%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP552-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 26
% Syntax : Number of formulae : 125 ( 103 unt; 0 typ; 0 def)
% Number of atoms : 153 ( 149 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 44 ( 19 ~; 15 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 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 : 91 ( 85 !; 0 ?; 91 :)
% 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/sandbox2/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,
^ [A: $i] :
refl(( ( identity = divide(A,A) )
<=> ( identity = divide(A,A) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [A: $i] : ( identity = divide(A,A) )
<=> ! [A: $i] : ( identity = divide(A,A) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [A: $i] : ( identity = divide(A,A) )
<=> ! [A: $i] : ( identity = divide(A,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [A: $i] : ( identity = divide(A,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
tff(15,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(identity,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
identity = divide(identity,identity),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
divide(identity,identity) = identity,
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(divide(identity,a),divide(identity,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
identity = divide(divide(identity,a),divide(identity,a)),
inference(unit_resolution,[status(thm)],[21,17]) ).
tff(23,plain,
divide(divide(identity,a),divide(identity,a)) = identity,
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
divide(divide(identity,identity),a) = divide(identity,a),
inference(monotonicity,[status(thm)],[20]) ).
tff(25,plain,
divide(divide(divide(identity,identity),a),divide(identity,a)) = divide(divide(identity,a),divide(identity,a)),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
divide(divide(divide(identity,identity),a),divide(identity,a)) = identity,
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
divide(divide(divide(divide(identity,identity),a),divide(identity,a)),divide(identity,identity)) = divide(identity,identity),
inference(monotonicity,[status(thm)],[26,20]) ).
tff(28,plain,
divide(identity,identity) = divide(divide(divide(divide(identity,identity),a),divide(identity,a)),divide(identity,identity)),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C )
<=> ( divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C )
<=> ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C )
<=> ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
tff(33,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C )
| ( divide(divide(identity,divide(identity,divide(divide(b,divide(identity,a)),a))),divide(divide(divide(divide(identity,b),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(identity,a)),divide(identity,b))) = divide(identity,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
divide(divide(identity,divide(identity,divide(divide(b,divide(identity,a)),a))),divide(divide(divide(divide(identity,b),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(identity,a)),divide(identity,b))) = divide(identity,a),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C )
| ( divide(divide(identity,divide(identity,a)),divide(divide(divide(divide(identity,a),divide(identity,a)),a),divide(identity,a))) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
divide(divide(identity,divide(identity,a)),divide(divide(divide(divide(identity,a),divide(identity,a)),a),divide(identity,a))) = a,
inference(unit_resolution,[status(thm)],[38,35]) ).
tff(40,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
identity = divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),
inference(unit_resolution,[status(thm)],[40,17]) ).
tff(42,plain,
divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) = identity,
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
divide(divide(identity,identity),divide(identity,a)) = divide(identity,divide(identity,a)),
inference(monotonicity,[status(thm)],[20]) ).
tff(44,plain,
divide(divide(divide(identity,identity),divide(identity,a)),divide(identity,divide(identity,a))) = divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
divide(divide(divide(identity,identity),divide(identity,a)),divide(identity,divide(identity,a))) = identity,
inference(transitivity,[status(thm)],[44,42]) ).
tff(46,plain,
divide(divide(divide(divide(identity,identity),divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,identity)) = divide(identity,identity),
inference(monotonicity,[status(thm)],[45,20]) ).
tff(47,plain,
divide(identity,identity) = divide(divide(divide(divide(identity,identity),divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,identity)),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
divide(divide(divide(identity,a),divide(identity,a)),a) = divide(identity,a),
inference(monotonicity,[status(thm)],[23]) ).
tff(49,plain,
divide(divide(divide(divide(identity,a),divide(identity,a)),a),divide(identity,a)) = divide(divide(identity,a),divide(identity,a)),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
divide(divide(divide(divide(identity,a),divide(identity,a)),a),divide(identity,a)) = divide(divide(divide(divide(identity,identity),divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,identity)),
inference(transitivity,[status(thm)],[49,23,19,47]) ).
