TSTP Solution File: RNG123+4 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : RNG123+4 : TPTP v8.1.2. Released v4.0.0.
% 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 : Fri May 3 02:57:46 EDT 2024
% Result : Theorem 7.51s 1.69s
% Output : CNFRefutation 7.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 38 ( 15 unt; 0 def)
% Number of atoms : 235 ( 62 equ)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 253 ( 56 ~; 52 |; 124 &)
% ( 9 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 12 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 55 !; 44 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,axiom,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( aElementOf0(X0,xI)
<=> ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) )
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xb))
<=> ? [X1] :
( sdtasdt0(xb,X1) = X0
& aElement0(X1) ) )
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xa))
<=> ? [X1] :
( sdtasdt0(xa,X1) = X0
& aElement0(X1) ) )
& aIdeal0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xI) )
& ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(f52,axiom,
( aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = smndt0(sdtasdt0(xq,xu))
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2690) ).
fof(f53,axiom,
( aElementOf0(xb,xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xb
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) )
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xb
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2699) ).
fof(f54,axiom,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2718) ).
fof(f55,conjecture,
( aElementOf0(xr,xI)
| ? [X0,X1] :
( sdtpldt0(X0,X1) = xr
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f56,negated_conjecture,
~ ( aElementOf0(xr,xI)
| ? [X0,X1] :
( sdtpldt0(X0,X1) = xr
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
inference(negated_conjecture,[],[f55]) ).
fof(f65,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( aElementOf0(X0,xI)
<=> ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xa))
<=> ? [X6] :
( sdtasdt0(xa,X6) = X5
& aElement0(X6) ) )
& aIdeal0(xI)
& ! [X7] :
( aElementOf0(X7,xI)
=> ( ! [X8] :
( aElement0(X8)
=> aElementOf0(sdtasdt0(X8,X7),xI) )
& ! [X9] :
( aElementOf0(X9,xI)
=> aElementOf0(sdtpldt0(X7,X9),xI) ) ) )
& aSet0(xI) ),
inference(rectify,[],[f42]) ).
fof(f71,plain,
( aElementOf0(xb,xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xb
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) )
& ? [X2,X3] :
( xb = sdtpldt0(X2,X3)
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) ),
inference(rectify,[],[f53]) ).
fof(f124,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( aElementOf0(X0,xI)
<=> ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xa))
<=> ? [X6] :
( sdtasdt0(xa,X6) = X5
& aElement0(X6) ) )
& aIdeal0(xI)
& ! [X7] :
( ( ! [X8] :
( aElementOf0(sdtasdt0(X8,X7),xI)
| ~ aElement0(X8) )
& ! [X9] :
( aElementOf0(sdtpldt0(X7,X9),xI)
| ~ aElementOf0(X9,xI) ) )
| ~ aElementOf0(X7,xI) )
& aSet0(xI) ),
inference(ennf_transformation,[],[f65]) ).
fof(f129,plain,
( ~ aElementOf0(xr,xI)
& ! [X0,X1] :
( sdtpldt0(X0,X1) != xr
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) ) ),
inference(ennf_transformation,[],[f56]) ).
fof(f195,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( ( aElementOf0(X0,xI)
| ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) )
& ( ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
| ~ aElementOf0(X0,xI) ) )
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) ) )
& ( ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X5] :
( ( aElementOf0(X5,slsdtgt0(xa))
| ! [X6] :
( sdtasdt0(xa,X6) != X5
| ~ aElement0(X6) ) )
& ( ? [X6] :
( sdtasdt0(xa,X6) = X5
& aElement0(X6) )
| ~ aElementOf0(X5,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [X7] :
( ( ! [X8] :
( aElementOf0(sdtasdt0(X8,X7),xI)
| ~ aElement0(X8) )
& ! [X9] :
( aElementOf0(sdtpldt0(X7,X9),xI)
| ~ aElementOf0(X9,xI) ) )
| ~ aElementOf0(X7,xI) )
& aSet0(xI) ),
inference(nnf_transformation,[],[f124]) ).
fof(f196,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( ( aElementOf0(X0,xI)
| ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) )
& ( ? [X3,X4] :
( sdtpldt0(X3,X4) = X0
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) )
| ~ aElementOf0(X0,xI) ) )
& ! [X5] :
( ( aElementOf0(X5,slsdtgt0(xb))
| ! [X6] :
( sdtasdt0(xb,X6) != X5
| ~ aElement0(X6) ) )
& ( ? [X7] :
( sdtasdt0(xb,X7) = X5
& aElement0(X7) )
| ~ aElementOf0(X5,slsdtgt0(xb)) ) )
& ! [X8] :
( ( aElementOf0(X8,slsdtgt0(xa))
| ! [X9] :
( sdtasdt0(xa,X9) != X8
| ~ aElement0(X9) ) )
& ( ? [X10] :
( sdtasdt0(xa,X10) = X8
& aElement0(X10) )
| ~ aElementOf0(X8,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [X11] :
( ( ! [X12] :
( aElementOf0(sdtasdt0(X12,X11),xI)
| ~ aElement0(X12) )
& ! [X13] :
( aElementOf0(sdtpldt0(X11,X13),xI)
| ~ aElementOf0(X13,xI) ) )
| ~ aElementOf0(X11,xI) )
& aSet0(xI) ),
inference(rectify,[],[f195]) ).
