%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV181+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %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 : Sat Jun 21 05:31:40 AM UTC 2025
% Result : Theorem 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 64
% Syntax : Number of formulae : 163 ( 76 unt; 0 typ; 0 def)
% Number of atoms : 642 ( 151 equ)
% Maximal formula atoms : 52 ( 3 avg)
% Number of connectives : 706 ( 264 ~; 224 |; 101 &)
% ( 86 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of FOOLs : 37 ( 37 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 15 con; 0-3 aty)
% Number of variables : 245 ( 225 !; 0 ?; 245 :)
% Comments :
%------------------------------------------------------------------------------
tff(gt_type,type,
gt: ( $i * $i ) > $o ).
tff(n5_type,type,
n5: $i ).
tff(succ_type,type,
succ: $i > $i ).
tff(n4_type,type,
n4: $i ).
tff(n0_type,type,
n0: $i ).
tff(plus_type,type,
plus: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(loopcounter_type,type,
loopcounter: $i ).
tff(pred_type,type,
pred: $i > $i ).
tff(init_type,type,
init: $i ).
tff(a_select2_type,type,
a_select2: ( $i * $i ) > $i ).
tff(sigma_init_type,type,
sigma_init: $i ).
tff(rho_init_type,type,
rho_init: $i ).
tff(mu_init_type,type,
mu_init: $i ).
tff(a_select3_type,type,
a_select3: ( $i * $i * $i ) > $i ).
tff(center_init_type,type,
center_init: $i ).
tff(q_init_type,type,
q_init: $i ).
tff(n135299_type,type,
n135299: $i ).
tff(pv76_type,type,
pv76: $i ).
tff(tptp_float_0_001_type,type,
tptp_float_0_001: $i ).
tff(muold_init_type,type,
muold_init: $i ).
tff(1,plain,
( ( succ(succ(succ(succ(n0)))) = n4 )
<=> ( succ(succ(succ(succ(n0)))) = n4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
succ(succ(succ(succ(n0)))) = n4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_4) ).
tff(3,plain,
succ(succ(succ(succ(n0)))) = n4,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
n4 = succ(succ(succ(succ(n0)))),
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
succ(n4) = succ(succ(succ(succ(succ(n0))))),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
succ(succ(succ(succ(succ(n0))))) = succ(n4),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( ( succ(succ(succ(succ(succ(n0))))) = n5 )
<=> ( succ(succ(succ(succ(succ(n0))))) = n5 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
succ(succ(succ(succ(succ(n0))))) = n5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_5) ).
tff(9,plain,
succ(succ(succ(succ(succ(n0))))) = n5,
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
n5 = succ(succ(succ(succ(succ(n0))))),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
n5 = succ(n4),
inference(transitivity,[status(thm)],[10,6]) ).
tff(12,plain,
( gt(n5,n5)
<=> gt(succ(n4),n5) ),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
( gt(succ(n4),n5)
<=> gt(n5,n5) ),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
^ [X: $i] :
refl(( ( plus(n5,X) = succ(succ(succ(succ(succ(X))))) )
<=> ( plus(n5,X) = succ(succ(succ(succ(succ(X))))) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [X: $i] : ( plus(n5,X) = succ(succ(succ(succ(succ(X))))) )
<=> ! [X: $i] : ( plus(n5,X) = succ(succ(succ(succ(succ(X))))) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [X: $i] : ( plus(n5,X) = succ(succ(succ(succ(succ(X))))) )
<=> ! [X: $i] : ( plus(n5,X) = succ(succ(succ(succ(succ(X))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
! [X: $i] : ( plus(n5,X) = succ(succ(succ(succ(succ(X))))) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',succ_plus_5_l) ).
tff(18,plain,
! [X: $i] : ( plus(n5,X) = succ(succ(succ(succ(succ(X))))) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [X: $i] : ( plus(n5,X) = succ(succ(succ(succ(succ(X))))) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [X: $i] : ( plus(n5,X) = succ(succ(succ(succ(succ(X))))) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
( ~ ! [X: $i] : ( plus(n5,X) = succ(succ(succ(succ(succ(X))))) )
| ( plus(n5,n0) = succ(succ(succ(succ(succ(n0))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
plus(n5,n0) = succ(succ(succ(succ(succ(n0))))),
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
( ! [X: $i] : ( pred(succ(X)) = X )
<=> ! [X: $i] : ( pred(succ(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ! [X: $i] : ( pred(succ(X)) = X )
<=> ! [X: $i] : ( pred(succ(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
! [X: $i] : ( pred(succ(X)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',pred_succ) ).
