TSTP Solution File: SWV409+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWV409+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n014.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 03:14:21 EDT 2024
% Result : Theorem 6.21s 1.69s
% Output : CNFRefutation 6.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 10 unt; 0 def)
% Number of atoms : 188 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 225 ( 96 ~; 86 |; 34 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 134 ( 0 sgn 77 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
fof(f4,axiom,
! [X0,X1] :
( strictly_less_than(X0,X1)
<=> ( ~ less_than(X1,X0)
& less_than(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).
fof(f19,axiom,
! [X0,X1] :
( contains_slb(X0,X1)
=> ? [X2] : pair_in_list(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_li4647) ).
fof(f20,axiom,
! [X0,X1,X2,X3] :
( ( strictly_less_than(X2,X3)
& strictly_less_than(X1,X3)
& pair_in_list(X0,X1,X2) )
=> pair_in_list(update_slb(X0,X3),X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_l48) ).
fof(f21,axiom,
! [X0,X1,X2,X3] :
( ( less_than(X3,X2)
& strictly_less_than(X1,X3)
& pair_in_list(X0,X1,X2) )
=> ? [X4] :
( less_than(X3,X4)
& pair_in_list(update_slb(X0,X3),X1,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_l49) ).
fof(f22,conjecture,
! [X0,X1,X2] :
( ( strictly_less_than(X1,X2)
& contains_slb(X0,X1) )
=> ( ? [X3] :
( less_than(X2,X3)
& pair_in_list(update_slb(X0,X2),X1,X3) )
| pair_in_list(update_slb(X0,X2),X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_co) ).
fof(f23,negated_conjecture,
~ ! [X0,X1,X2] :
( ( strictly_less_than(X1,X2)
& contains_slb(X0,X1) )
=> ( ? [X3] :
( less_than(X2,X3)
& pair_in_list(update_slb(X0,X2),X1,X3) )
| pair_in_list(update_slb(X0,X2),X1,X2) ) ),
inference(negated_conjecture,[],[f22]) ).
fof(f32,plain,
! [X0,X1] :
( ? [X2] : pair_in_list(X0,X1,X2)
| ~ contains_slb(X0,X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( pair_in_list(update_slb(X0,X3),X1,X3)
| ~ strictly_less_than(X2,X3)
| ~ strictly_less_than(X1,X3)
| ~ pair_in_list(X0,X1,X2) ),
inference(ennf_transformation,[],[f20]) ).
fof(f34,plain,
! [X0,X1,X2,X3] :
( pair_in_list(update_slb(X0,X3),X1,X3)
| ~ strictly_less_than(X2,X3)
| ~ strictly_less_than(X1,X3)
| ~ pair_in_list(X0,X1,X2) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( less_than(X3,X4)
& pair_in_list(update_slb(X0,X3),X1,X4) )
| ~ less_than(X3,X2)
| ~ strictly_less_than(X1,X3)
| ~ pair_in_list(X0,X1,X2) ),
inference(ennf_transformation,[],[f21]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( less_than(X3,X4)
& pair_in_list(update_slb(X0,X3),X1,X4) )
| ~ less_than(X3,X2)
| ~ strictly_less_than(X1,X3)
| ~ pair_in_list(X0,X1,X2) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
? [X0,X1,X2] :
( ! [X3] :
( ~ less_than(X2,X3)
| ~ pair_in_list(update_slb(X0,X2),X1,X3) )
& ~ pair_in_list(update_slb(X0,X2),X1,X2)
& strictly_less_than(X1,X2)
& contains_slb(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f38,plain,
? [X0,X1,X2] :
( ! [X3] :
( ~ less_than(X2,X3)
| ~ pair_in_list(update_slb(X0,X2),X1,X3) )
& ~ pair_in_list(update_slb(X0,X2),X1,X2)
& strictly_less_than(X1,X2)
& contains_slb(X0,X1) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( ( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) )
& ( ( ~ less_than(X1,X0)
& less_than(X0,X1) )
| ~ strictly_less_than(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f40,plain,
! [X0,X1] :
( ( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) )
& ( ( ~ less_than(X1,X0)
& less_than(X0,X1) )
| ~ strictly_less_than(X0,X1) ) ),
inference(flattening,[],[f39]) ).
fof(f45,plain,
! [X0,X1] :
( ? [X2] : pair_in_list(X0,X1,X2)
=> pair_in_list(X0,X1,sK0(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
! [X0,X1] :
( pair_in_list(X0,X1,sK0(X0,X1))
| ~ contains_slb(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f32,f45]) ).
fof(f47,plain,
! [X0,X1,X3] :
( ? [X4] :
( less_than(X3,X4)
& pair_in_list(update_slb(X0,X3),X1,X4) )
=> ( less_than(X3,sK1(X0,X1,X3))
& pair_in_list(update_slb(X0,X3),X1,sK1(X0,X1,X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( ( less_than(X3,sK1(X0,X1,X3))
& pair_in_list(update_slb(X0,X3),X1,sK1(X0,X1,X3)) )
| ~ less_than(X3,X2)
| ~ strictly_less_than(X1,X3)
| ~ pair_in_list(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f36,f47]) ).
