TSTP Solution File: RNG006-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG006-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 : Tue Sep 20 03:17:37 EDT 2022
% Result : Unsatisfiable 0.16s 0.46s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 39
% Syntax : Number of formulae : 68 ( 18 unt; 10 typ; 0 def)
% Number of atoms : 337 ( 0 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 509 ( 246 ~; 234 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 3 >; 4 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-1 aty)
% Number of variables : 237 ( 217 !; 0 ?; 237 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(additive_inverse_type,type,
additive_inverse: $i > $i ).
tff(aPc_type,type,
aPc: $i ).
tff(c_type,type,
c: $i ).
tff(a_type,type,
a: $i ).
tff(sum_type,type,
sum: ( $i * $i * $i ) > $o ).
tff(aPb_S_IaPc_type,type,
aPb_S_IaPc: $i ).
tff(aPb_type,type,
aPb: $i ).
tff(bS_Ic_type,type,
bS_Ic: $i ).
tff(b_type,type,
b: $i ).
tff(1,plain,
( product(a,c,aPc)
<=> product(a,c,aPc) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
product(a,c,aPc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c) ).
tff(3,plain,
product(a,c,aPc),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ~ product(A,B,C)
| product(A,additive_inverse(B),additive_inverse(C)) )
<=> ( ~ product(A,B,C)
| product(A,additive_inverse(B),additive_inverse(C)) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(A,additive_inverse(B),additive_inverse(C)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(A,additive_inverse(B),additive_inverse(C)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(A,additive_inverse(B),additive_inverse(C)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(A,additive_inverse(B),additive_inverse(C)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(A,additive_inverse(B),additive_inverse(C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_lemma1) ).
tff(8,plain,
! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(A,additive_inverse(B),additive_inverse(C)) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(A,additive_inverse(B),additive_inverse(C)) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(A,additive_inverse(B),additive_inverse(C)) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(A,additive_inverse(B),additive_inverse(C)) )
| ~ product(a,c,aPc)
| product(a,additive_inverse(c),additive_inverse(aPc)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(A,additive_inverse(B),additive_inverse(C)) )
| ~ product(a,c,aPc)
| product(a,additive_inverse(c),additive_inverse(aPc)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(A,additive_inverse(B),additive_inverse(C)) )
| ~ product(a,c,aPc)
| product(a,additive_inverse(c),additive_inverse(aPc)) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(A,additive_inverse(B),additive_inverse(C)) )
| ~ product(a,c,aPc)
| product(a,additive_inverse(c),additive_inverse(aPc)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
product(a,additive_inverse(c),additive_inverse(aPc)),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( sum(aPb,additive_inverse(aPc),aPb_S_IaPc)
<=> sum(aPb,additive_inverse(aPc),aPb_S_IaPc) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aPb_plus_IaPc) ).
tff(17,plain,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
<=> ( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
tff(22,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(aPb,additive_inverse(aPc),aPb_S_IaPc)
| sum(additive_inverse(aPc),aPb,aPb_S_IaPc) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(aPb,additive_inverse(aPc),aPb_S_IaPc)
| sum(additive_inverse(aPc),aPb,aPb_S_IaPc) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(aPb,additive_inverse(aPc),aPb_S_IaPc)
| sum(additive_inverse(aPc),aPb,aPb_S_IaPc) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(aPb,additive_inverse(aPc),aPb_S_IaPc)
| sum(additive_inverse(aPc),aPb,aPb_S_IaPc) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
sum(additive_inverse(aPc),aPb,aPb_S_IaPc),
inference(unit_resolution,[status(thm)],[27,24,17]) ).
tff(29,plain,
( sum(b,additive_inverse(c),bS_Ic)
<=> sum(b,additive_inverse(c),bS_Ic) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
sum(b,additive_inverse(c),bS_Ic),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_inverse_c) ).
tff(31,plain,
sum(b,additive_inverse(c),bS_Ic),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(b,additive_inverse(c),bS_Ic)
| sum(additive_inverse(c),b,bS_Ic) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(b,additive_inverse(c),bS_Ic)
| sum(additive_inverse(c),b,bS_Ic) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(b,additive_inverse(c),bS_Ic)
| sum(additive_inverse(c),b,bS_Ic) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(b,additive_inverse(c),bS_Ic)
| sum(additive_inverse(c),b,bS_Ic) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
sum(additive_inverse(c),b,bS_Ic),
inference(unit_resolution,[status(thm)],[34,24,31]) ).
