%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP548-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:08:04 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 23
% Syntax : Number of formulae : 101 ( 82 unt; 0 typ; 0 def)
% Number of atoms : 126 ( 122 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 38 ( 16 ~; 12 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 82 ( 76 !; 0 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(( ( multiply(A,B) = divide(A,divide(identity,B)) )
<=> ( multiply(A,B) = divide(A,divide(identity,B)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
<=> ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
<=> ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
tff(5,plain,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
| ( multiply(b,a) = divide(b,divide(identity,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiply(b,a) = divide(b,divide(identity,a)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
divide(b,divide(identity,a)) = multiply(b,a),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C )
<=> ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C )
<=> ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C )
<=> ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C )
| ( divide(divide(identity,divide(divide(identity,a),divide(divide(identity,a),divide(identity,a)))),divide(divide(divide(divide(identity,a),divide(identity,a)),divide(b,divide(identity,a))),divide(identity,a))) = divide(b,divide(identity,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
divide(divide(identity,divide(divide(identity,a),divide(divide(identity,a),divide(identity,a)))),divide(divide(divide(divide(identity,a),divide(identity,a)),divide(b,divide(identity,a))),divide(identity,a))) = divide(b,divide(identity,a)),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
^ [A: $i] :
refl(( ( identity = divide(A,A) )
<=> ( identity = divide(A,A) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [A: $i] : ( identity = divide(A,A) )
<=> ! [A: $i] : ( identity = divide(A,A) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [A: $i] : ( identity = divide(A,A) )
<=> ! [A: $i] : ( identity = divide(A,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [A: $i] : ( identity = divide(A,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
tff(24,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,a),divide(identity,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
identity = divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,a),divide(identity,a))),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(divide(identity,a),divide(identity,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
identity = divide(divide(identity,a),divide(identity,a)),
inference(unit_resolution,[status(thm)],[29,26]) ).
tff(31,plain,
divide(divide(identity,a),divide(identity,a)) = identity,
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
divide(divide(identity,a),divide(identity,a)) = divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,a),divide(identity,a))),
inference(transitivity,[status(thm)],[31,28]) ).
tff(33,plain,
divide(identity,divide(divide(identity,a),divide(identity,a))) = divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,a),divide(identity,a))),
inference(monotonicity,[status(thm)],[30]) ).
tff(34,plain,
divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,a),divide(identity,a))) = divide(identity,divide(divide(identity,a),divide(identity,a))),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
identity = divide(identity,divide(divide(identity,a),divide(identity,a))),
inference(transitivity,[status(thm)],[28,34]) ).
tff(36,plain,
divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(identity,a))) = divide(divide(identity,divide(divide(identity,a),divide(identity,a))),divide(divide(divide(identity,a),divide(identity,a)),divide(identity,a))),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
divide(divide(identity,divide(divide(identity,a),divide(identity,a))),divide(divide(divide(identity,a),divide(identity,a)),divide(identity,a))) = divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(identity,a))),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C )
| ( divide(divide(identity,divide(divide(identity,a),divide(identity,a))),divide(divide(divide(identity,a),divide(identity,a)),divide(identity,a))) = divide(identity,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
divide(divide(identity,divide(divide(identity,a),divide(identity,a))),divide(divide(divide(identity,a),divide(identity,a)),divide(identity,a))) = divide(identity,a),
inference(unit_resolution,[status(thm)],[38,17]) ).
tff(40,plain,
divide(identity,a) = divide(divide(identity,divide(divide(identity,a),divide(identity,a))),divide(divide(divide(identity,a),divide(identity,a)),divide(identity,a))),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C )
| ( divide(divide(identity,divide(b,divide(identity,a))),divide(divide(divide(identity,a),divide(identity,a)),b)) = divide(identity,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
divide(divide(identity,divide(b,divide(identity,a))),divide(divide(divide(identity,a),divide(identity,a)),b)) = divide(identity,a),
inference(unit_resolution,[status(thm)],[41,17]) ).
tff(43,plain,
divide(divide(divide(identity,a),divide(identity,a)),b) = divide(identity,b),
inference(monotonicity,[status(thm)],[31]) ).
tff(44,plain,
divide(identity,b) = divide(divide(divide(identity,a),divide(identity,a)),b),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)) = divide(divide(identity,divide(b,divide(identity,a))),divide(divide(divide(identity,a),divide(identity,a)),b)),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)) = divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(identity,a))),
inference(transitivity,[status(thm)],[45,42,40,37]) ).
tff(47,plain,
divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),divide(divide(identity,a),divide(identity,a))) = divide(divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(identity,a))),divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,a),divide(identity,a)))),
inference(monotonicity,[status(thm)],[46,32]) ).
