%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE170+1.002 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:13:08 AM UTC 2025
% Result : Theorem 0.50s 0.69s
% Output : Proof 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 55
% Syntax : Number of formulae : 186 ( 130 unt; 0 typ; 0 def)
% Number of atoms : 279 ( 212 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 126 ( 41 ~; 35 |; 0 &)
% ( 50 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 8 ( 8 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 187 ( 173 !; 0 ?; 187 :)
% Comments :
%------------------------------------------------------------------------------
tff(star_type,type,
star: $i > $i ).
tff(a_type,type,
a: $i ).
tff(addition_type,type,
addition: ( $i * $i ) > $i ).
tff(multiplication_type,type,
multiplication: ( $i * $i ) > $i ).
tff(one_type,type,
one: $i ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(1,plain,
^ [A: $i,B: $i] :
refl(( ( leq(A,B)
<=> ( addition(A,B) = B ) )
<=> ( leq(A,B)
<=> ( addition(A,B) = B ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [A: $i,B: $i] :
( leq(A,B)
<=> ( addition(A,B) = B ) )
<=> ! [A: $i,B: $i] :
( leq(A,B)
<=> ( addition(A,B) = B ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i,B: $i] :
( leq(A,B)
<=> ( addition(A,B) = B ) )
<=> ! [A: $i,B: $i] :
( leq(A,B)
<=> ( addition(A,B) = B ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [A: $i,B: $i] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',order) ).
tff(5,plain,
! [A: $i,B: $i] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A: $i,B: $i] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A: $i,B: $i] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [A: $i,B: $i] :
( leq(A,B)
<=> ( addition(A,B) = B ) )
| ( leq(addition(one,multiplication(a,star(a))),star(a))
<=> ( addition(addition(one,multiplication(a,star(a))),star(a)) = star(a) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
( leq(addition(one,multiplication(a,star(a))),star(a))
<=> ( addition(addition(one,multiplication(a,star(a))),star(a)) = star(a) ) ),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [A: $i] :
refl(( leq(addition(one,multiplication(A,star(A))),star(A))
<=> leq(addition(one,multiplication(A,star(A))),star(A)) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [A: $i] : leq(addition(one,multiplication(A,star(A))),star(A))
<=> ! [A: $i] : leq(addition(one,multiplication(A,star(A))),star(A)) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [A: $i] : leq(addition(one,multiplication(A,star(A))),star(A))
<=> ! [A: $i] : leq(addition(one,multiplication(A,star(A))),star(A)) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [A: $i] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).
tff(14,plain,
! [A: $i] : leq(addition(one,multiplication(A,star(A))),star(A)),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [A: $i] : leq(addition(one,multiplication(A,star(A))),star(A)),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [A: $i] : leq(addition(one,multiplication(A,star(A))),star(A)),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [A: $i] : leq(addition(one,multiplication(A,star(A))),star(A))
| leq(addition(one,multiplication(a,star(a))),star(a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
leq(addition(one,multiplication(a,star(a))),star(a)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ ( leq(addition(one,multiplication(a,star(a))),star(a))
<=> ( addition(addition(one,multiplication(a,star(a))),star(a)) = star(a) ) )
| ~ leq(addition(one,multiplication(a,star(a))),star(a))
| ( addition(addition(one,multiplication(a,star(a))),star(a)) = star(a) ) ),
inference(tautology,[status(thm)],[]) ).
tff(20,plain,
( ~ ( leq(addition(one,multiplication(a,star(a))),star(a))
<=> ( addition(addition(one,multiplication(a,star(a))),star(a)) = star(a) ) )
| ( addition(addition(one,multiplication(a,star(a))),star(a)) = star(a) ) ),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
addition(addition(one,multiplication(a,star(a))),star(a)) = star(a),
inference(unit_resolution,[status(thm)],[20,9]) ).
tff(22,plain,
^ [A: $i,B: $i] :
refl(( ( addition(A,B) = addition(B,A) )
<=> ( addition(A,B) = addition(B,A) ) )),
inference(bind,[status(th)],[]) ).
tff(23,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)],[22]) ).
tff(24,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(25,axiom,
! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
tff(26,plain,
! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ~ ! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(one,multiplication(a,star(a))) = addition(multiplication(a,star(a)),one) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
addition(one,multiplication(a,star(a))) = addition(multiplication(a,star(a)),one),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
addition(multiplication(a,star(a)),one) = addition(one,multiplication(a,star(a))),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
addition(addition(multiplication(a,star(a)),one),star(a)) = addition(addition(one,multiplication(a,star(a))),star(a)),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
^ [C: $i,B: $i,A: $i] :
refl(( ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
<=> ( addition(A,addition(B,C)) = addition(addition(A,B),C) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
<=> ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
<=> ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_associativity) ).
