%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE044-10 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:12:56 AM UTC 2025
% Result : Unsatisfiable 47.78s 47.99s
% Output : Proof 47.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 112
% Syntax : Number of formulae : 402 ( 308 unt; 0 typ; 0 def)
% Number of atoms : 530 ( 512 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 174 ( 63 ~; 59 |; 0 &)
% ( 52 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 17 ( 17 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 : 12 ( 12 usr; 4 con; 0-4 aty)
% Number of variables : 481 ( 443 !; 0 ?; 481 :)
% Comments :
%------------------------------------------------------------------------------
tff(tuple_type,type,
tuple: ( $i * $i ) > $i ).
tff(true_type,type,
true: $i ).
tff(leq_type,type,
leq: ( $i * $i ) > $i ).
tff(star_type,type,
star: $i > $i ).
tff(addition_type,type,
addition: ( $i * $i ) > $i ).
tff(sK1_goals_X0_type,type,
sK1_goals_X0: $i ).
tff(one_type,type,
one: $i ).
tff(sK2_goals_X0_type,type,
sK2_goals_X0: $i ).
tff(ifeq3_type,type,
ifeq3: ( $i * $i * $i * $i ) > $i ).
tff(multiplication_type,type,
multiplication: ( $i * $i ) > $i ).
tff(ifeq2_type,type,
ifeq2: ( $i * $i * $i * $i ) > $i ).
tff(ifeq_type,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(( ( ifeq3(addition(A,B),B,leq(A,B),true) = true )
<=> ( ifeq3(addition(A,B),B,leq(A,B),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( ifeq3(addition(A,B),B,leq(A,B),true) = true )
<=> ! [B: $i,A: $i] : ( ifeq3(addition(A,B),B,leq(A,B),true) = true ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : ( ifeq3(addition(A,B),B,leq(A,B),true) = true )
<=> ! [B: $i,A: $i] : ( ifeq3(addition(A,B),B,leq(A,B),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,A: $i] : ( ifeq3(addition(A,B),B,leq(A,B),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
tff(5,plain,
! [B: $i,A: $i] : ( ifeq3(addition(A,B),B,leq(A,B),true) = true ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( ifeq3(addition(A,B),B,leq(A,B),true) = true ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( ifeq3(addition(A,B),B,leq(A,B),true) = true ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( ifeq3(addition(A,B),B,leq(A,B),true) = true )
| ( ifeq3(addition(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ifeq3(addition(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),true) = true,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [A: $i] :
refl(( ( multiplication(one,A) = A )
<=> ( multiplication(one,A) = A ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [A: $i] : ( multiplication(one,A) = A )
<=> ! [A: $i] : ( multiplication(one,A) = A ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [A: $i] : ( multiplication(one,A) = A )
<=> ! [A: $i] : ( multiplication(one,A) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [A: $i] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
tff(14,plain,
! [A: $i] : ( multiplication(one,A) = A ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [A: $i] : ( multiplication(one,A) = A ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [A: $i] : ( multiplication(one,A) = A ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [A: $i] : ( multiplication(one,A) = A )
| ( multiplication(one,star(addition(one,sK1_goals_X0))) = star(addition(one,sK1_goals_X0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
multiplication(one,star(addition(one,sK1_goals_X0))) = star(addition(one,sK1_goals_X0)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
star(addition(one,sK1_goals_X0)) = multiplication(one,star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [B: $i,A: $i] :
refl(( ( ifeq2(leq(A,B),true,addition(A,B),B) = B )
<=> ( ifeq2(leq(A,B),true,addition(A,B),B) = B ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B )
<=> ! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B )
<=> ! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order_1) ).
tff(24,plain,
! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B )
| ( ifeq2(leq(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),true,addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = star(addition(one,sK1_goals_X0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
ifeq2(leq(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),true,addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = star(addition(one,sK1_goals_X0)),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
^ [A: $i] :
refl(( ( leq(addition(one,multiplication(A,star(A))),star(A)) = true )
<=> ( leq(addition(one,multiplication(A,star(A))),star(A)) = true ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [A: $i] : ( leq(addition(one,multiplication(A,star(A))),star(A)) = true )
<=> ! [A: $i] : ( leq(addition(one,multiplication(A,star(A))),star(A)) = true ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [A: $i] : ( leq(addition(one,multiplication(A,star(A))),star(A)) = true )
<=> ! [A: $i] : ( leq(addition(one,multiplication(A,star(A))),star(A)) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
! [A: $i] : ( leq(addition(one,multiplication(A,star(A))),star(A)) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold_right) ).
tff(33,plain,
! [A: $i] : ( leq(addition(one,multiplication(A,star(A))),star(A)) = true ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [A: $i] : ( leq(addition(one,multiplication(A,star(A))),star(A)) = true ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [A: $i] : ( leq(addition(one,multiplication(A,star(A))),star(A)) = true ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [A: $i] : ( leq(addition(one,multiplication(A,star(A))),star(A)) = true )
| ( leq(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
leq(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))) = true,
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
ifeq2(leq(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),true,addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = ifeq2(true,true,addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
ifeq2(true,true,addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = ifeq2(leq(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),true,addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ifeq2(A,A,B,C) = B )
<=> ( ifeq2(A,A,B,C) = B ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
tff(44,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
ifeq2(true,true,addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))) = ifeq2(true,true,addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
^ [B: $i,A: $i] :
refl(( ( addition(A,B) = addition(B,A) )
<=> ( addition(A,B) = addition(B,A) ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
<=> ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
<=> ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
tff(54,plain,
! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))) = addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),star(addition(one,sK1_goals_X0))) = addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
^ [B: $i,A: $i,C: $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(62,plain,
( ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,axiom,
! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
tff(65,plain,
! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0)))) = addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),star(addition(one,sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0)))) = addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),star(addition(one,sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[68,67]) ).