tff(48,plain,
divide(divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(identity,a))),divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,a),divide(identity,a)))) = divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),divide(divide(identity,a),divide(identity,a))),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C )
| ( divide(divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(identity,a))),divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,a),divide(identity,a)))) = divide(identity,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
divide(divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(identity,a))),divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,a),divide(identity,a)))) = divide(identity,a),
inference(unit_resolution,[status(thm)],[49,17]) ).
tff(51,plain,
divide(identity,a) = divide(divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(identity,a))),divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,a),divide(identity,a)))),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
divide(identity,a) = divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),divide(divide(identity,a),divide(identity,a))),
inference(transitivity,[status(thm)],[51,48]) ).
tff(53,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C )
| ( divide(divide(identity,divide(divide(b,divide(identity,a)),divide(b,divide(identity,a)))),divide(divide(divide(b,divide(identity,a)),divide(b,divide(identity,a))),divide(b,divide(identity,a)))) = divide(b,divide(identity,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
divide(divide(identity,divide(divide(b,divide(identity,a)),divide(b,divide(identity,a)))),divide(divide(divide(b,divide(identity,a)),divide(b,divide(identity,a))),divide(b,divide(identity,a)))) = divide(b,divide(identity,a)),
inference(unit_resolution,[status(thm)],[53,17]) ).
tff(55,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(divide(b,divide(identity,a)),divide(b,divide(identity,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
identity = divide(divide(b,divide(identity,a)),divide(b,divide(identity,a))),
inference(unit_resolution,[status(thm)],[55,26]) ).
tff(57,plain,
divide(divide(b,divide(identity,a)),divide(b,divide(identity,a))) = identity,
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
divide(divide(divide(b,divide(identity,a)),divide(b,divide(identity,a))),divide(b,divide(identity,a))) = divide(identity,divide(b,divide(identity,a))),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
divide(identity,divide(b,divide(identity,a))) = divide(divide(divide(b,divide(identity,a)),divide(b,divide(identity,a))),divide(b,divide(identity,a))),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
divide(divide(b,divide(identity,a)),divide(b,divide(identity,a))) = divide(divide(identity,a),divide(identity,a)),
inference(transitivity,[status(thm)],[57,30]) ).
tff(61,plain,
divide(identity,divide(divide(b,divide(identity,a)),divide(b,divide(identity,a)))) = divide(identity,divide(divide(identity,a),divide(identity,a))),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
divide(identity,divide(divide(identity,a),divide(identity,a))) = divide(identity,divide(divide(b,divide(identity,a)),divide(b,divide(identity,a)))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
divide(divide(identity,a),divide(identity,a)) = divide(identity,divide(divide(b,divide(identity,a)),divide(b,divide(identity,a)))),
inference(transitivity,[status(thm)],[31,28,34,62]) ).
tff(64,plain,
divide(divide(divide(identity,a),divide(identity,a)),divide(identity,divide(b,divide(identity,a)))) = divide(divide(identity,divide(divide(b,divide(identity,a)),divide(b,divide(identity,a)))),divide(divide(divide(b,divide(identity,a)),divide(b,divide(identity,a))),divide(b,divide(identity,a)))),
inference(monotonicity,[status(thm)],[63,59]) ).
tff(65,plain,
divide(divide(divide(identity,a),divide(identity,a)),divide(identity,divide(b,divide(identity,a)))) = divide(b,divide(identity,a)),
inference(transitivity,[status(thm)],[64,54]) ).
tff(66,plain,
divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(identity,divide(b,divide(identity,a))))) = divide(identity,divide(b,divide(identity,a))),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
divide(identity,divide(b,divide(identity,a))) = divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(identity,divide(b,divide(identity,a))))),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
divide(divide(divide(identity,a),divide(identity,a)),divide(b,divide(identity,a))) = divide(identity,divide(b,divide(identity,a))),
inference(monotonicity,[status(thm)],[31]) ).
tff(69,plain,
divide(divide(divide(identity,a),divide(identity,a)),divide(b,divide(identity,a))) = divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(identity,divide(b,divide(identity,a))))),
inference(transitivity,[status(thm)],[68,67]) ).
tff(70,plain,
divide(divide(divide(divide(identity,a),divide(identity,a)),divide(b,divide(identity,a))),divide(identity,a)) = divide(divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(identity,divide(b,divide(identity,a))))),divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),divide(divide(identity,a),divide(identity,a)))),
inference(monotonicity,[status(thm)],[69,52]) ).
tff(71,plain,
divide(divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(identity,divide(b,divide(identity,a))))),divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),divide(divide(identity,a),divide(identity,a)))) = divide(divide(divide(divide(identity,a),divide(identity,a)),divide(b,divide(identity,a))),divide(identity,a)),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C )
| ( divide(divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(identity,divide(b,divide(identity,a))))),divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),divide(divide(identity,a),divide(identity,a)))) = divide(identity,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
divide(divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(identity,divide(b,divide(identity,a))))),divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),divide(divide(identity,a),divide(identity,a)))) = divide(identity,b),
inference(unit_resolution,[status(thm)],[72,17]) ).
