%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP546-1 : TPTP v9.0.0. Released v2.6.0.
% 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 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 28
% Syntax : Number of formulae : 138 ( 115 unt; 0 typ; 0 def)
% Number of atoms : 169 ( 164 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 45 ( 18 ~; 14 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 10 ( 2 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 95 ( 88 !; 0 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
tff(a2_type,type,
a2: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b2_type,type,
b2: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,axiom,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
tff(5,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C )
| ( divide(divide(identity,divide(divide(inverse(b2),divide(identity,b2)),divide(multiply(inverse(b2),b2),divide(identity,a2)))),divide(divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),a2),divide(inverse(b2),divide(identity,b2)))) = a2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
divide(divide(identity,divide(divide(inverse(b2),divide(identity,b2)),divide(multiply(inverse(b2),b2),divide(identity,a2)))),divide(divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),a2),divide(inverse(b2),divide(identity,b2)))) = a2,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [A: $i] :
refl(( ( inverse(A) = divide(identity,A) )
<=> ( inverse(A) = divide(identity,A) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [A: $i] : ( inverse(A) = divide(identity,A) )
<=> ! [A: $i] : ( inverse(A) = divide(identity,A) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [A: $i] : ( inverse(A) = divide(identity,A) )
<=> ! [A: $i] : ( inverse(A) = divide(identity,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [A: $i] : ( inverse(A) = divide(identity,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
tff(14,plain,
! [A: $i] : ( inverse(A) = divide(identity,A) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [A: $i] : ( inverse(A) = divide(identity,A) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [A: $i] : ( inverse(A) = divide(identity,A) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [A: $i] : ( inverse(A) = divide(identity,A) )
| ( inverse(b2) = divide(identity,b2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
inverse(b2) = divide(identity,b2),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
divide(identity,b2) = inverse(b2),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
divide(divide(identity,b2),divide(identity,b2)) = divide(inverse(b2),divide(identity,b2)),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
^ [A: $i] :
refl(( ( identity = divide(A,A) )
<=> ( identity = divide(A,A) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [A: $i] : ( identity = divide(A,A) )
<=> ! [A: $i] : ( identity = divide(A,A) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [A: $i] : ( identity = divide(A,A) )
<=> ! [A: $i] : ( identity = divide(A,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [A: $i] : ( identity = divide(A,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
tff(25,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(divide(identity,b2),divide(identity,b2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
identity = divide(divide(identity,b2),divide(identity,b2)),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
identity = divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))),
inference(unit_resolution,[status(thm)],[30,27]) ).
tff(32,plain,
divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))) = identity,
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(divide(identity,a2),divide(identity,a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
identity = divide(divide(identity,a2),divide(identity,a2)),
inference(unit_resolution,[status(thm)],[33,27]) ).
tff(35,plain,
divide(divide(identity,a2),divide(identity,a2)) = identity,
inference(symmetry,[status(thm)],[34]) ).
tff(36,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,a2),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))))),divide(divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(identity,a2)),divide(identity,a2))) = divide(identity,a2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
divide(divide(identity,divide(divide(identity,a2),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))))),divide(divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(identity,a2)),divide(identity,a2))) = divide(identity,a2),
inference(unit_resolution,[status(thm)],[36,7]) ).
tff(38,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(39,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)],[38]) ).
tff(40,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(41,axiom,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
tff(42,plain,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
| ( multiply(inverse(b2),b2) = divide(inverse(b2),divide(identity,b2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
multiply(inverse(b2),b2) = divide(inverse(b2),divide(identity,b2)),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
divide(inverse(b2),divide(identity,b2)) = multiply(inverse(b2),b2),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C )
| ( divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))),a2)) = divide(inverse(b2),divide(identity,b2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))),a2)) = divide(inverse(b2),divide(identity,b2)),
inference(unit_resolution,[status(thm)],[48,7]) ).
tff(50,plain,
divide(divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))),a2) = divide(identity,a2),
inference(monotonicity,[status(thm)],[32]) ).
tff(51,plain,
divide(identity,a2) = divide(divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))),a2),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(identity,a2)) = divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))),a2)),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(identity,a2)) = multiply(inverse(b2),b2),
inference(transitivity,[status(thm)],[52,49,47]) ).
tff(54,plain,
divide(divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(identity,a2)),divide(identity,a2)) = divide(multiply(inverse(b2),b2),divide(identity,a2)),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
divide(multiply(inverse(b2),b2),divide(identity,a2)) = divide(divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(identity,a2)),divide(identity,a2)),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
identity = divide(inverse(b2),divide(identity,b2)),
inference(transitivity,[status(thm)],[29,20]) ).
