TSTP Solution File: ALG073+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : ALG073+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n002.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 02:03:34 EDT 2024
% Result : Theorem 3.95s 1.19s
% Output : CNFRefutation 3.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 70 ( 26 unt; 0 def)
% Number of atoms : 240 ( 92 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 270 ( 100 ~; 84 |; 53 &)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn 69 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> sorti1(op1(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f2,axiom,
! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> sorti2(op2(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f3,axiom,
? [X0] :
( ? [X1] :
( op1(X0,X1) != X0
& op1(X1,X1) = X0
& op1(X0,X0) = X1
& sorti1(X1) )
& sorti1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
~ ? [X0] :
( ? [X1] :
( op2(X0,X1) != X0
& op2(X1,X1) = X0
& op2(X0,X0) = X1
& sorti2(X1) )
& 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] :
( 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(f8,plain,
! [X0] :
( ! [X1] :
( sorti1(op1(X0,X1))
| ~ sorti1(X1) )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f9,plain,
! [X0] :
( ! [X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1) )
| ~ sorti2(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f10,plain,
! [X0] :
( ! [X1] :
( op2(X0,X1) = X0
| op2(X1,X1) != X0
| op2(X0,X0) != X1
| ~ sorti2(X1) )
| ~ sorti2(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f11,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(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(flattening,[],[f11]) ).
fof(f13,plain,
( ? [X0] :
( ? [X1] :
( op1(X0,X1) != X0
& op1(X1,X1) = X0
& op1(X0,X0) = X1
& sorti1(X1) )
& sorti1(X0) )
=> ( ? [X1] :
( sK0 != op1(sK0,X1)
& op1(X1,X1) = sK0
& op1(sK0,sK0) = X1
& sorti1(X1) )
& sorti1(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
( ? [X1] :
( sK0 != op1(sK0,X1)
& op1(X1,X1) = sK0
& op1(sK0,sK0) = X1
& sorti1(X1) )
=> ( sK0 != op1(sK0,sK1)
& sK0 = op1(sK1,sK1)
& op1(sK0,sK0) = sK1
& sorti1(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
( sK0 != op1(sK0,sK1)
& sK0 = op1(sK1,sK1)
& op1(sK0,sK0) = sK1
& sorti1(sK1)
& sorti1(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f3,f14,f13]) ).
fof(f16,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,[],[f12]) ).
fof(f17,plain,
! [X0,X1] :
( sorti1(op1(X0,X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f18,plain,
! [X0,X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f19,plain,
sorti1(sK0),
inference(cnf_transformation,[],[f15]) ).
fof(f20,plain,
sorti1(sK1),
inference(cnf_transformation,[],[f15]) ).
fof(f21,plain,
op1(sK0,sK0) = sK1,
inference(cnf_transformation,[],[f15]) ).
fof(f22,plain,
sK0 = op1(sK1,sK1),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
sK0 != op1(sK0,sK1),
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
! [X0,X1] :
( op2(X0,X1) = X0
| op2(X1,X1) != X0
| op2(X0,X0) != X1
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f10]) ).
fof(f25,plain,
! [X7] :
( sorti2(h(X7))
| ~ sorti1(X7) ),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
! [X4,X5] :
( h(op1(X4,X5)) = op2(h(X4),h(X5))
| ~ sorti1(X5)
| ~ sorti1(X4) ),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X0] :
( j(h(X0)) = X0
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
! [X1] :
( op2(X1,X1) = op2(op2(X1,X1),X1)
| op2(op2(X1,X1),op2(X1,X1)) != X1
| ~ sorti2(X1)
| ~ sorti2(op2(X1,X1)) ),
inference(equality_resolution,[],[f24]) ).
cnf(c_49,plain,
( ~ sorti1(X0)
| ~ sorti1(X1)
| sorti1(op1(X0,X1)) ),
inference(cnf_transformation,[],[f17]) ).
cnf(c_50,plain,
( ~ sorti2(X0)
| ~ sorti2(X1)
| sorti2(op2(X0,X1)) ),
inference(cnf_transformation,[],[f18]) ).
cnf(c_51,plain,
op1(sK0,sK1) != sK0,
inference(cnf_transformation,[],[f23]) ).
cnf(c_52,plain,
op1(sK1,sK1) = sK0,
inference(cnf_transformation,[],[f22]) ).
cnf(c_53,plain,
op1(sK0,sK0) = sK1,
inference(cnf_transformation,[],[f21]) ).
cnf(c_54,plain,
sorti1(sK1),
inference(cnf_transformation,[],[f20]) ).