tff(37,plain,
! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
( ~ ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(multiplication(a,star(a)),addition(one,star(a))) = addition(addition(multiplication(a,star(a)),one),star(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
addition(multiplication(a,star(a)),addition(one,star(a))) = addition(addition(multiplication(a,star(a)),one),star(a)),
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
( ~ ! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(one,multiplication(star(a),a)) = addition(multiplication(star(a),a),one) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
addition(one,multiplication(star(a),a)) = addition(multiplication(star(a),a),one),
inference(unit_resolution,[status(thm)],[42,28]) ).
tff(44,plain,
addition(multiplication(star(a),a),one) = addition(one,multiplication(star(a),a)),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
addition(addition(multiplication(star(a),a),one),star(a)) = addition(addition(one,multiplication(star(a),a)),star(a)),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
addition(addition(one,multiplication(star(a),a)),star(a)) = addition(addition(multiplication(star(a),a),one),star(a)),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
( ~ ! [A: $i,B: $i] :
( leq(A,B)
<=> ( addition(A,B) = B ) )
| ( leq(addition(one,multiplication(star(a),a)),star(a))
<=> ( addition(addition(one,multiplication(star(a),a)),star(a)) = star(a) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( leq(addition(one,multiplication(star(a),a)),star(a))
<=> ( addition(addition(one,multiplication(star(a),a)),star(a)) = star(a) ) ),
inference(unit_resolution,[status(thm)],[47,7]) ).
tff(49,plain,
^ [A: $i] :
refl(( leq(addition(one,multiplication(star(A),A)),star(A))
<=> leq(addition(one,multiplication(star(A),A)),star(A)) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [A: $i] : leq(addition(one,multiplication(star(A),A)),star(A))
<=> ! [A: $i] : leq(addition(one,multiplication(star(A),A)),star(A)) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [A: $i] : leq(addition(one,multiplication(star(A),A)),star(A))
<=> ! [A: $i] : leq(addition(one,multiplication(star(A),A)),star(A)) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
! [A: $i] : leq(addition(one,multiplication(star(A),A)),star(A)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_left) ).
tff(53,plain,
! [A: $i] : leq(addition(one,multiplication(star(A),A)),star(A)),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [A: $i] : leq(addition(one,multiplication(star(A),A)),star(A)),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [A: $i] : leq(addition(one,multiplication(star(A),A)),star(A)),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
( ~ ! [A: $i] : leq(addition(one,multiplication(star(A),A)),star(A))
| leq(addition(one,multiplication(star(a),a)),star(a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
leq(addition(one,multiplication(star(a),a)),star(a)),
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,plain,
( ~ ( leq(addition(one,multiplication(star(a),a)),star(a))
<=> ( addition(addition(one,multiplication(star(a),a)),star(a)) = star(a) ) )
| ~ leq(addition(one,multiplication(star(a),a)),star(a))
| ( addition(addition(one,multiplication(star(a),a)),star(a)) = star(a) ) ),
inference(tautology,[status(thm)],[]) ).
tff(59,plain,
( ~ ( leq(addition(one,multiplication(star(a),a)),star(a))
<=> ( addition(addition(one,multiplication(star(a),a)),star(a)) = star(a) ) )
| ( addition(addition(one,multiplication(star(a),a)),star(a)) = star(a) ) ),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
addition(addition(one,multiplication(star(a),a)),star(a)) = star(a),
inference(unit_resolution,[status(thm)],[59,48]) ).
tff(61,plain,
star(a) = addition(addition(one,multiplication(star(a),a)),star(a)),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
star(a) = addition(addition(multiplication(star(a),a),one),star(a)),
inference(transitivity,[status(thm)],[61,46]) ).
tff(63,plain,
multiplication(a,star(a)) = multiplication(a,addition(addition(multiplication(star(a),a),one),star(a))),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
multiplication(a,addition(addition(multiplication(star(a),a),one),star(a))) = multiplication(a,star(a)),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
^ [A: $i,B: $i,C: $i] :
refl(( ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
<=> ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ) )),
inference(bind,[status(th)],[]) ).
tff(66,plain,
( ! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
<=> ! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
<=> ! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,axiom,
! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',right_distributivity) ).
