%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : FLD034-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:04:59 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 34
% Syntax : Number of formulae : 72 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 338 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 466 ( 218 ~; 213 |; 0 &)
% ( 35 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 18 ( 18 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 170 ( 157 !; 0 ?; 170 :)
% Comments :
%------------------------------------------------------------------------------
tff(equalish_type,type,
equalish: ( $i * $i ) > $o ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(m_type,type,
m: $i ).
tff(multiplicative_identity_type,type,
multiplicative_identity: $i ).
tff(defined_type,type,
defined: $i > $o ).
tff(1,plain,
( equalish(m,multiplicative_identity)
<=> equalish(m,multiplicative_identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
equalish(m,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_equals_multiplicative_identity_3) ).
tff(3,plain,
equalish(m,multiplicative_identity),
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(multiplicative_identity,m)
| ~ equalish(m,multiplicative_identity) )
<=> ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(multiplicative_identity,m)
| ~ equalish(m,multiplicative_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(multiplicative_identity,m)
| ~ equalish(m,multiplicative_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(multiplicative_identity,m)
| ~ equalish(m,multiplicative_identity) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
equalish(multiplicative_identity,m),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( defined(a)
<=> defined(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
tff(17,plain,
defined(a),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,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(19,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)],[18]) ).
tff(20,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(21,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(22,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)],[21]) ).
tff(23,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(24,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) )
| ~ defined(a)
| ~ equalish(multiplicative_identity,m)
| equalish(multiply(multiplicative_identity,a),multiply(m,a)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) )
| ~ defined(a)
| ~ equalish(multiplicative_identity,m)
| equalish(multiply(multiplicative_identity,a),multiply(m,a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) )
| ~ defined(a)
| ~ equalish(multiplicative_identity,m)
| equalish(multiply(multiplicative_identity,a),multiply(m,a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) )
| ~ defined(a)
| ~ equalish(multiplicative_identity,m)
| equalish(multiply(multiplicative_identity,a),multiply(m,a)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
equalish(multiply(multiplicative_identity,a),multiply(m,a)),
inference(unit_resolution,[status(thm)],[30,27,17,14]) ).
tff(32,plain,
^ [X: $i] :
refl(( ( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) )
<=> ( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) )
<=> ! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) )
<=> ! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [X: $i] :
rewrite(( ( equalish(multiply(multiplicative_identity,X),X)
| ~ defined(X) )
<=> ( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [X: $i] :
( equalish(multiply(multiplicative_identity,X),X)
| ~ defined(X) )
<=> ! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [X: $i] :
( equalish(multiply(multiplicative_identity,X),X)
| ~ defined(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_multiplication) ).
tff(38,plain,
! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) )
| ~ defined(a)
| equalish(multiply(multiplicative_identity,a),a) )
<=> ( ~ ! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) )
| ~ defined(a)
| equalish(multiply(multiplicative_identity,a),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) )
| ~ defined(a)
| equalish(multiply(multiplicative_identity,a),a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [X: $i] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) )
| ~ defined(a)
| equalish(multiply(multiplicative_identity,a),a) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
equalish(multiply(multiplicative_identity,a),a),
inference(unit_resolution,[status(thm)],[44,41,17]) ).
tff(46,plain,
( ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(a,multiply(multiplicative_identity,a))
| ~ equalish(multiply(multiplicative_identity,a),a) )
<=> ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(a,multiply(multiplicative_identity,a))
| ~ equalish(multiply(multiplicative_identity,a),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(a,multiply(multiplicative_identity,a))
| ~ equalish(multiply(multiplicative_identity,a),a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(a,multiply(multiplicative_identity,a))
| ~ equalish(multiply(multiplicative_identity,a),a) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
equalish(a,multiply(multiplicative_identity,a)),
inference(unit_resolution,[status(thm)],[48,10,45]) ).
tff(50,plain,
( ~ equalish(multiply(m,a),a)
<=> ~ equalish(multiply(m,a),a) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,axiom,
~ equalish(multiply(m,a),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_not_equal_to_a_4) ).
tff(52,plain,
~ equalish(multiply(m,a),a),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
( ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(multiply(m,a),a)
| ~ equalish(a,multiply(m,a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(multiply(m,a),a)
| ~ equalish(a,multiply(m,a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(multiply(m,a),a)
| ~ equalish(a,multiply(m,a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(multiply(m,a),a)
| ~ equalish(a,multiply(m,a)) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
~ equalish(a,multiply(m,a)),
inference(unit_resolution,[status(thm)],[55,10,52]) ).
tff(57,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(58,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(59,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(60,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)],[59]) ).
tff(61,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(62,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(a,multiply(m,a))
| ~ equalish(a,multiply(multiplicative_identity,a))
| ~ equalish(multiply(multiplicative_identity,a),multiply(m,a)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(a,multiply(m,a))
| ~ equalish(a,multiply(multiplicative_identity,a))
| ~ equalish(multiply(multiplicative_identity,a),multiply(m,a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
( ( ~ equalish(multiply(multiplicative_identity,a),multiply(m,a))
| ~ equalish(a,multiply(multiplicative_identity,a))
| equalish(a,multiply(m,a)) )
<=> ( equalish(a,multiply(m,a))
| ~ equalish(a,multiply(multiplicative_identity,a))
| ~ equalish(multiply(multiplicative_identity,a),multiply(m,a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(multiply(multiplicative_identity,a),multiply(m,a))
| ~ equalish(a,multiply(multiplicative_identity,a))
| equalish(a,multiply(m,a)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(a,multiply(m,a))
| ~ equalish(a,multiply(multiplicative_identity,a))
| ~ equalish(multiply(multiplicative_identity,a),multiply(m,a)) ) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(multiply(multiplicative_identity,a),multiply(m,a))
| ~ equalish(a,multiply(multiplicative_identity,a))
| equalish(a,multiply(m,a)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(a,multiply(m,a))
| ~ equalish(a,multiply(multiplicative_identity,a))
| ~ equalish(multiply(multiplicative_identity,a),multiply(m,a)) ) ),
inference(transitivity,[status(thm)],[68,66]) ).
tff(70,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(multiply(multiplicative_identity,a),multiply(m,a))
| ~ equalish(a,multiply(multiplicative_identity,a))
| equalish(a,multiply(m,a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(a,multiply(m,a))
| ~ equalish(a,multiply(multiplicative_identity,a))
| ~ equalish(multiply(multiplicative_identity,a),multiply(m,a)) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
$false,
inference(unit_resolution,[status(thm)],[71,65,56,49,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : FLD034-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n004.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 13:35:38 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
%------------------------------------------------------------------------------