TSTP Solution File: ALG018+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : ALG018+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n007.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 02:03:13 EDT 2024
% Result : Theorem 0.42s 1.11s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 59 ( 12 unt; 0 def)
% Number of atoms : 198 ( 56 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 222 ( 83 ~; 69 |; 37 &)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 100 ( 0 sgn 71 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> sorti2(op2(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f3,axiom,
? [X0] :
( ! [X1] :
( sorti1(X1)
=> op1(X1,X1) = X0 )
& sorti1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
~ ? [X0] :
( ! [X1] :
( sorti2(X1)
=> op2(X1,X1) = X0 )
& sorti2(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f5,conjecture,
( ( ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) )
& ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) ) )
=> ~ ( ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f6,negated_conjecture,
~ ( ( ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) )
& ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) ) )
=> ~ ( ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) ) ) ),
inference(negated_conjecture,[],[f5]) ).
fof(f7,plain,
~ ( ( ! [X0] :
( sorti2(X0)
=> sorti1(j(X0)) )
& ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) ) )
=> ~ ( ! [X2] :
( sorti1(X2)
=> j(h(X2)) = X2 )
& ! [X3] :
( sorti2(X3)
=> h(j(X3)) = X3 )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X6] :
( sorti1(X6)
=> ! [X7] :
( sorti1(X7)
=> h(op1(X6,X7)) = op2(h(X6),h(X7)) ) ) ) ),
inference(rectify,[],[f6]) ).
fof(f9,plain,
! [X0] :
( ! [X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1) )
| ~ sorti2(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f10,plain,
? [X0] :
( ! [X1] :
( op1(X1,X1) = X0
| ~ sorti1(X1) )
& sorti1(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f11,plain,
! [X0] :
( ? [X1] :
( op2(X1,X1) != X0
& sorti2(X1) )
| ~ sorti2(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f12,plain,
( ! [X2] :
( j(h(X2)) = X2
| ~ sorti1(X2) )
& ! [X3] :
( h(j(X3)) = X3
| ~ sorti2(X3) )
& ! [X4] :
( ! [X5] :
( j(op2(X4,X5)) = op1(j(X4),j(X5))
| ~ sorti2(X5) )
| ~ sorti2(X4) )
& ! [X6] :
( ! [X7] :
( h(op1(X6,X7)) = op2(h(X6),h(X7))
| ~ sorti1(X7) )
| ~ sorti1(X6) )
& ! [X0] :
( sorti1(j(X0))
| ~ sorti2(X0) )
& ! [X1] :
( sorti2(h(X1))
| ~ sorti1(X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f13,plain,
( ! [X2] :
( j(h(X2)) = X2
| ~ sorti1(X2) )
& ! [X3] :
( h(j(X3)) = X3
| ~ sorti2(X3) )
& ! [X4] :
( ! [X5] :
( j(op2(X4,X5)) = op1(j(X4),j(X5))
| ~ sorti2(X5) )
| ~ sorti2(X4) )
& ! [X6] :
( ! [X7] :
( h(op1(X6,X7)) = op2(h(X6),h(X7))
| ~ sorti1(X7) )
| ~ sorti1(X6) )
& ! [X0] :
( sorti1(j(X0))
| ~ sorti2(X0) )
& ! [X1] :
( sorti2(h(X1))
| ~ sorti1(X1) ) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
( ? [X0] :
( ! [X1] :
( op1(X1,X1) = X0
| ~ sorti1(X1) )
& sorti1(X0) )
=> ( ! [X1] :
( op1(X1,X1) = sK0
| ~ sorti1(X1) )
& sorti1(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
( ! [X1] :
( op1(X1,X1) = sK0
| ~ sorti1(X1) )
& sorti1(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f10,f14]) ).
fof(f16,plain,
! [X0] :
( ? [X1] :
( op2(X1,X1) != X0
& sorti2(X1) )
=> ( op2(sK1(X0),sK1(X0)) != X0
& sorti2(sK1(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X0] :
( ( op2(sK1(X0),sK1(X0)) != X0
& sorti2(sK1(X0)) )
| ~ sorti2(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f11,f16]) ).
fof(f18,plain,
( ! [X0] :
( j(h(X0)) = X0
| ~ sorti1(X0) )
& ! [X1] :
( h(j(X1)) = X1
| ~ sorti2(X1) )
& ! [X2] :
( ! [X3] :
( j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X3) )
| ~ sorti2(X2) )
& ! [X4] :
( ! [X5] :
( h(op1(X4,X5)) = op2(h(X4),h(X5))
| ~ sorti1(X5) )
| ~ sorti1(X4) )
& ! [X6] :
( sorti1(j(X6))
| ~ sorti2(X6) )
& ! [X7] :
( sorti2(h(X7))
| ~ sorti1(X7) ) ),
inference(rectify,[],[f13]) ).