tff(69,plain,
! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
( ~ ! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
| ( multiplication(a,addition(addition(multiplication(star(a),a),one),star(a))) = addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
multiplication(a,addition(addition(multiplication(star(a),a),one),star(a))) = addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))) = multiplication(a,addition(addition(multiplication(star(a),a),one),star(a))),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
^ [A: $i] :
refl(( ( addition(A,A) = A )
<=> ( addition(A,A) = A ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [A: $i] : ( addition(A,A) = A )
<=> ! [A: $i] : ( addition(A,A) = A ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [A: $i] : ( addition(A,A) = A )
<=> ! [A: $i] : ( addition(A,A) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
! [A: $i] : ( addition(A,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
tff(79,plain,
! [A: $i] : ( addition(A,A) = A ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [A: $i] : ( addition(A,A) = A ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [A: $i] : ( addition(A,A) = A ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
( ~ ! [A: $i] : ( addition(A,A) = A )
| ( addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))) = addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))) = addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),
inference(unit_resolution,[status(thm)],[82,81]) ).
tff(84,plain,
addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))) = multiplication(a,star(a)),
inference(transitivity,[status(thm)],[83,74,64]) ).
tff(85,plain,
addition(addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),addition(one,star(a))) = addition(multiplication(a,star(a)),addition(one,star(a))),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
( ~ ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(one,star(a)))) = addition(addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),addition(one,star(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(one,star(a)))) = addition(addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),addition(one,star(a))),
inference(unit_resolution,[status(thm)],[86,39]) ).
tff(88,plain,
addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))) = multiplication(a,star(a)),
inference(transitivity,[status(thm)],[74,64]) ).
tff(89,plain,
addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(one,star(a))) = addition(multiplication(a,star(a)),addition(one,star(a))),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
addition(multiplication(a,star(a)),addition(one,star(a))) = addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(one,star(a))),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
addition(addition(multiplication(a,star(a)),one),star(a)) = addition(multiplication(a,star(a)),addition(one,star(a))),
inference(symmetry,[status(thm)],[41]) ).
tff(92,plain,
addition(addition(one,multiplication(a,star(a))),star(a)) = addition(addition(multiplication(a,star(a)),one),star(a)),
inference(symmetry,[status(thm)],[32]) ).
tff(93,plain,
star(a) = addition(addition(one,multiplication(a,star(a))),star(a)),
inference(symmetry,[status(thm)],[21]) ).
tff(94,plain,
star(a) = addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(one,star(a))),
inference(transitivity,[status(thm)],[93,92,91,90]) ).
tff(95,plain,
multiplication(a,star(a)) = addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),
inference(transitivity,[status(thm)],[63,73]) ).
tff(96,plain,
addition(multiplication(a,star(a)),star(a)) = addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(one,star(a)))),
inference(monotonicity,[status(thm)],[95,94]) ).
tff(97,plain,
addition(multiplication(a,star(a)),star(a)) = star(a),
inference(transitivity,[status(thm)],[96,87,85,41,32,21]) ).
tff(98,plain,
multiplication(a,addition(multiplication(a,star(a)),star(a))) = multiplication(a,star(a)),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),star(a)) = addition(multiplication(a,star(a)),star(a)),
inference(monotonicity,[status(thm)],[88]) ).
tff(100,plain,
multiplication(a,addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),star(a))) = multiplication(a,addition(multiplication(a,star(a)),star(a))),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
( ~ ! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
| ( multiplication(a,addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),star(a))) = addition(multiplication(a,addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),multiplication(a,star(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
multiplication(a,addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),star(a))) = addition(multiplication(a,addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),multiplication(a,star(a))),
inference(unit_resolution,[status(thm)],[101,71]) ).
tff(103,plain,
addition(multiplication(a,addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),multiplication(a,star(a))) = multiplication(a,addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),star(a))),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
( ~ ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(one,addition(multiplication(star(a),a),star(a))) = addition(addition(one,multiplication(star(a),a)),star(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
addition(one,addition(multiplication(star(a),a),star(a))) = addition(addition(one,multiplication(star(a),a)),star(a)),
inference(unit_resolution,[status(thm)],[104,39]) ).
tff(106,plain,
( ~ ! [A: $i] : ( addition(A,A) = A )
| ( addition(one,one) = one ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,plain,
addition(one,one) = one,
inference(unit_resolution,[status(thm)],[106,81]) ).
