TSTP Solution File: SET693+4 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET693+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n027.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 15:09:10 EDT 2023
% Result : Theorem 2.18s 1.21s
% Output : CNFRefutation 2.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 63 ( 4 unt; 0 def)
% Number of atoms : 182 ( 4 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 196 ( 77 ~; 87 |; 21 &)
% ( 7 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 112 ( 4 sgn; 59 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
fof(f5,axiom,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f12,conjecture,
! [X0,X1] :
( equal_set(X0,union(X0,X1))
<=> subset(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI20) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] :
( equal_set(X0,union(X0,X1))
<=> subset(X1,X0) ),
inference(negated_conjecture,[],[f12]) ).
fof(f16,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X2)
| member(X0,X1) ) ),
inference(rectify,[],[f5]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f25,plain,
? [X0,X1] :
( equal_set(X0,union(X0,X1))
<~> subset(X1,X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f26,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f27,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f27,f28]) ).
fof(f30,plain,
! [X0,X1] :
( ( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| ~ equal_set(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f31,plain,
! [X0,X1] :
( ( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| ~ equal_set(X0,X1) ) ),
inference(flattening,[],[f30]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) )
& ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) )
& ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f35]) ).
fof(f50,plain,
? [X0,X1] :
( ( ~ subset(X1,X0)
| ~ equal_set(X0,union(X0,X1)) )
& ( subset(X1,X0)
| equal_set(X0,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f51,plain,
( ? [X0,X1] :
( ( ~ subset(X1,X0)
| ~ equal_set(X0,union(X0,X1)) )
& ( subset(X1,X0)
| equal_set(X0,union(X0,X1)) ) )
=> ( ( ~ subset(sK4,sK3)
| ~ equal_set(sK3,union(sK3,sK4)) )
& ( subset(sK4,sK3)
| equal_set(sK3,union(sK3,sK4)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
( ( ~ subset(sK4,sK3)
| ~ equal_set(sK3,union(sK3,sK4)) )
& ( subset(sK4,sK3)
| equal_set(sK3,union(sK3,sK4)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f50,f51]) ).
fof(f53,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f54,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f55,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f57,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f58,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f64,plain,
! [X2,X0,X1] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f65,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f66,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f82,plain,
( subset(sK4,sK3)
| equal_set(sK3,union(sK3,sK4)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f83,plain,
( ~ subset(sK4,sK3)
| ~ equal_set(sK3,union(sK3,sK4)) ),
inference(cnf_transformation,[],[f52]) ).
cnf(c_49,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
cnf(c_50,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
cnf(c_51,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f53]) ).
cnf(c_52,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
cnf(c_53,plain,
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f57]) ).
cnf(c_60,plain,
( ~ member(X0,X1)
| member(X0,union(X2,X1)) ),
inference(cnf_transformation,[],[f66]) ).
cnf(c_61,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f65]) ).
cnf(c_62,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[],[f64]) ).
cnf(c_78,negated_conjecture,
( ~ equal_set(sK3,union(sK3,sK4))
| ~ subset(sK4,sK3) ),
inference(cnf_transformation,[],[f83]) ).
cnf(c_79,negated_conjecture,
( equal_set(sK3,union(sK3,sK4))
| subset(sK4,sK3) ),
inference(cnf_transformation,[],[f82]) ).
cnf(c_106,plain,
( ~ subset(sK4,sK3)
| ~ equal_set(sK3,union(sK3,sK4)) ),
inference(prop_impl_just,[status(thm)],[c_78]) ).
cnf(c_107,plain,
( ~ equal_set(sK3,union(sK3,sK4))
| ~ subset(sK4,sK3) ),
inference(renaming,[status(thm)],[c_106]) ).
cnf(c_108,plain,
( subset(sK4,sK3)
| equal_set(sK3,union(sK3,sK4)) ),
inference(prop_impl_just,[status(thm)],[c_79]) ).
cnf(c_109,plain,
( equal_set(sK3,union(sK3,sK4))
| subset(sK4,sK3) ),
inference(renaming,[status(thm)],[c_108]) ).
cnf(c_120,plain,
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_53]) ).
cnf(c_485,plain,
( union(sK3,sK4) != X1
| X0 != sK3
| ~ subset(X0,X1)
| ~ subset(X1,X0)
| ~ subset(sK4,sK3) ),
inference(resolution_lifted,[status(thm)],[c_52,c_107]) ).
cnf(c_486,plain,
( ~ subset(union(sK3,sK4),sK3)
| ~ subset(sK3,union(sK3,sK4))
| ~ subset(sK4,sK3) ),
inference(unflattening,[status(thm)],[c_485]) ).
cnf(c_504,plain,
( union(sK3,sK4) != X1
| X0 != sK3
| subset(X1,X0)
| subset(sK4,sK3) ),
inference(resolution_lifted,[status(thm)],[c_120,c_109]) ).
