TSTP Solution File: ALG019+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : ALG019+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n018.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 3.21s 1.08s
% Output : CNFRefutation 3.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 60 ( 12 unt; 0 def)
% Number of atoms : 201 ( 57 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 226 ( 85 ~; 69 |; 38 &)
% ( 0 <=>; 34 =>; 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 : 102 ( 0 sgn 72 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> sorti1(op1(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f3,axiom,
~ ? [X0] :
( ! [X1] :
( sorti1(X1)
=> op1(X1,X1) = X0 )
& sorti1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
~ ~ ? [X0] :
( ! [X1] :
( sorti2(X1)
=> op2(X1,X1) = X0 )
& sorti2(X0) ),
file('/export/starexec/sandbox2/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/sandbox2/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] :
( ! [X1] :
( sorti2(X1)
=> op2(X1,X1) = X0 )
& sorti2(X0) ),
inference(flattening,[],[f4]) ).
fof(f8,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] :
( sorti1(op1(X0,X1))
| ~ sorti1(X1) )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f11,plain,
! [X0] :
( ? [X1] :
( op1(X1,X1) != X0
& sorti1(X1) )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f12,plain,
? [X0] :
( ! [X1] :
( op2(X1,X1) = X0
| ~ sorti2(X1) )
& sorti2(X0) ),
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(ennf_transformation,[],[f8]) ).
fof(f14,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,[],[f13]) ).
fof(f15,plain,
! [X0] :
( ? [X1] :
( op1(X1,X1) != X0
& sorti1(X1) )
=> ( op1(sK0(X0),sK0(X0)) != X0
& sorti1(sK0(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
! [X0] :
( ( op1(sK0(X0),sK0(X0)) != X0
& sorti1(sK0(X0)) )
| ~ sorti1(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f11,f15]) ).
fof(f17,plain,
( ? [X0] :
( ! [X1] :
( op2(X1,X1) = X0
| ~ sorti2(X1) )
& sorti2(X0) )
=> ( ! [X1] :
( op2(X1,X1) = sK1
| ~ sorti2(X1) )
& sorti2(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
( ! [X1] :
( op2(X1,X1) = sK1
| ~ sorti2(X1) )
& sorti2(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f12,f17]) ).
fof(f19,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,[],[f14]) ).
fof(f20,plain,
! [X0,X1] :
( sorti1(op1(X0,X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f22,plain,
! [X0] :
( sorti1(sK0(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f23,plain,
! [X0] :
( op1(sK0(X0),sK0(X0)) != X0
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f24,plain,
sorti2(sK1),
inference(cnf_transformation,[],[f18]) ).
fof(f25,plain,
! [X1] :
( op2(X1,X1) = sK1
| ~ sorti2(X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f26,plain,
! [X7] :
( sorti2(h(X7))
| ~ sorti1(X7) ),
inference(cnf_transformation,[],[f19]) ).
fof(f27,plain,
! [X6] :
( sorti1(j(X6))
| ~ sorti2(X6) ),
inference(cnf_transformation,[],[f19]) ).
fof(f28,plain,
! [X4,X5] :
( h(op1(X4,X5)) = op2(h(X4),h(X5))
| ~ sorti1(X5)
| ~ sorti1(X4) ),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
! [X0] :
( j(h(X0)) = X0
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f19]) ).
cnf(c_49,plain,
( ~ sorti1(X0)
| ~ sorti1(X1)
| sorti1(op1(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
cnf(c_51,plain,
( op1(sK0(X0),sK0(X0)) != X0
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f23]) ).
cnf(c_52,plain,
( ~ sorti1(X0)
| sorti1(sK0(X0)) ),
inference(cnf_transformation,[],[f22]) ).
cnf(c_53,plain,
( ~ sorti2(X0)
| op2(X0,X0) = sK1 ),
inference(cnf_transformation,[],[f25]) ).
cnf(c_54,plain,
sorti2(sK1),
inference(cnf_transformation,[],[f24]) ).
cnf(c_55,negated_conjecture,
( ~ sorti1(X0)
| j(h(X0)) = X0 ),
inference(cnf_transformation,[],[f31]) ).
cnf(c_58,negated_conjecture,
( ~ sorti1(X0)
| ~ sorti1(X1)
| op2(h(X0),h(X1)) = h(op1(X0,X1)) ),
inference(cnf_transformation,[],[f28]) ).
cnf(c_59,negated_conjecture,
( ~ sorti2(X0)
| sorti1(j(X0)) ),
inference(cnf_transformation,[],[f27]) ).
cnf(c_60,negated_conjecture,
( ~ sorti1(X0)
| sorti2(h(X0)) ),
inference(cnf_transformation,[],[f26]) ).
cnf(c_62,plain,
( ~ sorti2(sK1)
| sorti1(j(sK1)) ),
inference(instantiation,[status(thm)],[c_59]) ).
