TSTP Solution File: SWV486+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWV486+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n024.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 22:37:53 EDT 2023
% Result : Theorem 3.77s 1.15s
% Output : CNFRefutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 74 ( 19 unt; 0 def)
% Number of atoms : 271 ( 61 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 326 ( 129 ~; 127 |; 52 &)
% ( 3 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 118 ( 0 sgn; 81 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( int_leq(X0,X1)
<=> ( X0 = X1
| int_less(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_leq) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( int_less(X1,X2)
& int_less(X0,X1) )
=> int_less(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_transitive) ).
fof(f9,axiom,
! [X0,X1] :
( int_less(X0,X1)
<=> ? [X2] :
( int_less(int_zero,X2)
& plus(X0,X2) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_and_inverse) ).
fof(f10,axiom,
! [X0] :
( int_less(int_zero,X0)
<=> int_leq(int_one,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_successor_of_zero) ).
fof(f12,axiom,
! [X0,X1] :
( ( int_leq(X1,n)
& int_leq(int_one,X1)
& int_leq(X0,n)
& int_leq(int_one,X0) )
=> ( ! [X7] :
( ( plus(X0,X7) = X1
& int_less(int_zero,X7) )
=> ! [X2] :
( ( int_leq(X2,X0)
& int_leq(int_one,X2) )
=> real_zero = a(X2,plus(X2,X7)) ) )
& ! [X7] :
( ( plus(X1,X7) = X0
& int_less(int_zero,X7) )
=> ! [X2] :
( ( int_leq(X2,X1)
& int_leq(int_one,X2) )
=> a(plus(X2,X7),X2) = qr(plus(X2,X7),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qih) ).
fof(f13,conjecture,
! [X0,X1] :
( ( int_leq(X1,n)
& int_less(X0,X1)
& int_leq(int_one,X0) )
=> real_zero = a(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lt) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( ( int_leq(X1,n)
& int_less(X0,X1)
& int_leq(int_one,X0) )
=> real_zero = a(X0,X1) ),
inference(negated_conjecture,[],[f13]) ).
fof(f16,plain,
! [X0,X1] :
( ( int_leq(X1,n)
& int_leq(int_one,X1)
& int_leq(X0,n)
& int_leq(int_one,X0) )
=> ( ! [X2] :
( ( plus(X0,X2) = X1
& int_less(int_zero,X2) )
=> ! [X3] :
( ( int_leq(X3,X0)
& int_leq(int_one,X3) )
=> real_zero = a(X3,plus(X3,X2)) ) )
& ! [X4] :
( ( plus(X1,X4) = X0
& int_less(int_zero,X4) )
=> ! [X5] :
( ( int_leq(X5,X1)
& int_leq(int_one,X5) )
=> a(plus(X5,X4),X5) = qr(plus(X5,X4),X5) ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f17,plain,
! [X0,X1,X2] :
( int_less(X0,X2)
| ~ int_less(X1,X2)
| ~ int_less(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f18,plain,
! [X0,X1,X2] :
( int_less(X0,X2)
| ~ int_less(X1,X2)
| ~ int_less(X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f22,plain,
! [X0,X1] :
( ( ! [X2] :
( ! [X3] :
( real_zero = a(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3) )
| plus(X0,X2) != X1
| ~ int_less(int_zero,X2) )
& ! [X4] :
( ! [X5] :
( a(plus(X5,X4),X5) = qr(plus(X5,X4),X5)
| ~ int_leq(X5,X1)
| ~ int_leq(int_one,X5) )
| plus(X1,X4) != X0
| ~ int_less(int_zero,X4) ) )
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f23,plain,
! [X0,X1] :
( ( ! [X2] :
( ! [X3] :
( real_zero = a(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3) )
| plus(X0,X2) != X1
| ~ int_less(int_zero,X2) )
& ! [X4] :
( ! [X5] :
( a(plus(X5,X4),X5) = qr(plus(X5,X4),X5)
| ~ int_leq(X5,X1)
| ~ int_leq(int_one,X5) )
| plus(X1,X4) != X0
| ~ int_less(int_zero,X4) ) )
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
? [X0,X1] :
( real_zero != a(X0,X1)
& int_leq(X1,n)
& int_less(X0,X1)
& int_leq(int_one,X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f25,plain,
? [X0,X1] :
( real_zero != a(X0,X1)
& int_leq(X1,n)
& int_less(X0,X1)
& int_leq(int_one,X0) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ( int_leq(X0,X1)
| ( X0 != X1
& ~ int_less(X0,X1) ) )