cnf(c_55,plain,
sorti1(sK0),
inference(cnf_transformation,[],[f19]) ).
cnf(c_56,plain,
( op2(op2(X0,X0),op2(X0,X0)) != X0
| ~ sorti2(op2(X0,X0))
| ~ sorti2(X0)
| op2(op2(X0,X0),X0) = op2(X0,X0) ),
inference(cnf_transformation,[],[f31]) ).
cnf(c_57,negated_conjecture,
( ~ sorti1(X0)
| j(h(X0)) = X0 ),
inference(cnf_transformation,[],[f30]) ).
cnf(c_60,negated_conjecture,
( ~ sorti1(X0)
| ~ sorti1(X1)
| op2(h(X0),h(X1)) = h(op1(X0,X1)) ),
inference(cnf_transformation,[],[f27]) ).
cnf(c_62,negated_conjecture,
( ~ sorti1(X0)
| sorti2(h(X0)) ),
inference(cnf_transformation,[],[f25]) ).
cnf(c_63,plain,
( ~ sorti1(sK0)
| sorti2(h(sK0)) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_90,negated_conjecture,
( ~ sorti1(X0_13)
| ~ sorti1(X1_13)
| op2(h(X0_13),h(X1_13)) = h(op1(X0_13,X1_13)) ),
inference(subtyping,[status(esa)],[c_60]) ).
cnf(c_93,negated_conjecture,
( ~ sorti1(X0_13)
| j(h(X0_13)) = X0_13 ),
inference(subtyping,[status(esa)],[c_57]) ).
cnf(c_94,plain,
( op2(op2(X0_14,X0_14),op2(X0_14,X0_14)) != X0_14
| ~ sorti2(op2(X0_14,X0_14))
| ~ sorti2(X0_14)
| op2(op2(X0_14,X0_14),X0_14) = op2(X0_14,X0_14) ),
inference(subtyping,[status(esa)],[c_56]) ).
cnf(c_95,plain,
sorti1(sK0),
inference(subtyping,[status(esa)],[c_55]) ).
cnf(c_96,plain,
sorti1(sK1),
inference(subtyping,[status(esa)],[c_54]) ).
cnf(c_97,plain,
op1(sK0,sK0) = sK1,
inference(subtyping,[status(esa)],[c_53]) ).
cnf(c_98,plain,
op1(sK1,sK1) = sK0,
inference(subtyping,[status(esa)],[c_52]) ).
cnf(c_99,plain,
op1(sK0,sK1) != sK0,
inference(subtyping,[status(esa)],[c_51]) ).
cnf(c_100,plain,
( ~ sorti2(X0_14)
| ~ sorti2(X1_14)
| sorti2(op2(X0_14,X1_14)) ),
inference(subtyping,[status(esa)],[c_50]) ).
cnf(c_101,plain,
( ~ sorti1(X0_13)
| ~ sorti1(X1_13)
| sorti1(op1(X0_13,X1_13)) ),
inference(subtyping,[status(esa)],[c_49]) ).
cnf(c_172,plain,
j(h(sK0)) = sK0,
inference(superposition,[status(thm)],[c_95,c_93]) ).
cnf(c_190,plain,
( ~ sorti1(X0_13)
| ~ sorti1(X1_13)
| j(h(op1(X0_13,X1_13))) = op1(X0_13,X1_13) ),
inference(superposition,[status(thm)],[c_101,c_93]) ).
cnf(c_230,plain,
( ~ sorti1(X0_13)
| op2(h(sK1),h(X0_13)) = h(op1(sK1,X0_13)) ),
inference(superposition,[status(thm)],[c_96,c_90]) ).
cnf(c_231,plain,
( ~ sorti1(X0_13)
| op2(h(sK0),h(X0_13)) = h(op1(sK0,X0_13)) ),
inference(superposition,[status(thm)],[c_95,c_90]) ).
cnf(c_303,plain,
( ~ sorti1(X0_13)
| j(h(op1(sK0,X0_13))) = op1(sK0,X0_13) ),
inference(superposition,[status(thm)],[c_95,c_190]) ).
cnf(c_419,plain,
op2(h(sK0),h(sK1)) = h(op1(sK0,sK1)),
inference(superposition,[status(thm)],[c_96,c_231]) ).
cnf(c_420,plain,
op2(h(sK0),h(sK0)) = h(op1(sK0,sK0)),
inference(superposition,[status(thm)],[c_95,c_231]) ).
cnf(c_423,plain,
op2(h(sK0),h(sK0)) = h(sK1),
inference(demodulation,[status(thm)],[c_420,c_97]) ).