cnf(c_505,plain,
( subset(union(sK3,sK4),sK3)
| subset(sK4,sK3) ),
inference(unflattening,[status(thm)],[c_504]) ).
cnf(c_565,plain,
( subset(sK4,sK3)
| subset(union(sK3,sK4),sK3) ),
inference(prop_impl_just,[status(thm)],[c_505]) ).
cnf(c_566,plain,
( subset(union(sK3,sK4),sK3)
| subset(sK4,sK3) ),
inference(renaming,[status(thm)],[c_565]) ).
cnf(c_1474,plain,
( ~ member(sK0(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) ),
inference(superposition,[status(thm)],[c_61,c_49]) ).
cnf(c_1486,plain,
( ~ subset(union(X0,X1),X2)
| ~ member(X3,X1)
| member(X3,X2) ),
inference(superposition,[status(thm)],[c_60,c_51]) ).
cnf(c_1495,plain,
( member(sK0(union(X0,X1),X2),X0)
| member(sK0(union(X0,X1),X2),X1)
| subset(union(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_50,c_62]) ).
cnf(c_1520,plain,
subset(X0,union(X0,X1)),
inference(superposition,[status(thm)],[c_50,c_1474]) ).
cnf(c_1524,plain,
( ~ subset(union(sK3,sK4),sK3)
| ~ subset(sK4,sK3) ),
inference(backward_subsumption_resolution,[status(thm)],[c_486,c_1520]) ).
cnf(c_1619,plain,
( ~ member(X0,sK4)
| member(X0,sK3)
| subset(sK4,sK3) ),
inference(superposition,[status(thm)],[c_566,c_1486]) ).
cnf(c_1635,plain,
( member(sK0(union(X0,X1),X0),X1)
| subset(union(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_1495,c_49]) ).
cnf(c_1934,plain,
( ~ member(X0,sK4)
| member(X0,sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1619,c_51]) ).
cnf(c_1937,plain,
( member(sK0(sK4,X0),sK3)
| subset(sK4,X0) ),
inference(superposition,[status(thm)],[c_50,c_1934]) ).
cnf(c_2020,plain,
( member(sK0(union(X0,sK4),X0),sK3)
| subset(union(X0,sK4),X0) ),
inference(superposition,[status(thm)],[c_1635,c_1934]) ).
cnf(c_4749,plain,
subset(sK4,sK3),
inference(superposition,[status(thm)],[c_1937,c_49]) ).
cnf(c_5685,plain,
subset(union(sK3,sK4),sK3),
inference(superposition,[status(thm)],[c_2020,c_49]) ).
cnf(c_5701,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5685,c_4749,c_1524]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET693+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.15 % Command : run_iprover %s %d THM
% 0.14/0.36 % Computer : n027.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 16:02:20 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.23/0.51 Running first-order theorem proving
% 0.23/0.51 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.18/1.21 % SZS status Started for theBenchmark.p
% 2.18/1.21 % SZS status Theorem for theBenchmark.p
% 2.18/1.21
% 2.18/1.21 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.18/1.21
% 2.18/1.21 ------ iProver source info
% 2.18/1.21
% 2.18/1.21 git: date: 2023-05-31 18:12:56 +0000
% 2.18/1.21 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.18/1.21 git: non_committed_changes: false
% 2.18/1.21 git: last_make_outside_of_git: false
% 2.18/1.21
% 2.18/1.21 ------ Parsing...
% 2.18/1.21 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.18/1.21
% 2.18/1.21 ------ 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
% 2.18/1.21
% 2.18/1.21 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.18/1.21
% 2.18/1.21 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.18/1.21 ------ Proving...
% 2.18/1.21 ------ Problem Properties
% 2.18/1.21
% 2.18/1.21
% 2.18/1.21 clauses 29
% 2.18/1.21 conjectures 0
% 2.18/1.21 EPR 2
% 2.18/1.21 Horn 22
% 2.18/1.21 unary 4
% 2.18/1.21 binary 17
% 2.18/1.21 lits 62
% 2.18/1.21 lits eq 3
% 2.18/1.21 fd_pure 0
% 2.18/1.21 fd_pseudo 0
% 2.18/1.21 fd_cond 0
% 2.18/1.21 fd_pseudo_cond 2
% 2.18/1.21 AC symbols 0
% 2.18/1.21
% 2.18/1.21 ------ Input Options Time Limit: Unbounded
% 2.18/1.21
% 2.18/1.21
% 2.18/1.21 ------
% 2.18/1.21 Current options:
% 2.18/1.21 ------
% 2.18/1.21
% 2.18/1.21
% 2.18/1.21
% 2.18/1.21
% 2.18/1.21 ------ Proving...
% 2.18/1.21
% 2.18/1.21
% 2.18/1.21 % SZS status Theorem for theBenchmark.p
% 2.18/1.21
% 2.18/1.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.18/1.21
% 2.18/1.22
%------------------------------------------------------------------------------