tff(51,plain,
divide(divide(identity,divide(identity,a)),divide(divide(divide(divide(identity,a),divide(identity,a)),a),divide(identity,a))) = divide(divide(identity,divide(identity,a)),divide(divide(divide(divide(identity,identity),divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,identity))),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
divide(divide(identity,divide(identity,a)),divide(divide(divide(divide(identity,identity),divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,identity))) = divide(divide(identity,divide(identity,a)),divide(divide(divide(divide(identity,a),divide(identity,a)),a),divide(identity,a))),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C )
| ( divide(divide(identity,divide(identity,a)),divide(divide(divide(divide(identity,identity),divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,identity))) = divide(identity,divide(identity,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
divide(divide(identity,divide(identity,a)),divide(divide(divide(divide(identity,identity),divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,identity))) = divide(identity,divide(identity,a)),
inference(unit_resolution,[status(thm)],[53,35]) ).
tff(55,plain,
divide(identity,divide(identity,a)) = divide(divide(identity,divide(identity,a)),divide(divide(divide(divide(identity,identity),divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,identity))),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C )
| ( divide(divide(identity,b),divide(divide(divide(divide(divide(b,divide(identity,a)),a),b),divide(identity,identity)),divide(divide(b,divide(identity,a)),a))) = divide(identity,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
divide(divide(identity,b),divide(divide(divide(divide(divide(b,divide(identity,a)),a),b),divide(identity,identity)),divide(divide(b,divide(identity,a)),a))) = divide(identity,identity),
inference(unit_resolution,[status(thm)],[56,35]) ).
tff(58,plain,
divide(divide(identity,a),divide(identity,a)) = divide(divide(divide(divide(identity,a),divide(identity,a)),a),divide(identity,a)),
inference(symmetry,[status(thm)],[49]) ).
tff(59,plain,
divide(identity,identity) = divide(divide(divide(divide(identity,a),divide(identity,a)),a),divide(identity,a)),
inference(transitivity,[status(thm)],[20,22,58]) ).
tff(60,plain,
a = divide(divide(identity,divide(identity,a)),divide(divide(divide(divide(identity,a),divide(identity,a)),a),divide(identity,a))),
inference(symmetry,[status(thm)],[39]) ).
tff(61,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C )
| ( divide(divide(identity,divide(identity,a)),divide(divide(divide(b,divide(identity,a)),a),b)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
divide(divide(identity,divide(identity,a)),divide(divide(divide(b,divide(identity,a)),a),b)) = a,
inference(unit_resolution,[status(thm)],[61,35]) ).
tff(63,plain,
divide(divide(divide(identity,identity),divide(identity,a)),divide(divide(divide(b,divide(identity,a)),a),b)) = divide(divide(identity,divide(identity,a)),divide(divide(divide(b,divide(identity,a)),a),b)),
inference(monotonicity,[status(thm)],[43]) ).
tff(64,plain,
divide(divide(divide(identity,identity),divide(identity,a)),divide(divide(divide(b,divide(identity,a)),a),b)) = divide(identity,divide(identity,a)),
inference(transitivity,[status(thm)],[63,62,60,51,54]) ).
tff(65,plain,
divide(divide(divide(divide(identity,identity),divide(identity,a)),divide(divide(divide(b,divide(identity,a)),a),b)),divide(identity,identity)) = divide(divide(identity,divide(identity,a)),divide(divide(divide(divide(identity,a),divide(identity,a)),a),divide(identity,a))),
inference(monotonicity,[status(thm)],[64,59]) ).
tff(66,plain,
divide(divide(divide(divide(identity,identity),divide(identity,a)),divide(divide(divide(b,divide(identity,a)),a),b)),divide(identity,identity)) = divide(identity,divide(identity,a)),
inference(transitivity,[status(thm)],[65,51,54]) ).