tff(26,plain,
! [X: $i] : ( pred(succ(X)) = X ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [X: $i] : ( pred(succ(X)) = X ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [X: $i] : ( pred(succ(X)) = X ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ~ ! [X: $i] : ( pred(succ(X)) = X )
| ( pred(succ(n0)) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
pred(succ(n0)) = n0,
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
( ( succ(n0) = n1 )
<=> ( succ(n0) = n1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_1) ).
tff(33,plain,
succ(n0) = n1,
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
n1 = succ(n0),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
pred(n1) = pred(succ(n0)),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
pred(n1) = n0,
inference(transitivity,[status(thm)],[35,30]) ).
tff(37,plain,
( leq(loopcounter,pred(n1))
<=> leq(loopcounter,n0) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
^ [X: $i,Y: $i] :
refl(( ( leq(X,pred(Y))
<=> gt(Y,X) )
<=> ( leq(X,pred(Y))
<=> gt(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) )
<=> ! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) )
<=> ! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt_pred) ).
tff(42,plain,
! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ~ ! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) )
| ( leq(loopcounter,pred(n1))
<=> gt(n1,loopcounter) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
( leq(loopcounter,pred(n1))
<=> gt(n1,loopcounter) ),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
( gt(n1,loopcounter)
<=> gt(n1,loopcounter) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ~ ( ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [A: $i] :
( ( leq(n0,A)
& leq(A,n135299) )
=> ! [B: $i] :
( ( leq(n0,B)
& leq(B,n4) )
=> ( a_select3(q_init,A,B) = init ) ) )
& ! [C: $i] :
( ( leq(n0,C)
& leq(C,n4) )
=> ( a_select3(center_init,C,n0) = init ) )
& ( gt(loopcounter,n0)
=> ! [D: $i] :
( ( leq(n0,D)
& leq(D,n4) )
=> ( a_select2(mu_init,D) = init ) ) )
& ( gt(loopcounter,n0)
=> ! [E: $i] :
( ( leq(n0,E)
& leq(E,n4) )
=> ( a_select2(rho_init,E) = init ) ) )
& ( gt(loopcounter,n0)
=> ! [F: $i] :
( ( leq(n0,F)
& leq(F,n4) )
=> ( a_select2(sigma_init,F) = init ) ) ) )
=> ! [G: $i] :
( ( leq(n0,G)
& leq(G,n4) )
=> ( a_select2(muold_init,G) = init ) ) )
<=> ~ ( ~ ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [A: $i] :
( ~ ( leq(n0,A)
& leq(A,n135299) )
| ! [B: $i] :
( ~ ( leq(n0,B)
& leq(B,n4) )
| ( a_select3(q_init,A,B) = init ) ) )
& ! [C: $i] :
( ~ ( leq(n0,C)
& leq(C,n4) )
| ( a_select3(center_init,C,n0) = init ) )
& ( ~ gt(loopcounter,n0)
| ! [D: $i] :
( ~ ( leq(n0,D)
& leq(D,n4) )
| ( a_select2(mu_init,D) = init ) ) )
& ( ~ gt(loopcounter,n0)
| ! [E: $i] :
( ~ ( leq(n0,E)
& leq(E,n4) )
| ( a_select2(rho_init,E) = init ) ) )
& ( ~ gt(loopcounter,n0)
| ! [F: $i] :
( ~ ( leq(n0,F)
& leq(F,n4) )
| ( a_select2(sigma_init,F) = init ) ) ) )
| ! [G: $i] :
( ~ ( leq(n0,G)
& leq(G,n4) )
| ( a_select2(muold_init,G) = init ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
~ ( ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [A: $i] :
( ( leq(n0,A)
& leq(A,n135299) )
=> ! [B: $i] :
( ( leq(n0,B)
& leq(B,n4) )
=> ( a_select3(q_init,A,B) = init ) ) )
& ! [C: $i] :
( ( leq(n0,C)
& leq(C,n4) )
=> ( a_select3(center_init,C,n0) = init ) )
& ( gt(loopcounter,n0)
=> ! [D: $i] :
( ( leq(n0,D)
& leq(D,n4) )
=> ( a_select2(mu_init,D) = init ) ) )
& ( gt(loopcounter,n0)
=> ! [E: $i] :
( ( leq(n0,E)
& leq(E,n4) )
=> ( a_select2(rho_init,E) = init ) ) )
& ( gt(loopcounter,n0)
=> ! [F: $i] :
( ( leq(n0,F)
& leq(F,n4) )
=> ( a_select2(sigma_init,F) = init ) ) ) )
=> ! [G: $i] :
( ( leq(n0,G)
& leq(G,n4) )
=> ( a_select2(muold_init,G) = init ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_init_0081) ).
