%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV056+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 : Sat Jun 21 05:31:24 AM UTC 2025
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of formulae : 56 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 121 ( 66 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 102 ( 39 ~; 17 |; 27 &)
% ( 17 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 29 ( 27 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
tff(sum_type,type,
sum: ( $i * $i * $i ) > $i ).
tff(a_select3_type,type,
a_select3: ( $i * $i * $i ) > $i ).
tff(pv25_type,type,
pv25: $i ).
tff(pv77_type,type,
pv77: $i ).
tff(q_type,type,
q: $i ).
tff(minus_type,type,
minus: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(n0_type,type,
n0: $i ).
tff(tptp_minus_1_type,type,
tptp_minus_1: $i ).
tff(pred_type,type,
pred: $i > $i ).
tff(succ_type,type,
succ: $i > $i ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(n5_type,type,
n5: $i ).
tff(1,plain,
( ! [X: $i] : ( pred(succ(X)) = X )
<=> ! [X: $i] : ( pred(succ(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ! [X: $i] : ( pred(succ(X)) = X )
<=> ! [X: $i] : ( pred(succ(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
! [X: $i] : ( pred(succ(X)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',pred_succ) ).
tff(4,plain,
! [X: $i] : ( pred(succ(X)) = X ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
! [X: $i] : ( pred(succ(X)) = X ),
inference(skolemize,[status(sab)],[4]) ).
tff(6,plain,
! [X: $i] : ( pred(succ(X)) = X ),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( ~ ! [X: $i] : ( pred(succ(X)) = X )
| ( pred(succ(tptp_minus_1)) = tptp_minus_1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(8,plain,
pred(succ(tptp_minus_1)) = tptp_minus_1,
inference(unit_resolution,[status(thm)],[7,6]) ).
tff(9,plain,
( ( succ(tptp_minus_1) = n0 )
<=> ( succ(tptp_minus_1) = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
succ(tptp_minus_1) = n0,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',succ_tptp_minus_1) ).
tff(11,plain,
succ(tptp_minus_1) = n0,
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
pred(succ(tptp_minus_1)) = pred(n0),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
pred(n0) = pred(succ(tptp_minus_1)),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
^ [X: $i] :
refl(( ( minus(X,n1) = pred(X) )
<=> ( minus(X,n1) = pred(X) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [X: $i] : ( minus(X,n1) = pred(X) )
<=> ! [X: $i] : ( minus(X,n1) = pred(X) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [X: $i] : ( minus(X,n1) = pred(X) )
<=> ! [X: $i] : ( minus(X,n1) = pred(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
! [X: $i] : ( minus(X,n1) = pred(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
tff(18,plain,
! [X: $i] : ( minus(X,n1) = pred(X) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [X: $i] : ( minus(X,n1) = pred(X) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [X: $i] : ( minus(X,n1) = pred(X) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
( ~ ! [X: $i] : ( minus(X,n1) = pred(X) )
| ( minus(n0,n1) = pred(n0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
minus(n0,n1) = pred(n0),
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
minus(n0,n1) = tptp_minus_1,
inference(transitivity,[status(thm)],[22,13,8]) ).
tff(24,plain,
sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) = sum(n0,tptp_minus_1,a_select3(q,pv77,pv25)),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
sum(n0,tptp_minus_1,a_select3(q,pv77,pv25)) = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
^ [Body: $i] :
refl(( ( sum(n0,tptp_minus_1,Body) = n0 )
<=> ( sum(n0,tptp_minus_1,Body) = n0 ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [Body: $i] : ( sum(n0,tptp_minus_1,Body) = n0 )
<=> ! [Body: $i] : ( sum(n0,tptp_minus_1,Body) = n0 ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [Body: $i] : ( sum(n0,tptp_minus_1,Body) = n0 )
<=> ! [Body: $i] : ( sum(n0,tptp_minus_1,Body) = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
! [Body: $i] : ( sum(n0,tptp_minus_1,Body) = n0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',sum_plus_base) ).
