TSTP Solution File: SEU194+2 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU194+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n021.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 : Fri May 3 03:04:56 EDT 2024
% Result : Theorem 25.05s 4.23s
% Output : CNFRefutation 25.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 13 unt; 0 def)
% Number of atoms : 193 ( 37 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 231 ( 88 ~; 99 |; 35 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 105 ( 1 sgn 76 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f21,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f153,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f175,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_relat_1) ).
fof(f180,conjecture,
! [X0,X1] :
( relation(X1)
=> relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_relat_1) ).
fof(f181,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0) ),
inference(negated_conjecture,[],[f180]) ).
fof(f325,plain,
! [X0,X1,X2] :
( ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(X0,X1) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f175]) ).
fof(f331,plain,
? [X0,X1] :
( relation_dom(relation_dom_restriction(X1,X0)) != set_intersection2(relation_dom(X1),X0)
& relation(X1) ),
inference(ennf_transformation,[],[f181]) ).
fof(f396,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f397,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f396]) ).
fof(f398,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0) )
& ( ( in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f397]) ).
fof(f399,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( ~ in(sK23(X0,X1,X2),X1)
| ~ in(sK23(X0,X1,X2),X0)
| ~ in(sK23(X0,X1,X2),X2) )
& ( ( in(sK23(X0,X1,X2),X1)
& in(sK23(X0,X1,X2),X0) )
| in(sK23(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f400,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ( ( ~ in(sK23(X0,X1,X2),X1)
| ~ in(sK23(X0,X1,X2),X0)
| ~ in(sK23(X0,X1,X2),X2) )
& ( ( in(sK23(X0,X1,X2),X1)
& in(sK23(X0,X1,X2),X0) )
| in(sK23(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0) )
& ( ( in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f398,f399]) ).
fof(f489,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1) )
& ( ( in(X0,relation_dom(X2))
& in(X0,X1) )
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1))) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f325]) ).
fof(f490,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1) )
& ( ( in(X0,relation_dom(X2))
& in(X0,X1) )
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1))) ) )
| ~ relation(X2) ),
inference(flattening,[],[f489]) ).
fof(f491,plain,
( ? [X0,X1] :
( relation_dom(relation_dom_restriction(X1,X0)) != set_intersection2(relation_dom(X1),X0)
& relation(X1) )
=> ( relation_dom(relation_dom_restriction(sK56,sK55)) != set_intersection2(relation_dom(sK56),sK55)
& relation(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f492,plain,
( relation_dom(relation_dom_restriction(sK56,sK55)) != set_intersection2(relation_dom(sK56),sK55)
& relation(sK56) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK55,sK56])],[f331,f491]) ).
fof(f502,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f572,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| in(sK23(X0,X1,X2),X0)
| in(sK23(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f400]) ).
fof(f573,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| in(sK23(X0,X1,X2),X1)
| in(sK23(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f400]) ).
fof(f574,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ in(sK23(X0,X1,X2),X1)
| ~ in(sK23(X0,X1,X2),X0)
| ~ in(sK23(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f400]) ).
fof(f757,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f153]) ).
fof(f788,plain,
! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f490]) ).
fof(f789,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f490]) ).
fof(f790,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f490]) ).
fof(f795,plain,
relation(sK56),
inference(cnf_transformation,[],[f492]) ).
fof(f796,plain,
relation_dom(relation_dom_restriction(sK56,sK55)) != set_intersection2(relation_dom(sK56),sK55),
inference(cnf_transformation,[],[f492]) ).
fof(f805,plain,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(definition_unfolding,[],[f502,f757,f757]) ).
fof(f831,plain,
! [X2,X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X2
| ~ in(sK23(X0,X1,X2),X1)
| ~ in(sK23(X0,X1,X2),X0)
| ~ in(sK23(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f574,f757]) ).
fof(f832,plain,
! [X2,X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X2
| in(sK23(X0,X1,X2),X1)
| in(sK23(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f573,f757]) ).
fof(f833,plain,
! [X2,X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X2
| in(sK23(X0,X1,X2),X0)
| in(sK23(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f572,f757]) ).