tff(70,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0)))) = addition(addition(one,star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0)))) = addition(addition(one,star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[70,56]) ).
tff(72,plain,
addition(addition(one,star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(one,addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
addition(one,addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[73,67]) ).
tff(75,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))) = addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))) = addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[75,67]) ).
tff(77,plain,
addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))) = addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
star(addition(one,sK1_goals_X0)) = ifeq2(leq(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),true,addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[28]) ).
tff(79,plain,
star(addition(one,sK1_goals_X0)) = addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),
inference(transitivity,[status(thm)],[78,38,48,77]) ).
tff(80,plain,
addition(one,star(addition(one,sK1_goals_X0))) = addition(one,addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
addition(one,star(addition(one,sK1_goals_X0))) = addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),
inference(transitivity,[status(thm)],[80,74]) ).
tff(82,plain,
addition(addition(one,star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
addition(addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(addition(one,star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(addition(one,one),addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))))) = addition(addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
addition(addition(one,one),addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))))) = addition(addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[84,67]) ).
tff(86,plain,
^ [A: $i] :
refl(( ( addition(A,A) = A )
<=> ( addition(A,A) = A ) )),
inference(bind,[status(th)],[]) ).
tff(87,plain,
( ! [A: $i] : ( addition(A,A) = A )
<=> ! [A: $i] : ( addition(A,A) = A ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,plain,
( ! [A: $i] : ( addition(A,A) = A )
<=> ! [A: $i] : ( addition(A,A) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,axiom,
! [A: $i] : ( addition(A,A) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
tff(90,plain,
! [A: $i] : ( addition(A,A) = A ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
! [A: $i] : ( addition(A,A) = A ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [A: $i] : ( addition(A,A) = A ),
inference(modus_ponens,[status(thm)],[91,87]) ).
tff(93,plain,
( ~ ! [A: $i] : ( addition(A,A) = A )
| ( addition(one,one) = one ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
addition(one,one) = one,
inference(unit_resolution,[status(thm)],[93,92]) ).
tff(95,plain,
addition(addition(one,one),addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))))) = addition(one,addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))))),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
addition(one,addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))))) = addition(addition(one,one),addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))))),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(one,addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))))) = addition(addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
addition(one,addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))))) = addition(addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[97,67]) ).
tff(99,plain,
addition(addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(one,addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))))),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))) = star(addition(one,sK1_goals_X0)),
inference(transitivity,[status(thm)],[76,49,39,28]) ).
tff(101,plain,
addition(addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(star(addition(one,sK1_goals_X0)),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
addition(star(addition(one,sK1_goals_X0)),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(star(addition(one,sK1_goals_X0)),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(star(addition(one,sK1_goals_X0)),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[103,56]) ).
tff(105,plain,
addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = multiplication(one,star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[104,102,99,96,85,83,72,69,60,49,39,28,19]) ).
tff(106,plain,
multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))) = multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))) = multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )
<=> ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ) )),
inference(bind,[status(th)],[]) ).
tff(109,plain,
( ! [B: $i,A: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,plain,
( ! [B: $i,A: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,axiom,
! [B: $i,A: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
tff(112,plain,
! [B: $i,A: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
! [B: $i,A: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ),
inference(skolemize,[status(sab)],[112]) ).
tff(114,plain,
! [B: $i,A: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ),
inference(modus_ponens,[status(thm)],[113,109]) ).
tff(115,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )
| ( multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))) = multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))) = multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[115,114]) ).
tff(117,plain,
multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))) = multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))) = multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),
inference(transitivity,[status(thm)],[117,107]) ).
tff(119,plain,
^ [A: $i] :
refl(( ( multiplication(A,one) = A )
<=> ( multiplication(A,one) = A ) )),
inference(bind,[status(th)],[]) ).
tff(120,plain,
( ! [A: $i] : ( multiplication(A,one) = A )
<=> ! [A: $i] : ( multiplication(A,one) = A ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,plain,
( ! [A: $i] : ( multiplication(A,one) = A )
<=> ! [A: $i] : ( multiplication(A,one) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,axiom,
! [A: $i] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
tff(123,plain,
! [A: $i] : ( multiplication(A,one) = A ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
! [A: $i] : ( multiplication(A,one) = A ),
inference(skolemize,[status(sab)],[123]) ).
tff(125,plain,
! [A: $i] : ( multiplication(A,one) = A ),
inference(modus_ponens,[status(thm)],[124,120]) ).
tff(126,plain,
( ~ ! [A: $i] : ( multiplication(A,one) = A )
| ( multiplication(star(sK1_goals_X0),one) = star(sK1_goals_X0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(127,plain,
multiplication(star(sK1_goals_X0),one) = star(sK1_goals_X0),
inference(unit_resolution,[status(thm)],[126,125]) ).
tff(128,plain,
star(sK1_goals_X0) = multiplication(star(sK1_goals_X0),one),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
addition(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = addition(multiplication(star(sK1_goals_X0),one),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
addition(multiplication(star(sK1_goals_X0),one),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = addition(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
^ [B: $i,A: $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(132,plain,
( ! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,plain,
( ! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,axiom,
! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
tff(135,plain,
! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
inference(skolemize,[status(sab)],[135]) ).
tff(137,plain,
! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
inference(modus_ponens,[status(thm)],[136,132]) ).
tff(138,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
| ( multiplication(star(sK1_goals_X0),addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = addition(multiplication(star(sK1_goals_X0),one),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,plain,
multiplication(star(sK1_goals_X0),addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = addition(multiplication(star(sK1_goals_X0),one),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),
inference(unit_resolution,[status(thm)],[138,137]) ).
tff(140,plain,
addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))) = multiplication(one,star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[76,49,39,28,19]) ).
tff(141,plain,
multiplication(star(sK1_goals_X0),addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))) = multiplication(star(sK1_goals_X0),addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))) = addition(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),
inference(transitivity,[status(thm)],[117,142,139,130]) ).