& ( X0 = X1
| int_less(X0,X1)
| ~ int_leq(X0,X1) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f27,plain,
! [X0,X1] :
( ( int_leq(X0,X1)
| ( X0 != X1
& ~ int_less(X0,X1) ) )
& ( X0 = X1
| int_less(X0,X1)
| ~ int_leq(X0,X1) ) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ( int_less(X0,X1)
| ! [X2] :
( ~ int_less(int_zero,X2)
| plus(X0,X2) != X1 ) )
& ( ? [X2] :
( int_less(int_zero,X2)
& plus(X0,X2) = X1 )
| ~ int_less(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f29,plain,
! [X0,X1] :
( ( int_less(X0,X1)
| ! [X2] :
( ~ int_less(int_zero,X2)
| plus(X0,X2) != X1 ) )
& ( ? [X3] :
( int_less(int_zero,X3)
& plus(X0,X3) = X1 )
| ~ int_less(X0,X1) ) ),
inference(rectify,[],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ? [X3] :
( int_less(int_zero,X3)
& plus(X0,X3) = X1 )
=> ( int_less(int_zero,sK0(X0,X1))
& plus(X0,sK0(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0,X1] :
( ( int_less(X0,X1)
| ! [X2] :
( ~ int_less(int_zero,X2)
| plus(X0,X2) != X1 ) )
& ( ( int_less(int_zero,sK0(X0,X1))
& plus(X0,sK0(X0,X1)) = X1 )
| ~ int_less(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f29,f30]) ).
fof(f32,plain,
! [X0] :
( ( int_less(int_zero,X0)
| ~ int_leq(int_one,X0) )
& ( int_leq(int_one,X0)
| ~ int_less(int_zero,X0) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f33,plain,
( ? [X0,X1] :
( real_zero != a(X0,X1)
& int_leq(X1,n)
& int_less(X0,X1)
& int_leq(int_one,X0) )
=> ( real_zero != a(sK1,sK2)
& int_leq(sK2,n)
& int_less(sK1,sK2)
& int_leq(int_one,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
( real_zero != a(sK1,sK2)
& int_leq(sK2,n)
& int_less(sK1,sK2)
& int_leq(int_one,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f25,f33]) ).
fof(f35,plain,
! [X0,X1] :
( X0 = X1
| int_less(X0,X1)
| ~ int_leq(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f36,plain,
! [X0,X1] :
( int_leq(X0,X1)
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f37,plain,
! [X0,X1] :
( int_leq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f27]) ).
fof(f38,plain,
! [X2,X0,X1] :
( int_less(X0,X2)
| ~ int_less(X1,X2)
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f45,plain,
! [X0,X1] :
( plus(X0,sK0(X0,X1)) = X1
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f46,plain,
! [X0,X1] :
( int_less(int_zero,sK0(X0,X1))
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f48,plain,
! [X0] :
( int_leq(int_one,X0)
| ~ int_less(int_zero,X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f49,plain,
! [X0] :
( int_less(int_zero,X0)
| ~ int_leq(int_one,X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( real_zero = a(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3)
| plus(X0,X2) != X1
| ~ int_less(int_zero,X2)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f53,plain,
int_leq(int_one,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f54,plain,
int_less(sK1,sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f55,plain,
int_leq(sK2,n),
inference(cnf_transformation,[],[f34]) ).
fof(f56,plain,
real_zero != a(sK1,sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f57,plain,
! [X1] : int_leq(X1,X1),
inference(equality_resolution,[],[f37]) ).
fof(f60,plain,
! [X2,X3,X0] :
( real_zero = a(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3)
| ~ int_less(int_zero,X2)
| ~ int_leq(plus(X0,X2),n)
| ~ int_leq(int_one,plus(X0,X2))
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(equality_resolution,[],[f52]) ).
cnf(c_49,plain,
int_leq(X0,X0),
inference(cnf_transformation,[],[f57]) ).
cnf(c_50,plain,
( ~ int_less(X0,X1)
| int_leq(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
cnf(c_51,plain,
( ~ int_leq(X0,X1)
| X0 = X1
| int_less(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
cnf(c_52,plain,
( ~ int_less(X0,X1)
| ~ int_less(X2,X0)
| int_less(X2,X1) ),
inference(cnf_transformation,[],[f38]) ).