tff(74,plain,
divide(identity,b) = divide(divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(identity,divide(b,divide(identity,a))))),divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),divide(divide(identity,a),divide(identity,a)))),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
divide(identity,b) = divide(divide(divide(divide(identity,a),divide(identity,a)),divide(b,divide(identity,a))),divide(identity,a)),
inference(transitivity,[status(thm)],[74,71]) ).
tff(76,plain,
divide(identity,a) = divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(identity,a))),
inference(transitivity,[status(thm)],[40,37]) ).
tff(77,plain,
divide(divide(identity,a),divide(divide(identity,a),divide(identity,a))) = divide(divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(identity,a))),divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,a),divide(identity,a)))),
inference(monotonicity,[status(thm)],[76,32]) ).
tff(78,plain,
divide(divide(identity,a),divide(divide(identity,a),divide(identity,a))) = divide(identity,a),
inference(transitivity,[status(thm)],[77,50]) ).
tff(79,plain,
divide(identity,divide(divide(identity,a),divide(divide(identity,a),divide(identity,a)))) = divide(identity,divide(identity,a)),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
divide(identity,divide(identity,a)) = divide(identity,divide(divide(identity,a),divide(divide(identity,a),divide(identity,a)))),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
divide(divide(divide(identity,a),divide(identity,a)),a) = divide(identity,a),
inference(monotonicity,[status(thm)],[31]) ).
tff(82,plain,
divide(divide(divide(identity,a),divide(identity,a)),a) = divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(identity,a))),
inference(transitivity,[status(thm)],[81,40,37]) ).
tff(83,plain,
divide(divide(divide(divide(identity,a),divide(identity,a)),a),divide(divide(identity,a),divide(identity,a))) = divide(divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(identity,a))),divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,a),divide(identity,a)))),
inference(monotonicity,[status(thm)],[82,32]) ).
tff(84,plain,
divide(divide(divide(divide(identity,a),divide(identity,a)),a),divide(divide(identity,a),divide(identity,a))) = divide(identity,a),
inference(transitivity,[status(thm)],[83,50]) ).
tff(85,plain,
divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,a),divide(identity,a))) = identity,
inference(symmetry,[status(thm)],[28]) ).
tff(86,plain,
divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,a),divide(identity,a))) = divide(divide(identity,a),divide(identity,a)),
inference(transitivity,[status(thm)],[85,30]) ).
tff(87,plain,
divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,a),divide(identity,a)))) = divide(identity,divide(divide(identity,a),divide(identity,a))),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,a),divide(identity,a)))) = identity,
inference(transitivity,[status(thm)],[87,33,85]) ).
tff(89,plain,
divide(divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,a),divide(identity,a)))),divide(divide(divide(divide(identity,a),divide(identity,a)),a),divide(divide(identity,a),divide(identity,a)))) = divide(identity,divide(identity,a)),
inference(monotonicity,[status(thm)],[88,84]) ).
tff(90,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C )
| ( divide(divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,a),divide(identity,a)))),divide(divide(divide(divide(identity,a),divide(identity,a)),a),divide(divide(identity,a),divide(identity,a)))) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
divide(divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,a),divide(identity,a)))),divide(divide(divide(divide(identity,a),divide(identity,a)),a),divide(divide(identity,a),divide(identity,a)))) = a,
inference(unit_resolution,[status(thm)],[90,17]) ).
tff(92,plain,
a = divide(divide(identity,divide(divide(divide(identity,a),divide(identity,a)),divide(divide(identity,a),divide(identity,a)))),divide(divide(divide(divide(identity,a),divide(identity,a)),a),divide(divide(identity,a),divide(identity,a)))),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
a = divide(identity,divide(divide(identity,a),divide(divide(identity,a),divide(identity,a)))),
inference(transitivity,[status(thm)],[92,89,80]) ).
tff(94,plain,
divide(a,divide(identity,b)) = divide(divide(identity,divide(divide(identity,a),divide(divide(identity,a),divide(identity,a)))),divide(divide(divide(divide(identity,a),divide(identity,a)),divide(b,divide(identity,a))),divide(identity,a))),
inference(monotonicity,[status(thm)],[93,75]) ).
tff(95,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
| ( multiply(a,b) = divide(a,divide(identity,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
multiply(a,b) = divide(a,divide(identity,b)),
inference(unit_resolution,[status(thm)],[95,7]) ).
tff(97,plain,
multiply(a,b) = multiply(b,a),
inference(transitivity,[status(thm)],[96,94,19,10]) ).
tff(98,plain,
( ( multiply(a,b) != multiply(b,a) )
<=> ( multiply(a,b) != multiply(b,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,axiom,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_4) ).
tff(100,plain,
multiply(a,b) != multiply(b,a),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
$false,
inference(unit_resolution,[status(thm)],[100,97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP548-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n005.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Jun 19 16:17:05 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40 % SZS output start Proof
% See solution above
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------