tff(144,plain,
ifeq3(multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),true) = ifeq3(addition(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),true),
inference(monotonicity,[status(thm)],[143,118]) ).
tff(145,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ifeq3(A,A,B,C) = B )
<=> ( ifeq3(A,A,B,C) = B ) )),
inference(bind,[status(th)],[]) ).
tff(146,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[145]) ).
tff(147,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(148,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
tff(149,plain,
! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[149]) ).
tff(151,plain,
! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[150,146]) ).
tff(152,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B )
| ( ifeq3(multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),true) = leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
ifeq3(multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),true) = leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),
inference(unit_resolution,[status(thm)],[152,151]) ).
tff(154,plain,
leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = ifeq3(multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),true),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(156,plain,
ifeq2(true,true,multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[155,46]) ).
tff(157,plain,
addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[19]) ).
tff(158,plain,
addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))) = addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[157]) ).
tff(159,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )
<=> ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ) )),
inference(bind,[status(th)],[]) ).
tff(160,plain,
( ! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ) ),
inference(quant_intro,[status(thm)],[159]) ).
tff(161,plain,
( ! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(162,axiom,
! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
tff(163,plain,
! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
inference(skolemize,[status(sab)],[163]) ).
tff(165,plain,
! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
inference(modus_ponens,[status(thm)],[164,160]) ).
tff(166,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )
| ( multiplication(addition(sK1_goals_X0,one),star(addition(one,sK1_goals_X0))) = addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(167,plain,
multiplication(addition(sK1_goals_X0,one),star(addition(one,sK1_goals_X0))) = addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[166,165]) ).
tff(168,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(one,sK1_goals_X0) = addition(sK1_goals_X0,one) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(169,plain,
addition(one,sK1_goals_X0) = addition(sK1_goals_X0,one),
inference(unit_resolution,[status(thm)],[168,56]) ).
tff(170,plain,
addition(sK1_goals_X0,one) = addition(one,sK1_goals_X0),
inference(symmetry,[status(thm)],[169]) ).
tff(171,plain,
multiplication(addition(sK1_goals_X0,one),star(addition(one,sK1_goals_X0))) = multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))) = multiplication(addition(sK1_goals_X0,one),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))) = addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[172,167,158]) ).
tff(174,plain,
addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[173]) ).
tff(175,plain,
addition(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(star(addition(one,sK1_goals_X0)),star(addition(one,sK1_goals_X0)))) = addition(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(177,plain,
addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(star(addition(one,sK1_goals_X0)),star(addition(one,sK1_goals_X0)))) = addition(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[176,67]) ).
tff(178,plain,
( ~ ! [A: $i] : ( addition(A,A) = A )
| ( addition(star(addition(one,sK1_goals_X0)),star(addition(one,sK1_goals_X0))) = star(addition(one,sK1_goals_X0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(179,plain,
addition(star(addition(one,sK1_goals_X0)),star(addition(one,sK1_goals_X0))) = star(addition(one,sK1_goals_X0)),
inference(unit_resolution,[status(thm)],[178,92]) ).
tff(180,plain,
addition(star(addition(one,sK1_goals_X0)),star(addition(one,sK1_goals_X0))) = multiplication(one,star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[179,19]) ).
tff(181,plain,
addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(star(addition(one,sK1_goals_X0)),star(addition(one,sK1_goals_X0)))) = addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))) = addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(star(addition(one,sK1_goals_X0)),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))) = star(addition(one,sK1_goals_X0)),
inference(transitivity,[status(thm)],[172,167,182,177,175,104,102,99,96,85,83,72,69,60,49,39,28]) ).
tff(184,plain,
addition(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))) = addition(multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[116]) ).
tff(185,plain,
addition(multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(star(addition(one,sK1_goals_X0)),multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(187,plain,
addition(multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(star(addition(one,sK1_goals_X0)),multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[186,56]) ).
tff(188,plain,
addition(star(addition(one,sK1_goals_X0)),multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0)))) = addition(multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))) = multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[19]) ).
tff(190,plain,
multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))) = multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))) = multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[117,190]) ).
tff(192,plain,
addition(star(addition(one,sK1_goals_X0)),multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0)))) = addition(multiplication(one,star(addition(one,sK1_goals_X0))),multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[19,191]) ).
tff(193,plain,
addition(multiplication(one,star(addition(one,sK1_goals_X0))),multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(star(addition(one,sK1_goals_X0)),multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )
| ( multiplication(addition(one,star(sK1_goals_X0)),star(addition(one,sK1_goals_X0))) = addition(multiplication(one,star(addition(one,sK1_goals_X0))),multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(195,plain,
multiplication(addition(one,star(sK1_goals_X0)),star(addition(one,sK1_goals_X0))) = addition(multiplication(one,star(addition(one,sK1_goals_X0))),multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[194,165]) ).
tff(196,plain,
( ~ ! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B )
| ( ifeq2(leq(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),true,addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),star(sK1_goals_X0)) = star(sK1_goals_X0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(197,plain,
ifeq2(leq(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),true,addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),star(sK1_goals_X0)) = star(sK1_goals_X0),
inference(unit_resolution,[status(thm)],[196,26]) ).
tff(198,plain,
^ [A: $i] :
refl(( ( leq(addition(one,multiplication(star(A),A)),star(A)) = true )
<=> ( leq(addition(one,multiplication(star(A),A)),star(A)) = true ) )),
inference(bind,[status(th)],[]) ).
tff(199,plain,
( ! [A: $i] : ( leq(addition(one,multiplication(star(A),A)),star(A)) = true )
<=> ! [A: $i] : ( leq(addition(one,multiplication(star(A),A)),star(A)) = true ) ),
inference(quant_intro,[status(thm)],[198]) ).
