TSTP Solution File: SEU104+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU104+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n025.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 17:03:44 EDT 2023
% Result : Theorem 0.61s 1.18s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 66 ( 22 unt; 0 def)
% Number of atoms : 194 ( 14 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 214 ( 86 ~; 76 |; 37 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 97 ( 1 sgn; 66 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f17,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f28,axiom,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(X2,X0)
& in(X1,X0) )
=> ( in(set_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_finsub_1) ).
fof(f29,conjecture,
! [X0] :
( ~ empty(X0)
=> ( ! [X1] :
( element(X1,X0)
=> ! [X2] :
( element(X2,X0)
=> ( in(set_difference(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_finsub_1) ).
fof(f30,negated_conjecture,
~ ! [X0] :
( ~ empty(X0)
=> ( ! [X1] :
( element(X1,X0)
=> ! [X2] :
( element(X2,X0)
=> ( in(set_difference(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
inference(negated_conjecture,[],[f29]) ).
fof(f32,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f34,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(f43,axiom,
! [X0,X1] : set_union2(X0,X1) = symmetric_difference(X0,set_difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_xboole_1) ).
fof(f44,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f17]) ).
fof(f71,plain,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(set_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) )
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f72,plain,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(set_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) )
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
? [X0] :
( ~ preboolean(X0)
& ! [X1] :
( ! [X2] :
( ( in(set_difference(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) )
| ~ element(X2,X0) )
| ~ element(X1,X0) )
& ~ empty(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f74,plain,
? [X0] :
( ~ preboolean(X0)
& ! [X1] :
( ! [X2] :
( ( in(set_difference(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) )
| ~ element(X2,X0) )
| ~ element(X1,X0) )
& ~ empty(X0) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f105,plain,
! [X0] :
( ( preboolean(X0)
| ? [X1,X2] :
( ( ~ in(set_difference(X1,X2),X0)
| ~ in(set_union2(X1,X2),X0) )
& in(X2,X0)
& in(X1,X0) ) )
& ( ! [X1,X2] :
( ( in(set_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) )
| ~ in(X2,X0)
| ~ in(X1,X0) )
| ~ preboolean(X0) ) ),
inference(nnf_transformation,[],[f72]) ).
fof(f106,plain,
! [X0] :
( ( preboolean(X0)
| ? [X1,X2] :
( ( ~ in(set_difference(X1,X2),X0)
| ~ in(set_union2(X1,X2),X0) )
& in(X2,X0)
& in(X1,X0) ) )
& ( ! [X3,X4] :
( ( in(set_difference(X3,X4),X0)
& in(set_union2(X3,X4),X0) )
| ~ in(X4,X0)
| ~ in(X3,X0) )
| ~ preboolean(X0) ) ),
inference(rectify,[],[f105]) ).
fof(f107,plain,
! [X0] :
( ? [X1,X2] :
( ( ~ in(set_difference(X1,X2),X0)
| ~ in(set_union2(X1,X2),X0) )
& in(X2,X0)
& in(X1,X0) )
=> ( ( ~ in(set_difference(sK10(X0),sK11(X0)),X0)
| ~ in(set_union2(sK10(X0),sK11(X0)),X0) )
& in(sK11(X0),X0)
& in(sK10(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f108,plain,
! [X0] :
( ( preboolean(X0)
| ( ( ~ in(set_difference(sK10(X0),sK11(X0)),X0)
| ~ in(set_union2(sK10(X0),sK11(X0)),X0) )
& in(sK11(X0),X0)
& in(sK10(X0),X0) ) )
& ( ! [X3,X4] :
( ( in(set_difference(X3,X4),X0)
& in(set_union2(X3,X4),X0) )
| ~ in(X4,X0)
| ~ in(X3,X0) )
| ~ preboolean(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f106,f107]) ).
fof(f109,plain,
( ? [X0] :
( ~ preboolean(X0)
& ! [X1] :
( ! [X2] :
( ( in(set_difference(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) )
| ~ element(X2,X0) )
| ~ element(X1,X0) )
& ~ empty(X0) )
=> ( ~ preboolean(sK12)
& ! [X1] :
( ! [X2] :
( ( in(set_difference(X1,X2),sK12)
& in(symmetric_difference(X1,X2),sK12) )
| ~ element(X2,sK12) )
| ~ element(X1,sK12) )
& ~ empty(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f110,plain,
( ~ preboolean(sK12)
& ! [X1] :
( ! [X2] :
( ( in(set_difference(X1,X2),sK12)
& in(symmetric_difference(X1,X2),sK12) )
| ~ element(X2,sK12) )
| ~ element(X1,sK12) )
& ~ empty(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f74,f109]) ).
fof(f117,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f128,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f44]) ).
