%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET881+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 2.12s 1.30s
% Output : CNFRefutation 2.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 17 unt; 3 def)
% Number of atoms : 103 ( 64 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 106 ( 42 ~; 40 |; 21 &)
% ( 3 <=>; 0 =>; 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 : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 48 ( 0 sgn 43 !; 5 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X1
| X3 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f5,axiom,
! [X0,X1] :
( set_difference(singleton(X0),X1) = empty_set
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).
fof(f8,conjecture,
! [X0,X1] : set_difference(singleton(X0),unordered_pair(X0,X1)) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] : set_difference(singleton(X0),unordered_pair(X0,X1)) = empty_set,
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f11,plain,
? [X0,X1] : empty_set != set_difference(singleton(X0),unordered_pair(X0,X1)),
inference(ennf_transformation,[],[f9]) ).
fof(f12,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,[],[f3]) ).
fof(f13,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,[],[f12]) ).
fof(f14,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,[],[f13]) ).
fof(f15,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))],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ( empty_set != set_difference(singleton(X0),X1)
| in(X0,X1) )
& ( ~ in(X0,X1)
| set_difference(singleton(X0),X1) = empty_set ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f19,plain,
empty_set != set_difference(singleton(sK3),unordered_pair(sK3,sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f11]) ).
fof(f24,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X0 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X0,X1] :
( ~ in(X0,X1)
| empty_set = set_difference(singleton(X0),X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f33,plain,
empty_set != set_difference(singleton(sK3),unordered_pair(sK3,sK4)),
inference(cnf_transformation,[],[f19]) ).
fof(f34,plain,
! [X2,X1,X4] :
( unordered_pair(X4,X1) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f24]) ).
fof(f35,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f34]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f35]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( set_difference(singleton(X0),X1) = empty_set )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_62,negated_conjecture,
set_difference(singleton(sK3),unordered_pair(sK3,sK4)) != empty_set,
inference(cnf_transformation,[],[f33]) ).
tcf(c_208,definition,
iPr_def_10 = singleton(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_209,definition,
iPr_def_11 = unordered_pair(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_210,definition,
iPr_def_12 = set_difference(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_211,negated_conjecture,
iPr_def_12 != empty_set,
inference(demodulation,[status(thm)],[c_62,c_209,c_208,c_210]) ).
tcf(c_522,plain,
in(sK3,iPr_def_11),
inference(superposition,[status(thm)],[c_209,c_54]) ).
tcf(c_549,plain,
set_difference(singleton(sK3),iPr_def_11) = empty_set,
inference(superposition,[status(thm)],[c_522,c_58]) ).
tcf(c_551,plain,
empty_set = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_549,c_208,c_210]) ).
tcf(c_555,plain,
iPr_def_12 != iPr_def_12,
inference(demodulation,[status(thm)],[c_211,c_551]) ).
tcf(c_556,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_555]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET881+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n011.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 12:19:12 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...
% 2.12/1.30 % SZS status Started for theBenchmark.p
% 2.12/1.30 % SZS status Theorem for theBenchmark.p
% 2.12/1.30
% 2.12/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.12/1.30
% 2.12/1.30 % ------ iProver source info
% 2.12/1.30
% 2.12/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.12/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.12/1.30 % git: non_committed_changes: false
% 2.12/1.30
% 2.12/1.30 % ------ Parsing...
% 2.12/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.12/1.30
% 2.12/1.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.12/1.30
% 2.12/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.12/1.30
% 2.12/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.12/1.30 % ------ Proving...
% 2.12/1.30 % ------ Problem Properties
% 2.12/1.30
% 2.12/1.30 %
% 2.12/1.30 % clauses 17
% 2.12/1.30 % conjectures 1
% 2.12/1.30 % EPR 5
% 2.12/1.30 % Horn 15
% 2.12/1.30 % unary 10
% 2.12/1.30 % binary 3
% 2.12/1.30 % lits 29
% 2.12/1.30 % lits eq 16
% 2.12/1.30 % fd_pure 0
% 2.12/1.30 % fd_pseudo 0
% 2.12/1.30 % fd_cond 0
% 2.12/1.30 % fd_pseudo_cond 3
% 2.12/1.30 % AC symbols 0
% 2.12/1.30
% 2.12/1.30 % ------ Schedule dynamic 5 is on
% 2.12/1.30
% 2.12/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.12/1.30
% 2.12/1.30
% 2.12/1.30 % ------
% 2.12/1.30 % Current options:
% 2.12/1.30 % ------
% 2.12/1.30
% 2.12/1.30
% 2.12/1.30 %
% 2.12/1.30
% 2.12/1.30 % ------ Proving...
% 2.12/1.30 %
% 2.12/1.30
% 2.12/1.30 % SZS status Theorem for theBenchmark.p
% 2.12/1.30
% 2.12/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.12/1.30
% 2.12/1.30
%------------------------------------------------------------------------------