cnf(c_60,plain,
( ~ int_less(X0,X1)
| int_less(int_zero,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f46]) ).
cnf(c_61,plain,
( ~ int_less(X0,X1)
| plus(X0,sK0(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f45]) ).
cnf(c_62,plain,
( ~ int_leq(int_one,X0)
| int_less(int_zero,X0) ),
inference(cnf_transformation,[],[f49]) ).
cnf(c_63,plain,
( ~ int_less(int_zero,X0)
| int_leq(int_one,X0) ),
inference(cnf_transformation,[],[f48]) ).
cnf(c_65,plain,
( ~ int_leq(plus(X0,X1),n)
| ~ int_leq(int_one,plus(X0,X1))
| ~ int_leq(X2,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| a(X2,plus(X2,X1)) = real_zero ),
inference(cnf_transformation,[],[f60]) ).
cnf(c_67,negated_conjecture,
a(sK1,sK2) != real_zero,
inference(cnf_transformation,[],[f56]) ).
cnf(c_68,negated_conjecture,
int_leq(sK2,n),
inference(cnf_transformation,[],[f55]) ).
cnf(c_69,negated_conjecture,
int_less(sK1,sK2),
inference(cnf_transformation,[],[f54]) ).
cnf(c_70,negated_conjecture,
int_leq(int_one,sK1),
inference(cnf_transformation,[],[f53]) ).
cnf(c_81,plain,
( ~ int_less(int_zero,X0)
| int_leq(int_one,X0) ),
inference(prop_impl_just,[status(thm)],[c_63]) ).
cnf(c_140,plain,
( ~ int_leq(plus(X0,X1),n)
| ~ int_leq(int_one,plus(X0,X1))
| ~ int_leq(X2,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X0)
| ~ int_less(int_zero,X1)
| a(X2,plus(X2,X1)) = real_zero ),
inference(bin_hyper_res,[status(thm)],[c_65,c_81]) ).
cnf(c_795,plain,
int_leq(sK1,sK2),
inference(superposition,[status(thm)],[c_69,c_50]) ).
cnf(c_803,plain,
int_less(int_zero,sK1),
inference(superposition,[status(thm)],[c_70,c_62]) ).
cnf(c_916,plain,
( n = sK2
| int_less(sK2,n) ),
inference(superposition,[status(thm)],[c_68,c_51]) ).
cnf(c_951,plain,
( ~ int_less(X0,sK1)
| int_less(X0,sK2) ),
inference(superposition,[status(thm)],[c_69,c_52]) ).
cnf(c_980,plain,
( ~ int_less(X0,sK2)
| n = sK2
| int_less(X0,n) ),
inference(superposition,[status(thm)],[c_916,c_52]) ).
cnf(c_1007,plain,
( ~ int_less(sK1,sK2)
| int_less(int_zero,sK0(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_1025,plain,
int_less(int_zero,sK2),
inference(superposition,[status(thm)],[c_803,c_951]) ).
cnf(c_1034,plain,
int_leq(int_one,sK2),
inference(superposition,[status(thm)],[c_1025,c_63]) ).
cnf(c_1082,plain,
( n = sK2
| int_less(sK1,n) ),
inference(superposition,[status(thm)],[c_69,c_980]) ).
cnf(c_1114,plain,
( n = sK2
| int_leq(sK1,n) ),
inference(superposition,[status(thm)],[c_1082,c_50]) ).
cnf(c_1181,plain,
plus(sK1,sK0(sK1,sK2)) = sK2,
inference(superposition,[status(thm)],[c_69,c_61]) ).
cnf(c_1395,plain,
( ~ int_leq(int_one,plus(sK1,sK0(sK1,sK2)))
| ~ int_less(int_zero,sK0(sK1,sK2))
| ~ int_leq(X0,sK1)
| ~ int_leq(int_one,X0)
| ~ int_leq(sK1,n)
| ~ int_leq(sK2,n)
| ~ int_less(int_zero,sK1)
| a(X0,plus(X0,sK0(sK1,sK2))) = real_zero ),
inference(superposition,[status(thm)],[c_1181,c_140]) ).