fof(f153,plain,
! [X0] :
( preboolean(X0)
| in(sK10(X0),X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f154,plain,
! [X0] :
( preboolean(X0)
| in(sK11(X0),X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f155,plain,
! [X0] :
( preboolean(X0)
| ~ in(set_difference(sK10(X0),sK11(X0)),X0)
| ~ in(set_union2(sK10(X0),sK11(X0)),X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f157,plain,
! [X2,X1] :
( in(symmetric_difference(X1,X2),sK12)
| ~ element(X2,sK12)
| ~ element(X1,sK12) ),
inference(cnf_transformation,[],[f110]) ).
fof(f158,plain,
! [X2,X1] :
( in(set_difference(X1,X2),sK12)
| ~ element(X2,sK12)
| ~ element(X1,sK12) ),
inference(cnf_transformation,[],[f110]) ).
fof(f159,plain,
~ preboolean(sK12),
inference(cnf_transformation,[],[f110]) ).
fof(f161,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f163,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f34]) ).
fof(f172,plain,
! [X0,X1] : set_union2(X0,X1) = symmetric_difference(X0,set_difference(X1,X0)),
inference(cnf_transformation,[],[f43]) ).
fof(f174,plain,
! [X0,X1] : symmetric_difference(X0,set_difference(X1,X0)) = symmetric_difference(X1,set_difference(X0,X1)),
inference(definition_unfolding,[],[f117,f172,f172]) ).
fof(f178,plain,
! [X0] : symmetric_difference(X0,set_difference(X0,X0)) = X0,
inference(definition_unfolding,[],[f128,f172]) ).
fof(f179,plain,
! [X0] :
( preboolean(X0)
| ~ in(set_difference(sK10(X0),sK11(X0)),X0)
| ~ in(symmetric_difference(sK10(X0),set_difference(sK11(X0),sK10(X0))),X0) ),
inference(definition_unfolding,[],[f155,f172]) ).
cnf(c_56,plain,
symmetric_difference(X0,set_difference(X1,X0)) = symmetric_difference(X1,set_difference(X0,X1)),
inference(cnf_transformation,[],[f174]) ).
cnf(c_66,plain,
symmetric_difference(X0,set_difference(X0,X0)) = X0,
inference(cnf_transformation,[],[f178]) ).
cnf(c_89,plain,
( ~ in(symmetric_difference(sK10(X0),set_difference(sK11(X0),sK10(X0))),X0)
| ~ in(set_difference(sK10(X0),sK11(X0)),X0)
| preboolean(X0) ),
inference(cnf_transformation,[],[f179]) ).
cnf(c_90,plain,
( in(sK11(X0),X0)
| preboolean(X0) ),
inference(cnf_transformation,[],[f154]) ).
cnf(c_91,plain,
( in(sK10(X0),X0)
| preboolean(X0) ),
inference(cnf_transformation,[],[f153]) ).
cnf(c_94,negated_conjecture,
~ preboolean(sK12),
inference(cnf_transformation,[],[f159]) ).
cnf(c_95,negated_conjecture,
( ~ element(X0,sK12)
| ~ element(X1,sK12)
| in(set_difference(X0,X1),sK12) ),
inference(cnf_transformation,[],[f158]) ).
cnf(c_96,negated_conjecture,
( ~ element(X0,sK12)
| ~ element(X1,sK12)
| in(symmetric_difference(X0,X1),sK12) ),
inference(cnf_transformation,[],[f157]) ).
cnf(c_99,plain,
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_101,plain,
set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f163]) ).
cnf(c_123,plain,
( in(sK10(sK12),sK12)
| preboolean(sK12) ),
inference(instantiation,[status(thm)],[c_91]) ).
cnf(c_124,plain,
( in(sK11(sK12),sK12)
| preboolean(sK12) ),
inference(instantiation,[status(thm)],[c_90]) ).
cnf(c_1634,plain,
( ~ element(X0,sK12)
| ~ element(empty_set,sK12)
| in(X0,sK12) ),
inference(superposition,[status(thm)],[c_101,c_95]) ).
cnf(c_1689,plain,
( element(sK11(X0),X0)
| preboolean(X0) ),
inference(superposition,[status(thm)],[c_90,c_99]) ).
cnf(c_1690,plain,
( element(sK10(X0),X0)
| preboolean(X0) ),
inference(superposition,[status(thm)],[c_91,c_99]) ).
cnf(c_1691,plain,
( ~ element(X0,sK12)
| ~ element(X1,sK12)
| element(set_difference(X0,X1),sK12) ),
inference(superposition,[status(thm)],[c_95,c_99]) ).
cnf(c_1712,plain,
( ~ element(empty_set,sK12)
| in(sK11(sK12),sK12)
| preboolean(sK12) ),
inference(superposition,[status(thm)],[c_1689,c_1634]) ).
cnf(c_1713,plain,
( ~ element(empty_set,sK12)
| in(sK11(sK12),sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1712,c_94]) ).
