) ).
tcf(c_634,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| member(X0,iPr_def_10)
| ~ member(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_341,c_51]) ).
tcf(c_638,plain,
( member(sK1,iPr_def_11)
| member(sK1,iPr_def_10)
| ~ member(sK1,iPr_def_12) ),
inference(instantiation,[status(thm)],[c_634]) ).
tcf(c_675,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| member(X0,sK3)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_339,c_52]) ).
tcf(c_676,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| member(X0,sK2)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_340,c_52]) ).
tcf(c_685,plain,
( member(sK1,iPr_def_11)
| member(sK1,sK2)
| ~ member(sK1,sK3) ),
inference(instantiation,[status(thm)],[c_676]) ).
tcf(c_686,plain,
( member(sK1,iPr_def_10)
| member(sK1,sK3)
| ~ member(sK1,sK2) ),
inference(instantiation,[status(thm)],[c_675]) ).
tcf(c_716,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_686,c_685,c_638,c_623,c_622,c_611,c_610,c_599,c_589,c_345,c_344,c_343,c_342]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET580+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 11:21:04 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 0.89/1.19 % SZS status Started for theBenchmark.p
% 0.89/1.19 % SZS status Theorem for theBenchmark.p
% 0.89/1.19
% 0.89/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.89/1.19
% 0.89/1.19 % ------ iProver source info
% 0.89/1.19
% 0.89/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 0.89/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.89/1.19 % git: non_committed_changes: false
% 0.89/1.19
% 0.89/1.19 % ------ Parsing...
% 0.89/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.89/1.19
% 0.89/1.19 % ------ 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 %
% 0.89/1.19
% 0.89/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.89/1.19
% 0.89/1.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.89/1.19 % ------ Proving...
% 0.89/1.19 % ------ Problem Properties
% 0.89/1.19
% 0.89/1.19 %
% 0.89/1.19 % clauses 16
% 0.89/1.19 % conjectures 4
% 0.89/1.19 % EPR 4
% 0.89/1.19 % Horn 12
% 0.89/1.19 % unary 4
% 0.89/1.19 % binary 4
% 0.89/1.19 % lits 36
% 0.89/1.19 % lits eq 6
% 0.89/1.19 % fd_pure 0
% 0.89/1.19 % fd_pseudo 0
% 0.89/1.19 % fd_cond 0
% 0.89/1.19 % fd_pseudo_cond 2
% 0.89/1.19 % AC symbols 0
% 0.89/1.19
% 0.89/1.19 % ------ Schedule dynamic 5 is on
% 0.89/1.19
% 0.89/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.89/1.19
% 0.89/1.19
% 0.89/1.19 % ------
% 0.89/1.19 % Current options:
% 0.89/1.19 % ------
% 0.89/1.19
% 0.89/1.19
% 0.89/1.19 %
% 0.89/1.19
% 0.89/1.19 % ------ Proving...
% 0.89/1.19 %
% 0.89/1.19
% 0.89/1.19 % SZS status Theorem for theBenchmark.p
% 0.89/1.19
% 0.89/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.89/1.19
% 0.89/1.19
%------------------------------------------------------------------------------