tff(67,plain,
divide(divide(identity,divide(identity,a)),divide(divide(divide(divide(identity,identity),divide(identity,a)),divide(divide(divide(b,divide(identity,a)),a),b)),divide(identity,identity))) = divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C )
| ( divide(divide(identity,divide(identity,a)),divide(divide(divide(divide(identity,identity),divide(identity,a)),divide(divide(divide(b,divide(identity,a)),a),b)),divide(identity,identity))) = divide(divide(divide(b,divide(identity,a)),a),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
divide(divide(identity,divide(identity,a)),divide(divide(divide(divide(identity,identity),divide(identity,a)),divide(divide(divide(b,divide(identity,a)),a),b)),divide(identity,identity))) = divide(divide(divide(b,divide(identity,a)),a),b),
inference(unit_resolution,[status(thm)],[68,35]) ).
tff(70,plain,
divide(divide(divide(b,divide(identity,a)),a),b) = divide(divide(identity,divide(identity,a)),divide(divide(divide(divide(identity,identity),divide(identity,a)),divide(divide(divide(b,divide(identity,a)),a),b)),divide(identity,identity))),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
divide(divide(divide(b,divide(identity,a)),a),b) = identity,
inference(transitivity,[status(thm)],[70,67,42]) ).
tff(72,plain,
divide(divide(divide(divide(b,divide(identity,a)),a),b),divide(identity,identity)) = divide(identity,identity),
inference(monotonicity,[status(thm)],[71,20]) ).
tff(73,plain,
divide(divide(divide(divide(b,divide(identity,a)),a),b),divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[72,20]) ).
tff(74,plain,
divide(divide(divide(divide(divide(b,divide(identity,a)),a),b),divide(identity,identity)),divide(divide(b,divide(identity,a)),a)) = divide(identity,divide(divide(b,divide(identity,a)),a)),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
divide(identity,divide(divide(b,divide(identity,a)),a)) = divide(divide(divide(divide(divide(b,divide(identity,a)),a),b),divide(identity,identity)),divide(divide(b,divide(identity,a)),a)),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
divide(divide(identity,b),divide(identity,divide(divide(b,divide(identity,a)),a))) = divide(divide(identity,b),divide(divide(divide(divide(divide(b,divide(identity,a)),a),b),divide(identity,identity)),divide(divide(b,divide(identity,a)),a))),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
divide(divide(identity,b),divide(identity,divide(divide(b,divide(identity,a)),a))) = identity,
inference(transitivity,[status(thm)],[76,57,20]) ).
tff(78,plain,
divide(divide(divide(identity,b),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(identity,a)) = divide(identity,divide(identity,a)),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
divide(divide(divide(identity,b),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(identity,a)) = a,
inference(transitivity,[status(thm)],[78,55,52,39]) ).
tff(80,plain,
divide(divide(divide(divide(identity,b),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(identity,a)),divide(identity,b)) = divide(a,divide(identity,b)),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
divide(a,divide(identity,b)) = divide(divide(divide(divide(identity,b),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(identity,a)),divide(identity,b)),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
divide(divide(identity,identity),divide(identity,divide(divide(b,divide(identity,a)),a))) = divide(identity,divide(identity,divide(divide(b,divide(identity,a)),a))),
inference(monotonicity,[status(thm)],[20]) ).
tff(83,plain,
divide(divide(divide(identity,identity),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(a,divide(identity,b))) = divide(divide(identity,divide(identity,divide(divide(b,divide(identity,a)),a))),divide(divide(divide(divide(identity,b),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(identity,a)),divide(identity,b))),
inference(monotonicity,[status(thm)],[82,81]) ).
tff(84,plain,
divide(divide(divide(identity,identity),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(a,divide(identity,b))) = divide(identity,a),
inference(transitivity,[status(thm)],[83,37]) ).