fof(f905,plain,
relation_dom(relation_dom_restriction(sK56,sK55)) != set_difference(relation_dom(sK56),set_difference(relation_dom(sK56),sK55)),
inference(definition_unfolding,[],[f796,f757]) ).
cnf(c_54,plain,
set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(cnf_transformation,[],[f805]) ).
cnf(c_121,plain,
( ~ in(sK23(X0,X1,X2),X0)
| ~ in(sK23(X0,X1,X2),X1)
| ~ in(sK23(X0,X1,X2),X2)
| set_difference(X0,set_difference(X0,X1)) = X2 ),
inference(cnf_transformation,[],[f831]) ).
cnf(c_122,plain,
( set_difference(X0,set_difference(X0,X1)) = X2
| in(sK23(X0,X1,X2),X1)
| in(sK23(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f832]) ).
cnf(c_123,plain,
( set_difference(X0,set_difference(X0,X1)) = X2
| in(sK23(X0,X1,X2),X0)
| in(sK23(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f833]) ).
cnf(c_337,plain,
( ~ in(X0,relation_dom(X1))
| ~ in(X0,X2)
| ~ relation(X1)
| in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f790]) ).
cnf(c_338,plain,
( ~ in(X0,relation_dom(relation_dom_restriction(X1,X2)))
| ~ relation(X1)
| in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f789]) ).
cnf(c_339,plain,
( ~ in(X0,relation_dom(relation_dom_restriction(X1,X2)))
| ~ relation(X1)
| in(X0,X2) ),
inference(cnf_transformation,[],[f788]) ).
cnf(c_344,negated_conjecture,
set_difference(relation_dom(sK56),set_difference(relation_dom(sK56),sK55)) != relation_dom(relation_dom_restriction(sK56,sK55)),
inference(cnf_transformation,[],[f905]) ).
cnf(c_345,negated_conjecture,
relation(sK56),
inference(cnf_transformation,[],[f795]) ).
cnf(c_3264,plain,
set_difference(sK55,set_difference(sK55,relation_dom(sK56))) != relation_dom(relation_dom_restriction(sK56,sK55)),
inference(demodulation,[status(thm)],[c_344,c_54]) ).
cnf(c_14683,plain,
( set_difference(sK55,set_difference(sK55,relation_dom(sK56))) = relation_dom(relation_dom_restriction(sK56,sK55))
| in(sK23(sK55,relation_dom(sK56),relation_dom(relation_dom_restriction(sK56,sK55))),relation_dom(relation_dom_restriction(sK56,sK55)))
| in(sK23(sK55,relation_dom(sK56),relation_dom(relation_dom_restriction(sK56,sK55))),relation_dom(sK56)) ),
inference(instantiation,[status(thm)],[c_122]) ).
cnf(c_14684,plain,
( set_difference(sK55,set_difference(sK55,relation_dom(sK56))) = relation_dom(relation_dom_restriction(sK56,sK55))
| in(sK23(sK55,relation_dom(sK56),relation_dom(relation_dom_restriction(sK56,sK55))),relation_dom(relation_dom_restriction(sK56,sK55)))
| in(sK23(sK55,relation_dom(sK56),relation_dom(relation_dom_restriction(sK56,sK55))),sK55) ),
inference(instantiation,[status(thm)],[c_123]) ).
cnf(c_15055,plain,
( ~ in(sK23(sK55,relation_dom(sK56),relation_dom(relation_dom_restriction(sK56,sK55))),relation_dom(relation_dom_restriction(sK56,sK55)))
| ~ in(sK23(sK55,relation_dom(sK56),relation_dom(relation_dom_restriction(sK56,sK55))),relation_dom(sK56))
| ~ in(sK23(sK55,relation_dom(sK56),relation_dom(relation_dom_restriction(sK56,sK55))),sK55)
| set_difference(sK55,set_difference(sK55,relation_dom(sK56))) = relation_dom(relation_dom_restriction(sK56,sK55)) ),
inference(instantiation,[status(thm)],[c_121]) ).
cnf(c_19890,plain,
( ~ in(sK23(sK55,relation_dom(sK56),relation_dom(relation_dom_restriction(sK56,sK55))),relation_dom(relation_dom_restriction(sK56,sK55)))
| ~ relation(sK56)
| in(sK23(sK55,relation_dom(sK56),relation_dom(relation_dom_restriction(sK56,sK55))),sK55) ),
inference(instantiation,[status(thm)],[c_339]) ).
