%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET577+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 : n019.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 0.88s 6.28s
% Output : CNFRefutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 74 ( 11 unt; 1 def)
% Number of atoms : 275 ( 35 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 255 ( 97 ~; 118 |; 29 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 125 ( 0 sgn 112 !; 13 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f7,conjecture,
! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X2)
| member(X3,X1) ) )
=> X0 = union(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th18) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X2)
| member(X3,X1) ) )
=> X0 = union(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,plain,
? [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X2)
| member(X3,X1) ) )
& union(X1,X2) != X0 ),
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(f15,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,[],[f9]) ).
fof(f16,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,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK0(X0,X1),X0)
& ~ member(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f16]) ).
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,
? [X0,X1,X2] :
( ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X2)
| member(X3,X1) )
& ( ( ~ member(X3,X2)
& ~ member(X3,X1) )
| member(X3,X0) ) )
& union(X1,X2) != X0 ),
inference(nnf_transformation,[],[f10]) ).
fof(f22,plain,
? [X0,X1,X2] :
( ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X2)
| member(X3,X1) )
& ( ( ~ member(X3,X2)
& ~ member(X3,X1) )
| member(X3,X0) ) )
& union(X1,X2) != X0 ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
( ! [X3] :
( ( ~ member(X3,sK2)
| member(X3,sK4)
| member(X3,sK3) )
& ( ( ~ member(X3,sK4)
& ~ member(X3,sK3) )
| member(X3,sK2) ) )
& sK2 != union(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f22]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f31,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f37,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X3] :
( ~ member(X3,sK2)
| member(X3,sK4)
| member(X3,sK3) ),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
! [X3] :
( ~ member(X3,sK4)
| member(X3,sK2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f41,plain,
! [X3] :
( ~ member(X3,sK3)
| member(X3,sK2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
sK2 != union(sK3,sK4),
inference(cnf_transformation,[],[f23]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_62,negated_conjecture,
union(sK3,sK4) != sK2,
inference(cnf_transformation,[],[f42]) ).
tcf(c_63,negated_conjecture,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,sK3) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_64,negated_conjecture,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,sK4) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_65,negated_conjecture,
! [X0: $i] :
( member(X0,sK4)
| member(X0,sK3)
| ~ member(X0,sK2) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_334,definition,
iPr_def_10 = union(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_335,negated_conjecture,
! [X0: $i] :
( member(X0,sK4)
| member(X0,sK3)
| ~ member(X0,sK2) ),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_336,negated_conjecture,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,sK4) ),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_337,negated_conjecture,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,sK3) ),
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_338,negated_conjecture,
iPr_def_10 != sK2,
inference(demodulation,[status(thm)],[c_62,c_334]) ).
tcf(c_339,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_341,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_544,plain,
! [X0: $i] :
( subset(sK3,X0)
| member(sK0(sK3,X0),sK2) ),
inference(superposition,[status(thm)],[c_57,c_337]) ).
tcf(c_546,plain,
! [X0: $i] :
( subset(sK4,X0)
| member(sK0(sK4,X0),sK2) ),
inference(superposition,[status(thm)],[c_57,c_336]) ).
tcf(c_562,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_334,c_49]) ).
tcf(c_572,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_334,c_50]) ).
tcf(c_617,plain,
! [X0: $i] :
( member(X0,sK4)
| member(X0,sK3)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_334,c_51]) ).
tcf(c_630,plain,
! [X0: $i] :
( subset(sK3,X0)
| member(sK0(sK3,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_57,c_562]) ).
tcf(c_638,plain,
! [X0: $i] :
( subset(sK4,X0)
| member(sK0(sK4,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_57,c_572]) ).
tcf(c_647,plain,
subset(sK3,sK2),
inference(superposition,[status(thm)],[c_544,c_56]) ).
tcf(c_660,plain,
subset(sK4,sK2),
inference(superposition,[status(thm)],[c_546,c_56]) ).
tcf(c_669,plain,
! [X0: $i] :
( ( iPr_def_10 = sK2 )
| ( iPr_def_10 != X0 )
| ( sK2 != X0 ) ),
inference(instantiation,[status(thm)],[c_341]) ).
tcf(c_692,plain,
( ( iPr_def_10 = sK2 )
| ~ member(sK1(iPr_def_10,sK2),iPr_def_10)
| ~ member(sK1(iPr_def_10,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_744,plain,
! [X0: $i] :
( member(sK1(X0,sK2),sK4)
| member(sK1(X0,sK2),sK3)
| member(sK1(X0,sK2),X0)
| ( X0 = sK2 ) ),
inference(superposition,[status(thm)],[c_61,c_335]) ).
tcf(c_826,plain,
( member(sK1(iPr_def_10,sK2),sK4)
| member(sK1(iPr_def_10,sK2),sK3)
| ~ member(sK1(iPr_def_10,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_335]) ).
