TSTP Solution File: SCT123+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SCT123+1 : TPTP v8.1.2. Released v5.2.0.
% 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 14:17:37 EDT 2023
% Result : Theorem 211.68s 28.85s
% Output : CNFRefutation 211.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 20 unt; 0 def)
% Number of atoms : 60 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 22 ~; 12 |; 4 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-5 aty)
% Number of variables : 99 ( 20 sgn; 55 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ! [X2] : hAPP(X1,X2) = hAPP(X0,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
fof(f110,axiom,
c_Arrow__Order__Mirabelle_OProf = c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Prof__def) ).
fof(f112,axiom,
! [X8,X1,X18,X9,X7] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X7),X2),X9))
=> hBOOL(hAPP(hAPP(c_member(X18),hAPP(X1,X2)),X8)) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X18)),X1),c_FuncSet_OPi(X7,X18,X9,c_COMBK(tc_fun(X18,tc_HOL_Obool),X7,X8)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcsetI) ).
fof(f520,axiom,
! [X88,X87,X18,X7] : hAPP(c_COMBK(X7,X18,X87),X88) = X87,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(f528,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_L),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f529,conjecture,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,v_L)),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(f530,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,v_L)),c_Arrow__Order__Mirabelle_OProf)),
inference(negated_conjecture,[],[f529]) ).
fof(f640,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( hBOOL(hAPP(hAPP(c_member(X4),X5),X3))
=> hBOOL(hAPP(hAPP(c_member(X2),hAPP(X1,X5)),X0)) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X2)),X1),c_FuncSet_OPi(X4,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X4,X0)))) ),
inference(rectify,[],[f112]) ).
fof(f1036,plain,
! [X0,X1,X2,X3] : hAPP(c_COMBK(X3,X2,X1),X0) = X1,
inference(rectify,[],[f520]) ).
fof(f1044,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,v_L)),c_Arrow__Order__Mirabelle_OProf)),
inference(flattening,[],[f530]) ).
fof(f1063,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] : hAPP(X1,X2) != hAPP(X0,X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1143,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X2)),X1),c_FuncSet_OPi(X4,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X4,X0))))
| ? [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),hAPP(X1,X5)),X0))
& hBOOL(hAPP(hAPP(c_member(X4),X5),X3)) ) ),
inference(ennf_transformation,[],[f640]) ).
fof(f1490,plain,
! [X0,X1] :
( ? [X2] : hAPP(X1,X2) != hAPP(X0,X2)
=> hAPP(X1,sK2(X0,X1)) != hAPP(X0,sK2(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f1491,plain,
! [X0,X1] :
( X0 = X1
| hAPP(X1,sK2(X0,X1)) != hAPP(X0,sK2(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f1063,f1490]) ).
fof(f1600,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),hAPP(X1,X5)),X0))
& hBOOL(hAPP(hAPP(c_member(X4),X5),X3)) )
=> ( ~ hBOOL(hAPP(hAPP(c_member(X2),hAPP(X1,sK29(X0,X1,X2,X3,X4))),X0))
& hBOOL(hAPP(hAPP(c_member(X4),sK29(X0,X1,X2,X3,X4)),X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f1601,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X2)),X1),c_FuncSet_OPi(X4,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X4,X0))))
| ( ~ hBOOL(hAPP(hAPP(c_member(X2),hAPP(X1,sK29(X0,X1,X2,X3,X4))),X0))
& hBOOL(hAPP(hAPP(c_member(X4),sK29(X0,X1,X2,X3,X4)),X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f1143,f1600]) ).
fof(f1782,plain,
! [X0,X1] :
( X0 = X1
| hAPP(X1,sK2(X0,X1)) != hAPP(X0,sK2(X0,X1)) ),
inference(cnf_transformation,[],[f1491]) ).
fof(f1983,plain,
c_Arrow__Order__Mirabelle_OProf = c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_OLin)),
inference(cnf_transformation,[],[f110]) ).
fof(f1987,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X2)),X1),c_FuncSet_OPi(X4,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X4,X0))))
| ~ hBOOL(hAPP(hAPP(c_member(X2),hAPP(X1,sK29(X0,X1,X2,X3,X4))),X0)) ),
inference(cnf_transformation,[],[f1601]) ).
fof(f2535,plain,
! [X2,X3,X0,X1] : hAPP(c_COMBK(X3,X2,X1),X0) = X1,
inference(cnf_transformation,[],[f1036]) ).
fof(f2543,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_L),c_Arrow__Order__Mirabelle_OLin)),
inference(cnf_transformation,[],[f528]) ).
fof(f2544,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,v_L)),c_Arrow__Order__Mirabelle_OProf)),
inference(cnf_transformation,[],[f1044]) ).
cnf(c_50,plain,
( hAPP(X0,sK2(X0,X1)) != hAPP(X1,sK2(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f1782]) ).