fof(f20,plain,
! [X0,X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f21,plain,
sorti1(sK0),
inference(cnf_transformation,[],[f15]) ).
fof(f22,plain,
! [X1] :
( op1(X1,X1) = sK0
| ~ sorti1(X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
! [X0] :
( sorti2(sK1(X0))
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f24,plain,
! [X0] :
( op2(sK1(X0),sK1(X0)) != X0
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f25,plain,
! [X7] :
( sorti2(h(X7))
| ~ sorti1(X7) ),
inference(cnf_transformation,[],[f18]) ).
fof(f26,plain,
! [X6] :
( sorti1(j(X6))
| ~ sorti2(X6) ),
inference(cnf_transformation,[],[f18]) ).
fof(f28,plain,
! [X2,X3] :
( j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X3)
| ~ sorti2(X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X1] :
( h(j(X1)) = X1
| ~ sorti2(X1) ),
inference(cnf_transformation,[],[f18]) ).
cnf(c_50,plain,
( ~ sorti2(X0)
| ~ sorti2(X1)
| sorti2(op2(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
cnf(c_51,plain,
( ~ sorti1(X0)
| op1(X0,X0) = sK0 ),
inference(cnf_transformation,[],[f22]) ).
cnf(c_52,plain,
sorti1(sK0),
inference(cnf_transformation,[],[f21]) ).
cnf(c_53,plain,
( op2(sK1(X0),sK1(X0)) != X0
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f24]) ).
cnf(c_54,plain,
( ~ sorti2(X0)
| sorti2(sK1(X0)) ),
inference(cnf_transformation,[],[f23]) ).
cnf(c_56,negated_conjecture,
( ~ sorti2(X0)
| h(j(X0)) = X0 ),
inference(cnf_transformation,[],[f29]) ).
cnf(c_57,negated_conjecture,
( ~ sorti2(X0)
| ~ sorti2(X1)
| op1(j(X0),j(X1)) = j(op2(X0,X1)) ),
inference(cnf_transformation,[],[f28]) ).
cnf(c_59,negated_conjecture,
( ~ sorti2(X0)
| sorti1(j(X0)) ),
inference(cnf_transformation,[],[f26]) ).
cnf(c_60,negated_conjecture,
( ~ sorti1(X0)
| sorti2(h(X0)) ),
inference(cnf_transformation,[],[f25]) ).
cnf(c_61,plain,
( ~ sorti1(sK0)
| sorti2(h(sK0)) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_185,negated_conjecture,
( ~ sorti1(X0)
| sorti2(h(X0)) ),
inference(demodulation,[status(thm)],[c_60]) ).
cnf(c_186,negated_conjecture,
( ~ sorti2(X0)
| sorti1(j(X0)) ),
inference(demodulation,[status(thm)],[c_59]) ).
cnf(c_188,negated_conjecture,
( ~ sorti2(X0)
| ~ sorti2(X1)
| op1(j(X0),j(X1)) = j(op2(X0,X1)) ),
inference(demodulation,[status(thm)],[c_57]) ).
cnf(c_189,negated_conjecture,
( ~ sorti2(X0)
| h(j(X0)) = X0 ),
inference(demodulation,[status(thm)],[c_56]) ).
cnf(c_476,plain,
( ~ sorti2(X0)
| h(j(sK1(X0))) = sK1(X0) ),
inference(superposition,[status(thm)],[c_54,c_189]) ).
cnf(c_492,plain,
( ~ sorti2(X0)
| op1(j(X0),j(X0)) = sK0 ),
inference(superposition,[status(thm)],[c_186,c_51]) ).
cnf(c_539,plain,
( ~ sorti2(X0)
| ~ sorti2(X1)
| h(j(op2(X0,X1))) = op2(X0,X1) ),
inference(superposition,[status(thm)],[c_50,c_189]) ).
cnf(c_561,plain,
( ~ sorti1(X0)
| h(j(sK1(h(X0)))) = sK1(h(X0)) ),
inference(superposition,[status(thm)],[c_185,c_476]) ).
cnf(c_575,plain,
( ~ sorti2(h(X0))
| sorti2(sK1(h(X0))) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_576,plain,
( ~ sorti2(h(sK0))
| sorti2(sK1(h(sK0))) ),
inference(instantiation,[status(thm)],[c_575]) ).
cnf(c_622,plain,
h(j(sK1(h(sK0)))) = sK1(h(sK0)),
inference(superposition,[status(thm)],[c_52,c_561]) ).
