%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG024-6 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:23:55 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 33 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 45 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 7 ~; 3 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 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 : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 60 ( 54 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
tff(additive_identity_type,type,
additive_identity: $i ).
tff(associator_type,type,
associator: ( $i * $i * $i ) > $i ).
tff(y_type,type,
y: $i ).
tff(x_type,type,
x: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(additive_inverse_type,type,
additive_inverse: $i > $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( add(X,additive_inverse(X)) = additive_identity )
<=> ( add(X,additive_inverse(X)) = additive_identity ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
<=> ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
<=> ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_additive_inverse) ).
tff(5,plain,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
| ( add(multiply(x,multiply(y,y)),additive_inverse(multiply(x,multiply(y,y)))) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
add(multiply(x,multiply(y,y)),additive_inverse(multiply(x,multiply(y,y)))) = additive_identity,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(( ( multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)) )
<=> ( multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Y: $i,X: $i] : ( multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)) )
<=> ! [Y: $i,X: $i] : ( multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)) )
<=> ! [Y: $i,X: $i] : ( multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Y: $i,X: $i] : ( multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_alternative) ).
tff(14,plain,
! [Y: $i,X: $i] : ( multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)) )
| ( multiply(multiply(x,y),y) = multiply(x,multiply(y,y)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
multiply(multiply(x,y),y) = multiply(x,multiply(y,y)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
add(multiply(multiply(x,y),y),additive_inverse(multiply(x,multiply(y,y)))) = add(multiply(x,multiply(y,y)),additive_inverse(multiply(x,multiply(y,y)))),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
<=> ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',associator) ).
tff(24,plain,
! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
| ( associator(x,y,y) = add(multiply(multiply(x,y),y),additive_inverse(multiply(x,multiply(y,y)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
associator(x,y,y) = add(multiply(multiply(x,y),y),additive_inverse(multiply(x,multiply(y,y)))),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
associator(x,y,y) = additive_identity,
inference(transitivity,[status(thm)],[28,19,9]) ).
tff(30,plain,
( ( associator(x,y,y) != additive_identity )
<=> ( associator(x,y,y) != additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
associator(x,y,y) != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_right_alternative) ).
tff(32,plain,
associator(x,y,y) != additive_identity,
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
$false,
inference(unit_resolution,[status(thm)],[32,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG024-6 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n014.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 : Fri Jun 20 03:10:09 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.38 % SZS status Unsatisfiable
% 0.13/0.38 % SZS output start Proof
% See solution above
% 0.13/0.38 % E exiting
%------------------------------------------------------------------------------