TSTP Solution File: SET873+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET873+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 15:10:25 EDT 2023
% Result : Theorem 1.92s 1.20s
% Output : CNFRefutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 14 unt; 0 def)
% Number of atoms : 89 ( 52 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 92 ( 37 ~; 33 |; 15 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 58 ( 1 sgn; 37 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f3,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f7,axiom,
! [X0,X1] :
( subset(set_union2(singleton(X0),X1),X1)
=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l21_zfmisc_1) ).
fof(f10,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f11,conjecture,
! [X0,X1] :
( singleton(X0) = set_union2(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] :
( singleton(X0) = set_union2(singleton(X0),singleton(X1))
=> X0 = X1 ),
inference(negated_conjecture,[],[f11]) ).
fof(f14,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f10]) ).
fof(f18,plain,
! [X0,X1] :
( in(X0,X1)
| ~ subset(set_union2(singleton(X0),X1),X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f19,plain,
? [X0,X1] :
( X0 != X1
& singleton(X0) = set_union2(singleton(X0),singleton(X1)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f20,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f21,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f21,f22]) ).
fof(f28,plain,
( ? [X0,X1] :
( X0 != X1
& singleton(X0) = set_union2(singleton(X0),singleton(X1)) )
=> ( sK3 != sK4
& singleton(sK3) = set_union2(singleton(sK3),singleton(sK4)) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
( sK3 != sK4
& singleton(sK3) = set_union2(singleton(sK3),singleton(sK4)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f19,f28]) ).
fof(f31,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f32,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f39,plain,
! [X0,X1] :
( in(X0,X1)
| ~ subset(set_union2(singleton(X0),X1),X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f42,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f14]) ).
fof(f43,plain,
singleton(sK3) = set_union2(singleton(sK3),singleton(sK4)),
inference(cnf_transformation,[],[f29]) ).
fof(f44,plain,
sK3 != sK4,
inference(cnf_transformation,[],[f29]) ).
fof(f47,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,singleton(X0)) ),
inference(equality_resolution,[],[f32]) ).
cnf(c_50,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f31]) ).
cnf(c_54,plain,
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f47]) ).
cnf(c_58,plain,
( ~ subset(set_union2(singleton(X0),X1),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_61,plain,
subset(X0,X0),
inference(cnf_transformation,[],[f42]) ).
cnf(c_62,negated_conjecture,
sK3 != sK4,
inference(cnf_transformation,[],[f44]) ).
cnf(c_63,negated_conjecture,
set_union2(singleton(sK3),singleton(sK4)) = singleton(sK3),
inference(cnf_transformation,[],[f43]) ).
cnf(c_160,plain,
( set_union2(singleton(X0),X1) != X2
| X1 != X2
| in(X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_58,c_61]) ).
cnf(c_161,plain,
( set_union2(singleton(X0),X1) != X1
| in(X0,X1) ),
inference(unflattening,[status(thm)],[c_160]) ).
cnf(c_479,plain,
( set_union2(X0,singleton(X1)) != X0
| in(X1,X0) ),
inference(superposition,[status(thm)],[c_50,c_161]) ).
cnf(c_495,plain,
in(sK4,singleton(sK3)),
inference(superposition,[status(thm)],[c_63,c_479]) ).
cnf(c_497,plain,
sK3 = sK4,
inference(superposition,[status(thm)],[c_495,c_54]) ).
cnf(c_498,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_497,c_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET873+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 09:19:33 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 1.92/1.20 % SZS status Started for theBenchmark.p
% 1.92/1.20 % SZS status Theorem for theBenchmark.p
% 1.92/1.20
% 1.92/1.20 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.92/1.20
% 1.92/1.20 ------ iProver source info
% 1.92/1.20
% 1.92/1.20 git: date: 2023-05-31 18:12:56 +0000
% 1.92/1.20 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.92/1.20 git: non_committed_changes: false
% 1.92/1.20 git: last_make_outside_of_git: false
% 1.92/1.20
% 1.92/1.20 ------ Parsing...
% 1.92/1.20 ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.92/1.20
% 1.92/1.20 ------ 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
% 1.92/1.20
% 1.92/1.20 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.92/1.20
% 1.92/1.20 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.92/1.20 ------ Proving...
% 1.92/1.20 ------ Problem Properties
% 1.92/1.20
% 1.92/1.20
% 1.92/1.20 clauses 14
% 1.92/1.20 conjectures 2
% 1.92/1.20 EPR 4
% 1.92/1.20 Horn 13
% 1.92/1.20 unary 7
% 1.92/1.20 binary 5
% 1.92/1.20 lits 23
% 1.92/1.20 lits eq 10
% 1.92/1.20 fd_pure 0
% 1.92/1.20 fd_pseudo 0
% 1.92/1.20 fd_cond 0
% 1.92/1.20 fd_pseudo_cond 2
% 1.92/1.20 AC symbols 0
% 1.92/1.20
% 1.92/1.20 ------ Schedule dynamic 5 is on
% 1.92/1.20
% 1.92/1.20 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.92/1.20
% 1.92/1.20
% 1.92/1.20 ------
% 1.92/1.20 Current options:
% 1.92/1.20 ------
% 1.92/1.20
% 1.92/1.20
% 1.92/1.20
% 1.92/1.20
% 1.92/1.20 ------ Proving...
% 1.92/1.20
% 1.92/1.20
% 1.92/1.20 % SZS status Theorem for theBenchmark.p
% 1.92/1.20
% 1.92/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.92/1.20
% 1.92/1.20
%------------------------------------------------------------------------------