tff(85,plain,
divide(divide(divide(divide(identity,identity),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(a,divide(identity,b))),divide(identity,identity)) = divide(divide(identity,a),divide(divide(divide(divide(identity,identity),a),divide(identity,a)),divide(identity,identity))),
inference(monotonicity,[status(thm)],[84,28]) ).
tff(86,plain,
divide(divide(identity,a),divide(divide(divide(divide(identity,identity),a),divide(identity,a)),divide(identity,identity))) = divide(divide(divide(divide(identity,identity),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(a,divide(identity,b))),divide(identity,identity)),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C )
| ( divide(divide(identity,a),divide(divide(divide(divide(identity,identity),a),divide(identity,a)),divide(identity,identity))) = divide(identity,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
divide(divide(identity,a),divide(divide(divide(divide(identity,identity),a),divide(identity,a)),divide(identity,identity))) = divide(identity,a),
inference(unit_resolution,[status(thm)],[87,35]) ).
tff(89,plain,
divide(identity,a) = divide(divide(identity,a),divide(divide(divide(divide(identity,identity),a),divide(identity,a)),divide(identity,identity))),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
divide(identity,a) = divide(divide(divide(divide(identity,identity),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(a,divide(identity,b))),divide(identity,identity)),
inference(transitivity,[status(thm)],[89,86]) ).
tff(91,plain,
divide(divide(identity,identity),b) = divide(identity,b),
inference(monotonicity,[status(thm)],[20]) ).
tff(92,plain,
divide(divide(divide(identity,identity),b),divide(identity,divide(divide(b,divide(identity,a)),a))) = divide(divide(identity,b),divide(divide(divide(divide(divide(b,divide(identity,a)),a),b),divide(identity,identity)),divide(divide(b,divide(identity,a)),a))),
inference(monotonicity,[status(thm)],[91,75]) ).
tff(93,plain,
divide(divide(divide(identity,identity),b),divide(identity,divide(divide(b,divide(identity,a)),a))) = identity,
inference(transitivity,[status(thm)],[92,57,20]) ).
tff(94,plain,
divide(divide(divide(divide(identity,identity),b),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(identity,identity)) = divide(identity,identity),
inference(monotonicity,[status(thm)],[93,20]) ).
tff(95,plain,
divide(identity,identity) = divide(divide(divide(divide(identity,identity),b),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(identity,identity)),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
divide(divide(identity,identity),divide(identity,identity)) = divide(identity,identity),
inference(monotonicity,[status(thm)],[20,20]) ).
tff(97,plain,
divide(divide(identity,identity),divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[96,20]) ).
tff(98,plain,
divide(divide(divide(identity,identity),divide(identity,identity)),b) = divide(identity,b),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
divide(divide(divide(divide(identity,identity),divide(identity,identity)),b),divide(identity,identity)) = divide(divide(identity,b),divide(divide(divide(divide(identity,identity),b),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(identity,identity))),
inference(monotonicity,[status(thm)],[98,95]) ).
tff(100,plain,
divide(divide(identity,b),divide(divide(divide(divide(identity,identity),b),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(identity,identity))) = divide(divide(divide(divide(identity,identity),divide(identity,identity)),b),divide(identity,identity)),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C )
| ( divide(divide(identity,b),divide(divide(divide(divide(identity,identity),b),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(identity,identity))) = divide(identity,divide(divide(b,divide(identity,a)),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
divide(divide(identity,b),divide(divide(divide(divide(identity,identity),b),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(identity,identity))) = divide(identity,divide(divide(b,divide(identity,a)),a)),
inference(unit_resolution,[status(thm)],[101,35]) ).
tff(103,plain,
divide(identity,divide(divide(b,divide(identity,a)),a)) = divide(divide(identity,b),divide(divide(divide(divide(identity,identity),b),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(identity,identity))),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
divide(identity,divide(divide(b,divide(identity,a)),a)) = divide(divide(divide(divide(identity,identity),divide(identity,identity)),b),divide(identity,identity)),
inference(transitivity,[status(thm)],[103,100]) ).
