%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG040-2 : TPTP v9.0.0. Released v1.0.0.
% 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 05:23:58 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 32
% Syntax : Number of formulae : 63 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 321 ( 0 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 469 ( 227 ~; 214 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 233 ( 213 !; 0 ?; 233 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(n_type,type,
n: $i ).
tff(c_type,type,
c: $i ).
tff(a_type,type,
a: $i ).
tff(l_type,type,
l: $i ).
tff(b_type,type,
b: $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(d_type,type,
d: $i ).
tff(sum_type,type,
sum: ( $i * $i * $i ) > $o ).
tff(1,plain,
( product(c,a,n)
<=> product(c,a,n) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
product(c,a,n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_plus_a) ).
tff(3,plain,
product(c,a,n),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ product(A,B,C)
| product(B,A,C) )
<=> ( ~ product(A,B,C)
| product(B,A,C) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(B,A,C) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(B,A,C) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(B,A,C) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(B,A,C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(B,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_symmetry) ).
tff(8,plain,
! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(B,A,C) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(B,A,C) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(B,A,C) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(B,A,C) )
| ~ product(c,a,n)
| product(a,c,n) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(B,A,C) )
| ~ product(c,a,n)
| product(a,c,n) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(B,A,C) )
| ~ product(c,a,n)
| product(a,c,n) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(B,A,C) )
| ~ product(c,a,n)
| product(a,c,n) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
product(a,c,n),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( product(b,a,l)
<=> product(b,a,l) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
product(b,a,l),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_a) ).
tff(17,plain,
product(b,a,l),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(B,A,C) )
| ~ product(b,a,l)
| product(a,b,l) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(B,A,C) )
| ~ product(b,a,l)
| product(a,b,l) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(B,A,C) )
| ~ product(b,a,l)
| product(a,b,l) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(B,A,C) )
| ~ product(b,a,l)
| product(a,b,l) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
product(a,b,l),
inference(unit_resolution,[status(thm)],[20,10,17]) ).
tff(22,plain,
( product(d,a,additive_identity)
<=> product(d,a,additive_identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
product(d,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_plus_a) ).
tff(24,plain,
product(d,a,additive_identity),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(B,A,C) )
| ~ product(d,a,additive_identity)
| product(a,d,additive_identity) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(B,A,C) )
| ~ product(d,a,additive_identity)
| product(a,d,additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(B,A,C) )
| ~ product(d,a,additive_identity)
| product(a,d,additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| product(B,A,C) )
| ~ product(d,a,additive_identity)
| product(a,d,additive_identity) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
product(a,d,additive_identity),
inference(unit_resolution,[status(thm)],[27,10,24]) ).
tff(29,plain,
( ~ sum(l,n,additive_identity)
<=> ~ sum(l,n,additive_identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
~ sum(l,n,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
tff(31,plain,
~ sum(l,n,additive_identity),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,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(33,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)],[32]) ).
tff(34,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(35,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(36,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(n,l,additive_identity)
| sum(l,n,additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(n,l,additive_identity)
| sum(l,n,additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(n,l,additive_identity)
| sum(l,n,additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(n,l,additive_identity)
| sum(l,n,additive_identity) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
~ sum(n,l,additive_identity),
inference(unit_resolution,[status(thm)],[41,38,31]) ).
tff(43,plain,
( sum(b,c,d)
<=> sum(b,c,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
sum(b,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_c) ).
tff(45,plain,
sum(b,c,d),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(b,c,d)
| sum(c,b,d) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(b,c,d)
| sum(c,b,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(b,c,d)
| sum(c,b,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) )
| ~ sum(b,c,d)
| sum(c,b,d) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
sum(c,b,d),
inference(unit_resolution,[status(thm)],[48,38,45]) ).
tff(50,plain,
^ [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
refl(( ( 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)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,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)
| ~ product(X,V3,V4) )
<=> ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ product(X,V3,V4) ) )),
rewrite(( ( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| ~ product(X,V3,V4) )
<=> ( ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) )),
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4) )
<=> ( ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) )),
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4)
| sum(V1,V2,V4) )
<=> ( ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| sum(V1,V2,V4) ) )),
rewrite(( ( ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1)
| sum(V1,V2,V4) )
<=> ( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) )),
( ( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4)
| sum(V1,V2,V4) )
<=> ( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) )),
inference(bind,[status(th)],[]) ).
tff(54,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)
| ~ product(X,V3,V4)
| sum(V1,V2,V4) )
<=> ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,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)
| ~ product(X,V3,V4)
| sum(V1,V2,V4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
tff(56,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(modus_ponens,[status(thm)],[58,51]) ).
tff(60,plain,
( ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
| sum(n,l,additive_identity)
| ~ product(a,d,additive_identity)
| ~ sum(c,b,d)
| ~ product(a,b,l)
| ~ product(a,c,n) )
<=> ( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
| sum(n,l,additive_identity)
| ~ product(a,d,additive_identity)
| ~ sum(c,b,d)
| ~ product(a,b,l)
| ~ product(a,c,n) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
| sum(n,l,additive_identity)
| ~ product(a,d,additive_identity)
| ~ sum(c,b,d)
| ~ product(a,b,l)
| ~ product(a,c,n) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [Z: $i,Y: $i,V1: $i,X: $i,V2: $i,V3: $i,V4: $i] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) )
| sum(n,l,additive_identity)
| ~ product(a,d,additive_identity)
| ~ sum(c,b,d)
| ~ product(a,b,l)
| ~ product(a,c,n) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
$false,
inference(unit_resolution,[status(thm)],[62,59,49,42,28,21,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : RNG040-2 : TPTP v9.0.0. Released v1.0.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 03:17:11 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.37 % SZS status Unsatisfiable
% 0.19/0.37 % SZS output start Proof
% See solution above
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------