fof(f197,plain,
! [X0] :
( ? [X3,X4] :
( sdtpldt0(X3,X4) = X0
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) )
=> ( sdtpldt0(sK28(X0),sK29(X0)) = X0
& aElementOf0(sK29(X0),slsdtgt0(xb))
& aElementOf0(sK28(X0),slsdtgt0(xa)) ) ),
introduced(choice_axiom,[]) ).
fof(f198,plain,
! [X5] :
( ? [X7] :
( sdtasdt0(xb,X7) = X5
& aElement0(X7) )
=> ( sdtasdt0(xb,sK30(X5)) = X5
& aElement0(sK30(X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f199,plain,
! [X8] :
( ? [X10] :
( sdtasdt0(xa,X10) = X8
& aElement0(X10) )
=> ( sdtasdt0(xa,sK31(X8)) = X8
& aElement0(sK31(X8)) ) ),
introduced(choice_axiom,[]) ).
fof(f200,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( ( aElementOf0(X0,xI)
| ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) )
& ( ( sdtpldt0(sK28(X0),sK29(X0)) = X0
& aElementOf0(sK29(X0),slsdtgt0(xb))
& aElementOf0(sK28(X0),slsdtgt0(xa)) )
| ~ aElementOf0(X0,xI) ) )
& ! [X5] :
( ( aElementOf0(X5,slsdtgt0(xb))
| ! [X6] :
( sdtasdt0(xb,X6) != X5
| ~ aElement0(X6) ) )
& ( ( sdtasdt0(xb,sK30(X5)) = X5
& aElement0(sK30(X5)) )
| ~ aElementOf0(X5,slsdtgt0(xb)) ) )
& ! [X8] :
( ( aElementOf0(X8,slsdtgt0(xa))
| ! [X9] :
( sdtasdt0(xa,X9) != X8
| ~ aElement0(X9) ) )
& ( ( sdtasdt0(xa,sK31(X8)) = X8
& aElement0(sK31(X8)) )
| ~ aElementOf0(X8,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [X11] :
( ( ! [X12] :
( aElementOf0(sdtasdt0(X12,X11),xI)
| ~ aElement0(X12) )
& ! [X13] :
( aElementOf0(sdtpldt0(X11,X13),xI)
| ~ aElementOf0(X13,xI) ) )
| ~ aElementOf0(X11,xI) )
& aSet0(xI) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29,sK30,sK31])],[f196,f199,f198,f197]) ).
fof(f221,plain,
( ? [X0,X1] :
( sdtpldt0(X0,X1) = smndt0(sdtasdt0(xq,xu))
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) )
=> ( smndt0(sdtasdt0(xq,xu)) = sdtpldt0(sK46,sK47)
& aElementOf0(sK47,slsdtgt0(xb))
& aElementOf0(sK46,slsdtgt0(xa)) ) ),
introduced(choice_axiom,[]) ).
fof(f222,plain,
( aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
& smndt0(sdtasdt0(xq,xu)) = sdtpldt0(sK46,sK47)
& aElementOf0(sK47,slsdtgt0(xb))
& aElementOf0(sK46,slsdtgt0(xa)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK46,sK47])],[f52,f221]) ).
fof(f223,plain,
( ? [X0,X1] :
( sdtpldt0(X0,X1) = xb
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) )
=> ( xb = sdtpldt0(sK48,sK49)
& aElementOf0(sK49,slsdtgt0(xb))
& aElementOf0(sK48,slsdtgt0(xa)) ) ),
introduced(choice_axiom,[]) ).
fof(f224,plain,
( ? [X2,X3] :
( xb = sdtpldt0(X2,X3)
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) )
=> ( xb = sdtpldt0(sK50,sK51)
& aElementOf0(sK51,slsdtgt0(xb))
& aElementOf0(sK50,slsdtgt0(xa)) ) ),
introduced(choice_axiom,[]) ).
fof(f225,plain,
( aElementOf0(xb,xI)
& xb = sdtpldt0(sK48,sK49)
& aElementOf0(sK49,slsdtgt0(xb))
& aElementOf0(sK48,slsdtgt0(xa))
& xb = sdtpldt0(sK50,sK51)
& aElementOf0(sK51,slsdtgt0(xb))
& aElementOf0(sK50,slsdtgt0(xa)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48,sK49,sK50,sK51])],[f71,f224,f223]) ).
