TSTP Solution File: SEU037+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU037+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n010.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 17:03:29 EDT 2023
% Result : Theorem 3.23s 1.17s
% Output : CNFRefutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 16 unt; 0 def)
% Number of atoms : 218 ( 62 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 275 ( 113 ~; 103 |; 44 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 113 ( 4 sgn; 74 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f6,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f9,axiom,
! [X0,X1] :
( ( relation_empty_yielding(X0)
& relation(X0) )
=> ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_relat_1) ).
fof(f13,axiom,
! [X0,X1] :
( ( function(X0)
& relation(X0) )
=> ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(f35,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_dom_restriction(X2,X0) = X1
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).
fof(f37,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,set_intersection2(relation_dom(X2),X0))
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_funct_1) ).
fof(f38,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,set_intersection2(relation_dom(X2),X0))
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
inference(negated_conjecture,[],[f37]) ).
fof(f51,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f52,plain,
! [X0,X1] :
( ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f53,plain,
! [X0,X1] :
( ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ),
inference(flattening,[],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f57,plain,
! [X0,X1] :
( ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f56]) ).
fof(f69,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_dom_restriction(X2,X0) = X1
<=> ( ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f70,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_dom_restriction(X2,X0) = X1
<=> ( ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f69]) ).
fof(f72,plain,
? [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
& in(X1,set_intersection2(relation_dom(X2),X0))
& function(X2)
& relation(X2) ),
inference(ennf_transformation,[],[f38]) ).
fof(f73,plain,
? [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
& in(X1,set_intersection2(relation_dom(X2),X0))
& function(X2)
& relation(X2) ),
inference(flattening,[],[f72]) ).
fof(f98,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f70]) ).
fof(f99,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(rectify,[],[f99]) ).
fof(f101,plain,
! [X1,X2] :
( ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) )
=> ( apply(X1,sK11(X1,X2)) != apply(X2,sK11(X1,X2))
& in(sK11(X1,X2),relation_dom(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ( apply(X1,sK11(X1,X2)) != apply(X2,sK11(X1,X2))
& in(sK11(X1,X2),relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f100,f101]) ).
fof(f103,plain,
( ? [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
& in(X1,set_intersection2(relation_dom(X2),X0))
& function(X2)
& relation(X2) )
=> ( apply(relation_dom_restriction(sK14,sK12),sK13) != apply(sK14,sK13)
& in(sK13,set_intersection2(relation_dom(sK14),sK12))
& function(sK14)
& relation(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f104,plain,
( apply(relation_dom_restriction(sK14,sK12),sK13) != apply(sK14,sK13)
& in(sK13,set_intersection2(relation_dom(sK14),sK12))
& function(sK14)
& relation(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f73,f103]) ).
fof(f110,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f111,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f116,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f122,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f155,plain,
! [X2,X0,X1] :
( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
| relation_dom_restriction(X2,X0) != X1
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f156,plain,
! [X2,X0,X1,X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1))
| relation_dom_restriction(X2,X0) != X1
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f160,plain,
relation(sK14),
inference(cnf_transformation,[],[f104]) ).
fof(f161,plain,
function(sK14),
inference(cnf_transformation,[],[f104]) ).
fof(f162,plain,
in(sK13,set_intersection2(relation_dom(sK14),sK12)),
inference(cnf_transformation,[],[f104]) ).
fof(f163,plain,
apply(relation_dom_restriction(sK14,sK12),sK13) != apply(sK14,sK13),
inference(cnf_transformation,[],[f104]) ).
fof(f166,plain,
! [X2,X0,X4] :
( apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4)
| ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X0))
| ~ relation(relation_dom_restriction(X2,X0)) ),
inference(equality_resolution,[],[f156]) ).
fof(f167,plain,
! [X2,X0] :
( set_intersection2(relation_dom(X2),X0) = relation_dom(relation_dom_restriction(X2,X0))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_dom_restriction(X2,X0))
| ~ relation(relation_dom_restriction(X2,X0)) ),
inference(equality_resolution,[],[f155]) ).
cnf(c_52,plain,
set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f110]) ).
cnf(c_53,plain,
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f111]) ).
cnf(c_59,plain,
( ~ relation(X0)
| ~ relation_empty_yielding(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f116]) ).
cnf(c_63,plain,
( ~ function(X0)
| ~ relation(X0)
| function(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f122]) ).
cnf(c_99,plain,
( ~ in(X0,relation_dom(relation_dom_restriction(X1,X2)))
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| apply(relation_dom_restriction(X1,X2),X0) = apply(X1,X0) ),
inference(cnf_transformation,[],[f166]) ).
cnf(c_100,plain,
( ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0)
| set_intersection2(relation_dom(X0),X1) = relation_dom(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f167]) ).