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_187,negated_conjecture,
( ~ sorti1(X0)
| ~ sorti1(X1)
| op2(h(X0),h(X1)) = h(op1(X0,X1)) ),
inference(demodulation,[status(thm)],[c_58]) ).
cnf(c_190,negated_conjecture,
( ~ sorti1(X0)
| j(h(X0)) = X0 ),
inference(demodulation,[status(thm)],[c_55]) ).
cnf(c_479,plain,
( ~ sorti1(X0)
| j(h(sK0(X0))) = sK0(X0) ),
inference(superposition,[status(thm)],[c_52,c_190]) ).
cnf(c_499,plain,
( ~ sorti1(X0)
| op2(h(X0),h(X0)) = sK1 ),
inference(superposition,[status(thm)],[c_185,c_53]) ).
cnf(c_512,plain,
( ~ sorti1(X0)
| ~ sorti1(X1)
| j(h(op1(X0,X1))) = op1(X0,X1) ),
inference(superposition,[status(thm)],[c_49,c_190]) ).
cnf(c_569,plain,
( ~ sorti2(X0)
| j(h(sK0(j(X0)))) = sK0(j(X0)) ),
inference(superposition,[status(thm)],[c_186,c_479]) ).
cnf(c_583,plain,
( ~ sorti1(j(X0))
| sorti1(sK0(j(X0))) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_584,plain,
( ~ sorti1(j(sK1))
| sorti1(sK0(j(sK1))) ),
inference(instantiation,[status(thm)],[c_583]) ).
cnf(c_659,plain,
j(h(sK0(j(sK1)))) = sK0(j(sK1)),
inference(superposition,[status(thm)],[c_54,c_569]) ).
cnf(c_749,plain,
( ~ sorti2(h(sK0(j(sK1))))
| sorti1(sK0(j(sK1))) ),
inference(superposition,[status(thm)],[c_659,c_186]) ).
cnf(c_757,plain,
sorti1(sK0(j(sK1))),
inference(global_subsumption_just,[status(thm)],[c_749,c_54,c_62,c_584]) ).
cnf(c_759,plain,
( ~ sorti1(X0)
| op2(h(X0),h(sK0(j(sK1)))) = h(op1(X0,sK0(j(sK1)))) ),
inference(superposition,[status(thm)],[c_757,c_187]) ).
cnf(c_762,plain,
op2(h(sK0(j(sK1))),h(sK0(j(sK1)))) = sK1,
inference(superposition,[status(thm)],[c_757,c_499]) ).
cnf(c_1021,plain,
( ~ sorti1(X0)
| j(h(op1(X0,sK0(j(sK1))))) = op1(X0,sK0(j(sK1))) ),
inference(superposition,[status(thm)],[c_757,c_512]) ).
cnf(c_2078,plain,
j(h(op1(sK0(j(sK1)),sK0(j(sK1))))) = op1(sK0(j(sK1)),sK0(j(sK1))),
inference(superposition,[status(thm)],[c_757,c_1021]) ).
cnf(c_2153,plain,
op2(h(sK0(j(sK1))),h(sK0(j(sK1)))) = h(op1(sK0(j(sK1)),sK0(j(sK1)))),
inference(superposition,[status(thm)],[c_757,c_759]) ).
cnf(c_2156,plain,
h(op1(sK0(j(sK1)),sK0(j(sK1)))) = sK1,
inference(light_normalisation,[status(thm)],[c_2153,c_762]) ).
cnf(c_3757,plain,
op1(sK0(j(sK1)),sK0(j(sK1))) = j(sK1),
inference(light_normalisation,[status(thm)],[c_2078,c_2156]) ).
cnf(c_3759,plain,
( ~ sorti1(sK0(j(sK1)))
| sorti1(j(sK1)) ),
inference(superposition,[status(thm)],[c_3757,c_49]) ).
cnf(c_3760,plain,
~ sorti1(j(sK1)),
inference(superposition,[status(thm)],[c_3757,c_51]) ).
cnf(c_3761,plain,
~ sorti1(sK0(j(sK1))),
inference(forward_subsumption_resolution,[status(thm)],[c_3759,c_3760]) ).
cnf(c_3762,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3761,c_757]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : ALG019+1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.08 % Command : run_iprover %s %d THM
% 0.08/0.28 % Computer : n018.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Thu May 2 23:04:01 EDT 2024
% 0.08/0.28 % CPUTime :
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.21/1.08 % SZS status Started for theBenchmark.p
% 3.21/1.08 % SZS status Theorem for theBenchmark.p
% 3.21/1.08
% 3.21/1.08 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.21/1.08
% 3.21/1.08 ------ iProver source info
% 3.21/1.08
% 3.21/1.08 git: date: 2024-05-02 19:28:25 +0000
% 3.21/1.08 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.21/1.08 git: non_committed_changes: false
% 3.21/1.08
% 3.21/1.08 ------ Parsing...
% 3.21/1.08 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.21/1.08
% 3.21/1.08 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 3.21/1.08
% 3.21/1.08 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.21/1.08
% 3.21/1.08 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.21/1.08 ------ Proving...
% 3.21/1.08 ------ Problem Properties
% 3.21/1.08
% 3.21/1.08
% 3.21/1.08 clauses 12
% 3.21/1.08 conjectures 6
% 3.21/1.08 EPR 1
% 3.21/1.08 Horn 12
% 3.21/1.08 unary 1
% 3.21/1.08 binary 7
% 3.21/1.08 lits 27
% 3.21/1.08 lits eq 6
% 3.21/1.08 fd_pure 0
% 3.21/1.08 fd_pseudo 0
% 3.21/1.08 fd_cond 0
% 3.21/1.08 fd_pseudo_cond 0
% 3.21/1.08 AC symbols 0
% 3.21/1.08
% 3.21/1.08 ------ Schedule dynamic 5 is on
% 3.21/1.08
% 3.21/1.08 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.21/1.08
% 3.21/1.08
% 3.21/1.08 ------
% 3.21/1.08 Current options:
% 3.21/1.08 ------
% 3.21/1.08
% 3.21/1.08
% 3.21/1.08
% 3.21/1.08
% 3.21/1.08 ------ Proving...
% 3.21/1.08
% 3.21/1.08
% 3.21/1.08 % SZS status Theorem for theBenchmark.p
% 3.21/1.08
% 3.21/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.21/1.08
% 3.21/1.08
%------------------------------------------------------------------------------