tcf(c_832,plain,
( ( iPr_def_10 = sK2 )
| ( iPr_def_10 != iPr_def_10 )
| ( sK2 != iPr_def_10 ) ),
inference(instantiation,[status(thm)],[c_669]) ).
tcf(c_833,plain,
iPr_def_10 = iPr_def_10,
inference(instantiation,[status(thm)],[c_339]) ).
tcf(c_858,plain,
subset(sK3,iPr_def_10),
inference(superposition,[status(thm)],[c_630,c_56]) ).
tcf(c_863,plain,
! [X0: $i] :
( member(sK1(iPr_def_10,sK2),X0)
| ~ subset(sK3,X0)
| ~ member(sK1(iPr_def_10,sK2),sK3) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_868,plain,
( member(sK1(iPr_def_10,sK2),sK2)
| ~ subset(sK3,sK2)
| ~ member(sK1(iPr_def_10,sK2),sK3) ),
inference(instantiation,[status(thm)],[c_863]) ).
tcf(c_880,plain,
subset(sK4,iPr_def_10),
inference(superposition,[status(thm)],[c_638,c_56]) ).
tcf(c_1221,plain,
! [X0: $i] :
( member(sK1(iPr_def_10,sK2),X0)
| ~ subset(sK4,X0)
| ~ member(sK1(iPr_def_10,sK2),sK4) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_1226,plain,
( member(sK1(iPr_def_10,sK2),sK2)
| ~ subset(sK4,sK2)
| ~ member(sK1(iPr_def_10,sK2),sK4) ),
inference(instantiation,[status(thm)],[c_1221]) ).
tcf(c_1720,plain,
( member(sK1(iPr_def_10,sK2),sK4)
| member(sK1(iPr_def_10,sK2),sK3)
| ( sK2 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_744,c_617]) ).
tcf(c_2156,plain,
( member(sK1(iPr_def_10,sK2),iPr_def_10)
| ~ subset(sK3,iPr_def_10)
| ~ member(sK1(iPr_def_10,sK2),sK3) ),
inference(instantiation,[status(thm)],[c_863]) ).
tcf(c_2211,plain,
( member(sK1(iPr_def_10,sK2),iPr_def_10)
| ~ subset(sK4,iPr_def_10)
| ~ member(sK1(iPr_def_10,sK2),sK4) ),
inference(instantiation,[status(thm)],[c_1221]) ).
tcf(c_3465,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2211,c_2156,c_1720,c_1226,c_880,c_868,c_858,c_833,c_832,c_826,c_692,c_660,c_647,c_338]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET577+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.37 % Computer : n019.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Thu Sep 24 11:19:56 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.41 Running first-order theorem proving
% 0.15/5.41 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
% 0.15/5.42
% 0.15/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.42
% 0.15/5.43 % Detected problem language: tptp
% 0.15/5.44 % Proving...
% 0.88/6.28 % SZS status Started for theBenchmark.p
% 0.88/6.28 % SZS status Theorem for theBenchmark.p
% 0.88/6.28
% 0.88/6.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.88/6.28
% 0.88/6.28 % ------ iProver source info
% 0.88/6.28
% 0.88/6.28 % git: date: 2026-07-19 20:42:38 +0200
% 0.88/6.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.88/6.28 % git: non_committed_changes: false
% 0.88/6.28
% 0.88/6.28 % ------ Parsing...
% 0.88/6.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.88/6.28
% 0.88/6.28 % ------ 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 %
% 0.88/6.28
% 0.88/6.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.88/6.28
% 0.88/6.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.88/6.28 % ------ Proving...
% 0.88/6.28 % ------ Problem Properties
% 0.88/6.28
% 0.88/6.28 %
% 0.88/6.28 % clauses 16
% 0.88/6.28 % conjectures 4
% 0.88/6.28 % EPR 7
% 0.88/6.28 % Horn 12
% 0.88/6.28 % unary 4
% 0.88/6.28 % binary 6
% 0.88/6.28 % lits 34
% 0.88/6.28 % lits eq 6
% 0.88/6.28 % fd_pure 0
% 0.88/6.28 % fd_pseudo 0
% 0.88/6.28 % fd_cond 0
% 0.88/6.28 % fd_pseudo_cond 3
% 0.88/6.28 % AC symbols 0
% 0.88/6.28
% 0.88/6.28 % ------ Schedule dynamic 5 is on
% 0.88/6.28
% 0.88/6.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.88/6.28
% 0.88/6.28
% 0.88/6.28 % ------
% 0.88/6.28 % Current options:
% 0.88/6.28 % ------
% 0.88/6.28
% 0.88/6.28
% 0.88/6.28 %
% 0.88/6.28
% 0.88/6.28 % ------ Proving...
% 0.88/6.28 %
% 0.88/6.28
% 0.88/6.28 % SZS status Theorem for theBenchmark.p
% 0.88/6.28
% 0.88/6.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.88/6.29
% 0.88/6.29
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