cnf(c_19891,plain,
( ~ in(sK23(sK55,relation_dom(sK56),relation_dom(relation_dom_restriction(sK56,sK55))),relation_dom(relation_dom_restriction(sK56,sK55)))
| ~ relation(sK56)
| in(sK23(sK55,relation_dom(sK56),relation_dom(relation_dom_restriction(sK56,sK55))),relation_dom(sK56)) ),
inference(instantiation,[status(thm)],[c_338]) ).
cnf(c_31999,plain,
( ~ in(sK23(sK55,relation_dom(sK56),relation_dom(relation_dom_restriction(sK56,sK55))),relation_dom(X0))
| ~ in(sK23(sK55,relation_dom(sK56),relation_dom(relation_dom_restriction(sK56,sK55))),sK55)
| ~ relation(X0)
| in(sK23(sK55,relation_dom(sK56),relation_dom(relation_dom_restriction(sK56,sK55))),relation_dom(relation_dom_restriction(X0,sK55))) ),
inference(instantiation,[status(thm)],[c_337]) ).
cnf(c_64091,plain,
( ~ in(sK23(sK55,relation_dom(sK56),relation_dom(relation_dom_restriction(sK56,sK55))),relation_dom(sK56))
| ~ in(sK23(sK55,relation_dom(sK56),relation_dom(relation_dom_restriction(sK56,sK55))),sK55)
| ~ relation(sK56)
| in(sK23(sK55,relation_dom(sK56),relation_dom(relation_dom_restriction(sK56,sK55))),relation_dom(relation_dom_restriction(sK56,sK55))) ),
inference(instantiation,[status(thm)],[c_31999]) ).
cnf(c_64092,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_64091,c_19890,c_19891,c_15055,c_14684,c_14683,c_3264,c_345]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU194+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu May 2 17:57:28 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 25.05/4.23 % SZS status Started for theBenchmark.p
% 25.05/4.23 % SZS status Theorem for theBenchmark.p
% 25.05/4.23
% 25.05/4.23 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 25.05/4.23
% 25.05/4.23 ------ iProver source info
% 25.05/4.23
% 25.05/4.23 git: date: 2024-05-02 19:28:25 +0000
% 25.05/4.23 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 25.05/4.23 git: non_committed_changes: false
% 25.05/4.23
% 25.05/4.23 ------ Parsing...
% 25.05/4.23 ------ Clausification by vclausify_rel & Parsing by iProver...
% 25.05/4.23
% 25.05/4.23 ------ Preprocessing... sup_sim: 30 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 25.05/4.23
% 25.05/4.23 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 25.05/4.23
% 25.05/4.23 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 25.05/4.23 ------ Proving...
% 25.05/4.23 ------ Problem Properties
% 25.05/4.23
% 25.05/4.23
% 25.05/4.23 clauses 271
% 25.05/4.23 conjectures 1
% 25.05/4.23 EPR 34
% 25.05/4.23 Horn 215
% 25.05/4.23 unary 46
% 25.05/4.23 binary 93
% 25.05/4.23 lits 693
% 25.05/4.23 lits eq 148
% 25.05/4.23 fd_pure 0
% 25.05/4.23 fd_pseudo 0
% 25.05/4.23 fd_cond 13
% 25.05/4.23 fd_pseudo_cond 57
% 25.05/4.23 AC symbols 0
% 25.05/4.23
% 25.05/4.23 ------ Schedule dynamic 5 is on
% 25.05/4.23
% 25.05/4.23 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 25.05/4.23
% 25.05/4.23
% 25.05/4.23 ------
% 25.05/4.23 Current options:
% 25.05/4.23 ------
% 25.05/4.23
% 25.05/4.23
% 25.05/4.23
% 25.05/4.23
% 25.05/4.23 ------ Proving...
% 25.05/4.23
% 25.05/4.23
% 25.05/4.23 % SZS status Theorem for theBenchmark.p
% 25.05/4.23
% 25.05/4.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 25.05/4.23
% 25.05/4.23
%------------------------------------------------------------------------------