TSTP Solution File: SWV381+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWV381+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n010.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 22:32:47 EDT 2023
% Result : Theorem 3.69s 1.13s
% Output : CNFRefutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 10 unt; 0 def)
% Number of atoms : 129 ( 8 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 129 ( 55 ~; 50 |; 12 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 117 ( 0 sgn; 65 !; 9 ?)
% 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(f10,axiom,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
<=> ! [X2] :
( contains_pq(X0,X2)
=> less_than(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10) ).
fof(f53,axiom,
! [X0] : findmin_cpq_res(X0) = removemin_cpq_res(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
fof(f63,axiom,
! [X0,X1,X2,X3] :
( contains_cpq(triple(X0,X1,X2),X3)
<=> contains_pq(i(triple(X0,X1,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l17_li56) ).
fof(f64,axiom,
! [X0,X1,X2] :
( ? [X3] :
( strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
& contains_cpq(triple(X0,X1,X2),X3) )
=> ~ phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l17_l18) ).
fof(f65,conjecture,
! [X0,X1,X2] :
( phi(findmin_cpq_eff(triple(X0,X1,X2)))
=> issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l17_co) ).
fof(f66,negated_conjecture,
~ ! [X0,X1,X2] :
( phi(findmin_cpq_eff(triple(X0,X1,X2)))
=> issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
inference(negated_conjecture,[],[f65]) ).
fof(f75,plain,
! [X0,X1] :
( ! [X2] :
( contains_pq(X0,X2)
=> less_than(X1,X2) )
=> issmallestelement_pq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f76,plain,
! [X0,X1] :
( ( ~ less_than(X1,X0)
& less_than(X0,X1) )
=> strictly_less_than(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f79,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(ennf_transformation,[],[f76]) ).
fof(f80,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(flattening,[],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
| ? [X2] :
( ~ less_than(X1,X2)
& contains_pq(X0,X2) ) ),
inference(ennf_transformation,[],[f75]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| ! [X3] :
( ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
| ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
inference(ennf_transformation,[],[f64]) ).
fof(f118,plain,
? [X0,X1,X2] :
( ~ issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2)))
& phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(ennf_transformation,[],[f66]) ).
fof(f121,plain,
! [X0,X1] :
( ? [X2] :
( ~ less_than(X1,X2)
& contains_pq(X0,X2) )
=> ( ~ less_than(X1,sK0(X0,X1))
& contains_pq(X0,sK0(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f122,plain,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
| ( ~ less_than(X1,sK0(X0,X1))
& contains_pq(X0,sK0(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f81,f121]) ).
fof(f133,plain,
! [X0,X1,X2,X3] :
( ( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_pq(i(triple(X0,X1,X2)),X3) )
& ( contains_pq(i(triple(X0,X1,X2)),X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f134,plain,
( ? [X0,X1,X2] :
( ~ issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2)))
& phi(findmin_cpq_eff(triple(X0,X1,X2))) )
=> ( ~ issmallestelement_pq(i(triple(sK2,sK3,sK4)),findmin_cpq_res(triple(sK2,sK3,sK4)))
& phi(findmin_cpq_eff(triple(sK2,sK3,sK4))) ) ),
introduced(choice_axiom,[]) ).
fof(f135,plain,
( ~ issmallestelement_pq(i(triple(sK2,sK3,sK4)),findmin_cpq_res(triple(sK2,sK3,sK4)))
& phi(findmin_cpq_eff(triple(sK2,sK3,sK4))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f118,f134]) ).
fof(f137,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
fof(f139,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f147,plain,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
| contains_pq(X0,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f122]) ).
fof(f148,plain,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
| ~ less_than(X1,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f122]) ).
fof(f198,plain,
! [X0] : findmin_cpq_res(X0) = removemin_cpq_res(X0),
inference(cnf_transformation,[],[f53]) ).
fof(f206,plain,
! [X2,X3,X0,X1] :
( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_pq(i(triple(X0,X1,X2)),X3) ),
inference(cnf_transformation,[],[f133]) ).
fof(f207,plain,
! [X2,X3,X0,X1] :
( ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
| ~ contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[],[f117]) ).
fof(f208,plain,
phi(findmin_cpq_eff(triple(sK2,sK3,sK4))),
inference(cnf_transformation,[],[f135]) ).