tff(50,plain,
~ ( ~ ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [A: $i] :
( ~ ( leq(n0,A)
& leq(A,n135299) )
| ! [B: $i] :
( ~ ( leq(n0,B)
& leq(B,n4) )
| ( a_select3(q_init,A,B) = init ) ) )
& ! [C: $i] :
( ~ ( leq(n0,C)
& leq(C,n4) )
| ( a_select3(center_init,C,n0) = init ) )
& ( ~ gt(loopcounter,n0)
| ! [D: $i] :
( ~ ( leq(n0,D)
& leq(D,n4) )
| ( a_select2(mu_init,D) = init ) ) )
& ( ~ gt(loopcounter,n0)
| ! [E: $i] :
( ~ ( leq(n0,E)
& leq(E,n4) )
| ( a_select2(rho_init,E) = init ) ) )
& ( ~ gt(loopcounter,n0)
| ! [F: $i] :
( ~ ( leq(n0,F)
& leq(F,n4) )
| ( a_select2(sigma_init,F) = init ) ) ) )
| ! [G: $i] :
( ~ ( leq(n0,G)
& leq(G,n4) )
| ( a_select2(muold_init,G) = init ) ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [A: $i] :
( ~ ( leq(n0,A)
& leq(A,n135299) )
| ! [B: $i] :
( ~ ( leq(n0,B)
& leq(B,n4) )
| ( a_select3(q_init,A,B) = init ) ) )
& ! [C: $i] :
( ~ ( leq(n0,C)
& leq(C,n4) )
| ( a_select3(center_init,C,n0) = init ) )
& ( ~ gt(loopcounter,n0)
| ! [D: $i] :
( ~ ( leq(n0,D)
& leq(D,n4) )
| ( a_select2(mu_init,D) = init ) ) )
& ( ~ gt(loopcounter,n0)
| ! [E: $i] :
( ~ ( leq(n0,E)
& leq(E,n4) )
| ( a_select2(rho_init,E) = init ) ) )
& ( ~ gt(loopcounter,n0)
| ! [F: $i] :
( ~ ( leq(n0,F)
& leq(F,n4) )
| ( a_select2(sigma_init,F) = init ) ) ) ),
inference(or_elim,[status(thm)],[50]) ).
tff(52,plain,
gt(n1,loopcounter),
inference(and_elim,[status(thm)],[51]) ).
tff(53,plain,
gt(n1,loopcounter),
inference(modus_ponens,[status(thm)],[52,47]) ).
tff(54,plain,
( ~ ( leq(loopcounter,pred(n1))
<=> gt(n1,loopcounter) )
| leq(loopcounter,pred(n1))
| ~ gt(n1,loopcounter) ),
inference(tautology,[status(thm)],[]) ).
tff(55,plain,
( ~ ( leq(loopcounter,pred(n1))
<=> gt(n1,loopcounter) )
| leq(loopcounter,pred(n1)) ),
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
leq(loopcounter,pred(n1)),
inference(unit_resolution,[status(thm)],[55,46]) ).
tff(57,plain,
leq(loopcounter,n0),
inference(modus_ponens,[status(thm)],[56,37]) ).
tff(58,plain,
( leq(n1,loopcounter)
<=> leq(n1,loopcounter) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
leq(n1,loopcounter),
inference(and_elim,[status(thm)],[51]) ).