tff(57,plain,
divide(identity,divide(inverse(b2),divide(identity,b2))) = divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))) = divide(identity,divide(inverse(b2),divide(identity,b2))),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
divide(divide(identity,b2),divide(identity,b2)) = identity,
inference(symmetry,[status(thm)],[29]) ).
tff(60,plain,
divide(inverse(b2),divide(identity,b2)) = divide(divide(identity,b2),divide(identity,b2)),
inference(symmetry,[status(thm)],[20]) ).
tff(61,plain,
divide(inverse(b2),divide(identity,b2)) = divide(identity,divide(inverse(b2),divide(identity,b2))),
inference(transitivity,[status(thm)],[60,59,31,58]) ).
tff(62,plain,
divide(a2,divide(inverse(b2),divide(identity,b2))) = divide(a2,divide(identity,divide(inverse(b2),divide(identity,b2)))),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
divide(a2,divide(identity,divide(inverse(b2),divide(identity,b2)))) = divide(a2,divide(inverse(b2),divide(identity,b2))),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
divide(identity,divide(a2,divide(identity,divide(inverse(b2),divide(identity,b2))))) = divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))) = divide(identity,divide(a2,divide(identity,divide(inverse(b2),divide(identity,b2))))),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
divide(divide(identity,a2),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2))))) = divide(divide(identity,a2),divide(identity,divide(a2,divide(identity,divide(inverse(b2),divide(identity,b2)))))),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
divide(divide(identity,a2),divide(identity,divide(a2,divide(identity,divide(inverse(b2),divide(identity,b2)))))) = divide(divide(identity,a2),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2))))),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
divide(inverse(b2),divide(identity,b2)) = identity,
inference(transitivity,[status(thm)],[60,59]) ).
tff(69,plain,
divide(divide(inverse(b2),divide(identity,b2)),divide(divide(identity,a2),divide(identity,divide(a2,divide(identity,divide(inverse(b2),divide(identity,b2))))))) = divide(identity,divide(divide(identity,a2),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))))),
inference(monotonicity,[status(thm)],[68,67]) ).
tff(70,plain,
divide(divide(divide(inverse(b2),divide(identity,b2)),divide(divide(identity,a2),divide(identity,divide(a2,divide(identity,divide(inverse(b2),divide(identity,b2))))))),divide(multiply(inverse(b2),b2),divide(identity,a2))) = divide(divide(identity,divide(divide(identity,a2),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))))),divide(divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(identity,a2)),divide(identity,a2))),
inference(monotonicity,[status(thm)],[69,55]) ).
tff(71,plain,
divide(divide(divide(inverse(b2),divide(identity,b2)),divide(divide(identity,a2),divide(identity,divide(a2,divide(identity,divide(inverse(b2),divide(identity,b2))))))),divide(multiply(inverse(b2),b2),divide(identity,a2))) = divide(identity,a2),
inference(transitivity,[status(thm)],[70,37]) ).
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(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),divide(inverse(b2),divide(identity,b2)))) = divide(identity,a2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
divide(divide(identity,divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),divide(inverse(b2),divide(identity,b2)))) = divide(identity,a2),
inference(unit_resolution,[status(thm)],[72,7]) ).
tff(74,plain,
divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)) = divide(multiply(inverse(b2),b2),divide(identity,a2)),
inference(monotonicity,[status(thm)],[47]) ).
tff(75,plain,
divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),divide(inverse(b2),divide(identity,b2))) = divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2))),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2))) = divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),divide(inverse(b2),divide(identity,b2))),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))) = divide(inverse(b2),divide(identity,b2)),
inference(transitivity,[status(thm)],[32,29,20]) ).
tff(78,plain,
divide(identity,divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2)))) = divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))),
inference(monotonicity,[status(thm)],[56,77]) ).
tff(79,plain,
divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))) = divide(identity,divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2)))),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
identity = divide(identity,divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2)))),
inference(transitivity,[status(thm)],[31,79]) ).
tff(81,plain,
divide(identity,divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2)))) = divide(divide(identity,divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),divide(inverse(b2),divide(identity,b2)))),
inference(monotonicity,[status(thm)],[80,76]) ).
tff(82,plain,
divide(identity,divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2)))) = divide(identity,a2),
inference(transitivity,[status(thm)],[81,73]) ).