tff(200,plain,
( ! [A: $i] : ( leq(addition(one,multiplication(star(A),A)),star(A)) = true )
<=> ! [A: $i] : ( leq(addition(one,multiplication(star(A),A)),star(A)) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(201,axiom,
! [A: $i] : ( leq(addition(one,multiplication(star(A),A)),star(A)) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold_left) ).
tff(202,plain,
! [A: $i] : ( leq(addition(one,multiplication(star(A),A)),star(A)) = true ),
inference(modus_ponens,[status(thm)],[201,200]) ).
tff(203,plain,
! [A: $i] : ( leq(addition(one,multiplication(star(A),A)),star(A)) = true ),
inference(skolemize,[status(sab)],[202]) ).
tff(204,plain,
! [A: $i] : ( leq(addition(one,multiplication(star(A),A)),star(A)) = true ),
inference(modus_ponens,[status(thm)],[203,199]) ).
tff(205,plain,
( ~ ! [A: $i] : ( leq(addition(one,multiplication(star(A),A)),star(A)) = true )
| ( leq(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(206,plain,
leq(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)) = true,
inference(unit_resolution,[status(thm)],[205,204]) ).
tff(207,plain,
true = leq(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),
inference(symmetry,[status(thm)],[206]) ).
tff(208,plain,
ifeq2(true,true,addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),star(sK1_goals_X0)) = ifeq2(leq(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),true,addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),star(sK1_goals_X0)),
inference(monotonicity,[status(thm)],[207]) ).
tff(209,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),star(sK1_goals_X0)) = addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(210,plain,
ifeq2(true,true,addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),star(sK1_goals_X0)) = addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),
inference(unit_resolution,[status(thm)],[209,46]) ).
tff(211,plain,
addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)) = ifeq2(true,true,addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),star(sK1_goals_X0)),
inference(symmetry,[status(thm)],[210]) ).
tff(212,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(one,addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(sK1_goals_X0))) = addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(213,plain,
addition(one,addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(sK1_goals_X0))) = addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),
inference(unit_resolution,[status(thm)],[212,67]) ).
tff(214,plain,
addition(addition(one,one),addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(sK1_goals_X0))) = addition(one,addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(sK1_goals_X0))),
inference(monotonicity,[status(thm)],[94]) ).
tff(215,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(one,addition(one,addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(sK1_goals_X0)))) = addition(addition(one,one),addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(216,plain,
addition(one,addition(one,addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(sK1_goals_X0)))) = addition(addition(one,one),addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[215,67]) ).
tff(217,plain,
addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)) = addition(one,addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(sK1_goals_X0))),
inference(symmetry,[status(thm)],[213]) ).
tff(218,plain,
ifeq2(leq(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),true,addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),star(sK1_goals_X0)) = ifeq2(true,true,addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),star(sK1_goals_X0)),
inference(symmetry,[status(thm)],[208]) ).
tff(219,plain,
star(sK1_goals_X0) = ifeq2(leq(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),true,addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),star(sK1_goals_X0)),
inference(symmetry,[status(thm)],[197]) ).
tff(220,plain,
star(sK1_goals_X0) = addition(one,addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(sK1_goals_X0))),
inference(transitivity,[status(thm)],[219,218,210,217]) ).
tff(221,plain,
addition(one,star(sK1_goals_X0)) = addition(one,addition(one,addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[220]) ).
tff(222,plain,
addition(one,star(sK1_goals_X0)) = star(sK1_goals_X0),
inference(transitivity,[status(thm)],[221,216,214,213,211,208,197]) ).
tff(223,plain,
multiplication(addition(one,star(sK1_goals_X0)),star(addition(one,sK1_goals_X0))) = multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[222,19]) ).
tff(224,plain,
multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))) = multiplication(addition(one,star(sK1_goals_X0)),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[223]) ).
tff(225,plain,
multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))) = addition(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[117,224,195,193,188,185]) ).
tff(226,plain,
addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))) = multiplication(addition(sK1_goals_X0,one),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[167]) ).
tff(227,plain,
addition(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(star(addition(one,sK1_goals_X0)),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[177]) ).
tff(228,plain,
addition(star(addition(one,sK1_goals_X0)),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[104]) ).
tff(229,plain,
addition(addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(addition(one,one),addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))))),
inference(symmetry,[status(thm)],[85]) ).
tff(230,plain,
addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),star(addition(one,sK1_goals_X0))) = addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[69]) ).
tff(231,plain,
star(addition(one,sK1_goals_X0)) = multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[78,38,48,59,230,71,82,229,95,98,101,228,174,227,181,226,171]) ).
tff(232,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
| ( multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0))))) = addition(multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(233,plain,
multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0))))) = addition(multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0))))),
inference(unit_resolution,[status(thm)],[232,137]) ).
tff(234,plain,
addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0)))) = multiplication(one,star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[69,60,49,39,28,19]) ).
tff(235,plain,
multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0))))) = multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[234]) ).
tff(236,plain,
multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))) = multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0))))),
inference(symmetry,[status(thm)],[235]) ).
tff(237,plain,
multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))) = addition(multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0))))),
inference(transitivity,[status(thm)],[236,233]) ).
tff(238,plain,
leq(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))) = leq(addition(multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0))))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[237,231]) ).
tff(239,plain,
leq(addition(multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0))))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = leq(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[238]) ).
tff(240,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(one,star(addition(one,sK1_goals_X0))) = addition(star(addition(one,sK1_goals_X0)),one) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(241,plain,
addition(one,star(addition(one,sK1_goals_X0))) = addition(star(addition(one,sK1_goals_X0)),one),
inference(unit_resolution,[status(thm)],[240,56]) ).