tff(108,plain,
addition(addition(one,one),addition(multiplication(star(a),a),star(a))) = addition(one,addition(multiplication(star(a),a),star(a))),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( ~ ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(one,addition(one,addition(multiplication(star(a),a),star(a)))) = addition(addition(one,one),addition(multiplication(star(a),a),star(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
addition(one,addition(one,addition(multiplication(star(a),a),star(a)))) = addition(addition(one,one),addition(multiplication(star(a),a),star(a))),
inference(unit_resolution,[status(thm)],[109,39]) ).
tff(111,plain,
addition(addition(one,multiplication(star(a),a)),star(a)) = addition(one,addition(multiplication(star(a),a),star(a))),
inference(symmetry,[status(thm)],[105]) ).
tff(112,plain,
star(a) = addition(one,addition(multiplication(star(a),a),star(a))),
inference(transitivity,[status(thm)],[61,111]) ).
tff(113,plain,
addition(one,star(a)) = addition(one,addition(one,addition(multiplication(star(a),a),star(a)))),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
addition(one,star(a)) = star(a),
inference(transitivity,[status(thm)],[113,110,108,105,60]) ).
tff(115,plain,
multiplication(a,addition(one,star(a))) = multiplication(a,star(a)),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
( ~ ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(one,addition(multiplication(a,star(a)),star(a))) = addition(addition(one,multiplication(a,star(a))),star(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
addition(one,addition(multiplication(a,star(a)),star(a))) = addition(addition(one,multiplication(a,star(a))),star(a)),
inference(unit_resolution,[status(thm)],[116,39]) ).
tff(118,plain,
addition(one,addition(multiplication(a,star(a)),star(a))) = star(a),
inference(transitivity,[status(thm)],[117,21]) ).
tff(119,plain,
multiplication(a,addition(one,addition(multiplication(a,star(a)),star(a)))) = multiplication(a,star(a)),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
( ~ ! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
| ( multiplication(a,addition(one,addition(multiplication(a,star(a)),star(a)))) = addition(multiplication(a,one),multiplication(a,addition(multiplication(a,star(a)),star(a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
multiplication(a,addition(one,addition(multiplication(a,star(a)),star(a)))) = addition(multiplication(a,one),multiplication(a,addition(multiplication(a,star(a)),star(a)))),
inference(unit_resolution,[status(thm)],[120,71]) ).
tff(122,plain,
addition(multiplication(a,one),multiplication(a,addition(multiplication(a,star(a)),star(a)))) = multiplication(a,addition(one,addition(multiplication(a,star(a)),star(a)))),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
addition(multiplication(a,one),multiplication(a,addition(multiplication(a,star(a)),star(a)))) = addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),
inference(transitivity,[status(thm)],[122,119,63,73]) ).
tff(124,plain,
multiplication(a,addition(multiplication(a,one),multiplication(a,addition(multiplication(a,star(a)),star(a))))) = multiplication(a,addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
( ~ ! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
| ( multiplication(a,addition(multiplication(a,one),multiplication(a,addition(multiplication(a,star(a)),star(a))))) = addition(multiplication(a,multiplication(a,one)),multiplication(a,multiplication(a,addition(multiplication(a,star(a)),star(a))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
multiplication(a,addition(multiplication(a,one),multiplication(a,addition(multiplication(a,star(a)),star(a))))) = addition(multiplication(a,multiplication(a,one)),multiplication(a,multiplication(a,addition(multiplication(a,star(a)),star(a))))),
inference(unit_resolution,[status(thm)],[125,71]) ).
tff(127,plain,
addition(multiplication(a,multiplication(a,one)),multiplication(a,multiplication(a,addition(multiplication(a,star(a)),star(a))))) = multiplication(a,addition(multiplication(a,one),multiplication(a,addition(multiplication(a,star(a)),star(a))))),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
multiplication(a,addition(multiplication(a,star(a)),star(a))) = addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),
inference(transitivity,[status(thm)],[98,63,73]) ).
tff(129,plain,
multiplication(a,multiplication(a,addition(multiplication(a,star(a)),star(a)))) = multiplication(a,addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
multiplication(a,addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))) = multiplication(a,multiplication(a,addition(multiplication(a,star(a)),star(a)))),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
^ [A: $i] :
refl(( ( multiplication(A,one) = A )
<=> ( multiplication(A,one) = A ) )),
inference(bind,[status(th)],[]) ).
