%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : FLD030-2 : TPTP v9.0.0. Bugfixed v2.1.0.
% 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 05:04:58 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 28
% Syntax : Number of formulae : 57 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 276 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 382 ( 179 ~; 174 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 145 ( 134 !; 0 ?; 145 :)
% Comments :
%------------------------------------------------------------------------------
tff(equalish_type,type,
equalish: ( $i * $i ) > $o ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(d_type,type,
d: $i ).
tff(c_type,type,
c: $i ).
tff(a_type,type,
a: $i ).
tff(defined_type,type,
defined: $i > $o ).
tff(1,plain,
( ~ equalish(multiply(d,b),c)
<=> ~ equalish(multiply(d,b),c) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ equalish(multiply(d,b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_not_equal_to_c_7) ).
tff(3,plain,
~ equalish(multiply(d,b),c),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Y: $i,X: $i] :
refl(( ( equalish(X,Y)
| ~ equalish(Y,X) )
<=> ( equalish(X,Y)
| ~ equalish(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
<=> ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
<=> ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
tff(8,plain,
! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(multiply(d,b),c)
| ~ equalish(c,multiply(d,b)) )
<=> ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(multiply(d,b),c)
| ~ equalish(c,multiply(d,b)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(multiply(d,b),c)
| ~ equalish(c,multiply(d,b)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(multiply(d,b),c)
| ~ equalish(c,multiply(d,b)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ equalish(c,multiply(d,b)),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( equalish(multiply(a,b),c)
<=> equalish(multiply(a,b),c) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
equalish(multiply(a,b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_equals_c_5) ).
tff(17,plain,
equalish(multiply(a,b),c),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(c,multiply(a,b))
| ~ equalish(multiply(a,b),c) )
<=> ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(c,multiply(a,b))
| ~ equalish(multiply(a,b),c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(c,multiply(a,b))
| ~ equalish(multiply(a,b),c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(c,multiply(a,b))
| ~ equalish(multiply(a,b),c) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
equalish(c,multiply(a,b)),
inference(unit_resolution,[status(thm)],[20,10,17]) ).
tff(22,plain,
( equalish(a,d)
<=> equalish(a,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
equalish(a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_d_6) ).
tff(24,plain,
equalish(a,d),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
( defined(b)
<=> defined(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
tff(27,plain,
defined(b),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) )
<=> ( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( equalish(multiply(X,Z),multiply(Y,Z))
| ~ defined(Z) )
<=> ( ~ defined(Z)
| equalish(multiply(X,Z),multiply(Y,Z)) ) )),
( ( equalish(multiply(X,Z),multiply(Y,Z))
| ~ defined(Z)
| ~ equalish(X,Y) )
<=> ( ~ defined(Z)
| equalish(multiply(X,Z),multiply(Y,Z))
| ~ equalish(X,Y) ) )),
rewrite(( ( ~ defined(Z)
| equalish(multiply(X,Z),multiply(Y,Z))
| ~ equalish(X,Y) )
<=> ( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ) )),
( ( equalish(multiply(X,Z),multiply(Y,Z))
| ~ defined(Z)
| ~ equalish(X,Y) )
<=> ( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [Z: $i,Y: $i,X: $i] :
( equalish(multiply(X,Z),multiply(Y,Z))
| ~ defined(Z)
| ~ equalish(X,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,axiom,
! [Z: $i,Y: $i,X: $i] :
( equalish(multiply(X,Z),multiply(Y,Z))
| ~ defined(Z)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_multiplication) ).
tff(34,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[36,29]) ).
tff(38,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) )
| ~ defined(b)
| ~ equalish(a,d)
| equalish(multiply(a,b),multiply(d,b)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) )
| ~ defined(b)
| ~ equalish(a,d)
| equalish(multiply(a,b),multiply(d,b)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) )
| ~ defined(b)
| ~ equalish(a,d)
| equalish(multiply(a,b),multiply(d,b)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) )
| ~ defined(b)
| ~ equalish(a,d)
| equalish(multiply(a,b),multiply(d,b)) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
equalish(multiply(a,b),multiply(d,b)),
inference(unit_resolution,[status(thm)],[40,37,27,24]) ).
tff(42,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( equalish(X,Z)
| ~ equalish(X,Y) )
<=> ( ~ equalish(X,Y)
| equalish(X,Z) ) )),
( ( equalish(X,Z)
| ~ equalish(X,Y)
| ~ equalish(Y,Z) )
<=> ( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) ) )),
rewrite(( ( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
<=> ( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ) )),
( ( equalish(X,Z)
| ~ equalish(X,Y)
| ~ equalish(Y,Z) )
<=> ( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [Z: $i,Y: $i,X: $i] :
( equalish(X,Z)
| ~ equalish(X,Y)
| ~ equalish(Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [Z: $i,Y: $i,X: $i] :
( equalish(X,Z)
| ~ equalish(X,Y)
| ~ equalish(Y,Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
tff(47,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(c,multiply(d,b))
| ~ equalish(c,multiply(a,b))
| ~ equalish(multiply(a,b),multiply(d,b)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(c,multiply(d,b))
| ~ equalish(c,multiply(a,b))
| ~ equalish(multiply(a,b),multiply(d,b)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ( ~ equalish(multiply(a,b),multiply(d,b))
| ~ equalish(c,multiply(a,b))
| equalish(c,multiply(d,b)) )
<=> ( equalish(c,multiply(d,b))
| ~ equalish(c,multiply(a,b))
| ~ equalish(multiply(a,b),multiply(d,b)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(multiply(a,b),multiply(d,b))
| ~ equalish(c,multiply(a,b))
| equalish(c,multiply(d,b)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(c,multiply(d,b))
| ~ equalish(c,multiply(a,b))
| ~ equalish(multiply(a,b),multiply(d,b)) ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(multiply(a,b),multiply(d,b))
| ~ equalish(c,multiply(a,b))
| equalish(c,multiply(d,b)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(c,multiply(d,b))
| ~ equalish(c,multiply(a,b))
| ~ equalish(multiply(a,b),multiply(d,b)) ) ),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(multiply(a,b),multiply(d,b))
| ~ equalish(c,multiply(a,b))
| equalish(c,multiply(d,b)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(c,multiply(d,b))
| ~ equalish(c,multiply(a,b))
| ~ equalish(multiply(a,b),multiply(d,b)) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
$false,
inference(unit_resolution,[status(thm)],[56,50,41,21,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : FLD030-2 : TPTP v9.0.0. Bugfixed v2.1.0.
% 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 13:35:54 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% See solution above
% 0.13/0.40 % E exiting
%------------------------------------------------------------------------------