cnf(c_233,plain,
c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_OLin)) = c_Arrow__Order__Mirabelle_OProf,
inference(cnf_transformation,[],[f1983]) ).
cnf(c_236,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X0),hAPP(X1,sK29(X2,X1,X0,X3,X4))),X2))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X0)),X1),c_FuncSet_OPi(X4,X0,X3,c_COMBK(tc_fun(X0,tc_HOL_Obool),X4,X2)))) ),
inference(cnf_transformation,[],[f1987]) ).
cnf(c_774,plain,
hAPP(c_COMBK(X0,X1,X2),X3) = X2,
inference(cnf_transformation,[],[f2535]) ).
cnf(c_782,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_L),c_Arrow__Order__Mirabelle_OLin)),
inference(cnf_transformation,[],[f2543]) ).
cnf(c_783,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,v_L)),c_Arrow__Order__Mirabelle_OProf)),
inference(cnf_transformation,[],[f2544]) ).
cnf(c_22615,plain,
( hAPP(X0,sK2(X0,c_COMBK(X1,X2,X3))) != X3
| c_COMBK(X1,X2,X3) = X0 ),
inference(superposition,[status(thm)],[c_774,c_50]) ).
cnf(c_22624,plain,
( X0 != X1
| c_COMBK(X2,X3,X0) = c_COMBK(X4,X5,X1) ),
inference(superposition,[status(thm)],[c_774,c_22615]) ).
cnf(c_22625,plain,
c_COMBK(X0,X1,X2) = c_COMBK(X3,X4,X2),
inference(unflattening,[status(thm)],[c_22624]) ).
cnf(c_22647,plain,
c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),c_COMBK(X0,X1,c_Arrow__Order__Mirabelle_OLin)) = c_Arrow__Order__Mirabelle_OProf,
inference(superposition,[status(thm)],[c_22625,c_233]) ).
cnf(c_22751,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3,X0)),c_COMBK(X4,X5,X1)),c_FuncSet_OPi(X3,X0,X6,c_COMBK(tc_fun(X0,tc_HOL_Obool),X3,X2)))) ),
inference(superposition,[status(thm)],[c_774,c_236]) ).
cnf(c_23029,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(X0,X1,v_L)),c_Arrow__Order__Mirabelle_OProf)),
inference(superposition,[status(thm)],[c_22625,c_783]) ).
cnf(c_23052,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(X1,X2,X0)),c_Arrow__Order__Mirabelle_OProf)) ),
inference(superposition,[status(thm)],[c_22647,c_22751]) ).
cnf(c_24328,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_L),c_Arrow__Order__Mirabelle_OLin)),
inference(superposition,[status(thm)],[c_23052,c_23029]) ).
cnf(c_24329,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_24328,c_782]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SCT123+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.13 % 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 : Thu Aug 24 16:24:39 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 211.68/28.85 % SZS status Started for theBenchmark.p
% 211.68/28.85 % SZS status Theorem for theBenchmark.p
% 211.68/28.85
% 211.68/28.85 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 211.68/28.85
% 211.68/28.85 ------ iProver source info
% 211.68/28.85
% 211.68/28.85 git: date: 2023-05-31 18:12:56 +0000
% 211.68/28.85 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 211.68/28.85 git: non_committed_changes: false
% 211.68/28.85 git: last_make_outside_of_git: false
% 211.68/28.85
% 211.68/28.85 ------ Parsing...
% 211.68/28.85 ------ Clausification by vclausify_rel & Parsing by iProver...
% 211.68/28.85
% 211.68/28.85 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 211.68/28.85
% 211.68/28.85 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 211.68/28.85
% 211.68/28.85 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 211.68/28.85 ------ Proving...
% 211.68/28.85 ------ Problem Properties
% 211.68/28.85
% 211.68/28.85
% 211.68/28.85 clauses 589
% 211.68/28.85 conjectures 1
% 211.68/28.85 EPR 21
% 211.68/28.85 Horn 452
% 211.68/28.85 unary 140
% 211.68/28.85 binary 266
% 211.68/28.85 lits 1282
% 211.68/28.85 lits eq 324
% 211.68/28.85 fd_pure 0
% 211.68/28.85 fd_pseudo 0
% 211.68/28.85 fd_cond 0
% 211.68/28.85 fd_pseudo_cond 79
% 211.68/28.85 AC symbols 0
% 211.68/28.85
% 211.68/28.85 ------ Input Options Time Limit: Unbounded
% 211.68/28.85
% 211.68/28.85
% 211.68/28.85 ------
% 211.68/28.85 Current options:
% 211.68/28.85 ------
% 211.68/28.85
% 211.68/28.85
% 211.68/28.85
% 211.68/28.85
% 211.68/28.85 ------ Proving...
% 211.68/28.85
% 211.68/28.85
% 211.68/28.85 % SZS status Theorem for theBenchmark.p
% 211.68/28.85
% 211.68/28.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 211.68/28.85
% 211.68/28.86
%------------------------------------------------------------------------------