tff(36,plain,
( ~ product(a,bS_Ic,aPb_S_IaPc)
<=> ~ product(a,bS_Ic,aPb_S_IaPc) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
~ product(a,bS_Ic,aPb_S_IaPc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_times_bS_Ic_is_aPb_S__IaPc) ).
tff(38,plain,
~ product(a,bS_Ic,aPb_S_IaPc),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
( product(a,b,aPb)
<=> product(a,b,aPb) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
product(a,b,aPb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
tff(41,plain,
product(a,b,aPb),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
^ [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
refl(
( ( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
<=> ( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
^ [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) )),
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ) )),
rewrite(
( ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ) )),
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ) )),
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(X,V3,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4)
| product(X,V3,V4) ) )),
rewrite(
( ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4)
| product(X,V3,V4) )
<=> ( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ) )),
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(X,V3,V4) )
<=> ( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(X,V3,V4) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,axiom,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(X,V3,V4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
tff(48,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) ),
inference(modus_ponens,[status(thm)],[50,43]) ).
tff(52,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
| product(a,bS_Ic,aPb_S_IaPc)
| ~ product(a,b,aPb)
| ~ sum(additive_inverse(c),b,bS_Ic)
| ~ product(a,additive_inverse(c),additive_inverse(aPc))
| ~ sum(additive_inverse(aPc),aPb,aPb_S_IaPc) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
| product(a,bS_Ic,aPb_S_IaPc)
| ~ product(a,b,aPb)
| ~ sum(additive_inverse(c),b,bS_Ic)
| ~ product(a,additive_inverse(c),additive_inverse(aPc))
| ~ sum(additive_inverse(aPc),aPb,aPb_S_IaPc) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ( product(a,bS_Ic,aPb_S_IaPc)
| ~ sum(additive_inverse(c),b,bS_Ic)
| ~ product(a,b,aPb)
| ~ product(a,additive_inverse(c),additive_inverse(aPc))
| ~ sum(additive_inverse(aPc),aPb,aPb_S_IaPc) )
<=> ( product(a,bS_Ic,aPb_S_IaPc)
| ~ product(a,b,aPb)
| ~ sum(additive_inverse(c),b,bS_Ic)
| ~ product(a,additive_inverse(c),additive_inverse(aPc))
| ~ sum(additive_inverse(aPc),aPb,aPb_S_IaPc) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
| product(a,bS_Ic,aPb_S_IaPc)
| ~ sum(additive_inverse(c),b,bS_Ic)
| ~ product(a,b,aPb)
| ~ product(a,additive_inverse(c),additive_inverse(aPc))
| ~ sum(additive_inverse(aPc),aPb,aPb_S_IaPc) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
| product(a,bS_Ic,aPb_S_IaPc)
| ~ product(a,b,aPb)
| ~ sum(additive_inverse(c),b,bS_Ic)
| ~ product(a,additive_inverse(c),additive_inverse(aPc))
| ~ sum(additive_inverse(aPc),aPb,aPb_S_IaPc) ) ),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
| product(a,bS_Ic,aPb_S_IaPc)
| ~ sum(additive_inverse(c),b,bS_Ic)
| ~ product(a,b,aPb)
| ~ product(a,additive_inverse(c),additive_inverse(aPc))
| ~ sum(additive_inverse(aPc),aPb,aPb_S_IaPc) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
| product(a,bS_Ic,aPb_S_IaPc)
| ~ product(a,b,aPb)
| ~ sum(additive_inverse(c),b,bS_Ic)
| ~ product(a,additive_inverse(c),additive_inverse(aPc))
| ~ sum(additive_inverse(aPc),aPb,aPb_S_IaPc) ) ),
inference(transitivity,[status(thm)],[54,52]) ).
tff(56,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
| product(a,bS_Ic,aPb_S_IaPc)
| ~ sum(additive_inverse(c),b,bS_Ic)
| ~ product(a,b,aPb)
| ~ product(a,additive_inverse(c),additive_inverse(aPc))
| ~ sum(additive_inverse(aPc),aPb,aPb_S_IaPc) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ sum(V1,V2,V4) )
| product(a,bS_Ic,aPb_S_IaPc)
| ~ product(a,b,aPb)
| ~ sum(additive_inverse(c),b,bS_Ic)
| ~ product(a,additive_inverse(c),additive_inverse(aPc))
| ~ sum(additive_inverse(aPc),aPb,aPb_S_IaPc) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
$false,
inference(unit_resolution,[status(thm)],[57,51,41,38,35,28,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : RNG006-2 : TPTP v8.1.0. Released v1.0.0.
% 0.05/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.31 % Computer : n019.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Sep 2 21:19:35 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.16/0.46 % SZS status Unsatisfiable
% 0.16/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------