TSTP Solution File: NUM423+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM423+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n027.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 02:49:13 EDT 2024
% Result : Theorem 2.13s 1.16s
% Output : CNFRefutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 67 ( 16 unt; 0 def)
% Number of atoms : 250 ( 100 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 311 ( 128 ~; 134 |; 36 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 60 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).
fof(f6,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> aInteger0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
fof(f10,axiom,
! [X0] :
( aInteger0(X0)
=> ( sz00 = sdtpldt0(smndt0(X0),X0)
& sz00 = sdtpldt0(X0,smndt0(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
fof(f15,axiom,
! [X0] :
( aInteger0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(f17,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> ( sz00 = sdtasdt0(X0,X1)
=> ( sz00 = X1
| sz00 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).
fof(f18,axiom,
! [X0] :
( aInteger0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).
fof(f19,axiom,
! [X0,X1,X2] :
( ( sz00 != X2
& aInteger0(X2)
& aInteger0(X1)
& aInteger0(X0) )
=> ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).
fof(f20,axiom,
( sz00 != xq
& aInteger0(xq)
& aInteger0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__671) ).
fof(f21,conjecture,
sdteqdtlpzmzozddtrp0(xa,xa,xq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f22,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(negated_conjecture,[],[f21]) ).
fof(f24,plain,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(flattening,[],[f22]) ).
fof(f28,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f29,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(flattening,[],[f28]) ).
fof(f35,plain,
! [X0] :
( ( sz00 = sdtpldt0(smndt0(X0),X0)
& sz00 = sdtpldt0(X0,smndt0(X0)) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f43,plain,
! [X0] :
( ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f45,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f46,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) ) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1) )
& ( ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(nnf_transformation,[],[f47]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1) )
& ( ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1) )
& ( ( ? [X3] :
( sdtasdt0(X1,X3) = X0
& aInteger0(X3) )
& sz00 != X1
& aInteger0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(rectify,[],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X1,X3) = X0
& aInteger0(X3) )
=> ( sdtasdt0(X1,sK0(X0,X1)) = X0
& aInteger0(sK0(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1) )
& ( ( sdtasdt0(X1,sK0(X0,X1)) = X0
& aInteger0(sK0(X0,X1))
& sz00 != X1
& aInteger0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f52,f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
& ( aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ) )
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(nnf_transformation,[],[f49]) ).
fof(f56,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f60,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f65,plain,
! [X0] :
( sz00 = sdtpldt0(X0,smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f73,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f77,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f82,plain,
! [X2,X0,X1] :
( aDivisorOf0(X1,X0)
| sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2)
| sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f84,plain,
! [X2,X0,X1] :
( sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f85,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f20]) ).
fof(f86,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f20]) ).
fof(f87,plain,
sz00 != xq,
inference(cnf_transformation,[],[f20]) ).
fof(f88,plain,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(cnf_transformation,[],[f24]) ).
fof(f89,plain,
! [X2,X1] :
( aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(X2)
| sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(sdtasdt0(X1,X2)) ),
inference(equality_resolution,[],[f82]) ).
cnf(c_49,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f56]) ).
cnf(c_53,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f60]) ).
cnf(c_59,plain,
( ~ aInteger0(X0)
| sdtpldt0(X0,smndt0(X0)) = sz00 ),
inference(cnf_transformation,[],[f65]) ).
cnf(c_67,plain,
( ~ aInteger0(X0)
| sdtasdt0(X0,sz00) = sz00 ),
inference(cnf_transformation,[],[f73]) ).
cnf(c_70,plain,
( sdtasdt0(X0,X1) != sz00
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| X0 = sz00
| X1 = sz00 ),
inference(cnf_transformation,[],[f77]) ).
cnf(c_71,plain,
( ~ aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| X0 = sz00
| aDivisorOf0(X0,sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f89]) ).
cnf(c_76,plain,
( ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(X2)))
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| X0 = sz00
| sdteqdtlpzmzozddtrp0(X1,X2,X0) ),
inference(cnf_transformation,[],[f84]) ).
cnf(c_78,plain,
sz00 != xq,
inference(cnf_transformation,[],[f87]) ).
cnf(c_79,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f86]) ).
cnf(c_80,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f85]) ).
cnf(c_81,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(cnf_transformation,[],[f88]) ).
cnf(c_84,plain,
( ~ aInteger0(sz00)
| sdtasdt0(sz00,sz00) = sz00 ),
inference(instantiation,[status(thm)],[c_67]) ).
cnf(c_97,plain,
( sdtasdt0(sz00,sz00) != sz00
| ~ aInteger0(sz00)
| sz00 = sz00 ),
inference(instantiation,[status(thm)],[c_70]) ).
cnf(c_104,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| X0 = sz00
| aDivisorOf0(X0,sdtasdt0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_71,c_53,c_71]) ).
cnf(c_456,plain,
( X0 != xq
| X1 != xa
| X2 != xa
| ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(X2)))
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| X0 = sz00 ),
inference(resolution_lifted,[status(thm)],[c_76,c_81]) ).
