%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET906+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n017.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 02:49:04 PM UTC 2026
% Result : Theorem 1.96s 1.28s
% Output : CNFRefutation 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 18 unt; 2 def)
% Number of atoms : 193 ( 64 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 218 ( 81 ~; 85 |; 42 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 103 ( 0 sgn 94 !; 9 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X1
| X3 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f6,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( subset(set_union2(unordered_pair(X0,X1),X2),X2)
=> in(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_zfmisc_1) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(set_union2(unordered_pair(X0,X1),X2),X2)
=> in(X0,X2) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f19,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f22,plain,
? [X0,X1,X2] :
( subset(set_union2(unordered_pair(X0,X1),X2),X2)
& ~ in(X0,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(rectify,[],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| sK0(X0,X1,X2) = X1
| sK0(X0,X1,X2) = X0 )
& ( ~ in(sK0(X0,X1,X2),X2)
| ( sK0(X0,X1,X2) != X1
& sK0(X0,X1,X2) != X0 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(rectify,[],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ( ( in(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X0) )
& ( ~ in(sK1(X0,X1,X2),X2)
| ( ~ in(sK1(X0,X1,X2),X1)
& ~ in(sK1(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f29]) ).
fof(f33,plain,
( subset(set_union2(unordered_pair(sK4,sK5),sK6),sK6)
& ~ in(sK4,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f22]) ).
fof(f36,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f39,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X0 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f45,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f56,plain,
subset(set_union2(unordered_pair(sK4,sK5),sK6),sK6),
inference(cnf_transformation,[],[f33]) ).
fof(f57,plain,
~ in(sK4,sK6),
inference(cnf_transformation,[],[f33]) ).
fof(f58,plain,
! [X2,X1,X4] :
( unordered_pair(X4,X1) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f39]) ).
fof(f59,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f58]) ).
fof(f63,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f45]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f36]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f59]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_71,negated_conjecture,
~ in(sK4,sK6),
inference(cnf_transformation,[],[f57]) ).
tcf(c_72,negated_conjecture,
subset(set_union2(unordered_pair(sK4,sK5),sK6),sK6),
inference(cnf_transformation,[],[f56]) ).
tcf(c_188,plain,
subset(set_union2(sK6,unordered_pair(sK4,sK5)),sK6),
inference(demodulation,[status(thm)],[c_72,c_51]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ~ in(X2,X0)
| ( X1 != sK6 )
| ( set_union2(sK6,unordered_pair(sK4,sK5)) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_64,c_188]) ).
tcf(c_270,plain,
! [X0: $i] :
( in(X0,sK6)
| ~ in(X0,set_union2(sK6,unordered_pair(sK4,sK5))) ),
inference(unflattening,[status(thm)],[c_269]) ).
tcf(c_453,definition,
iPr_def_10 = unordered_pair(sK4,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_454,definition,
iPr_def_11 = set_union2(sK6,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_455,plain,
! [X0: $i] :
( in(X0,sK6)
| ~ in(X0,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_270,c_453,c_454]) ).
tcf(c_456,negated_conjecture,
~ in(sK4,sK6),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_732,plain,
in(sK4,iPr_def_10),
inference(superposition,[status(thm)],[c_453,c_55]) ).
tcf(c_733,plain,
set_union2(iPr_def_10,sK6) = iPr_def_11,
inference(demodulation,[status(thm)],[c_454,c_51]) ).
tcf(c_788,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_733,c_61]) ).
tcf(c_804,plain,
in(sK4,iPr_def_11),
inference(superposition,[status(thm)],[c_732,c_788]) ).
tcf(c_885,plain,
in(sK4,sK6),
inference(superposition,[status(thm)],[c_804,c_455]) ).
tcf(c_886,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_885,c_456]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET906+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 12:16:47 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 1.96/1.28 % SZS status Started for theBenchmark.p
% 1.96/1.28 % SZS status Theorem for theBenchmark.p
% 1.96/1.28
% 1.96/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.96/1.28
% 1.96/1.28 % ------ iProver source info
% 1.96/1.28
% 1.96/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.96/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.96/1.28 % git: non_committed_changes: false
% 1.96/1.28
% 1.96/1.28 % ------ Parsing...
% 1.96/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.96/1.28
% 1.96/1.28 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 1.96/1.28
% 1.96/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.96/1.28
% 1.96/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.96/1.28 % ------ Proving...
% 1.96/1.28 % ------ Problem Properties
% 1.96/1.28
% 1.96/1.28 %
% 1.96/1.28 % clauses 24
% 1.96/1.28 % conjectures 1
% 1.96/1.28 % EPR 5
% 1.96/1.28 % Horn 20
% 1.96/1.28 % unary 10
% 1.96/1.28 % binary 6
% 1.96/1.28 % lits 48
% 1.96/1.28 % lits eq 17
% 1.96/1.28 % fd_pure 0
% 1.96/1.28 % fd_pseudo 0
% 1.96/1.28 % fd_cond 0
% 1.96/1.28 % fd_pseudo_cond 6
% 1.96/1.28 % AC symbols 0
% 1.96/1.28
% 1.96/1.28 % ------ Schedule dynamic 5 is on
% 1.96/1.28
% 1.96/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.96/1.28
% 1.96/1.28
% 1.96/1.28 % ------
% 1.96/1.28 % Current options:
% 1.96/1.28 % ------
% 1.96/1.28
% 1.96/1.28
% 1.96/1.28 %
% 1.96/1.28
% 1.96/1.28 % ------ Proving...
% 1.96/1.28 %
% 1.96/1.28
% 1.96/1.28 % SZS status Theorem for theBenchmark.p
% 1.96/1.28
% 1.96/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.96/1.28
% 1.96/1.28
%------------------------------------------------------------------------------