tff(242,plain,
addition(star(addition(one,sK1_goals_X0)),one) = addition(one,star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
addition(multiplication(one,star(addition(one,sK1_goals_X0))),one) = addition(star(addition(one,sK1_goals_X0)),one),
inference(monotonicity,[status(thm)],[18]) ).
tff(244,plain,
addition(multiplication(one,star(addition(one,sK1_goals_X0))),one) = addition(one,star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[243,242]) ).
tff(245,plain,
multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)) = multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[244]) ).
tff(246,plain,
multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0)))) = multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),
inference(symmetry,[status(thm)],[245]) ).
tff(247,plain,
addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))) = addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[94]) ).
tff(248,plain,
addition(one,star(addition(one,sK1_goals_X0))) = multiplication(one,star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[80,74,247,76,49,39,28,19]) ).
tff(249,plain,
multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0)))) = multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[248]) ).
tff(250,plain,
multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))) = multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[249]) ).
tff(251,plain,
addition(multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0))))) = multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0))))),
inference(symmetry,[status(thm)],[233]) ).
tff(252,plain,
addition(multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0))))) = multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),
inference(transitivity,[status(thm)],[251,235,250,246]) ).
tff(253,plain,
leq(addition(multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0))))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[252,183]) ).
tff(254,plain,
leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))) = leq(addition(multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0))))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[253]) ).
tff(255,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ifeq(A,A,B,C) = B )
<=> ( ifeq(A,A,B,C) = B ) )),
inference(bind,[status(th)],[]) ).
tff(256,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[255]) ).
tff(257,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(258,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_002) ).
tff(259,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[258,257]) ).
tff(260,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[259]) ).
tff(261,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[260,256]) ).
tff(262,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true) = leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(263,plain,
ifeq(true,true,leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true) = leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[262,261]) ).
tff(264,plain,
addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one) = addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[58]) ).
tff(265,plain,
addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))) = multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[226,171]) ).
tff(266,plain,
addition(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))),one) = addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),
inference(monotonicity,[status(thm)],[265]) ).
tff(267,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)) = addition(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))),one) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(268,plain,
addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)) = addition(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))),one),
inference(unit_resolution,[status(thm)],[267,67]) ).
tff(269,plain,
addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)) = addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(transitivity,[status(thm)],[268,266,264]) ).
tff(270,plain,
leq(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))) = leq(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[269]) ).
tff(271,plain,
leq(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))) = leq(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[270]) ).
tff(272,plain,
true = leq(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[37]) ).
tff(273,plain,
true = leq(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[272,271]) ).
tff(274,plain,
ifeq(true,true,leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true) = ifeq(leq(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true,leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true),
inference(monotonicity,[status(thm)],[273]) ).
tff(275,plain,
ifeq(leq(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true,leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true) = ifeq(true,true,leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true),
inference(symmetry,[status(thm)],[274]) ).
tff(276,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true )
<=> ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(277,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true ) ),
inference(quant_intro,[status(thm)],[276]) ).
tff(278,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(279,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction_left) ).
tff(280,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true ),
inference(modus_ponens,[status(thm)],[279,278]) ).
tff(281,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true ),
inference(skolemize,[status(sab)],[280]) ).
tff(282,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true ),
inference(modus_ponens,[status(thm)],[281,277]) ).
tff(283,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true )
| ( ifeq(leq(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true,leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(284,plain,
ifeq(leq(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true,leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true) = true,
inference(unit_resolution,[status(thm)],[283,282]) ).
tff(285,plain,
true = ifeq(leq(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true,leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true),
inference(symmetry,[status(thm)],[284]) ).
tff(286,plain,
true = leq(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[285,275,263,254,239]) ).
tff(287,plain,
ifeq2(true,true,multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = ifeq2(leq(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),true,addition(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[286,225,183]) ).
tff(288,plain,
ifeq2(leq(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),true,addition(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = ifeq2(true,true,multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[287]) ).
tff(289,plain,
( ~ ! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B )
| ( ifeq2(leq(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),true,addition(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = star(addition(one,sK1_goals_X0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(290,plain,
ifeq2(leq(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),true,addition(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = star(addition(one,sK1_goals_X0)),
inference(unit_resolution,[status(thm)],[289,26]) ).
tff(291,plain,
star(addition(one,sK1_goals_X0)) = ifeq2(leq(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),true,addition(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[290]) ).
tff(292,plain,
multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))) = multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),
inference(transitivity,[status(thm)],[172,167,182,177,175,104,102,99,96,85,83,72,69,60,49,39,28,291,288,156,117,107]) ).
tff(293,plain,
leq(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),
inference(monotonicity,[status(thm)],[292]) ).
tff(294,plain,
leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))) = leq(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[231]) ).
tff(295,plain,
leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))) = true,
inference(transitivity,[status(thm)],[294,293,154,144,9]) ).
tff(296,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ifeq(leq(addition(multiplication(A,B),C),A),true,leq(multiplication(C,star(B)),A),true) = true )
<=> ( ifeq(leq(addition(multiplication(A,B),C),A),true,leq(multiplication(C,star(B)),A),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(297,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),A),true,leq(multiplication(C,star(B)),A),true) = true )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),A),true,leq(multiplication(C,star(B)),A),true) = true ) ),
inference(quant_intro,[status(thm)],[296]) ).
tff(298,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),A),true,leq(multiplication(C,star(B)),A),true) = true )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),A),true,leq(multiplication(C,star(B)),A),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(299,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),A),true,leq(multiplication(C,star(B)),A),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction_right) ).
tff(300,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),A),true,leq(multiplication(C,star(B)),A),true) = true ),
inference(modus_ponens,[status(thm)],[299,298]) ).
tff(301,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),A),true,leq(multiplication(C,star(B)),A),true) = true ),
inference(skolemize,[status(sab)],[300]) ).