fof(f209,plain,
~ issmallestelement_pq(i(triple(sK2,sK3,sK4)),findmin_cpq_res(triple(sK2,sK3,sK4))),
inference(cnf_transformation,[],[f135]) ).
fof(f214,plain,
! [X2,X3,X0,X1] :
( ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| ~ strictly_less_than(X3,removemin_cpq_res(triple(X0,X1,X2)))
| ~ contains_cpq(triple(X0,X1,X2),X3) ),
inference(definition_unfolding,[],[f207,f198]) ).
fof(f215,plain,
~ issmallestelement_pq(i(triple(sK2,sK3,sK4)),removemin_cpq_res(triple(sK2,sK3,sK4))),
inference(definition_unfolding,[],[f209,f198]) ).
cnf(c_50,plain,
( less_than(X0,X1)
| less_than(X1,X0) ),
inference(cnf_transformation,[],[f137]) ).
cnf(c_52,plain,
( ~ less_than(X0,X1)
| less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
cnf(c_60,plain,
( ~ less_than(X0,sK0(X1,X0))
| issmallestelement_pq(X1,X0) ),
inference(cnf_transformation,[],[f148]) ).
cnf(c_61,plain,
( contains_pq(X0,sK0(X0,X1))
| issmallestelement_pq(X0,X1) ),
inference(cnf_transformation,[],[f147]) ).
cnf(c_116,plain,
( ~ contains_pq(i(triple(X0,X1,X2)),X3)
| contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[],[f206]) ).
cnf(c_118,plain,
( ~ strictly_less_than(X0,removemin_cpq_res(triple(X1,X2,X3)))
| ~ contains_cpq(triple(X1,X2,X3),X0)
| ~ phi(findmin_cpq_eff(triple(X1,X2,X3))) ),
inference(cnf_transformation,[],[f214]) ).
cnf(c_119,negated_conjecture,
~ issmallestelement_pq(i(triple(sK2,sK3,sK4)),removemin_cpq_res(triple(sK2,sK3,sK4))),
inference(cnf_transformation,[],[f215]) ).
cnf(c_120,negated_conjecture,
phi(findmin_cpq_eff(triple(sK2,sK3,sK4))),
inference(cnf_transformation,[],[f208]) ).
cnf(c_176,plain,
( less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_50,c_52]) ).
cnf(c_177,plain,
( less_than(X0,X1)
| strictly_less_than(X1,X0) ),
inference(renaming,[status(thm)],[c_176]) ).
cnf(c_189,plain,
( less_than(X0,X1)
| strictly_less_than(X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_177]) ).
cnf(c_197,plain,
( ~ less_than(X0,sK0(X1,X0))
| issmallestelement_pq(X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_60]) ).
cnf(c_199,plain,
( issmallestelement_pq(X0,X1)
| contains_pq(X0,sK0(X0,X1)) ),
inference(prop_impl_just,[status(thm)],[c_61]) ).
cnf(c_200,plain,
( contains_pq(X0,sK0(X0,X1))
| issmallestelement_pq(X0,X1) ),
inference(renaming,[status(thm)],[c_199]) ).
cnf(c_1023,plain,
( removemin_cpq_res(triple(X0,X1,X2)) != X3
| X4 != X5
| ~ contains_cpq(triple(X0,X1,X2),X4)
| ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| less_than(X3,X5) ),
inference(resolution_lifted,[status(thm)],[c_118,c_189]) ).
cnf(c_1024,plain,
( ~ contains_cpq(triple(X0,X1,X2),X3)
| ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| less_than(removemin_cpq_res(triple(X0,X1,X2)),X3) ),
inference(unflattening,[status(thm)],[c_1023]) ).
cnf(c_1351,plain,
( removemin_cpq_res(triple(sK2,sK3,sK4)) != X0
| i(triple(sK2,sK3,sK4)) != X1
| ~ less_than(X0,sK0(X1,X0)) ),
inference(resolution_lifted,[status(thm)],[c_197,c_119]) ).
cnf(c_1352,plain,
~ less_than(removemin_cpq_res(triple(sK2,sK3,sK4)),sK0(i(triple(sK2,sK3,sK4)),removemin_cpq_res(triple(sK2,sK3,sK4)))),
inference(unflattening,[status(thm)],[c_1351]) ).
