%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : BOO013-4 : TPTP v9.0.0. Released v1.1.0.
% 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 05:00:08 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 36
% Syntax : Number of formulae : 100 ( 73 unt; 0 typ; 0 def)
% Number of atoms : 139 ( 132 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 49 ( 16 ~; 12 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 6 ( 6 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; 4 con; 0-2 aty)
% Number of variables : 111 ( 101 !; 0 ?; 111 :)
% Comments :
%------------------------------------------------------------------------------
tff(inverse_type,type,
inverse: $i > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(multiplicative_identity_type,type,
multiplicative_identity: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( multiply(X,multiplicative_identity) = X )
<=> ( multiply(X,multiplicative_identity) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( multiply(X,multiplicative_identity) = X )
<=> ! [X: $i] : ( multiply(X,multiplicative_identity) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( multiply(X,multiplicative_identity) = X )
<=> ! [X: $i] : ( multiply(X,multiplicative_identity) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( multiply(X,multiplicative_identity) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_id1) ).
tff(5,plain,
! [X: $i] : ( multiply(X,multiplicative_identity) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( multiply(X,multiplicative_identity) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( multiply(X,multiplicative_identity) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( multiply(X,multiplicative_identity) = X )
| ( multiply(inverse(a),multiplicative_identity) = inverse(a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiply(inverse(a),multiplicative_identity) = inverse(a),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( add(a,b) = multiplicative_identity )
<=> ( add(a,b) = multiplicative_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
add(a,b) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_a_multiplicative_identity) ).
tff(12,plain,
add(a,b) = multiplicative_identity,
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
multiplicative_identity = add(a,b),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
multiply(multiplicative_identity,multiplicative_identity) = multiply(add(a,b),add(a,b)),
inference(monotonicity,[status(thm)],[13,13]) ).
tff(15,plain,
( ~ ! [X: $i] : ( multiply(X,multiplicative_identity) = X )
| ( multiply(multiplicative_identity,multiplicative_identity) = multiplicative_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
multiply(multiplicative_identity,multiplicative_identity) = multiplicative_identity,
inference(unit_resolution,[status(thm)],[15,7]) ).
tff(17,plain,
multiplicative_identity = multiply(multiplicative_identity,multiplicative_identity),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
multiplicative_identity = multiply(add(a,b),add(a,b)),
inference(transitivity,[status(thm)],[17,14]) ).
tff(19,plain,
multiply(inverse(a),multiplicative_identity) = multiply(inverse(a),multiply(add(a,b),add(a,b))),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
multiply(inverse(a),multiply(add(a,b),add(a,b))) = multiply(inverse(a),multiplicative_identity),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
^ [Y: $i,X: $i] :
refl(( ( add(X,Y) = add(Y,X) )
<=> ( add(X,Y) = add(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
<=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
<=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',commutativity_of_add) ).
tff(25,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(a,b) = add(b,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
add(a,b) = add(b,a),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
multiply(add(a,b),add(a,b)) = multiply(multiplicative_identity,multiplicative_identity),
inference(symmetry,[status(thm)],[14]) ).
tff(31,plain,
multiply(add(a,b),add(a,b)) = add(b,a),
inference(transitivity,[status(thm)],[30,16,13,29]) ).
tff(32,plain,
multiply(inverse(a),multiply(add(a,b),add(a,b))) = multiply(inverse(a),add(b,a)),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
multiply(inverse(a),add(b,a)) = multiply(inverse(a),multiply(add(a,b),add(a,b))),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
<=> ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',distributivity2) ).
tff(38,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(inverse(a),add(b,a)) = add(multiply(inverse(a),b),multiply(inverse(a),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
multiply(inverse(a),add(b,a)) = add(multiply(inverse(a),b),multiply(inverse(a),a)),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
add(multiply(inverse(a),b),multiply(inverse(a),a)) = multiply(inverse(a),add(b,a)),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
^ [Y: $i,X: $i] :
refl(( ( multiply(X,Y) = multiply(Y,X) )
<=> ( multiply(X,Y) = multiply(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
<=> ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
<=> ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',commutativity_of_multiply) ).
tff(48,plain,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(a,b) = multiply(b,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
multiply(a,b) = multiply(b,a),
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
( ( multiply(a,b) = additive_identity )
<=> ( multiply(a,b) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,axiom,
multiply(a,b) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_an_additive_identity) ).