tff(302,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),A),true,leq(multiplication(C,star(B)),A),true) = true ),
inference(modus_ponens,[status(thm)],[301,297]) ).
tff(303,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),A),true,leq(multiplication(C,star(B)),A),true) = true )
| ( ifeq(leq(addition(multiplication(star(sK2_goals_X0),addition(sK2_goals_X0,one)),one),star(sK2_goals_X0)),true,leq(multiplication(one,star(addition(sK2_goals_X0,one))),star(sK2_goals_X0)),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(304,plain,
ifeq(leq(addition(multiplication(star(sK2_goals_X0),addition(sK2_goals_X0,one)),one),star(sK2_goals_X0)),true,leq(multiplication(one,star(addition(sK2_goals_X0,one))),star(sK2_goals_X0)),true) = true,
inference(unit_resolution,[status(thm)],[303,302]) ).
tff(305,plain,
( ~ ! [A: $i] : ( multiplication(one,A) = A )
| ( multiplication(one,star(addition(one,sK2_goals_X0))) = star(addition(one,sK2_goals_X0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(306,plain,
multiplication(one,star(addition(one,sK2_goals_X0))) = star(addition(one,sK2_goals_X0)),
inference(unit_resolution,[status(thm)],[305,16]) ).
tff(307,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(one,sK2_goals_X0) = addition(sK2_goals_X0,one) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(308,plain,
addition(one,sK2_goals_X0) = addition(sK2_goals_X0,one),
inference(unit_resolution,[status(thm)],[307,56]) ).
tff(309,plain,
addition(sK2_goals_X0,one) = addition(one,sK2_goals_X0),
inference(symmetry,[status(thm)],[308]) ).
tff(310,plain,
star(addition(sK2_goals_X0,one)) = star(addition(one,sK2_goals_X0)),
inference(monotonicity,[status(thm)],[309]) ).
tff(311,plain,
multiplication(one,star(addition(sK2_goals_X0,one))) = multiplication(one,star(addition(one,sK2_goals_X0))),
inference(monotonicity,[status(thm)],[310]) ).
tff(312,plain,
multiplication(one,star(addition(sK2_goals_X0,one))) = star(addition(one,sK2_goals_X0)),
inference(transitivity,[status(thm)],[311,306]) ).
tff(313,plain,
leq(multiplication(one,star(addition(sK2_goals_X0,one))),star(sK2_goals_X0)) = leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),
inference(monotonicity,[status(thm)],[312]) ).
tff(314,plain,
leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)) = leq(multiplication(one,star(addition(sK2_goals_X0,one))),star(sK2_goals_X0)),
inference(symmetry,[status(thm)],[313]) ).
tff(315,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(one,star(sK2_goals_X0))) = addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(316,plain,
addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(one,star(sK2_goals_X0))) = addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)),
inference(unit_resolution,[status(thm)],[315,67]) ).
tff(317,plain,
addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)) = addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(one,star(sK2_goals_X0))),
inference(symmetry,[status(thm)],[316]) ).
tff(318,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))) = addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(319,plain,
addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))) = addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),
inference(unit_resolution,[status(thm)],[318,56]) ).
tff(320,plain,
addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one) = addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),
inference(symmetry,[status(thm)],[319]) ).
tff(321,plain,
addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)) = addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),
inference(monotonicity,[status(thm)],[320]) ).
tff(322,plain,
addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)) = addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)),
inference(symmetry,[status(thm)],[321]) ).
tff(323,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(one,addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0))) = addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(324,plain,
addition(one,addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0))) = addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),
inference(unit_resolution,[status(thm)],[323,67]) ).
tff(325,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(one,addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0))) = addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)),one) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(326,plain,
addition(one,addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0))) = addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)),one),
inference(unit_resolution,[status(thm)],[325,56]) ).
tff(327,plain,
addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)),one) = addition(one,addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0))),
inference(symmetry,[status(thm)],[326]) ).
tff(328,plain,
( ~ ! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B )
| ( ifeq2(leq(addition(one,multiplication(star(sK2_goals_X0),sK2_goals_X0)),star(sK2_goals_X0)),true,addition(addition(one,multiplication(star(sK2_goals_X0),sK2_goals_X0)),star(sK2_goals_X0)),star(sK2_goals_X0)) = star(sK2_goals_X0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(329,plain,
ifeq2(leq(addition(one,multiplication(star(sK2_goals_X0),sK2_goals_X0)),star(sK2_goals_X0)),true,addition(addition(one,multiplication(star(sK2_goals_X0),sK2_goals_X0)),star(sK2_goals_X0)),star(sK2_goals_X0)) = star(sK2_goals_X0),
inference(unit_resolution,[status(thm)],[328,26]) ).
tff(330,plain,
( ~ ! [A: $i] : ( leq(addition(one,multiplication(star(A),A)),star(A)) = true )
| ( leq(addition(one,multiplication(star(sK2_goals_X0),sK2_goals_X0)),star(sK2_goals_X0)) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(331,plain,
leq(addition(one,multiplication(star(sK2_goals_X0),sK2_goals_X0)),star(sK2_goals_X0)) = true,
inference(unit_resolution,[status(thm)],[330,204]) ).
tff(332,plain,
true = leq(addition(one,multiplication(star(sK2_goals_X0),sK2_goals_X0)),star(sK2_goals_X0)),
inference(symmetry,[status(thm)],[331]) ).
tff(333,plain,
ifeq2(true,true,addition(addition(one,multiplication(star(sK2_goals_X0),sK2_goals_X0)),star(sK2_goals_X0)),star(sK2_goals_X0)) = ifeq2(leq(addition(one,multiplication(star(sK2_goals_X0),sK2_goals_X0)),star(sK2_goals_X0)),true,addition(addition(one,multiplication(star(sK2_goals_X0),sK2_goals_X0)),star(sK2_goals_X0)),star(sK2_goals_X0)),
inference(monotonicity,[status(thm)],[332]) ).