cnf(c_1404,plain,
( ~ int_less(int_zero,sK0(sK1,sK2))
| ~ int_leq(X0,sK1)
| ~ int_leq(int_one,X0)
| ~ int_leq(int_one,sK2)
| ~ int_leq(sK1,n)
| ~ int_leq(sK2,n)
| ~ int_less(int_zero,sK1)
| a(X0,plus(X0,sK0(sK1,sK2))) = real_zero ),
inference(light_normalisation,[status(thm)],[c_1395,c_1181]) ).
cnf(c_1405,plain,
( ~ int_less(int_zero,sK0(sK1,sK2))
| ~ int_leq(X0,sK1)
| ~ int_leq(int_one,X0)
| ~ int_leq(sK1,n)
| a(X0,plus(X0,sK0(sK1,sK2))) = real_zero ),
inference(forward_subsumption_resolution,[status(thm)],[c_1404,c_803,c_68,c_1034]) ).
cnf(c_1423,plain,
( ~ int_leq(X0,sK1)
| ~ int_leq(int_one,X0)
| ~ int_leq(sK1,n)
| a(X0,plus(X0,sK0(sK1,sK2))) = real_zero ),
inference(global_subsumption_just,[status(thm)],[c_1405,c_69,c_1007,c_1405]) ).
cnf(c_1438,plain,
( ~ int_leq(sK1,n)
| ~ int_leq(sK1,sK1)
| a(sK1,plus(sK1,sK0(sK1,sK2))) = real_zero ),
inference(superposition,[status(thm)],[c_70,c_1423]) ).
cnf(c_1447,plain,
( ~ int_leq(sK1,n)
| ~ int_leq(sK1,sK1)
| a(sK1,sK2) = real_zero ),
inference(light_normalisation,[status(thm)],[c_1438,c_1181]) ).
cnf(c_1448,plain,
~ int_leq(sK1,n),
inference(forward_subsumption_resolution,[status(thm)],[c_1447,c_67,c_49]) ).
cnf(c_1449,plain,
n = sK2,
inference(backward_subsumption_resolution,[status(thm)],[c_1114,c_1448]) ).
cnf(c_1459,plain,
int_leq(sK1,n),
inference(demodulation,[status(thm)],[c_795,c_1449]) ).
cnf(c_1473,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1448,c_1459]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV486+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 03:55:23 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.77/1.15 % SZS status Started for theBenchmark.p
% 3.77/1.15 % SZS status Theorem for theBenchmark.p
% 3.77/1.15
% 3.77/1.15 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.77/1.15
% 3.77/1.15 ------ iProver source info
% 3.77/1.15
% 3.77/1.15 git: date: 2023-05-31 18:12:56 +0000
% 3.77/1.15 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.77/1.15 git: non_committed_changes: false
% 3.77/1.15 git: last_make_outside_of_git: false
% 3.77/1.15
% 3.77/1.15 ------ Parsing...
% 3.77/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.77/1.15
% 3.77/1.15 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 3.77/1.15
% 3.77/1.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.77/1.15
% 3.77/1.15 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.77/1.15 ------ Proving...
% 3.77/1.15 ------ Problem Properties
% 3.77/1.15
% 3.77/1.15
% 3.77/1.15 clauses 22
% 3.77/1.15 conjectures 4
% 3.77/1.15 EPR 13
% 3.77/1.15 Horn 20
% 3.77/1.15 unary 10
% 3.77/1.15 binary 7
% 3.77/1.15 lits 49
% 3.77/1.15 lits eq 8
% 3.77/1.15 fd_pure 0
% 3.77/1.15 fd_pseudo 0
% 3.77/1.15 fd_cond 0
% 3.77/1.15 fd_pseudo_cond 1
% 3.77/1.15 AC symbols 0
% 3.77/1.15
% 3.77/1.15 ------ Schedule dynamic 5 is on
% 3.77/1.15
% 3.77/1.15 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.77/1.15
% 3.77/1.15
% 3.77/1.15 ------
% 3.77/1.15 Current options:
% 3.77/1.15 ------
% 3.77/1.15
% 3.77/1.15
% 3.77/1.15
% 3.77/1.15
% 3.77/1.15 ------ Proving...
% 3.77/1.15
% 3.77/1.15
% 3.77/1.15 % SZS status Theorem for theBenchmark.p
% 3.77/1.15
% 3.77/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.77/1.15
% 3.77/1.16
%------------------------------------------------------------------------------