%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE138+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:13:04 AM UTC 2025
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 47 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 68 ( 63 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 8 ~; 4 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 45 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
tff(one_type,type,
one: $i ).
tff(strong_iteration_type,type,
strong_iteration: $i > $i ).
tff(zero_type,type,
zero: $i ).
tff(addition_type,type,
addition: ( $i * $i ) > $i ).
tff(multiplication_type,type,
multiplication: ( $i * $i ) > $i ).
tff(1,plain,
^ [A: $i] :
refl(( ( addition(A,zero) = A )
<=> ( addition(A,zero) = A ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [A: $i] : ( addition(A,zero) = A )
<=> ! [A: $i] : ( addition(A,zero) = A ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i] : ( addition(A,zero) = A )
<=> ! [A: $i] : ( addition(A,zero) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [A: $i] : ( addition(A,zero) = A ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
tff(5,plain,
! [A: $i] : ( addition(A,zero) = A ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A: $i] : ( addition(A,zero) = A ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A: $i] : ( addition(A,zero) = A ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [A: $i] : ( addition(A,zero) = A )
| ( addition(one,zero) = one ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
addition(one,zero) = one,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [A: $i] :
refl(( ( strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) )
<=> ( strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [A: $i] : ( strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) )
<=> ! [A: $i] : ( strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [A: $i] : ( strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) )
<=> ! [A: $i] : ( strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [A: $i] : ( strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
tff(14,plain,
! [A: $i] : ( strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [A: $i] : ( strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [A: $i] : ( strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [A: $i] : ( strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) )
| ( strong_iteration(zero) = addition(multiplication(zero,strong_iteration(zero)),one) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
strong_iteration(zero) = addition(multiplication(zero,strong_iteration(zero)),one),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
multiplication(zero,strong_iteration(zero)) = multiplication(zero,addition(multiplication(zero,strong_iteration(zero)),one)),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
multiplication(zero,addition(multiplication(zero,strong_iteration(zero)),one)) = multiplication(zero,strong_iteration(zero)),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
^ [A: $i] :
refl(( ( multiplication(zero,A) = zero )
<=> ( multiplication(zero,A) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [A: $i] : ( multiplication(zero,A) = zero )
<=> ! [A: $i] : ( multiplication(zero,A) = zero ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [A: $i] : ( multiplication(zero,A) = zero )
<=> ! [A: $i] : ( multiplication(zero,A) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [A: $i] : ( multiplication(zero,A) = zero ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
tff(25,plain,
! [A: $i] : ( multiplication(zero,A) = zero ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [A: $i] : ( multiplication(zero,A) = zero ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [A: $i] : ( multiplication(zero,A) = zero ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [A: $i] : ( multiplication(zero,A) = zero )
| ( multiplication(zero,addition(multiplication(zero,strong_iteration(zero)),one)) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
multiplication(zero,addition(multiplication(zero,strong_iteration(zero)),one)) = zero,
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
zero = multiplication(zero,addition(multiplication(zero,strong_iteration(zero)),one)),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
zero = multiplication(zero,strong_iteration(zero)),
inference(transitivity,[status(thm)],[30,20]) ).
tff(32,plain,
addition(one,zero) = addition(one,multiplication(zero,strong_iteration(zero))),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
addition(one,multiplication(zero,strong_iteration(zero))) = addition(one,zero),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
^ [A: $i,B: $i] :
refl(( ( addition(A,B) = addition(B,A) )
<=> ( addition(A,B) = addition(B,A) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) )
<=> ! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) )
<=> ! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
tff(38,plain,
! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(multiplication(zero,strong_iteration(zero)),one) = addition(one,multiplication(zero,strong_iteration(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
addition(multiplication(zero,strong_iteration(zero)),one) = addition(one,multiplication(zero,strong_iteration(zero))),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
strong_iteration(zero) = one,
inference(transitivity,[status(thm)],[18,42,33,9]) ).
tff(44,plain,
( ( strong_iteration(zero) != one )
<=> ( strong_iteration(zero) != one ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
strong_iteration(zero) != one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(46,plain,
strong_iteration(zero) != one,
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
$false,
inference(unit_resolution,[status(thm)],[46,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : KLE138+1 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n004.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 Jun 19 19:02:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% See solution above
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------