tff(60,plain,
leq(n1,loopcounter),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
( ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
<=> ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( leq(X,Y)
& leq(Y,Z) )
<=> ~ ( ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
( ~ ( leq(X,Y)
& leq(Y,Z) )
<=> ~ ~ ( ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
rewrite(( ~ ~ ( ~ leq(Y,Z)
| ~ leq(X,Y) )
<=> ( ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
( ~ ( leq(X,Y)
& leq(Y,Z) )
<=> ( ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
( ( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) )
<=> ( ~ leq(Y,Z)
| ~ leq(X,Y)
| leq(X,Z) ) )),
rewrite(( ( ~ leq(Y,Z)
| ~ leq(X,Y)
| leq(X,Z) )
<=> ( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
( ( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) )
<=> ( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(( ( ( leq(X,Y)
& leq(Y,Z) )
=> leq(X,Z) )
<=> ( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(66,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( leq(X,Y)
& leq(Y,Z) )
=> leq(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( leq(X,Y)
& leq(Y,Z) )
=> leq(X,Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',transitivity_leq) ).
tff(68,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(modus_ponens,[status(thm)],[70,63]) ).
tff(72,plain,
! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(modus_ponens,[status(thm)],[71,61]) ).
tff(73,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| ~ leq(loopcounter,n0)
| ~ leq(n1,loopcounter)
| leq(n1,n0) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| ~ leq(loopcounter,n0)
| ~ leq(n1,loopcounter)
| leq(n1,n0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ( leq(n1,n0)
| ~ leq(loopcounter,n0)
| ~ leq(n1,loopcounter) )
<=> ( ~ leq(loopcounter,n0)
| ~ leq(n1,loopcounter)
| leq(n1,n0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| leq(n1,n0)
| ~ leq(loopcounter,n0)
| ~ leq(n1,loopcounter) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| ~ leq(loopcounter,n0)
| ~ leq(n1,loopcounter)
| leq(n1,n0) ) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| leq(n1,n0)
| ~ leq(loopcounter,n0)
| ~ leq(n1,loopcounter) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| ~ leq(loopcounter,n0)
| ~ leq(n1,loopcounter)
| leq(n1,n0) ) ),
inference(transitivity,[status(thm)],[75,73]) ).
tff(77,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| leq(n1,n0)
| ~ leq(loopcounter,n0)
| ~ leq(n1,loopcounter) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| ~ leq(loopcounter,n0)
| ~ leq(n1,loopcounter)
| leq(n1,n0) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
leq(n1,n0),
inference(unit_resolution,[status(thm)],[78,72,60,57]) ).
tff(80,plain,
( gt(n1,n0)
<=> gt(n1,n0) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,axiom,
gt(n1,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_0) ).
tff(82,plain,
gt(n1,n0),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ gt(Y,X)
| leq(X,Y) )
<=> ( ~ gt(Y,X)
| leq(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(84,plain,
( ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
^ [X: $i,Y: $i] :
rewrite(( ( gt(Y,X)
=> leq(X,Y) )
<=> ( ~ gt(Y,X)
| leq(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(87,plain,
( ! [X: $i,Y: $i] :
( gt(Y,X)
=> leq(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,axiom,
! [X: $i,Y: $i] :
( gt(Y,X)
=> leq(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt1) ).
tff(89,plain,
! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[91,84]) ).
tff(93,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
| ~ gt(n1,n0)
| leq(n0,n1) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
| ~ gt(n1,n0)
| leq(n0,n1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
( ~ ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
| ~ gt(n1,n0)
| leq(n0,n1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
( ~ ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
| ~ gt(n1,n0)
| leq(n0,n1) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
leq(n0,n1),
inference(unit_resolution,[status(thm)],[95,92,82]) ).
tff(97,plain,
^ [X: $i] :
refl(( ( ( X = n0 )
| ~ leq(n0,X)
| ~ leq(X,n0) )
<=> ( ( X = n0 )
| ~ leq(n0,X)
| ~ leq(X,n0) ) )),
inference(bind,[status(th)],[]) ).