fof(f49,plain,
( ? [X0,X1,X2] :
( ! [X3] :
( ~ less_than(X2,X3)
| ~ pair_in_list(update_slb(X0,X2),X1,X3) )
& ~ pair_in_list(update_slb(X0,X2),X1,X2)
& strictly_less_than(X1,X2)
& contains_slb(X0,X1) )
=> ( ! [X3] :
( ~ less_than(sK4,X3)
| ~ pair_in_list(update_slb(sK2,sK4),sK3,X3) )
& ~ pair_in_list(update_slb(sK2,sK4),sK3,sK4)
& strictly_less_than(sK3,sK4)
& contains_slb(sK2,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f50,plain,
( ! [X3] :
( ~ less_than(sK4,X3)
| ~ pair_in_list(update_slb(sK2,sK4),sK3,X3) )
& ~ pair_in_list(update_slb(sK2,sK4),sK3,sK4)
& strictly_less_than(sK3,sK4)
& contains_slb(sK2,sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f38,f49]) ).
fof(f52,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
fof(f56,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f76,plain,
! [X0,X1] :
( pair_in_list(X0,X1,sK0(X0,X1))
| ~ contains_slb(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f77,plain,
! [X2,X3,X0,X1] :
( pair_in_list(update_slb(X0,X3),X1,X3)
| ~ strictly_less_than(X2,X3)
| ~ strictly_less_than(X1,X3)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( pair_in_list(update_slb(X0,X3),X1,sK1(X0,X1,X3))
| ~ less_than(X3,X2)
| ~ strictly_less_than(X1,X3)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f79,plain,
! [X2,X3,X0,X1] :
( less_than(X3,sK1(X0,X1,X3))
| ~ less_than(X3,X2)
| ~ strictly_less_than(X1,X3)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f80,plain,
contains_slb(sK2,sK3),
inference(cnf_transformation,[],[f50]) ).
fof(f81,plain,
strictly_less_than(sK3,sK4),
inference(cnf_transformation,[],[f50]) ).
fof(f82,plain,
~ pair_in_list(update_slb(sK2,sK4),sK3,sK4),
inference(cnf_transformation,[],[f50]) ).
fof(f83,plain,
! [X3] :
( ~ less_than(sK4,X3)
| ~ pair_in_list(update_slb(sK2,sK4),sK3,X3) ),
inference(cnf_transformation,[],[f50]) ).
cnf(c_50,plain,
( less_than(X0,X1)
| less_than(X1,X0) ),
inference(cnf_transformation,[],[f52]) ).
cnf(c_52,plain,
( ~ less_than(X0,X1)
| less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
cnf(c_74,plain,
( ~ contains_slb(X0,X1)
| pair_in_list(X0,X1,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f76]) ).
cnf(c_75,plain,
( ~ pair_in_list(X0,X1,X2)
| ~ strictly_less_than(X1,X3)
| ~ strictly_less_than(X2,X3)
| pair_in_list(update_slb(X0,X3),X1,X3) ),
inference(cnf_transformation,[],[f77]) ).
cnf(c_76,plain,
( ~ pair_in_list(X0,X1,X2)
| ~ less_than(X3,X2)
| ~ strictly_less_than(X1,X3)
| less_than(X3,sK1(X0,X1,X3)) ),
inference(cnf_transformation,[],[f79]) ).
cnf(c_77,plain,
( ~ pair_in_list(X0,X1,X2)
| ~ less_than(X3,X2)
| ~ strictly_less_than(X1,X3)
| pair_in_list(update_slb(X0,X3),X1,sK1(X0,X1,X3)) ),
inference(cnf_transformation,[],[f78]) ).
cnf(c_78,negated_conjecture,
( ~ pair_in_list(update_slb(sK2,sK4),sK3,X0)
| ~ less_than(sK4,X0) ),
inference(cnf_transformation,[],[f83]) ).
cnf(c_79,negated_conjecture,
~ pair_in_list(update_slb(sK2,sK4),sK3,sK4),
inference(cnf_transformation,[],[f82]) ).
cnf(c_80,negated_conjecture,
strictly_less_than(sK3,sK4),
inference(cnf_transformation,[],[f81]) ).
cnf(c_81,negated_conjecture,
contains_slb(sK2,sK3),
inference(cnf_transformation,[],[f80]) ).
cnf(c_98,plain,
( less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_50,c_52]) ).
cnf(c_99,plain,
( less_than(X0,X1)
| strictly_less_than(X1,X0) ),
inference(renaming,[status(thm)],[c_98]) ).
cnf(c_332,plain,
( strictly_less_than(X1,X0)
| less_than(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_99]) ).
cnf(c_333,plain,
( less_than(X0,X1)
| strictly_less_than(X1,X0) ),
inference(renaming,[status(thm)],[c_332]) ).
cnf(c_1249,plain,
( ~ contains_slb(sK2,sK3)
| pair_in_list(sK2,sK3,sK0(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_74]) ).