cnf(c_457,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| xq = sz00 ),
inference(unflattening,[status(thm)],[c_456]) ).
cnf(c_458,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| xq = sz00 ),
inference(global_subsumption_just,[status(thm)],[c_457,c_80,c_79,c_457]) ).
cnf(c_508,plain,
( sdtpldt0(xa,smndt0(xa)) != sdtasdt0(X0,X1)
| X0 != xq
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| X0 = sz00
| sz00 = xq ),
inference(resolution_lifted,[status(thm)],[c_104,c_458]) ).
cnf(c_509,plain,
( sdtpldt0(xa,smndt0(xa)) != sdtasdt0(xq,X0)
| ~ aInteger0(X0)
| ~ aInteger0(xq)
| sz00 = xq
| xq = sz00 ),
inference(unflattening,[status(thm)],[c_508]) ).
cnf(c_511,plain,
( sdtpldt0(xa,smndt0(xa)) != sdtasdt0(xq,X0)
| ~ aInteger0(X0)
| xq = sz00 ),
inference(global_subsumption_just,[status(thm)],[c_509,c_79,c_78,c_509]) ).
cnf(c_513,plain,
( sdtpldt0(xa,smndt0(xa)) != sdtasdt0(xq,sz00)
| ~ aInteger0(sz00)
| xq = sz00 ),
inference(instantiation,[status(thm)],[c_511]) ).
cnf(c_816,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_1256,plain,
sdtasdt0(xq,sz00) = sz00,
inference(superposition,[status(thm)],[c_79,c_67]) ).
cnf(c_1347,plain,
( sz00 != X0
| xq != X0
| sz00 = xq ),
inference(instantiation,[status(thm)],[c_816]) ).
cnf(c_1348,plain,
( sz00 != sz00
| xq != sz00
| sz00 = xq ),
inference(instantiation,[status(thm)],[c_1347]) ).
cnf(c_1349,plain,
( sdtpldt0(xa,smndt0(xa)) != X0
| sdtasdt0(xq,X1) != X0
| sdtpldt0(xa,smndt0(xa)) = sdtasdt0(xq,X1) ),
inference(instantiation,[status(thm)],[c_816]) ).
cnf(c_1350,plain,
( sdtpldt0(xa,smndt0(xa)) != sz00
| sdtasdt0(xq,sz00) != sz00
| sdtpldt0(xa,smndt0(xa)) = sdtasdt0(xq,sz00) ),
inference(instantiation,[status(thm)],[c_1349]) ).
cnf(c_1385,plain,
( ~ aInteger0(xa)
| sdtpldt0(xa,smndt0(xa)) = sz00 ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_1386,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1385,c_1350,c_1348,c_1256,c_513,c_97,c_84,c_78,c_49,c_80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM423+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu May 2 19:51:35 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 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
% 2.13/1.16 % SZS status Started for theBenchmark.p
% 2.13/1.16 % SZS status Theorem for theBenchmark.p
% 2.13/1.16
% 2.13/1.16 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.13/1.16
% 2.13/1.16 ------ iProver source info
% 2.13/1.16
% 2.13/1.16 git: date: 2024-05-02 19:28:25 +0000
% 2.13/1.16 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.13/1.16 git: non_committed_changes: false
% 2.13/1.16
% 2.13/1.16 ------ Parsing...
% 2.13/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.13/1.16
% 2.13/1.16 ------ 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: 3 0s sf_e pe_s pe_e
% 2.13/1.16
% 2.13/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.13/1.16
% 2.13/1.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.13/1.16 ------ Proving...
% 2.13/1.16 ------ Problem Properties
% 2.13/1.16
% 2.13/1.16
% 2.13/1.16 clauses 28
% 2.13/1.16 conjectures 0
% 2.13/1.16 EPR 5
% 2.13/1.16 Horn 25
% 2.13/1.16 unary 5
% 2.13/1.16 binary 11
% 2.13/1.16 lits 71
% 2.13/1.16 lits eq 25
% 2.13/1.16 fd_pure 0
% 2.13/1.16 fd_pseudo 0
% 2.13/1.16 fd_cond 3
% 2.13/1.16 fd_pseudo_cond 0
% 2.13/1.16 AC symbols 0
% 2.13/1.16
% 2.13/1.16 ------ Schedule dynamic 5 is on
% 2.13/1.16
% 2.13/1.16 ------ no conjectures: strip conj schedule
% 2.13/1.16
% 2.13/1.16 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.13/1.16
% 2.13/1.16
% 2.13/1.16 ------
% 2.13/1.16 Current options:
% 2.13/1.16 ------
% 2.13/1.16
% 2.13/1.16
% 2.13/1.16
% 2.13/1.16
% 2.13/1.16 ------ Proving...
% 2.13/1.16
% 2.13/1.16
% 2.13/1.16 % SZS status Theorem for theBenchmark.p
% 2.13/1.16
% 2.13/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.13/1.16
% 2.13/1.16
%------------------------------------------------------------------------------