tff(132,plain,
( ! [A: $i] : ( multiplication(A,one) = A )
<=> ! [A: $i] : ( multiplication(A,one) = A ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,plain,
( ! [A: $i] : ( multiplication(A,one) = A )
<=> ! [A: $i] : ( multiplication(A,one) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,axiom,
! [A: $i] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
tff(135,plain,
! [A: $i] : ( multiplication(A,one) = A ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
! [A: $i] : ( multiplication(A,one) = A ),
inference(skolemize,[status(sab)],[135]) ).
tff(137,plain,
! [A: $i] : ( multiplication(A,one) = A ),
inference(modus_ponens,[status(thm)],[136,132]) ).
tff(138,plain,
( ~ ! [A: $i] : ( multiplication(A,one) = A )
| ( multiplication(a,one) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,plain,
multiplication(a,one) = a,
inference(unit_resolution,[status(thm)],[138,137]) ).
tff(140,plain,
multiplication(a,multiplication(a,one)) = multiplication(a,a),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
multiplication(a,a) = multiplication(a,multiplication(a,one)),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
addition(multiplication(a,a),multiplication(a,addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))))) = addition(multiplication(a,multiplication(a,one)),multiplication(a,multiplication(a,addition(multiplication(a,star(a)),star(a))))),
inference(monotonicity,[status(thm)],[141,130]) ).
tff(143,plain,
addition(multiplication(a,a),multiplication(a,addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))))) = multiplication(a,addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),
inference(transitivity,[status(thm)],[142,127,124]) ).
tff(144,plain,
addition(addition(multiplication(a,a),multiplication(a,addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))))),multiplication(a,addition(one,star(a)))) = addition(multiplication(a,addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),multiplication(a,star(a))),
inference(monotonicity,[status(thm)],[143,115]) ).
tff(145,plain,
( ~ ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(multiplication(a,a),addition(multiplication(a,addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),multiplication(a,addition(one,star(a))))) = addition(addition(multiplication(a,a),multiplication(a,addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))))),multiplication(a,addition(one,star(a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(146,plain,
addition(multiplication(a,a),addition(multiplication(a,addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),multiplication(a,addition(one,star(a))))) = addition(addition(multiplication(a,a),multiplication(a,addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))))),multiplication(a,addition(one,star(a)))),
inference(unit_resolution,[status(thm)],[145,39]) ).
tff(147,plain,
( ~ ! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
| ( multiplication(a,addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(one,star(a)))) = addition(multiplication(a,addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),multiplication(a,addition(one,star(a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(148,plain,
multiplication(a,addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(one,star(a)))) = addition(multiplication(a,addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),multiplication(a,addition(one,star(a)))),
inference(unit_resolution,[status(thm)],[147,71]) ).
tff(149,plain,
addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(one,star(a))) = star(a),
inference(transitivity,[status(thm)],[89,41,32,21]) ).
tff(150,plain,
multiplication(a,addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(one,star(a)))) = multiplication(a,star(a)),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,plain,
multiplication(a,star(a)) = multiplication(a,addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(one,star(a)))),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))) = addition(multiplication(a,addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),multiplication(a,addition(one,star(a)))),
inference(transitivity,[status(thm)],[74,64,151,148]) ).
tff(153,plain,
addition(multiplication(a,a),addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))) = addition(multiplication(a,a),addition(multiplication(a,addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),multiplication(a,addition(one,star(a))))),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
( ~ ! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(multiplication(a,a),addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))) = addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),multiplication(a,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(155,plain,
addition(multiplication(a,a),addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))) = addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),multiplication(a,a)),
inference(unit_resolution,[status(thm)],[154,28]) ).
tff(156,plain,
addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),multiplication(a,a)) = addition(multiplication(a,a),addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),multiplication(a,a)) = multiplication(a,star(a)),
inference(transitivity,[status(thm)],[156,153,146,144,103,100,98]) ).
tff(158,plain,
addition(addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),multiplication(a,a)),star(a)) = addition(multiplication(a,star(a)),star(a)),
inference(monotonicity,[status(thm)],[157]) ).
tff(159,plain,
( ~ ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(multiplication(a,a),star(a))) = addition(addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),multiplication(a,a)),star(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(160,plain,
addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(multiplication(a,a),star(a))) = addition(addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),multiplication(a,a)),star(a)),
inference(unit_resolution,[status(thm)],[159,39]) ).
tff(161,plain,
( ~ ! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(multiplication(a,a),star(a)) = addition(star(a),multiplication(a,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(162,plain,
addition(multiplication(a,a),star(a)) = addition(star(a),multiplication(a,a)),
inference(unit_resolution,[status(thm)],[161,28]) ).