tff(55,plain,
multiply(a,b) = additive_identity,
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
additive_identity = multiply(a,b),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
^ [X: $i] :
refl(( ( multiply(X,inverse(X)) = additive_identity )
<=> ( multiply(X,inverse(X)) = additive_identity ) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity )
<=> ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity )
<=> ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,axiom,
! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_inverse1) ).
tff(61,plain,
! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
( ~ ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity )
| ( multiply(a,inverse(a)) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
multiply(a,inverse(a)) = additive_identity,
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(a,inverse(a)) = multiply(inverse(a),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
multiply(a,inverse(a)) = multiply(inverse(a),a),
inference(unit_resolution,[status(thm)],[66,50]) ).
tff(68,plain,
multiply(inverse(a),a) = multiply(a,inverse(a)),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
multiply(inverse(a),a) = multiply(b,a),
inference(transitivity,[status(thm)],[68,65,56,52]) ).
tff(70,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(b,inverse(a)) = multiply(inverse(a),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
multiply(b,inverse(a)) = multiply(inverse(a),b),
inference(unit_resolution,[status(thm)],[70,50]) ).
tff(72,plain,
multiply(inverse(a),b) = multiply(b,inverse(a)),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
add(multiply(inverse(a),b),multiply(inverse(a),a)) = add(multiply(b,inverse(a)),multiply(b,a)),
inference(monotonicity,[status(thm)],[72,69]) ).
tff(74,plain,
add(multiply(b,inverse(a)),multiply(b,a)) = add(multiply(inverse(a),b),multiply(inverse(a),a)),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(b,add(inverse(a),a)) = add(multiply(b,inverse(a)),multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
multiply(b,add(inverse(a),a)) = add(multiply(b,inverse(a)),multiply(b,a)),
inference(unit_resolution,[status(thm)],[75,40]) ).
tff(77,plain,
^ [X: $i] :
refl(( ( add(X,inverse(X)) = multiplicative_identity )
<=> ( add(X,inverse(X)) = multiplicative_identity ) )),
inference(bind,[status(th)],[]) ).
tff(78,plain,
( ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity )
<=> ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,plain,
( ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity )
<=> ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,axiom,
! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',additive_inverse1) ).
tff(81,plain,
! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
( ~ ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity )
| ( add(a,inverse(a)) = multiplicative_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
add(a,inverse(a)) = multiplicative_identity,
inference(unit_resolution,[status(thm)],[84,83]) ).
tff(86,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(a,inverse(a)) = add(inverse(a),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
add(a,inverse(a)) = add(inverse(a),a),
inference(unit_resolution,[status(thm)],[86,27]) ).
tff(88,plain,
add(inverse(a),a) = add(a,inverse(a)),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
add(inverse(a),a) = multiply(add(a,b),add(a,b)),
inference(transitivity,[status(thm)],[88,85,17,14]) ).
tff(90,plain,
multiply(b,add(inverse(a),a)) = multiply(b,multiply(add(a,b),add(a,b))),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
multiply(b,multiply(add(a,b),add(a,b))) = multiply(b,add(inverse(a),a)),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
multiply(b,multiplicative_identity) = multiply(b,multiply(add(a,b),add(a,b))),
inference(monotonicity,[status(thm)],[18]) ).
tff(93,plain,
( ~ ! [X: $i] : ( multiply(X,multiplicative_identity) = X )
| ( multiply(b,multiplicative_identity) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
multiply(b,multiplicative_identity) = b,
inference(unit_resolution,[status(thm)],[93,7]) ).
tff(95,plain,
b = multiply(b,multiplicative_identity),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
b = inverse(a),
inference(transitivity,[status(thm)],[95,92,91,76,74,43,33,20,9]) ).
tff(97,plain,
( ( b != inverse(a) )
<=> ( b != inverse(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,axiom,
b != inverse(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_inverse_is_b) ).
tff(99,plain,
b != inverse(a),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
$false,
inference(unit_resolution,[status(thm)],[99,96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO013-4 : TPTP v9.0.0. Released v1.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.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 : Thu Jun 19 11:32:48 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
%------------------------------------------------------------------------------