tff(98,plain,
( ! [X: $i] :
( ( X = n0 )
| ~ leq(n0,X)
| ~ leq(X,n0) )
<=> ! [X: $i] :
( ( X = n0 )
| ~ leq(n0,X)
| ~ leq(X,n0) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
^ [X: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( leq(n0,X)
& leq(X,n0) )
<=> ~ ( ~ leq(n0,X)
| ~ leq(X,n0) ) )),
( ~ ( leq(n0,X)
& leq(X,n0) )
<=> ~ ~ ( ~ leq(n0,X)
| ~ leq(X,n0) ) )),
rewrite(( ~ ~ ( ~ leq(n0,X)
| ~ leq(X,n0) )
<=> ( ~ leq(n0,X)
| ~ leq(X,n0) ) )),
( ~ ( leq(n0,X)
& leq(X,n0) )
<=> ( ~ leq(n0,X)
| ~ leq(X,n0) ) )),
( ( ~ ( leq(n0,X)
& leq(X,n0) )
| ( X = n0 ) )
<=> ( ~ leq(n0,X)
| ~ leq(X,n0)
| ( X = n0 ) ) )),
rewrite(( ( ~ leq(n0,X)
| ~ leq(X,n0)
| ( X = n0 ) )
<=> ( ( X = n0 )
| ~ leq(n0,X)
| ~ leq(X,n0) ) )),
( ( ~ ( leq(n0,X)
& leq(X,n0) )
| ( X = n0 ) )
<=> ( ( X = n0 )
| ~ leq(n0,X)
| ~ leq(X,n0) ) )),
inference(bind,[status(th)],[]) ).
tff(100,plain,
( ! [X: $i] :
( ~ ( leq(n0,X)
& leq(X,n0) )
| ( X = n0 ) )
<=> ! [X: $i] :
( ( X = n0 )
| ~ leq(n0,X)
| ~ leq(X,n0) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
( ! [X: $i] :
( ~ ( leq(n0,X)
& leq(X,n0) )
| ( X = n0 ) )
<=> ! [X: $i] :
( ~ ( leq(n0,X)
& leq(X,n0) )
| ( X = n0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
^ [X: $i] :
rewrite(( ( ( leq(n0,X)
& leq(X,n0) )
=> ( X = n0 ) )
<=> ( ~ ( leq(n0,X)
& leq(X,n0) )
| ( X = n0 ) ) )),
inference(bind,[status(th)],[]) ).
tff(103,plain,
( ! [X: $i] :
( ( leq(n0,X)
& leq(X,n0) )
=> ( X = n0 ) )
<=> ! [X: $i] :
( ~ ( leq(n0,X)
& leq(X,n0) )
| ( X = n0 ) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,axiom,
! [X: $i] :
( ( leq(n0,X)
& leq(X,n0) )
=> ( X = n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_0) ).
tff(105,plain,
! [X: $i] :
( ~ ( leq(n0,X)
& leq(X,n0) )
| ( X = n0 ) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
! [X: $i] :
( ~ ( leq(n0,X)
& leq(X,n0) )
| ( X = n0 ) ),
inference(modus_ponens,[status(thm)],[105,101]) ).
tff(107,plain,
! [X: $i] :
( ~ ( leq(n0,X)
& leq(X,n0) )
| ( X = n0 ) ),
inference(skolemize,[status(sab)],[106]) ).
tff(108,plain,
! [X: $i] :
( ( X = n0 )
| ~ leq(n0,X)
| ~ leq(X,n0) ),
inference(modus_ponens,[status(thm)],[107,100]) ).
tff(109,plain,
! [X: $i] :
( ( X = n0 )
| ~ leq(n0,X)
| ~ leq(X,n0) ),
inference(modus_ponens,[status(thm)],[108,98]) ).