cnf(c_1356,plain,
( removemin_cpq_res(triple(sK2,sK3,sK4)) != X1
| i(triple(sK2,sK3,sK4)) != X0
| contains_pq(X0,sK0(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_200,c_119]) ).
cnf(c_1357,plain,
contains_pq(i(triple(sK2,sK3,sK4)),sK0(i(triple(sK2,sK3,sK4)),removemin_cpq_res(triple(sK2,sK3,sK4)))),
inference(unflattening,[status(thm)],[c_1356]) ).
cnf(c_4580,plain,
( ~ contains_cpq(triple(sK2,sK3,sK4),X0)
| ~ phi(findmin_cpq_eff(triple(sK2,sK3,sK4)))
| less_than(removemin_cpq_res(triple(sK2,sK3,sK4)),X0) ),
inference(instantiation,[status(thm)],[c_1024]) ).
cnf(c_5021,plain,
( ~ contains_pq(i(triple(sK2,sK3,sK4)),sK0(i(triple(sK2,sK3,sK4)),removemin_cpq_res(triple(sK2,sK3,sK4))))
| contains_cpq(triple(sK2,sK3,sK4),sK0(i(triple(sK2,sK3,sK4)),removemin_cpq_res(triple(sK2,sK3,sK4)))) ),
inference(instantiation,[status(thm)],[c_116]) ).
cnf(c_8494,plain,
( ~ contains_cpq(triple(sK2,sK3,sK4),sK0(i(triple(sK2,sK3,sK4)),removemin_cpq_res(triple(sK2,sK3,sK4))))
| ~ phi(findmin_cpq_eff(triple(sK2,sK3,sK4)))
| less_than(removemin_cpq_res(triple(sK2,sK3,sK4)),sK0(i(triple(sK2,sK3,sK4)),removemin_cpq_res(triple(sK2,sK3,sK4)))) ),
inference(instantiation,[status(thm)],[c_4580]) ).
cnf(c_8495,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_8494,c_5021,c_1357,c_1352,c_120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : SWV381+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.16 % Command : run_iprover %s %d THM
% 0.12/0.37 % Computer : n010.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8042.1875MB
% 0.12/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Tue Aug 29 03:30:19 EDT 2023
% 0.12/0.37 % CPUTime :
% 0.19/0.48 Running first-order theorem proving
% 0.19/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.69/1.13 % SZS status Started for theBenchmark.p
% 3.69/1.13 % SZS status Theorem for theBenchmark.p
% 3.69/1.13
% 3.69/1.13 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.69/1.13
% 3.69/1.13 ------ iProver source info
% 3.69/1.13
% 3.69/1.13 git: date: 2023-05-31 18:12:56 +0000
% 3.69/1.13 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.69/1.13 git: non_committed_changes: false
% 3.69/1.13 git: last_make_outside_of_git: false
% 3.69/1.13
% 3.69/1.13 ------ Parsing...
% 3.69/1.13 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.69/1.13
% 3.69/1.13 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 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
% 3.69/1.13
% 3.69/1.13 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.69/1.13
% 3.69/1.13 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.69/1.13 ------ Proving...
% 3.69/1.13 ------ Problem Properties
% 3.69/1.13
% 3.69/1.13
% 3.69/1.13 clauses 69
% 3.69/1.13 conjectures 2
% 3.69/1.13 EPR 9
% 3.69/1.13 Horn 52
% 3.69/1.13 unary 25
% 3.69/1.13 binary 24
% 3.69/1.13 lits 135
% 3.69/1.13 lits eq 40
% 3.69/1.13 fd_pure 0
% 3.69/1.13 fd_pseudo 0
% 3.69/1.13 fd_cond 5
% 3.69/1.13 fd_pseudo_cond 7
% 3.69/1.13 AC symbols 0
% 3.69/1.13
% 3.69/1.13 ------ Schedule dynamic 5 is on
% 3.69/1.13
% 3.69/1.13 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.69/1.13
% 3.69/1.13
% 3.69/1.13 ------
% 3.69/1.13 Current options:
% 3.69/1.13 ------
% 3.69/1.13
% 3.69/1.13
% 3.69/1.13
% 3.69/1.13
% 3.69/1.13 ------ Proving...
% 3.69/1.13
% 3.69/1.13
% 3.69/1.13 % SZS status Theorem for theBenchmark.p
% 3.69/1.13
% 3.69/1.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.69/1.13
% 3.69/1.13
%------------------------------------------------------------------------------