cnf(c_102,negated_conjecture,
apply(relation_dom_restriction(sK14,sK12),sK13) != apply(sK14,sK13),
inference(cnf_transformation,[],[f163]) ).
cnf(c_103,negated_conjecture,
in(sK13,set_intersection2(relation_dom(sK14),sK12)),
inference(cnf_transformation,[],[f162]) ).
cnf(c_104,negated_conjecture,
function(sK14),
inference(cnf_transformation,[],[f161]) ).
cnf(c_105,negated_conjecture,
relation(sK14),
inference(cnf_transformation,[],[f160]) ).
cnf(c_134,plain,
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_59,c_53]) ).
cnf(c_136,plain,
( ~ function(X0)
| ~ relation(X0)
| set_intersection2(relation_dom(X0),X1) = relation_dom(relation_dom_restriction(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_100,c_53,c_63,c_100]) ).
cnf(c_239,plain,
( ~ in(X0,relation_dom(relation_dom_restriction(X1,X2)))
| ~ function(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| apply(relation_dom_restriction(X1,X2),X0) = apply(X1,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_99,c_134]) ).
cnf(c_279,plain,
( ~ in(X0,relation_dom(relation_dom_restriction(X1,X2)))
| ~ function(X1)
| ~ relation(X1)
| apply(relation_dom_restriction(X1,X2),X0) = apply(X1,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_239,c_63]) ).
cnf(c_383,plain,
in(sK13,set_intersection2(sK12,relation_dom(sK14))),
inference(demodulation,[status(thm)],[c_103,c_52]) ).
cnf(c_1339,plain,
( ~ relation(sK14)
| set_intersection2(relation_dom(sK14),X0) = relation_dom(relation_dom_restriction(sK14,X0)) ),
inference(superposition,[status(thm)],[c_104,c_136]) ).
cnf(c_1340,plain,
set_intersection2(relation_dom(sK14),X0) = relation_dom(relation_dom_restriction(sK14,X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_1339,c_105]) ).
cnf(c_1513,plain,
set_intersection2(X0,relation_dom(sK14)) = relation_dom(relation_dom_restriction(sK14,X0)),
inference(superposition,[status(thm)],[c_52,c_1340]) ).
cnf(c_1516,plain,
in(sK13,relation_dom(relation_dom_restriction(sK14,sK12))),
inference(demodulation,[status(thm)],[c_383,c_1513]) ).
cnf(c_1833,plain,
( ~ function(sK14)
| ~ relation(sK14)
| apply(relation_dom_restriction(sK14,sK12),sK13) = apply(sK14,sK13) ),
inference(superposition,[status(thm)],[c_1516,c_279]) ).
cnf(c_1842,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1833,c_102,c_105,c_104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU037+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 13:05:51 EDT 2023
% 0.13/0.35 % 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
% 3.23/1.17 % SZS status Started for theBenchmark.p
% 3.23/1.17 % SZS status Theorem for theBenchmark.p
% 3.23/1.17
% 3.23/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.23/1.17
% 3.23/1.17 ------ iProver source info
% 3.23/1.17
% 3.23/1.17 git: date: 2023-05-31 18:12:56 +0000
% 3.23/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.23/1.17 git: non_committed_changes: false
% 3.23/1.17 git: last_make_outside_of_git: false
% 3.23/1.17
% 3.23/1.17 ------ Parsing...
% 3.23/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.23/1.17
% 3.23/1.17 ------ Preprocessing... sup_sim: 1 sf_s rm: 5 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 3.23/1.17
% 3.23/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.23/1.17
% 3.23/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.23/1.17 ------ Proving...
% 3.23/1.17 ------ Problem Properties
% 3.23/1.17
% 3.23/1.17
% 3.23/1.17 clauses 50
% 3.23/1.17 conjectures 3
% 3.23/1.17 EPR 26
% 3.23/1.17 Horn 47
% 3.23/1.17 unary 28
% 3.23/1.17 binary 11
% 3.23/1.17 lits 92
% 3.23/1.17 lits eq 13
% 3.23/1.17 fd_pure 0
% 3.23/1.17 fd_pseudo 0
% 3.23/1.17 fd_cond 1
% 3.23/1.17 fd_pseudo_cond 3
% 3.23/1.17 AC symbols 0
% 3.23/1.17
% 3.23/1.17 ------ Schedule dynamic 5 is on
% 3.23/1.17
% 3.23/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.23/1.17
% 3.23/1.17
% 3.23/1.17 ------
% 3.23/1.17 Current options:
% 3.23/1.17 ------
% 3.23/1.17
% 3.23/1.17
% 3.23/1.17
% 3.23/1.17
% 3.23/1.17 ------ Proving...
% 3.23/1.17
% 3.23/1.17
% 3.23/1.17 % SZS status Theorem for theBenchmark.p
% 3.23/1.17
% 3.23/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.23/1.17
% 3.23/1.17
%------------------------------------------------------------------------------