cnf(c_1720,plain,
( ~ element(empty_set,sK12)
| in(sK10(sK12),sK12)
| preboolean(sK12) ),
inference(superposition,[status(thm)],[c_1690,c_1634]) ).
cnf(c_1721,plain,
( ~ element(empty_set,sK12)
| in(sK10(sK12),sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1720,c_94]) ).
cnf(c_1724,plain,
in(sK11(sK12),sK12),
inference(global_subsumption_just,[status(thm)],[c_1713,c_94,c_124]) ).
cnf(c_1726,plain,
element(sK11(sK12),sK12),
inference(superposition,[status(thm)],[c_1724,c_99]) ).
cnf(c_1727,plain,
in(sK10(sK12),sK12),
inference(global_subsumption_just,[status(thm)],[c_1721,c_94,c_123]) ).
cnf(c_1729,plain,
element(sK10(sK12),sK12),
inference(superposition,[status(thm)],[c_1727,c_99]) ).
cnf(c_1937,plain,
( ~ element(set_difference(X0,X0),sK12)
| ~ element(X0,sK12)
| in(X0,sK12) ),
inference(superposition,[status(thm)],[c_66,c_96]) ).
cnf(c_2037,plain,
( ~ element(X0,sK12)
| in(X0,sK12) ),
inference(superposition,[status(thm)],[c_1691,c_1937]) ).
cnf(c_2145,plain,
( ~ element(set_difference(X0,X1),sK12)
| ~ element(X1,sK12)
| in(symmetric_difference(X0,set_difference(X1,X0)),sK12) ),
inference(superposition,[status(thm)],[c_56,c_96]) ).
cnf(c_2440,plain,
( ~ in(set_difference(sK10(sK12),sK11(sK12)),sK12)
| ~ element(set_difference(sK10(sK12),sK11(sK12)),sK12)
| ~ element(sK11(sK12),sK12)
| preboolean(sK12) ),
inference(superposition,[status(thm)],[c_2145,c_89]) ).
cnf(c_2441,plain,
( ~ in(set_difference(sK10(sK12),sK11(sK12)),sK12)
| ~ element(set_difference(sK10(sK12),sK11(sK12)),sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2440,c_94,c_1726]) ).
cnf(c_2523,plain,
~ element(set_difference(sK10(sK12),sK11(sK12)),sK12),
inference(forward_subsumption_resolution,[status(thm)],[c_2441,c_2037]) ).
cnf(c_2524,plain,
( ~ element(sK10(sK12),sK12)
| ~ element(sK11(sK12),sK12) ),
inference(superposition,[status(thm)],[c_1691,c_2523]) ).
cnf(c_2525,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2524,c_1726,c_1729]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU104+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n025.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 15:46:06 EDT 2023
% 0.13/0.35 % 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 --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.61/1.18 % SZS status Started for theBenchmark.p
% 0.61/1.18 % SZS status Theorem for theBenchmark.p
% 0.61/1.18
% 0.61/1.18 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.61/1.18
% 0.61/1.18 ------ iProver source info
% 0.61/1.18
% 0.61/1.18 git: date: 2023-05-31 18:12:56 +0000
% 0.61/1.18 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.61/1.18 git: non_committed_changes: false
% 0.61/1.18 git: last_make_outside_of_git: false
% 0.61/1.18
% 0.61/1.18 ------ Parsing...
% 0.61/1.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.61/1.18
% 0.61/1.18 ------ Preprocessing... sup_sim: 1 sf_s rm: 11 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e
% 0.61/1.18
% 0.61/1.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.61/1.18
% 0.61/1.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.61/1.18 ------ Proving...
% 0.61/1.18 ------ Problem Properties
% 0.61/1.18
% 0.61/1.18
% 0.61/1.18 clauses 45
% 0.61/1.18 conjectures 4
% 0.61/1.18 EPR 14
% 0.61/1.18 Horn 39
% 0.61/1.18 unary 22
% 0.61/1.18 binary 14
% 0.61/1.18 lits 79
% 0.61/1.18 lits eq 9
% 0.61/1.18 fd_pure 0
% 0.61/1.18 fd_pseudo 0
% 0.61/1.18 fd_cond 1
% 0.61/1.18 fd_pseudo_cond 1
% 0.61/1.18 AC symbols 0
% 0.61/1.18
% 0.61/1.18 ------ Schedule dynamic 5 is on
% 0.61/1.18
% 0.61/1.18 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.61/1.18
% 0.61/1.18
% 0.61/1.18 ------
% 0.61/1.18 Current options:
% 0.61/1.18 ------
% 0.61/1.18
% 0.61/1.18
% 0.61/1.18
% 0.61/1.18
% 0.61/1.18 ------ Proving...
% 0.61/1.18
% 0.61/1.18
% 0.61/1.18 % SZS status Theorem for theBenchmark.p
% 0.61/1.18
% 0.61/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.61/1.18
% 0.61/1.18
%------------------------------------------------------------------------------