%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : BOO013-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 29
% Syntax : Number of formulae : 74 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 102 ( 97 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 35 ( 11 ~; 7 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 4 ( 4 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; 5 con; 0-2 aty)
% Number of variables : 86 ( 78 !; 0 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_type,type,
c: $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(a_type,type,
a: $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( multiply(multiplicative_identity,X) = X )
<=> ( multiply(multiplicative_identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( multiply(multiplicative_identity,X) = X )
<=> ! [X: $i] : ( multiply(multiplicative_identity,X) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( multiply(multiplicative_identity,X) = X )
<=> ! [X: $i] : ( multiply(multiplicative_identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( multiply(multiplicative_identity,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_id2) ).
tff(5,plain,
! [X: $i] : ( multiply(multiplicative_identity,X) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( multiply(multiplicative_identity,X) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( multiply(multiplicative_identity,X) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( multiply(multiplicative_identity,X) = X )
| ( multiply(multiplicative_identity,c) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiply(multiplicative_identity,c) = c,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(( ( add(X,Y) = add(Y,X) )
<=> ( add(X,Y) = add(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(11,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)],[10]) ).
tff(12,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(13,axiom,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',commutativity_of_add) ).
tff(14,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(a,b) = add(b,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
add(a,b) = add(b,a),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ( add(a,b) = multiplicative_identity )
<=> ( add(a,b) = multiplicative_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
add(a,b) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_and_multiplicative_identity) ).
tff(21,plain,
add(a,b) = multiplicative_identity,
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
multiplicative_identity = add(a,b),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
multiplicative_identity = add(b,a),
inference(transitivity,[status(thm)],[22,18]) ).
tff(24,plain,
multiply(multiplicative_identity,c) = multiply(add(b,a),c),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
multiply(add(b,a),c) = multiply(multiplicative_identity,c),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
<=> ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity3) ).
tff(30,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
| ( multiply(add(b,a),c) = add(multiply(b,c),multiply(a,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
multiply(add(b,a),c) = add(multiply(b,c),multiply(a,c)),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
add(multiply(b,c),multiply(a,c)) = multiply(add(b,a),c),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
( ( multiply(a,b) = additive_identity )
<=> ( multiply(a,b) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
multiply(a,b) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_a_additive_identity) ).
tff(38,plain,
multiply(a,b) = additive_identity,
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
additive_identity = multiply(a,b),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
( ( multiply(a,c) = additive_identity )
<=> ( multiply(a,c) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
multiply(a,c) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_a_additive_identity) ).
tff(42,plain,
multiply(a,c) = additive_identity,
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
multiply(a,c) = multiply(a,b),
inference(transitivity,[status(thm)],[42,39]) ).
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/sandbox/benchmark/Axioms/BOO003-0.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(c,b) = multiply(b,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
multiply(c,b) = multiply(b,c),
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
multiply(b,c) = multiply(c,b),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
add(multiply(b,c),multiply(a,c)) = add(multiply(c,b),multiply(a,b)),
inference(monotonicity,[status(thm)],[53,43]) ).
tff(55,plain,
add(multiply(c,b),multiply(a,b)) = add(multiply(b,c),multiply(a,c)),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
| ( multiply(add(c,a),b) = add(multiply(c,b),multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
multiply(add(c,a),b) = add(multiply(c,b),multiply(a,b)),
inference(unit_resolution,[status(thm)],[56,32]) ).
tff(58,plain,
( ( add(a,c) = multiplicative_identity )
<=> ( add(a,c) = multiplicative_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
add(a,c) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_and_multiplicative_identity) ).
tff(60,plain,
add(a,c) = multiplicative_identity,
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(a,c) = add(c,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
add(a,c) = add(c,a),
inference(unit_resolution,[status(thm)],[61,16]) ).
tff(63,plain,
add(c,a) = add(a,c),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
add(c,a) = multiplicative_identity,
inference(transitivity,[status(thm)],[63,60]) ).
tff(65,plain,
multiply(add(c,a),b) = multiply(multiplicative_identity,b),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
multiply(multiplicative_identity,b) = multiply(add(c,a),b),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
( ~ ! [X: $i] : ( multiply(multiplicative_identity,X) = X )
| ( multiply(multiplicative_identity,b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
multiply(multiplicative_identity,b) = b,
inference(unit_resolution,[status(thm)],[67,7]) ).
tff(69,plain,
b = multiply(multiplicative_identity,b),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
b = c,
inference(transitivity,[status(thm)],[69,66,57,55,35,25,9]) ).
tff(71,plain,
( ( b != c )
<=> ( b != c ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,axiom,
b != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_is_a) ).
tff(73,plain,
b != c,
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
$false,
inference(unit_resolution,[status(thm)],[73,70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : BOO013-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n003.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 : Thu Jun 19 11:33:09 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.37 % SZS status Unsatisfiable
% 0.13/0.37 % SZS output start Proof
% See solution above
% 0.13/0.37 % E exiting
%------------------------------------------------------------------------------