TSTP Solution File: SEU129+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU129+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n031.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 03:04:36 EDT 2024
% Result : Theorem 3.37s 1.15s
% Output : CNFRefutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 7 unt; 0 def)
% Number of atoms : 179 ( 16 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 222 ( 90 ~; 85 |; 37 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 109 ( 2 sgn 74 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f4,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f12,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
inference(negated_conjecture,[],[f12]) ).
fof(f21,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f22,plain,
? [X0,X1,X2] :
( ~ subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
& subset(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f26,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f27,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f27,f28]) ).
fof(f30,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,[],[f4]) ).
fof(f31,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,[],[f30]) ).
fof(f32,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,[],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0)
| ~ in(sK1(X0,X1,X2),X2) )
& ( ( in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) )
| in(sK1(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ( ( ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0)
| ~ in(sK1(X0,X1,X2),X2) )
& ( ( in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) )
| in(sK1(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,[sK1])],[f32,f33]) ).
fof(f39,plain,
( ? [X0,X1,X2] :
( ~ subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
& subset(X0,X1) )
=> ( ~ subset(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6))
& subset(sK4,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
( ~ subset(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6))
& subset(sK4,sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f22,f39]) ).
fof(f43,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f44,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f45,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f46,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f34]) ).
fof(f47,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f34]) ).
fof(f48,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f34]) ).
fof(f57,plain,
subset(sK4,sK5),
inference(cnf_transformation,[],[f40]) ).
fof(f58,plain,
~ subset(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6)),
inference(cnf_transformation,[],[f40]) ).
fof(f63,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f48]) ).
fof(f64,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f47]) ).
fof(f65,plain,
! [X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f46]) ).
cnf(c_51,plain,
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
cnf(c_52,plain,
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
cnf(c_53,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f43]) ).
cnf(c_57,plain,
( ~ in(X0,X1)
| ~ in(X0,X2)
| in(X0,set_intersection2(X2,X1)) ),
inference(cnf_transformation,[],[f63]) ).
cnf(c_58,plain,
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X2) ),
inference(cnf_transformation,[],[f64]) ).
cnf(c_59,plain,
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
cnf(c_65,negated_conjecture,
~ subset(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6)),
inference(cnf_transformation,[],[f58]) ).
cnf(c_66,negated_conjecture,
subset(sK4,sK5),
inference(cnf_transformation,[],[f57]) ).
cnf(c_191,plain,
( set_intersection2(sK4,sK6) != X0
| set_intersection2(sK5,sK6) != X1
| in(sK0(X0,X1),X0) ),
inference(resolution_lifted,[status(thm)],[c_52,c_65]) ).
cnf(c_192,plain,
in(sK0(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6)),set_intersection2(sK4,sK6)),
inference(unflattening,[status(thm)],[c_191]) ).
cnf(c_196,plain,
( set_intersection2(sK4,sK6) != X0
| set_intersection2(sK5,sK6) != X1
| ~ in(sK0(X0,X1),X1) ),
inference(resolution_lifted,[status(thm)],[c_51,c_65]) ).
cnf(c_197,plain,
~ in(sK0(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6)),set_intersection2(sK5,sK6)),
inference(unflattening,[status(thm)],[c_196]) ).
cnf(c_520,plain,
( ~ in(sK0(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6)),set_intersection2(sK4,sK6))
| in(sK0(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6)),sK4) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_521,plain,
( ~ in(sK0(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6)),set_intersection2(sK4,sK6))
| in(sK0(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6)),sK6) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_654,plain,
( ~ in(sK0(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6)),sK4)
| ~ subset(sK4,X0)
| in(sK0(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6)),X0) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_1289,plain,
( ~ in(sK0(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6)),sK4)
| ~ subset(sK4,sK5)
| in(sK0(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6)),sK5) ),
inference(instantiation,[status(thm)],[c_654]) ).
cnf(c_3496,plain,
( ~ in(sK0(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6)),X0)
| ~ in(sK0(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6)),sK5)
| in(sK0(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6)),set_intersection2(sK5,X0)) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_8018,plain,
( ~ in(sK0(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6)),sK6)
| ~ in(sK0(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6)),sK5)
| in(sK0(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6)),set_intersection2(sK5,sK6)) ),
inference(instantiation,[status(thm)],[c_3496]) ).
cnf(c_8019,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_8018,c_1289,c_520,c_521,c_197,c_192,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU129+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n031.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 : Thu May 2 18:13:31 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.37/1.15 % SZS status Started for theBenchmark.p
% 3.37/1.15 % SZS status Theorem for theBenchmark.p
% 3.37/1.15
% 3.37/1.15 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.37/1.15
% 3.37/1.15 ------ iProver source info
% 3.37/1.15
% 3.37/1.15 git: date: 2024-05-02 19:28:25 +0000
% 3.37/1.15 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.37/1.15 git: non_committed_changes: false
% 3.37/1.15
% 3.37/1.15 ------ Parsing...
% 3.37/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.37/1.15
% 3.37/1.15 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 3.37/1.15
% 3.37/1.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.37/1.15
% 3.37/1.15 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.37/1.15 ------ Proving...
% 3.37/1.15 ------ Problem Properties
% 3.37/1.15
% 3.37/1.15
% 3.37/1.15 clauses 22
% 3.37/1.15 conjectures 2
% 3.37/1.15 EPR 10
% 3.37/1.15 Horn 19
% 3.37/1.15 unary 9
% 3.37/1.15 binary 7
% 3.37/1.15 lits 42
% 3.37/1.15 lits eq 8
% 3.37/1.15 fd_pure 0
% 3.37/1.15 fd_pseudo 0
% 3.37/1.15 fd_cond 1
% 3.37/1.15 fd_pseudo_cond 4
% 3.37/1.15 AC symbols 0
% 3.37/1.15
% 3.37/1.15 ------ Input Options Time Limit: Unbounded
% 3.37/1.15
% 3.37/1.15
% 3.37/1.15 ------
% 3.37/1.15 Current options:
% 3.37/1.15 ------
% 3.37/1.15
% 3.37/1.15
% 3.37/1.15
% 3.37/1.15
% 3.37/1.15 ------ Proving...
% 3.37/1.15
% 3.37/1.15
% 3.37/1.15 % SZS status Theorem for theBenchmark.p
% 3.37/1.15
% 3.37/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.37/1.15
% 3.37/1.15
%------------------------------------------------------------------------------