%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET878+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 : 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 02:48:52 PM UTC 2026
% Result : Theorem 1.00s 1.05s
% Output : CNFRefutation 1.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 21 unt; 3 def)
% Number of atoms : 110 ( 67 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 : 54 ( 0 sgn 49 !; 5 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_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(f6,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_intersection2(X1,singleton(X0)) = singleton(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1] : set_intersection2(singleton(X0),unordered_pair(X0,X1)) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] : set_intersection2(singleton(X0),unordered_pair(X0,X1)) = singleton(X0),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f13,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_intersection2(X1,singleton(X0)) = singleton(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f14,plain,
? [X0,X1] : singleton(X0) != set_intersection2(singleton(X0),unordered_pair(X0,X1)),
inference(ennf_transformation,[],[f10]) ).
fof(f15,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(f16,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,[],[f15]) ).
fof(f17,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,[],[f16]) ).
fof(f18,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))],[f17]) ).
fof(f21,plain,
singleton(sK3) != set_intersection2(singleton(sK3),unordered_pair(sK3,sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f14]) ).
fof(f24,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f27,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X0 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
! [X0,X1] :
( ~ in(X0,X1)
| singleton(X0) = set_intersection2(X1,singleton(X0)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f35,plain,
singleton(sK3) != set_intersection2(singleton(sK3),unordered_pair(sK3,sK4)),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
! [X2,X1,X4] :
( unordered_pair(X4,X1) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f27]) ).
fof(f37,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f36]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f24]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f37]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,singleton(X0)) = singleton(X0) )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_62,negated_conjecture,
set_intersection2(singleton(sK3),unordered_pair(sK3,sK4)) != singleton(sK3),
inference(cnf_transformation,[],[f35]) ).
tcf(c_253,definition,
iPr_def_10 = singleton(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_254,definition,
iPr_def_11 = unordered_pair(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_255,definition,
iPr_def_12 = set_intersection2(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_256,negated_conjecture,
iPr_def_12 != iPr_def_10,
inference(demodulation,[status(thm)],[c_62,c_254,c_253,c_255]) ).
tcf(c_442,plain,
in(sK3,iPr_def_11),
inference(superposition,[status(thm)],[c_254,c_55]) ).
tcf(c_461,plain,
set_intersection2(iPr_def_11,singleton(sK3)) = singleton(sK3),
inference(superposition,[status(thm)],[c_442,c_59]) ).
tcf(c_463,plain,
set_intersection2(iPr_def_11,iPr_def_10) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_461,c_253]) ).
tcf(c_470,plain,
iPr_def_10 = iPr_def_12,
inference(demodulation,[status(thm)],[c_463,c_51,c_255]) ).
tcf(c_472,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_256,c_470]) ).
tcf(c_473,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_472]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET878+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Thu Sep 24 12:18:35 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.29 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/0.31 Running first-order theorem proving
% 0.02/0.31 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
% 0.02/0.32
% 0.02/0.32 % ======== iProver multi-core TPTP/SMT =========
% 0.02/0.32
% 0.02/0.32 % Detected problem language: tptp
% 0.06/0.33 % Proving...
% 1.00/1.05 % SZS status Started for theBenchmark.p
% 1.00/1.05 % SZS status Theorem for theBenchmark.p
% 1.00/1.05
% 1.00/1.05 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.00/1.05
% 1.00/1.05 % ------ iProver source info
% 1.00/1.05
% 1.00/1.05 % git: date: 2026-07-19 20:42:38 +0200
% 1.00/1.05 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.00/1.05 % git: non_committed_changes: false
% 1.00/1.05
% 1.00/1.05 % ------ Parsing...
% 1.00/1.05 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.00/1.05
% 1.00/1.05 % ------ Preprocessing... sup_sim: 0 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 %
% 1.00/1.05
% 1.00/1.05 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.00/1.05
% 1.00/1.05 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.00/1.05 % ------ Proving...
% 1.00/1.05 % ------ Problem Properties
% 1.00/1.05
% 1.00/1.05 %
% 1.00/1.05 % clauses 16
% 1.00/1.05 % conjectures 1
% 1.00/1.05 % EPR 3
% 1.00/1.05 % Horn 14
% 1.00/1.05 % unary 10
% 1.00/1.05 % binary 2
% 1.00/1.05 % lits 27
% 1.00/1.05 % lits eq 18
% 1.00/1.05 % fd_pure 0
% 1.00/1.05 % fd_pseudo 0
% 1.00/1.05 % fd_cond 0
% 1.00/1.05 % fd_pseudo_cond 3
% 1.00/1.05 % AC symbols 0
% 1.00/1.05
% 1.00/1.05 % ------ Schedule dynamic 5 is on
% 1.00/1.05
% 1.00/1.05 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.00/1.05
% 1.00/1.05
% 1.00/1.05 % ------
% 1.00/1.05 % Current options:
% 1.00/1.05 % ------
% 1.00/1.05
% 1.00/1.05
% 1.00/1.05 %
% 1.00/1.05
% 1.00/1.05 % ------ Proving...
% 1.00/1.05 %
% 1.00/1.05
% 1.00/1.05 % SZS status Theorem for theBenchmark.p
% 1.00/1.05
% 1.00/1.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.00/1.05
% 1.00/1.05
%------------------------------------------------------------------------------