tff(163,plain,
addition(star(a),multiplication(a,a)) = addition(multiplication(a,a),star(a)),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(star(a),multiplication(a,a))) = addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(multiplication(a,a),star(a))),
inference(monotonicity,[status(thm)],[163]) ).
tff(165,plain,
addition(star(a),multiplication(a,a)) = addition(addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(one,star(a))),multiplication(a,a)),
inference(monotonicity,[status(thm)],[94]) ).
tff(166,plain,
addition(addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(one,star(a))),multiplication(a,a)) = addition(star(a),multiplication(a,a)),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
( ~ ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(addition(one,star(a)),multiplication(a,a))) = addition(addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(one,star(a))),multiplication(a,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(168,plain,
addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(addition(one,star(a)),multiplication(a,a))) = addition(addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(one,star(a))),multiplication(a,a)),
inference(unit_resolution,[status(thm)],[167,39]) ).
tff(169,plain,
addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(addition(one,star(a)),multiplication(a,a))) = addition(star(a),multiplication(a,a)),
inference(transitivity,[status(thm)],[168,166]) ).
tff(170,plain,
addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(addition(one,star(a)),multiplication(a,a)))) = addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(star(a),multiplication(a,a))),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
( ~ ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(addition(one,star(a)),multiplication(a,a)))) = addition(addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),addition(addition(one,star(a)),multiplication(a,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(addition(one,star(a)),multiplication(a,a)))) = addition(addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),addition(addition(one,star(a)),multiplication(a,a))),
inference(unit_resolution,[status(thm)],[171,39]) ).
tff(173,plain,
addition(addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),addition(addition(one,star(a)),multiplication(a,a))) = addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(addition(one,star(a)),multiplication(a,a)))),
inference(symmetry,[status(thm)],[172]) ).
tff(174,plain,
addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))) = addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),
inference(symmetry,[status(thm)],[83]) ).
tff(175,plain,
addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(addition(one,star(a)),multiplication(a,a))) = addition(addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a)))),addition(addition(one,star(a)),multiplication(a,a))),
inference(monotonicity,[status(thm)],[174]) ).
tff(176,plain,
addition(addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(one,star(a))),multiplication(a,a)) = addition(addition(multiplication(a,addition(multiplication(star(a),a),one)),multiplication(a,star(a))),addition(addition(one,star(a)),multiplication(a,a))),
inference(symmetry,[status(thm)],[168]) ).
tff(177,plain,
addition(multiplication(a,a),star(a)) = star(a),
inference(transitivity,[status(thm)],[162,165,176,175,173,170,164,160,158,96,87,85,41,32,21]) ).
tff(178,plain,
( ~ ! [A: $i,B: $i] :
( leq(A,B)
<=> ( addition(A,B) = B ) )
| ( leq(multiplication(a,a),star(a))
<=> ( addition(multiplication(a,a),star(a)) = star(a) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(179,plain,
( leq(multiplication(a,a),star(a))
<=> ( addition(multiplication(a,a),star(a)) = star(a) ) ),
inference(unit_resolution,[status(thm)],[178,7]) ).
tff(180,plain,
( ~ leq(multiplication(a,a),star(a))
<=> ~ leq(multiplication(a,a),star(a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(181,axiom,
~ leq(multiplication(a,a),star(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a) ).
tff(182,plain,
~ leq(multiplication(a,a),star(a)),
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
( ~ ( leq(multiplication(a,a),star(a))
<=> ( addition(multiplication(a,a),star(a)) = star(a) ) )
| leq(multiplication(a,a),star(a))
| ( addition(multiplication(a,a),star(a)) != star(a) ) ),
inference(tautology,[status(thm)],[]) ).
tff(184,plain,
( ~ ( leq(multiplication(a,a),star(a))
<=> ( addition(multiplication(a,a),star(a)) = star(a) ) )
| ( addition(multiplication(a,a),star(a)) != star(a) ) ),
inference(unit_resolution,[status(thm)],[183,182]) ).
tff(185,plain,
addition(multiplication(a,a),star(a)) != star(a),
inference(unit_resolution,[status(thm)],[184,179]) ).
tff(186,plain,
$false,
inference(unit_resolution,[status(thm)],[185,177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE170+1.002 : TPTP v9.0.0. Released v5.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 19:05:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.50/0.69 % SZS status Theorem
% 0.50/0.69 % SZS output start Proof
% See solution above
% 0.50/0.71 % E exiting
%------------------------------------------------------------------------------