cnf(c_1404,plain,
( ~ pair_in_list(X0,X1,X2)
| ~ strictly_less_than(X1,sK4)
| ~ strictly_less_than(X2,sK4)
| pair_in_list(update_slb(X0,sK4),X1,sK4) ),
inference(instantiation,[status(thm)],[c_75]) ).
cnf(c_2567,plain,
( ~ pair_in_list(sK2,sK3,sK0(sK2,sK3))
| ~ strictly_less_than(sK0(sK2,sK3),sK4)
| ~ strictly_less_than(sK3,sK4)
| pair_in_list(update_slb(sK2,sK4),sK3,sK4) ),
inference(instantiation,[status(thm)],[c_1404]) ).
cnf(c_2648,plain,
( ~ strictly_less_than(sK0(X0,X1),X2)
| ~ strictly_less_than(X1,X2)
| ~ contains_slb(X0,X1)
| pair_in_list(update_slb(X0,X2),X1,X2) ),
inference(superposition,[status(thm)],[c_74,c_75]) ).
cnf(c_2672,plain,
( ~ less_than(X0,sK0(X1,X2))
| ~ strictly_less_than(X2,X0)
| ~ contains_slb(X1,X2)
| less_than(X0,sK1(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_74,c_76]) ).
cnf(c_2682,plain,
( ~ less_than(X0,sK0(X1,X2))
| ~ strictly_less_than(X2,X0)
| ~ contains_slb(X1,X2)
| pair_in_list(update_slb(X1,X0),X2,sK1(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_74,c_77]) ).
cnf(c_2777,plain,
( ~ strictly_less_than(sK0(sK2,sK3),sK4)
| ~ strictly_less_than(sK3,sK4)
| ~ contains_slb(sK2,sK3) ),
inference(superposition,[status(thm)],[c_2648,c_79]) ).
cnf(c_2920,plain,
~ strictly_less_than(sK0(sK2,sK3),sK4),
inference(global_subsumption_just,[status(thm)],[c_2777,c_81,c_80,c_79,c_1249,c_2567]) ).
cnf(c_2922,plain,
less_than(sK4,sK0(sK2,sK3)),
inference(superposition,[status(thm)],[c_333,c_2920]) ).
cnf(c_3683,plain,
( ~ less_than(sK4,sK1(sK2,sK3,sK4))
| ~ less_than(sK4,sK0(sK2,sK3))
| ~ strictly_less_than(sK3,sK4)
| ~ contains_slb(sK2,sK3) ),
inference(superposition,[status(thm)],[c_2682,c_78]) ).
cnf(c_3802,plain,
~ less_than(sK4,sK1(sK2,sK3,sK4)),
inference(global_subsumption_just,[status(thm)],[c_3683,c_81,c_80,c_2922,c_3683]) ).
cnf(c_3807,plain,
( ~ less_than(sK4,sK0(sK2,sK3))
| ~ strictly_less_than(sK3,sK4)
| ~ contains_slb(sK2,sK3) ),
inference(superposition,[status(thm)],[c_2672,c_3802]) ).
cnf(c_3808,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3807,c_2922,c_80,c_81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWV409+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 2 23:59:02 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 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
% 6.21/1.69 % SZS status Started for theBenchmark.p
% 6.21/1.69 % SZS status Theorem for theBenchmark.p
% 6.21/1.69
% 6.21/1.69 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 6.21/1.69
% 6.21/1.69 ------ iProver source info
% 6.21/1.69
% 6.21/1.69 git: date: 2024-05-02 19:28:25 +0000
% 6.21/1.69 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 6.21/1.69 git: non_committed_changes: false
% 6.21/1.69
% 6.21/1.69 ------ Parsing...
% 6.21/1.69 ------ Clausification by vclausify_rel & Parsing by iProver...
% 6.21/1.69
% 6.21/1.69 ------ 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
% 6.21/1.69
% 6.21/1.69 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 6.21/1.69
% 6.21/1.69 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.21/1.69 ------ Proving...
% 6.21/1.69 ------ Problem Properties
% 6.21/1.69
% 6.21/1.69
% 6.21/1.69 clauses 31
% 6.21/1.69 conjectures 4
% 6.21/1.69 EPR 10
% 6.21/1.69 Horn 23
% 6.21/1.69 unary 13
% 6.21/1.69 binary 9
% 6.21/1.69 lits 61
% 6.21/1.69 lits eq 13
% 6.21/1.69 fd_pure 0
% 6.21/1.69 fd_pseudo 0
% 6.21/1.69 fd_cond 0
% 6.21/1.69 fd_pseudo_cond 5
% 6.21/1.69 AC symbols 0
% 6.21/1.69
% 6.21/1.69 ------ Input Options Time Limit: Unbounded
% 6.21/1.69
% 6.21/1.69
% 6.21/1.69 ------
% 6.21/1.69 Current options:
% 6.21/1.69 ------
% 6.21/1.69
% 6.21/1.69
% 6.21/1.69
% 6.21/1.69
% 6.21/1.69 ------ Proving...
% 6.21/1.69
% 6.21/1.69
% 6.21/1.69 % SZS status Theorem for theBenchmark.p
% 6.21/1.69
% 6.21/1.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.21/1.69
% 6.21/1.69
%------------------------------------------------------------------------------