cnf(c_746,plain,
( ~ sorti1(j(sK1(h(sK0))))
| sorti2(sK1(h(sK0))) ),
inference(superposition,[status(thm)],[c_622,c_185]) ).
cnf(c_749,plain,
sorti2(sK1(h(sK0))),
inference(global_subsumption_just,[status(thm)],[c_746,c_52,c_61,c_576]) ).
cnf(c_751,plain,
( ~ sorti2(X0)
| op1(j(X0),j(sK1(h(sK0)))) = j(op2(X0,sK1(h(sK0)))) ),
inference(superposition,[status(thm)],[c_749,c_188]) ).
cnf(c_754,plain,
op1(j(sK1(h(sK0))),j(sK1(h(sK0)))) = sK0,
inference(superposition,[status(thm)],[c_749,c_492]) ).
cnf(c_954,plain,
( ~ sorti2(X0)
| h(j(op2(X0,sK1(h(sK0))))) = op2(X0,sK1(h(sK0))) ),
inference(superposition,[status(thm)],[c_749,c_539]) ).
cnf(c_2092,plain,
h(j(op2(sK1(h(sK0)),sK1(h(sK0))))) = op2(sK1(h(sK0)),sK1(h(sK0))),
inference(superposition,[status(thm)],[c_749,c_954]) ).
cnf(c_2125,plain,
op1(j(sK1(h(sK0))),j(sK1(h(sK0)))) = j(op2(sK1(h(sK0)),sK1(h(sK0)))),
inference(superposition,[status(thm)],[c_749,c_751]) ).
cnf(c_2129,plain,
j(op2(sK1(h(sK0)),sK1(h(sK0)))) = sK0,
inference(light_normalisation,[status(thm)],[c_2125,c_754]) ).
cnf(c_6336,plain,
op2(sK1(h(sK0)),sK1(h(sK0))) = h(sK0),
inference(light_normalisation,[status(thm)],[c_2092,c_2129]) ).
cnf(c_6338,plain,
( ~ sorti2(sK1(h(sK0)))
| sorti2(h(sK0)) ),
inference(superposition,[status(thm)],[c_6336,c_50]) ).
cnf(c_6339,plain,
~ sorti2(h(sK0)),
inference(superposition,[status(thm)],[c_6336,c_53]) ).
cnf(c_6340,plain,
~ sorti2(sK1(h(sK0))),
inference(forward_subsumption_resolution,[status(thm)],[c_6338,c_6339]) ).
cnf(c_6341,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6340,c_749]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ALG018+1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.11 % Command : run_iprover %s %d THM
% 0.10/0.31 % Computer : n007.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu May 2 22:42:35 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.16/0.41 Running first-order theorem proving
% 0.16/0.41 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
% 0.42/1.11 % SZS status Started for theBenchmark.p
% 0.42/1.11 % SZS status Theorem for theBenchmark.p
% 0.42/1.11
% 0.42/1.11 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.42/1.11
% 0.42/1.11 ------ iProver source info
% 0.42/1.11
% 0.42/1.11 git: date: 2024-05-02 19:28:25 +0000
% 0.42/1.11 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.42/1.11 git: non_committed_changes: false
% 0.42/1.11
% 0.42/1.11 ------ Parsing...
% 0.42/1.11 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.42/1.11
% 0.42/1.11 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 0.42/1.11
% 0.42/1.11 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.42/1.11
% 0.42/1.11 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.42/1.11 ------ Proving...
% 0.42/1.11 ------ Problem Properties
% 0.42/1.11
% 0.42/1.11
% 0.42/1.11 clauses 12
% 0.42/1.11 conjectures 6
% 0.42/1.11 EPR 1
% 0.42/1.11 Horn 12
% 0.42/1.11 unary 1
% 0.42/1.11 binary 7
% 0.42/1.11 lits 27
% 0.42/1.11 lits eq 6
% 0.42/1.11 fd_pure 0
% 0.42/1.11 fd_pseudo 0
% 0.42/1.11 fd_cond 0
% 0.42/1.11 fd_pseudo_cond 0
% 0.42/1.11 AC symbols 0
% 0.42/1.11
% 0.42/1.11 ------ Schedule dynamic 5 is on
% 0.42/1.11
% 0.42/1.11 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.42/1.11
% 0.42/1.11
% 0.42/1.11 ------
% 0.42/1.11 Current options:
% 0.42/1.11 ------
% 0.42/1.11
% 0.42/1.11
% 0.42/1.11
% 0.42/1.11
% 0.42/1.11 ------ Proving...
% 0.42/1.11
% 0.42/1.11
% 0.42/1.11 % SZS status Theorem for theBenchmark.p
% 0.42/1.11
% 0.42/1.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.42/1.12
% 0.42/1.12
%------------------------------------------------------------------------------