cnf(c_438,plain,
op2(h(sK1),h(sK1)) = h(op1(sK1,sK1)),
inference(superposition,[status(thm)],[c_96,c_230]) ).
cnf(c_442,plain,
op2(h(sK1),h(sK1)) = h(sK0),
inference(demodulation,[status(thm)],[c_438,c_98]) ).
cnf(c_618,plain,
j(h(op1(sK0,sK1))) = op1(sK0,sK1),
inference(superposition,[status(thm)],[c_96,c_303]) ).
cnf(c_993,plain,
( ~ sorti2(h(sK0))
| sorti2(h(sK1)) ),
inference(superposition,[status(thm)],[c_423,c_100]) ).
cnf(c_1071,plain,
( op2(h(sK0),h(sK0)) != h(sK1)
| ~ sorti2(op2(h(sK1),h(sK1)))
| ~ sorti2(h(sK1))
| op2(op2(h(sK1),h(sK1)),h(sK1)) = op2(h(sK1),h(sK1)) ),
inference(superposition,[status(thm)],[c_442,c_94]) ).
cnf(c_1082,plain,
( h(sK1) != h(sK1)
| ~ sorti2(h(sK0))
| ~ sorti2(h(sK1))
| h(op1(sK0,sK1)) = h(sK0) ),
inference(demodulation,[status(thm)],[c_1071,c_419,c_423,c_442]) ).
cnf(c_1083,plain,
( ~ sorti2(h(sK0))
| ~ sorti2(h(sK1))
| h(op1(sK0,sK1)) = h(sK0) ),
inference(equality_resolution_simp,[status(thm)],[c_1082]) ).
cnf(c_1087,plain,
( ~ sorti2(h(sK0))
| h(op1(sK0,sK1)) = h(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1083,c_993]) ).
cnf(c_3843,plain,
h(op1(sK0,sK1)) = h(sK0),
inference(global_subsumption_just,[status(thm)],[c_1087,c_55,c_63,c_1087]) ).
cnf(c_3871,plain,
op1(sK0,sK1) = j(h(sK0)),
inference(demodulation,[status(thm)],[c_618,c_3843]) ).
cnf(c_3873,plain,
op1(sK0,sK1) = sK0,
inference(demodulation,[status(thm)],[c_3871,c_172]) ).
cnf(c_3891,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3873,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG073+1 : TPTP v8.1.2. Released v2.7.0.
% 0.03/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu May 2 23:03:42 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 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
% 3.95/1.19 % SZS status Started for theBenchmark.p
% 3.95/1.19 % SZS status Theorem for theBenchmark.p
% 3.95/1.19
% 3.95/1.19 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.95/1.19
% 3.95/1.19 ------ iProver source info
% 3.95/1.19
% 3.95/1.19 git: date: 2024-05-02 19:28:25 +0000
% 3.95/1.19 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.95/1.19 git: non_committed_changes: false
% 3.95/1.19
% 3.95/1.19 ------ Parsing...
% 3.95/1.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.95/1.19
% 3.95/1.19 ------ Preprocessing... sup_sim: 0 pe_s pe_e
% 3.95/1.19
% 3.95/1.19 ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 0 0s scvd_e snvd_s sp: 0 0s snvd_e
% 3.95/1.19
% 3.95/1.19 ------ Preprocessing...
% 3.95/1.19 ------ Proving...
% 3.95/1.19 ------ Problem Properties
% 3.95/1.19
% 3.95/1.19
% 3.95/1.19 clauses 14
% 3.95/1.19 conjectures 6
% 3.95/1.19 EPR 2
% 3.95/1.19 Horn 14
% 3.95/1.19 unary 5
% 3.95/1.19 binary 4
% 3.95/1.19 lits 29
% 3.95/1.19 lits eq 9
% 3.95/1.19 fd_pure 0
% 3.95/1.19 fd_pseudo 0
% 3.95/1.19 fd_cond 0
% 3.95/1.19 fd_pseudo_cond 0
% 3.95/1.19 AC symbols 0
% 3.95/1.19
% 3.95/1.19 ------ Input Options Time Limit: Unbounded
% 3.95/1.19
% 3.95/1.19
% 3.95/1.19 ------
% 3.95/1.19 Current options:
% 3.95/1.19 ------
% 3.95/1.19
% 3.95/1.19
% 3.95/1.19
% 3.95/1.19
% 3.95/1.19 ------ Proving...
% 3.95/1.19
% 3.95/1.19
% 3.95/1.19 % SZS status Theorem for theBenchmark.p
% 3.95/1.19
% 3.95/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.95/1.19
% 3.95/1.20
%------------------------------------------------------------------------------