%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET874+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 : n005.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 02:48:51 PM UTC 2026
% Result : Theorem 1.76s 1.28s
% Output : CNFRefutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 17 unt; 3 def)
% Number of atoms : 104 ( 63 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 103 ( 41 ~; 39 |; 20 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 48 ( 0 sgn 43 !; 5 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
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(f8,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(f11,conjecture,
! [X0,X1] : set_union2(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] : set_union2(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(X0,X1),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f17,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(singleton(X0),X1) = X1 ),
inference(ennf_transformation,[],[f8]) ).
fof(f18,plain,
? [X0,X1] : unordered_pair(X0,X1) != set_union2(singleton(X0),unordered_pair(X0,X1)),
inference(ennf_transformation,[],[f12]) ).
fof(f19,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(f20,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,[],[f19]) ).
fof(f21,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,[],[f20]) ).
fof(f22,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))],[f21]) ).
fof(f25,plain,
unordered_pair(sK3,sK4) != set_union2(singleton(sK3),unordered_pair(sK3,sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f18]) ).
fof(f31,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X0 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(singleton(X0),X1) = X1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f41,plain,
unordered_pair(sK3,sK4) != set_union2(singleton(sK3),unordered_pair(sK3,sK4)),
inference(cnf_transformation,[],[f25]) ).
fof(f42,plain,
! [X2,X1,X4] :
( unordered_pair(X4,X1) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f31]) ).
fof(f43,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f42]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f43]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( set_union2(singleton(X0),X1) = X1 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_64,negated_conjecture,
set_union2(singleton(sK3),unordered_pair(sK3,sK4)) != unordered_pair(sK3,sK4),
inference(cnf_transformation,[],[f41]) ).
tcf(c_180,definition,
iPr_def_10 = singleton(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_181,definition,
iPr_def_11 = unordered_pair(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_182,definition,
iPr_def_12 = set_union2(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_183,negated_conjecture,
iPr_def_12 != iPr_def_11,
inference(demodulation,[status(thm)],[c_64,c_181,c_180,c_182]) ).
tcf(c_402,plain,
in(sK3,iPr_def_11),
inference(superposition,[status(thm)],[c_181,c_55]) ).
tcf(c_455,plain,
set_union2(singleton(sK3),iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_402,c_61]) ).
tcf(c_456,plain,
iPr_def_11 = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_455,c_180,c_182]) ).
tcf(c_460,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_183,c_456]) ).
tcf(c_461,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_460]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET874+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:18:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.42
% 0.14/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.42
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.44 % Proving...
% 1.76/1.28 % SZS status Started for theBenchmark.p
% 1.76/1.28 % SZS status Theorem for theBenchmark.p
% 1.76/1.28
% 1.76/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.76/1.28
% 1.76/1.28 % ------ iProver source info
% 1.76/1.28
% 1.76/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.76/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.76/1.28 % git: non_committed_changes: false
% 1.76/1.28
% 1.76/1.28 % ------ Parsing...
% 1.76/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.76/1.28
% 1.76/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.76/1.28
% 1.76/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.76/1.28
% 1.76/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.76/1.28 % ------ Proving...
% 1.76/1.28 % ------ Problem Properties
% 1.76/1.28
% 1.76/1.28 %
% 1.76/1.28 % clauses 19
% 1.76/1.28 % conjectures 1
% 1.76/1.28 % EPR 4
% 1.76/1.28 % Horn 17
% 1.76/1.28 % unary 11
% 1.76/1.28 % binary 4
% 1.76/1.28 % lits 32
% 1.76/1.28 % lits eq 17
% 1.76/1.28 % fd_pure 0
% 1.76/1.28 % fd_pseudo 0
% 1.76/1.28 % fd_cond 0
% 1.76/1.28 % fd_pseudo_cond 3
% 1.76/1.28 % AC symbols 0
% 1.76/1.28
% 1.76/1.28 % ------ Schedule dynamic 5 is on
% 1.76/1.28
% 1.76/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.76/1.28
% 1.76/1.28
% 1.76/1.28 % ------
% 1.76/1.28 % Current options:
% 1.76/1.28 % ------
% 1.76/1.28
% 1.76/1.28
% 1.76/1.28 %
% 1.76/1.28
% 1.76/1.28 % ------ Proving...
% 1.76/1.28 %
% 1.76/1.28
% 1.76/1.28 % SZS status Theorem for theBenchmark.p
% 1.76/1.28
% 1.76/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.76/1.28
% 1.76/1.28
%------------------------------------------------------------------------------