tff(105,plain,
divide(identity,divide(identity,identity)) = divide(identity,identity),
inference(monotonicity,[status(thm)],[20]) ).
tff(106,plain,
divide(identity,identity) = divide(identity,divide(identity,identity)),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
identity = divide(identity,divide(identity,identity)),
inference(transitivity,[status(thm)],[19,106]) ).
tff(108,plain,
divide(identity,divide(identity,divide(divide(b,divide(identity,a)),a))) = divide(divide(identity,divide(identity,identity)),divide(divide(divide(divide(identity,identity),divide(identity,identity)),b),divide(identity,identity))),
inference(monotonicity,[status(thm)],[107,104]) ).
tff(109,plain,
divide(divide(identity,divide(identity,identity)),divide(divide(divide(divide(identity,identity),divide(identity,identity)),b),divide(identity,identity))) = divide(identity,divide(identity,divide(divide(b,divide(identity,a)),a))),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C )
| ( divide(divide(identity,divide(identity,identity)),divide(divide(divide(divide(identity,identity),divide(identity,identity)),b),divide(identity,identity))) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
divide(divide(identity,divide(identity,identity)),divide(divide(divide(divide(identity,identity),divide(identity,identity)),b),divide(identity,identity))) = b,
inference(unit_resolution,[status(thm)],[110,35]) ).
tff(112,plain,
b = divide(divide(identity,divide(identity,identity)),divide(divide(divide(divide(identity,identity),divide(identity,identity)),b),divide(identity,identity))),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
b = divide(identity,divide(identity,divide(divide(b,divide(identity,a)),a))),
inference(transitivity,[status(thm)],[112,109]) ).
tff(114,plain,
divide(b,divide(identity,a)) = divide(divide(identity,divide(identity,divide(divide(b,divide(identity,a)),a))),divide(divide(divide(divide(identity,identity),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(a,divide(identity,b))),divide(identity,identity))),
inference(monotonicity,[status(thm)],[113,90]) ).
tff(115,plain,
divide(divide(identity,divide(identity,divide(divide(b,divide(identity,a)),a))),divide(divide(divide(divide(identity,identity),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(a,divide(identity,b))),divide(identity,identity))) = divide(b,divide(identity,a)),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C )
| ( divide(divide(identity,divide(identity,divide(divide(b,divide(identity,a)),a))),divide(divide(divide(divide(identity,identity),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(a,divide(identity,b))),divide(identity,identity))) = divide(a,divide(identity,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
divide(divide(identity,divide(identity,divide(divide(b,divide(identity,a)),a))),divide(divide(divide(divide(identity,identity),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(a,divide(identity,b))),divide(identity,identity))) = divide(a,divide(identity,b)),
inference(unit_resolution,[status(thm)],[116,35]) ).
tff(118,plain,
divide(a,divide(identity,b)) = divide(divide(identity,divide(identity,divide(divide(b,divide(identity,a)),a))),divide(divide(divide(divide(identity,identity),divide(identity,divide(divide(b,divide(identity,a)),a))),divide(a,divide(identity,b))),divide(identity,identity))),
inference(symmetry,[status(thm)],[117]) ).
tff(119,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(120,plain,
multiply(a,b) = divide(a,divide(identity,b)),
inference(unit_resolution,[status(thm)],[119,7]) ).
tff(121,plain,
multiply(a,b) = multiply(b,a),
inference(transitivity,[status(thm)],[120,118,115,10]) ).
tff(122,plain,
( ( multiply(a,b) != multiply(b,a) )
<=> ( multiply(a,b) != multiply(b,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(123,axiom,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_4) ).
tff(124,plain,
multiply(a,b) != multiply(b,a),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
$false,
inference(unit_resolution,[status(thm)],[124,121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : GRP552-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% 0.05/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n016.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 16:17:17 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40 % SZS output start Proof
% See solution above
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------