tff(334,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,addition(addition(one,multiplication(star(sK2_goals_X0),sK2_goals_X0)),star(sK2_goals_X0)),star(sK2_goals_X0)) = addition(addition(one,multiplication(star(sK2_goals_X0),sK2_goals_X0)),star(sK2_goals_X0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(335,plain,
ifeq2(true,true,addition(addition(one,multiplication(star(sK2_goals_X0),sK2_goals_X0)),star(sK2_goals_X0)),star(sK2_goals_X0)) = addition(addition(one,multiplication(star(sK2_goals_X0),sK2_goals_X0)),star(sK2_goals_X0)),
inference(unit_resolution,[status(thm)],[334,46]) ).
tff(336,plain,
addition(addition(one,multiplication(star(sK2_goals_X0),sK2_goals_X0)),star(sK2_goals_X0)) = ifeq2(true,true,addition(addition(one,multiplication(star(sK2_goals_X0),sK2_goals_X0)),star(sK2_goals_X0)),star(sK2_goals_X0)),
inference(symmetry,[status(thm)],[335]) ).
tff(337,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(one,multiplication(star(sK2_goals_X0),sK2_goals_X0)) = addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(338,plain,
addition(one,multiplication(star(sK2_goals_X0),sK2_goals_X0)) = addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one),
inference(unit_resolution,[status(thm)],[337,56]) ).
tff(339,plain,
addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one) = addition(one,multiplication(star(sK2_goals_X0),sK2_goals_X0)),
inference(symmetry,[status(thm)],[338]) ).
tff(340,plain,
addition(addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one),star(sK2_goals_X0)) = addition(addition(one,multiplication(star(sK2_goals_X0),sK2_goals_X0)),star(sK2_goals_X0)),
inference(monotonicity,[status(thm)],[339]) ).
tff(341,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one),star(sK2_goals_X0)) = addition(star(sK2_goals_X0),addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(342,plain,
addition(addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one),star(sK2_goals_X0)) = addition(star(sK2_goals_X0),addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one)),
inference(unit_resolution,[status(thm)],[341,56]) ).
tff(343,plain,
addition(star(sK2_goals_X0),addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one)) = addition(addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one),star(sK2_goals_X0)),
inference(symmetry,[status(thm)],[342]) ).
tff(344,plain,
addition(star(sK2_goals_X0),addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one)) = star(sK2_goals_X0),
inference(transitivity,[status(thm)],[343,340,336,333,329]) ).
tff(345,plain,
addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(star(sK2_goals_X0),addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one))) = addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)),
inference(monotonicity,[status(thm)],[344]) ).
tff(346,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(star(sK2_goals_X0),addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one))) = addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)),addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(347,plain,
addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(star(sK2_goals_X0),addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one))) = addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)),addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one)),
inference(unit_resolution,[status(thm)],[346,67]) ).
tff(348,plain,
addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)),addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one)) = addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(star(sK2_goals_X0),addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one))),
inference(symmetry,[status(thm)],[347]) ).
tff(349,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)),addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one)) = addition(addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one),addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(350,plain,
addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)),addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one)) = addition(addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one),addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0))),
inference(unit_resolution,[status(thm)],[349,56]) ).
tff(351,plain,
addition(addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one),addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0))) = addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)),addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one)),
inference(symmetry,[status(thm)],[350]) ).
tff(352,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),addition(one,addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)))) = addition(addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one),addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(353,plain,
addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),addition(one,addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)))) = addition(addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),one),addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0))),
inference(unit_resolution,[status(thm)],[352,67]) ).
tff(354,plain,
addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)) = addition(one,addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0))),
inference(symmetry,[status(thm)],[324]) ).
tff(355,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),star(sK2_goals_X0)) = addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(356,plain,
ifeq2(true,true,addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),star(sK2_goals_X0)) = addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),
inference(unit_resolution,[status(thm)],[355,46]) ).
tff(357,plain,
( ~ ! [A: $i] : ( leq(addition(one,multiplication(A,star(A))),star(A)) = true )
| ( leq(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(358,plain,
leq(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)) = true,
inference(unit_resolution,[status(thm)],[357,35]) ).
tff(359,plain,
true = leq(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),
inference(symmetry,[status(thm)],[358]) ).
tff(360,plain,
ifeq2(true,true,addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),star(sK2_goals_X0)) = ifeq2(leq(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),true,addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),star(sK2_goals_X0)),
inference(monotonicity,[status(thm)],[359]) ).
tff(361,plain,
ifeq2(leq(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),true,addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),star(sK2_goals_X0)) = ifeq2(true,true,addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),star(sK2_goals_X0)),
inference(symmetry,[status(thm)],[360]) ).
tff(362,plain,
( ~ ! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B )
| ( ifeq2(leq(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),true,addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),star(sK2_goals_X0)) = star(sK2_goals_X0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(363,plain,
ifeq2(leq(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),true,addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),star(sK2_goals_X0)) = star(sK2_goals_X0),
inference(unit_resolution,[status(thm)],[362,26]) ).
tff(364,plain,
star(sK2_goals_X0) = ifeq2(leq(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),true,addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),star(sK2_goals_X0)),
inference(symmetry,[status(thm)],[363]) ).
tff(365,plain,
star(sK2_goals_X0) = addition(one,addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0))),
inference(transitivity,[status(thm)],[364,361,356,354]) ).
tff(366,plain,
addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),star(sK2_goals_X0)) = addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),addition(one,addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)))),
inference(monotonicity,[status(thm)],[365]) ).
tff(367,plain,
( ~ ! [A: $i] : ( multiplication(A,one) = A )
| ( multiplication(star(sK2_goals_X0),one) = star(sK2_goals_X0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(368,plain,
multiplication(star(sK2_goals_X0),one) = star(sK2_goals_X0),
inference(unit_resolution,[status(thm)],[367,125]) ).