tff(30,plain,
! [Body: $i] : ( sum(n0,tptp_minus_1,Body) = n0 ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [Body: $i] : ( sum(n0,tptp_minus_1,Body) = n0 ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [Body: $i] : ( sum(n0,tptp_minus_1,Body) = n0 ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ~ ! [Body: $i] : ( sum(n0,tptp_minus_1,Body) = n0 )
| ( sum(n0,tptp_minus_1,a_select3(q,pv77,pv25)) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
sum(n0,tptp_minus_1,a_select3(q,pv77,pv25)) = n0,
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
n0 = sum(n0,tptp_minus_1,a_select3(q,pv77,pv25)),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)),
inference(transitivity,[status(thm)],[35,25]) ).
tff(37,plain,
( leq(pv25,minus(n5,n1))
<=> leq(pv25,minus(n5,n1)) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ~ ( ( leq(n0,pv25)
& leq(pv25,minus(n5,n1)) )
=> ( ( n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) )
& leq(n0,pv25)
& leq(pv25,minus(n5,n1)) ) )
<=> ~ ( ~ ( leq(n0,pv25)
& leq(pv25,minus(n5,n1)) )
| ( ( n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) )
& leq(n0,pv25)
& leq(pv25,minus(n5,n1)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
~ ( ( leq(n0,pv25)
& leq(pv25,minus(n5,n1)) )
=> ( ( n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) )
& leq(n0,pv25)
& leq(pv25,minus(n5,n1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_norm_0040) ).
tff(40,plain,
~ ( ~ ( leq(n0,pv25)
& leq(pv25,minus(n5,n1)) )
| ( ( n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) )
& leq(n0,pv25)
& leq(pv25,minus(n5,n1)) ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( leq(n0,pv25)
& leq(pv25,minus(n5,n1)) ),
inference(or_elim,[status(thm)],[40]) ).
tff(42,plain,
leq(pv25,minus(n5,n1)),
inference(and_elim,[status(thm)],[41]) ).
tff(43,plain,
leq(pv25,minus(n5,n1)),
inference(modus_ponens,[status(thm)],[42,37]) ).
tff(44,plain,
( leq(n0,pv25)
<=> leq(n0,pv25) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
leq(n0,pv25),
inference(and_elim,[status(thm)],[41]) ).
tff(46,plain,
leq(n0,pv25),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
( ~ ~ ( ( n0 != sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) )
| ~ leq(n0,pv25)
| ~ leq(pv25,minus(n5,n1)) )
<=> ( ( n0 != sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) )
| ~ leq(n0,pv25)
| ~ leq(pv25,minus(n5,n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ( ( n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) )
& leq(n0,pv25)
& leq(pv25,minus(n5,n1)) )
<=> ~ ( ( n0 != sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) )
| ~ leq(n0,pv25)
| ~ leq(pv25,minus(n5,n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ~ ( ( n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) )
& leq(n0,pv25)
& leq(pv25,minus(n5,n1)) )
<=> ~ ~ ( ( n0 != sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) )
| ~ leq(n0,pv25)
| ~ leq(pv25,minus(n5,n1)) ) ),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
( ~ ( ( n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) )
& leq(n0,pv25)
& leq(pv25,minus(n5,n1)) )
<=> ( ( n0 != sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) )
| ~ leq(n0,pv25)
| ~ leq(pv25,minus(n5,n1)) ) ),
inference(transitivity,[status(thm)],[49,47]) ).
tff(51,plain,
( ~ ( ( n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) )
& leq(n0,pv25)
& leq(pv25,minus(n5,n1)) )
<=> ~ ( ( n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) )
& leq(n0,pv25)
& leq(pv25,minus(n5,n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
~ ( ( n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) )
& leq(n0,pv25)
& leq(pv25,minus(n5,n1)) ),
inference(or_elim,[status(thm)],[40]) ).
tff(53,plain,
~ ( ( n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) )
& leq(n0,pv25)
& leq(pv25,minus(n5,n1)) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
( ( n0 != sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) )
| ~ leq(n0,pv25)
| ~ leq(pv25,minus(n5,n1)) ),
inference(modus_ponens,[status(thm)],[53,50]) ).
tff(55,plain,
n0 != sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)),
inference(unit_resolution,[status(thm)],[54,46,43]) ).
tff(56,plain,
$false,
inference(unit_resolution,[status(thm)],[55,36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWV056+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n012.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 09:25:55 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% See solution above
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------