tff(110,plain,
( ( ~ ! [X: $i] :
( ( X = n0 )
| ~ leq(n0,X)
| ~ leq(X,n0) )
| ~ leq(n0,n1)
| ~ leq(n1,n0)
| ( n1 = n0 ) )
<=> ( ~ ! [X: $i] :
( ( X = n0 )
| ~ leq(n0,X)
| ~ leq(X,n0) )
| ~ leq(n0,n1)
| ~ leq(n1,n0)
| ( n1 = n0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,plain,
( ( ( n1 = n0 )
| ~ leq(n0,n1)
| ~ leq(n1,n0) )
<=> ( ~ leq(n0,n1)
| ~ leq(n1,n0)
| ( n1 = n0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(112,plain,
( ( ~ ! [X: $i] :
( ( X = n0 )
| ~ leq(n0,X)
| ~ leq(X,n0) )
| ( n1 = n0 )
| ~ leq(n0,n1)
| ~ leq(n1,n0) )
<=> ( ~ ! [X: $i] :
( ( X = n0 )
| ~ leq(n0,X)
| ~ leq(X,n0) )
| ~ leq(n0,n1)
| ~ leq(n1,n0)
| ( n1 = n0 ) ) ),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
( ( ~ ! [X: $i] :
( ( X = n0 )
| ~ leq(n0,X)
| ~ leq(X,n0) )
| ( n1 = n0 )
| ~ leq(n0,n1)
| ~ leq(n1,n0) )
<=> ( ~ ! [X: $i] :
( ( X = n0 )
| ~ leq(n0,X)
| ~ leq(X,n0) )
| ~ leq(n0,n1)
| ~ leq(n1,n0)
| ( n1 = n0 ) ) ),
inference(transitivity,[status(thm)],[112,110]) ).
tff(114,plain,
( ~ ! [X: $i] :
( ( X = n0 )
| ~ leq(n0,X)
| ~ leq(X,n0) )
| ( n1 = n0 )
| ~ leq(n0,n1)
| ~ leq(n1,n0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
( ~ ! [X: $i] :
( ( X = n0 )
| ~ leq(n0,X)
| ~ leq(X,n0) )
| ~ leq(n0,n1)
| ~ leq(n1,n0)
| ( n1 = n0 ) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
n1 = n0,
inference(unit_resolution,[status(thm)],[115,109,96,79]) ).
tff(117,plain,
plus(n5,n1) = plus(n5,n0),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
( ~ ! [X: $i] : ( plus(n5,X) = succ(succ(succ(succ(succ(X))))) )
| ( plus(n5,n1) = succ(succ(succ(succ(succ(n1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(119,plain,
plus(n5,n1) = succ(succ(succ(succ(succ(n1))))),
inference(unit_resolution,[status(thm)],[118,20]) ).
tff(120,plain,
succ(succ(succ(succ(succ(n1))))) = plus(n5,n1),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
^ [X: $i] :
refl(( ( plus(X,n4) = succ(succ(succ(succ(X)))) )
<=> ( plus(X,n4) = succ(succ(succ(succ(X)))) ) )),
inference(bind,[status(th)],[]) ).
tff(122,plain,
( ! [X: $i] : ( plus(X,n4) = succ(succ(succ(succ(X)))) )
<=> ! [X: $i] : ( plus(X,n4) = succ(succ(succ(succ(X)))) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,plain,
( ! [X: $i] : ( plus(X,n4) = succ(succ(succ(succ(X)))) )
<=> ! [X: $i] : ( plus(X,n4) = succ(succ(succ(succ(X)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(124,axiom,
! [X: $i] : ( plus(X,n4) = succ(succ(succ(succ(X)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',succ_plus_4_r) ).
tff(125,plain,
! [X: $i] : ( plus(X,n4) = succ(succ(succ(succ(X)))) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
! [X: $i] : ( plus(X,n4) = succ(succ(succ(succ(X)))) ),
inference(skolemize,[status(sab)],[125]) ).
tff(127,plain,
! [X: $i] : ( plus(X,n4) = succ(succ(succ(succ(X)))) ),
inference(modus_ponens,[status(thm)],[126,122]) ).
tff(128,plain,
( ~ ! [X: $i] : ( plus(X,n4) = succ(succ(succ(succ(X)))) )
| ( plus(n1,n4) = succ(succ(succ(succ(n1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(129,plain,
plus(n1,n4) = succ(succ(succ(succ(n1)))),
inference(unit_resolution,[status(thm)],[128,127]) ).
tff(130,plain,
^ [X: $i] :
refl(( ( plus(n1,X) = succ(X) )
<=> ( plus(n1,X) = succ(X) ) )),
inference(bind,[status(th)],[]) ).