fof(f341,plain,
! [X11,X13] :
( aElementOf0(sdtpldt0(X11,X13),xI)
| ~ aElementOf0(X13,xI)
| ~ aElementOf0(X11,xI) ),
inference(cnf_transformation,[],[f200]) ).
fof(f406,plain,
smndt0(sdtasdt0(xq,xu)) = sdtpldt0(sK46,sK47),
inference(cnf_transformation,[],[f222]) ).
fof(f407,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(cnf_transformation,[],[f222]) ).
fof(f414,plain,
aElementOf0(xb,xI),
inference(cnf_transformation,[],[f225]) ).
fof(f415,plain,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(cnf_transformation,[],[f54]) ).
fof(f417,plain,
~ aElementOf0(xr,xI),
inference(cnf_transformation,[],[f129]) ).
cnf(c_176,plain,
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xI)
| aElementOf0(sdtpldt0(X0,X1),xI) ),
inference(cnf_transformation,[],[f341]) ).
cnf(c_227,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(cnf_transformation,[],[f407]) ).
cnf(c_228,plain,
smndt0(sdtasdt0(xq,xu)) = sdtpldt0(sK46,sK47),
inference(cnf_transformation,[],[f406]) ).
cnf(c_231,plain,
aElementOf0(xb,xI),
inference(cnf_transformation,[],[f414]) ).
cnf(c_238,plain,
sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = xr,
inference(cnf_transformation,[],[f415]) ).
cnf(c_239,negated_conjecture,
~ aElementOf0(xr,xI),
inference(cnf_transformation,[],[f417]) ).
cnf(c_1392,plain,
sdtpldt0(sdtpldt0(sK46,sK47),xb) = xr,
inference(demodulation,[status(thm)],[c_238,c_228]) ).
cnf(c_1393,plain,
aElementOf0(sdtpldt0(sK46,sK47),xI),
inference(demodulation,[status(thm)],[c_227,c_228]) ).
cnf(c_7849,negated_conjecture,
~ aElementOf0(xr,xI),
inference(demodulation,[status(thm)],[c_239]) ).
cnf(c_13038,plain,
( ~ aElementOf0(sdtpldt0(sK46,sK47),xI)
| ~ aElementOf0(xb,xI)
| aElementOf0(xr,xI) ),
inference(superposition,[status(thm)],[c_1392,c_176]) ).
cnf(c_13075,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_13038,c_7849,c_231,c_1393]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG123+4 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 2 21:18:06 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 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
% 7.51/1.69 % SZS status Started for theBenchmark.p
% 7.51/1.69 % SZS status Theorem for theBenchmark.p
% 7.51/1.69
% 7.51/1.69 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.51/1.69
% 7.51/1.69 ------ iProver source info
% 7.51/1.69
% 7.51/1.69 git: date: 2024-05-02 19:28:25 +0000
% 7.51/1.69 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.51/1.69 git: non_committed_changes: false
% 7.51/1.69
% 7.51/1.69 ------ Parsing...
% 7.51/1.69 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.51/1.69
% 7.51/1.69 ------ Preprocessing... sup_sim: 3 sf_s rm: 2 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 7.51/1.69
% 7.51/1.69 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.51/1.69
% 7.51/1.69 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.51/1.69 ------ Proving...
% 7.51/1.69 ------ Problem Properties
% 7.51/1.69
% 7.51/1.69
% 7.51/1.69 clauses 181
% 7.51/1.69 conjectures 2
% 7.51/1.69 EPR 49
% 7.51/1.69 Horn 154
% 7.51/1.69 unary 68
% 7.51/1.69 binary 33
% 7.51/1.69 lits 465
% 7.51/1.69 lits eq 79
% 7.51/1.69 fd_pure 0
% 7.51/1.69 fd_pseudo 0
% 7.51/1.69 fd_cond 5
% 7.51/1.69 fd_pseudo_cond 11
% 7.51/1.69 AC symbols 0
% 7.51/1.69
% 7.51/1.69 ------ Schedule dynamic 5 is on
% 7.51/1.69
% 7.51/1.69 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.51/1.69
% 7.51/1.69
% 7.51/1.69 ------
% 7.51/1.69 Current options:
% 7.51/1.69 ------
% 7.51/1.69
% 7.51/1.69
% 7.51/1.69
% 7.51/1.69
% 7.51/1.69 ------ Proving...
% 7.51/1.69
% 7.51/1.69
% 7.51/1.69 % SZS status Theorem for theBenchmark.p
% 7.51/1.69
% 7.51/1.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.51/1.69
% 7.51/1.70
%------------------------------------------------------------------------------