TSTP Solution File: SET881+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET881+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n014.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 15:10:27 EDT 2023
% Result : Theorem 1.76s 1.17s
% Output : CNFRefutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 10 unt; 0 def)
% Number of atoms : 99 ( 68 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 124 ( 48 ~; 46 |; 25 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 56 ( 2 sgn; 42 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f5,axiom,
! [X0,X1] :
( empty_set = set_difference(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l36_zfmisc_1) ).
fof(f8,conjecture,
! [X0,X1] : empty_set = set_difference(singleton(X0),unordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] : empty_set = set_difference(singleton(X0),unordered_pair(X0,X1)),
inference(negated_conjecture,[],[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] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X1 != X4
& X0 != X4 ) )
& ( X1 = X4
| X0 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,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
| in(sK0(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = 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
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X1 != X4
& X0 != X4 ) )
& ( X1 = X4
| X0 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f14,f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( empty_set = set_difference(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| empty_set != set_difference(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f22,plain,
( ? [X0,X1] : empty_set != set_difference(singleton(X0),unordered_pair(X0,X1))
=> empty_set != set_difference(singleton(sK3),unordered_pair(sK3,sK4)) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
empty_set != set_difference(singleton(sK3),unordered_pair(sK3,sK4)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f11,f22]) ).
fof(f27,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f34,plain,
! [X0,X1] :
( empty_set = set_difference(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f37,plain,
empty_set != set_difference(singleton(sK3),unordered_pair(sK3,sK4)),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
! [X2,X1,X4] :
( in(X4,X2)
| unordered_pair(X4,X1) != X2 ),
inference(equality_resolution,[],[f27]) ).
fof(f41,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f40]) ).
cnf(c_55,plain,
in(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f41]) ).
cnf(c_58,plain,
( ~ in(X0,X1)
| set_difference(singleton(X0),X1) = empty_set ),
inference(cnf_transformation,[],[f34]) ).
cnf(c_62,negated_conjecture,
set_difference(singleton(sK3),unordered_pair(sK3,sK4)) != empty_set,
inference(cnf_transformation,[],[f37]) ).
cnf(c_515,plain,
set_difference(singleton(X0),unordered_pair(X0,X1)) = empty_set,
inference(superposition,[status(thm)],[c_55,c_58]) ).
cnf(c_516,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_62,c_515]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET881+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.36 % Computer : n014.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 12:04:17 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 1.76/1.17 % SZS status Started for theBenchmark.p
% 1.76/1.17 % SZS status Theorem for theBenchmark.p
% 1.76/1.17
% 1.76/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.76/1.17
% 1.76/1.17 ------ iProver source info
% 1.76/1.17
% 1.76/1.17 git: date: 2023-05-31 18:12:56 +0000
% 1.76/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.76/1.17 git: non_committed_changes: false
% 1.76/1.17 git: last_make_outside_of_git: false
% 1.76/1.17
% 1.76/1.17 ------ Parsing...
% 1.76/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.76/1.17
% 1.76/1.17 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 1.76/1.17
% 1.76/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.76/1.17
% 1.76/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.76/1.17 ------ Proving...
% 1.76/1.17 ------ Problem Properties
% 1.76/1.17
% 1.76/1.17
% 1.76/1.17 clauses 14
% 1.76/1.17 conjectures 1
% 1.76/1.17 EPR 4
% 1.76/1.17 Horn 12
% 1.76/1.17 unary 7
% 1.76/1.17 binary 3
% 1.76/1.17 lits 26
% 1.76/1.17 lits eq 13
% 1.76/1.17 fd_pure 0
% 1.76/1.17 fd_pseudo 0
% 1.76/1.17 fd_cond 0
% 1.76/1.17 fd_pseudo_cond 3
% 1.76/1.17 AC symbols 0
% 1.76/1.17
% 1.76/1.17 ------ Schedule dynamic 5 is on
% 1.76/1.17
% 1.76/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.76/1.17
% 1.76/1.17
% 1.76/1.17 ------
% 1.76/1.17 Current options:
% 1.76/1.17 ------
% 1.76/1.17
% 1.76/1.17
% 1.76/1.17
% 1.76/1.17
% 1.76/1.17 ------ Proving...
% 1.76/1.17
% 1.76/1.17
% 1.76/1.17 % SZS status Theorem for theBenchmark.p
% 1.76/1.17
% 1.76/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.76/1.17
% 1.76/1.17
%------------------------------------------------------------------------------