tff(131,plain,
( ! [X: $i] : ( plus(n1,X) = succ(X) )
<=> ! [X: $i] : ( plus(n1,X) = succ(X) ) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,plain,
( ! [X: $i] : ( plus(n1,X) = succ(X) )
<=> ! [X: $i] : ( plus(n1,X) = succ(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(133,axiom,
! [X: $i] : ( plus(n1,X) = succ(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',succ_plus_1_l) ).
tff(134,plain,
! [X: $i] : ( plus(n1,X) = succ(X) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
! [X: $i] : ( plus(n1,X) = succ(X) ),
inference(skolemize,[status(sab)],[134]) ).
tff(136,plain,
! [X: $i] : ( plus(n1,X) = succ(X) ),
inference(modus_ponens,[status(thm)],[135,131]) ).
tff(137,plain,
( ~ ! [X: $i] : ( plus(n1,X) = succ(X) )
| ( plus(n1,n4) = succ(n4) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(138,plain,
plus(n1,n4) = succ(n4),
inference(unit_resolution,[status(thm)],[137,136]) ).
tff(139,plain,
succ(n4) = plus(n1,n4),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
n5 = succ(succ(succ(succ(n1)))),
inference(transitivity,[status(thm)],[10,6,139,129]) ).
tff(141,plain,
succ(n5) = succ(succ(succ(succ(succ(n1))))),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
succ(n5) = succ(n4),
inference(transitivity,[status(thm)],[141,120,117,22,6]) ).
tff(143,plain,
( gt(succ(n5),n5)
<=> gt(succ(n4),n5) ),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
( gt(succ(n5),n5)
<=> gt(n5,n5) ),
inference(transitivity,[status(thm)],[143,13]) ).
tff(145,plain,
^ [X: $i] :
refl(( gt(succ(X),X)
<=> gt(succ(X),X) )),
inference(bind,[status(th)],[]) ).
tff(146,plain,
( ! [X: $i] : gt(succ(X),X)
<=> ! [X: $i] : gt(succ(X),X) ),
inference(quant_intro,[status(thm)],[145]) ).
tff(147,plain,
( ! [X: $i] : gt(succ(X),X)
<=> ! [X: $i] : gt(succ(X),X) ),
inference(rewrite,[status(thm)],[]) ).
tff(148,axiom,
! [X: $i] : gt(succ(X),X),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',gt_succ) ).
tff(149,plain,
! [X: $i] : gt(succ(X),X),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
! [X: $i] : gt(succ(X),X),
inference(skolemize,[status(sab)],[149]) ).
tff(151,plain,
! [X: $i] : gt(succ(X),X),
inference(modus_ponens,[status(thm)],[150,146]) ).
tff(152,plain,
( ~ ! [X: $i] : gt(succ(X),X)
| gt(succ(n5),n5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
gt(succ(n5),n5),
inference(unit_resolution,[status(thm)],[152,151]) ).
tff(154,plain,
gt(n5,n5),
inference(modus_ponens,[status(thm)],[153,144]) ).
tff(155,plain,
^ [X: $i] :
refl(( ~ gt(X,X)
<=> ~ gt(X,X) )),
inference(bind,[status(th)],[]) ).
tff(156,plain,
( ! [X: $i] : ~ gt(X,X)
<=> ! [X: $i] : ~ gt(X,X) ),
inference(quant_intro,[status(thm)],[155]) ).
tff(157,plain,
( ! [X: $i] : ~ gt(X,X)
<=> ! [X: $i] : ~ gt(X,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(158,axiom,
! [X: $i] : ~ gt(X,X),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',irreflexivity_gt) ).
tff(159,plain,
! [X: $i] : ~ gt(X,X),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
! [X: $i] : ~ gt(X,X),
inference(skolemize,[status(sab)],[159]) ).
tff(161,plain,
! [X: $i] : ~ gt(X,X),
inference(modus_ponens,[status(thm)],[160,156]) ).
tff(162,plain,
( ~ ! [X: $i] : ~ gt(X,X)
| ~ gt(n5,n5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(163,plain,
$false,
inference(unit_resolution,[status(thm)],[162,161,154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV181+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n002.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 : Fri Jun 20 09:32:46 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 % SZS output start Proof
% See solution above
% 0.20/0.48 % E exiting
%------------------------------------------------------------------------------