tff(369,plain,
addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),multiplication(star(sK2_goals_X0),one)) = addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),star(sK2_goals_X0)),
inference(monotonicity,[status(thm)],[368]) ).
tff(370,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
| ( multiplication(star(sK2_goals_X0),addition(sK2_goals_X0,one)) = addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),multiplication(star(sK2_goals_X0),one)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(371,plain,
multiplication(star(sK2_goals_X0),addition(sK2_goals_X0,one)) = addition(multiplication(star(sK2_goals_X0),sK2_goals_X0),multiplication(star(sK2_goals_X0),one)),
inference(unit_resolution,[status(thm)],[370,137]) ).
tff(372,plain,
multiplication(star(sK2_goals_X0),addition(sK2_goals_X0,one)) = addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)),
inference(transitivity,[status(thm)],[371,369,366,353,351,348,345]) ).
tff(373,plain,
addition(multiplication(star(sK2_goals_X0),addition(sK2_goals_X0,one)),one) = addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)),one),
inference(monotonicity,[status(thm)],[372]) ).
tff(374,plain,
addition(multiplication(star(sK2_goals_X0),addition(sK2_goals_X0,one)),one) = addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(one,star(sK2_goals_X0))),
inference(transitivity,[status(thm)],[373,327,324,322,317]) ).
tff(375,plain,
leq(addition(multiplication(star(sK2_goals_X0),addition(sK2_goals_X0,one)),one),star(sK2_goals_X0)) = leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(one,star(sK2_goals_X0))),star(sK2_goals_X0)),
inference(monotonicity,[status(thm)],[374]) ).
tff(376,plain,
leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(one,star(sK2_goals_X0))),star(sK2_goals_X0)) = leq(addition(multiplication(star(sK2_goals_X0),addition(sK2_goals_X0,one)),one),star(sK2_goals_X0)),
inference(symmetry,[status(thm)],[375]) ).
tff(377,plain,
star(sK2_goals_X0) = multiplication(star(sK2_goals_X0),one),
inference(symmetry,[status(thm)],[368]) ).
tff(378,plain,
addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)) = ifeq2(true,true,addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),star(sK2_goals_X0)),
inference(symmetry,[status(thm)],[356]) ).
tff(379,plain,
addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(one,star(sK2_goals_X0))) = multiplication(star(sK2_goals_X0),one),
inference(transitivity,[status(thm)],[316,321,378,360,363,377]) ).
tff(380,plain,
leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(one,star(sK2_goals_X0))),star(sK2_goals_X0)) = leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),
inference(monotonicity,[status(thm)],[379]) ).
tff(381,plain,
leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)) = leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(one,star(sK2_goals_X0))),star(sK2_goals_X0)),
inference(symmetry,[status(thm)],[380]) ).
tff(382,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),true) = leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(383,plain,
ifeq(true,true,leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),true) = leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),
inference(unit_resolution,[status(thm)],[382,261]) ).
tff(384,plain,
leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)) = leq(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),
inference(monotonicity,[status(thm)],[320]) ).
tff(385,plain,
leq(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)) = leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)),
inference(symmetry,[status(thm)],[384]) ).
tff(386,plain,
true = leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)),
inference(transitivity,[status(thm)],[359,385]) ).
tff(387,plain,
ifeq(true,true,leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),true) = ifeq(leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)),true,leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),true),
inference(monotonicity,[status(thm)],[386]) ).
tff(388,plain,
ifeq(leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)),true,leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),true) = ifeq(true,true,leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),true),
inference(symmetry,[status(thm)],[387]) ).
tff(389,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true )
| ( ifeq(leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)),true,leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(390,plain,
ifeq(leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)),true,leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),true) = true,
inference(unit_resolution,[status(thm)],[389,282]) ).
tff(391,plain,
true = ifeq(leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)),true,leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),true),
inference(symmetry,[status(thm)],[390]) ).
tff(392,plain,
true = leq(addition(multiplication(star(sK2_goals_X0),addition(sK2_goals_X0,one)),one),star(sK2_goals_X0)),
inference(transitivity,[status(thm)],[391,388,383,381,376]) ).
tff(393,plain,
ifeq(true,true,leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),true) = ifeq(leq(addition(multiplication(star(sK2_goals_X0),addition(sK2_goals_X0,one)),one),star(sK2_goals_X0)),true,leq(multiplication(one,star(addition(sK2_goals_X0,one))),star(sK2_goals_X0)),true),
inference(monotonicity,[status(thm)],[392,314]) ).
tff(394,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),true) = leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(395,plain,
ifeq(true,true,leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),true) = leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),
inference(unit_resolution,[status(thm)],[394,261]) ).
tff(396,plain,
leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)) = ifeq(true,true,leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),true),
inference(symmetry,[status(thm)],[395]) ).
tff(397,plain,
leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)) = true,
inference(transitivity,[status(thm)],[396,393,304]) ).
tff(398,plain,
tuple(leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = tuple(true,true),
inference(monotonicity,[status(thm)],[397,295]) ).
tff(399,plain,
( ( tuple(leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) != tuple(true,true) )
<=> ( tuple(leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) != tuple(true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(400,axiom,
tuple(leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) != tuple(true,true),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
tff(401,plain,
tuple(leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) != tuple(true,true),
inference(modus_ponens,[status(thm)],[400,399]) ).
tff(402,plain,
$false,
inference(unit_resolution,[status(thm)],[401,398]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KLE044-10 : TPTP v9.0.0. Released v7.3.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n010.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 18:57:41 EDT 2025
% 0.13/0.34 % CPUTime :
% 47.78/47.99 % SZS status Unsatisfiable
% 47.78/47.99 % SZS output start Proof
% See solution above
% 47.88/48.05 % E exiting
%------------------------------------------------------------------------------