%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : BOO021-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:00:09 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of formulae : 63 ( 48 unt; 0 typ; 0 def)
% Number of atoms : 84 ( 80 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 30 ( 12 ~; 8 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 3 ( 3 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 74 !; 0 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( add(multiply(X,Y),Y) = Y )
<=> ( add(multiply(X,Y),Y) = Y ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
<=> ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
<=> ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_multiply) ).
tff(5,plain,
! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(b,b),b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
add(multiply(b,b),b) = b,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(a,b),b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(11,plain,
add(multiply(a,b),b) = b,
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
b = add(multiply(a,b),b),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
multiply(b,b) = multiply(add(multiply(a,b),b),b),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
multiply(add(multiply(a,b),b),b) = multiply(b,b),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
^ [Y: $i,X: $i] :
refl(( ( multiply(add(X,Y),Y) = Y )
<=> ( multiply(add(X,Y),Y) = Y ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
<=> ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
<=> ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add) ).
tff(19,plain,
! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
| ( multiply(add(multiply(a,b),b),b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
multiply(add(multiply(a,b),b),b) = b,
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
b = multiply(add(multiply(a,b),b),b),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
b = multiply(b,b),
inference(transitivity,[status(thm)],[24,14]) ).
tff(26,plain,
add(b,b) = add(multiply(b,b),b),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
add(b,b) = b,
inference(transitivity,[status(thm)],[26,9]) ).
tff(28,plain,
multiply(a,add(b,b)) = multiply(a,b),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
<=> ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add_property) ).
tff(33,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(a,add(b,b)) = add(multiply(b,a),multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
multiply(a,add(b,b)) = add(multiply(b,a),multiply(b,a)),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
add(multiply(b,a),multiply(b,a)) = multiply(a,add(b,b)),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(b,a),a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
add(multiply(b,a),a) = a,
inference(unit_resolution,[status(thm)],[39,7]) ).
tff(41,plain,
a = add(multiply(b,a),a),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
multiply(b,a) = multiply(b,add(multiply(b,a),a)),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
multiply(b,add(multiply(b,a),a)) = multiply(b,a),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(b,add(multiply(b,a),a)) = add(multiply(multiply(b,a),b),multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
multiply(b,add(multiply(b,a),a)) = add(multiply(multiply(b,a),b),multiply(a,b)),
inference(unit_resolution,[status(thm)],[44,35]) ).
tff(46,plain,
add(multiply(multiply(b,a),b),multiply(a,b)) = multiply(b,add(multiply(b,a),a)),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
add(multiply(multiply(b,a),b),multiply(a,b)) = multiply(b,a),
inference(transitivity,[status(thm)],[46,43]) ).
tff(48,plain,
add(add(multiply(multiply(b,a),b),multiply(a,b)),add(multiply(multiply(b,a),b),multiply(a,b))) = add(multiply(b,a),multiply(b,a)),
inference(monotonicity,[status(thm)],[47,47]) ).
tff(49,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
| ( multiply(add(multiply(multiply(a,b),a),add(multiply(multiply(b,a),b),multiply(a,b))),add(multiply(multiply(b,a),b),multiply(a,b))) = add(multiply(multiply(b,a),b),multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
multiply(add(multiply(multiply(a,b),a),add(multiply(multiply(b,a),b),multiply(a,b))),add(multiply(multiply(b,a),b),multiply(a,b))) = add(multiply(multiply(b,a),b),multiply(a,b)),
inference(unit_resolution,[status(thm)],[49,21]) ).
tff(51,plain,
add(multiply(multiply(a,b),a),add(multiply(multiply(b,a),b),multiply(a,b))) = add(multiply(multiply(a,b),a),multiply(b,a)),
inference(monotonicity,[status(thm)],[47]) ).
tff(52,plain,
add(multiply(multiply(a,b),a),multiply(b,a)) = add(multiply(multiply(a,b),a),add(multiply(multiply(b,a),b),multiply(a,b))),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(b,a),b),multiply(a,b))) = multiply(add(multiply(multiply(a,b),a),add(multiply(multiply(b,a),b),multiply(a,b))),add(multiply(multiply(b,a),b),multiply(a,b))),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(b,a),b),multiply(a,b))) = add(multiply(multiply(b,a),b),multiply(a,b)),
inference(transitivity,[status(thm)],[53,50]) ).
tff(55,plain,
add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(b,a),b),multiply(a,b))),add(multiply(multiply(b,a),b),multiply(a,b))) = add(add(multiply(multiply(b,a),b),multiply(a,b)),add(multiply(multiply(b,a),b),multiply(a,b))),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(b,a),b),multiply(a,b))),add(multiply(multiply(b,a),b),multiply(a,b))) = add(multiply(multiply(b,a),b),multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(b,a),b),multiply(a,b))),add(multiply(multiply(b,a),b),multiply(a,b))) = add(multiply(multiply(b,a),b),multiply(a,b)),
inference(unit_resolution,[status(thm)],[56,7]) ).
tff(58,plain,
add(multiply(multiply(b,a),b),multiply(a,b)) = add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(b,a),b),multiply(a,b))),add(multiply(multiply(b,a),b),multiply(a,b))),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
multiply(b,a) = multiply(a,b),
inference(transitivity,[status(thm)],[42,45,58,55,48,38,28]) ).
tff(60,plain,
( ( multiply(b,a) != multiply(a,b) )
<=> ( multiply(b,a) != multiply(a,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
multiply(b,a) != multiply(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity_of_multiply) ).
tff(62,plain,
multiply(b,a) != multiply(a,b),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
$false,
inference(unit_resolution,[status(thm)],[62,59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO021-1 : TPTP v9.0.0. Released v2.2.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 11:33:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.36 % SZS status Unsatisfiable
% 0.19/0.36 % SZS output start Proof
% See solution above
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------