tff(83,plain,
divide(divide(identity,divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(divide(identity,a2),divide(identity,divide(a2,divide(identity,divide(inverse(b2),divide(identity,b2))))))),divide(multiply(inverse(b2),b2),divide(identity,a2)))) = divide(divide(identity,a2),divide(identity,a2)),
inference(monotonicity,[status(thm)],[82,71]) ).
tff(84,plain,
divide(divide(identity,divide(divide(identity,a2),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))))),divide(divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(identity,a2)),divide(identity,a2))) = divide(divide(divide(inverse(b2),divide(identity,b2)),divide(divide(identity,a2),divide(identity,divide(a2,divide(identity,divide(inverse(b2),divide(identity,b2))))))),divide(multiply(inverse(b2),b2),divide(identity,a2))),
inference(symmetry,[status(thm)],[70]) ).
tff(85,plain,
divide(identity,a2) = divide(divide(identity,divide(divide(identity,a2),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))))),divide(divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(identity,a2)),divide(identity,a2))),
inference(symmetry,[status(thm)],[37]) ).
tff(86,plain,
divide(identity,a2) = divide(divide(divide(inverse(b2),divide(identity,b2)),divide(divide(identity,a2),divide(identity,divide(a2,divide(identity,divide(inverse(b2),divide(identity,b2))))))),divide(multiply(inverse(b2),b2),divide(identity,a2))),
inference(transitivity,[status(thm)],[85,84]) ).
tff(87,plain,
divide(divide(identity,divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),divide(inverse(b2),divide(identity,b2)))) = divide(identity,divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2)))),
inference(symmetry,[status(thm)],[81]) ).
tff(88,plain,
divide(identity,a2) = divide(divide(identity,divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),divide(inverse(b2),divide(identity,b2)))),
inference(symmetry,[status(thm)],[73]) ).
tff(89,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C )
| ( divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),a2)) = divide(identity,a2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,plain,
divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),a2)) = divide(identity,a2),
inference(unit_resolution,[status(thm)],[89,7]) ).
tff(91,plain,
divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),a2)) = divide(identity,divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2)))),
inference(transitivity,[status(thm)],[90,88,87]) ).
tff(92,plain,
divide(divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),a2)),divide(identity,a2)) = divide(divide(identity,divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(divide(identity,a2),divide(identity,divide(a2,divide(identity,divide(inverse(b2),divide(identity,b2))))))),divide(multiply(inverse(b2),b2),divide(identity,a2)))),
inference(monotonicity,[status(thm)],[91,86]) ).
tff(93,plain,
divide(divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),a2)),divide(identity,a2)) = divide(inverse(b2),divide(identity,b2)),
inference(transitivity,[status(thm)],[92,83,35,29,20]) ).
tff(94,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C )
| ( divide(divide(identity,divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(divide(identity,a2),divide(identity,divide(a2,divide(identity,divide(inverse(b2),divide(identity,b2))))))),divide(multiply(inverse(b2),b2),divide(identity,a2)))) = divide(divide(identity,a2),divide(identity,divide(a2,divide(identity,divide(inverse(b2),divide(identity,b2)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
divide(divide(identity,divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(divide(identity,a2),divide(identity,divide(a2,divide(identity,divide(inverse(b2),divide(identity,b2))))))),divide(multiply(inverse(b2),b2),divide(identity,a2)))) = divide(divide(identity,a2),divide(identity,divide(a2,divide(identity,divide(inverse(b2),divide(identity,b2)))))),
inference(unit_resolution,[status(thm)],[94,7]) ).
tff(96,plain,
divide(divide(identity,a2),divide(identity,divide(a2,divide(identity,divide(inverse(b2),divide(identity,b2)))))) = divide(divide(identity,divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(divide(identity,a2),divide(identity,divide(a2,divide(identity,divide(inverse(b2),divide(identity,b2))))))),divide(multiply(inverse(b2),b2),divide(identity,a2)))),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
divide(divide(identity,a2),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2))))) = divide(inverse(b2),divide(identity,b2)),
inference(transitivity,[status(thm)],[66,96,83,35,29,20]) ).
tff(98,plain,
divide(identity,divide(divide(identity,a2),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))))) = divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))),
inference(monotonicity,[status(thm)],[56,97]) ).
tff(99,plain,
divide(identity,divide(divide(identity,a2),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))))) = divide(inverse(b2),divide(identity,b2)),
inference(transitivity,[status(thm)],[98,32,29,20]) ).
tff(100,plain,
divide(divide(identity,divide(divide(identity,a2),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))))),divide(divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),a2)),divide(identity,a2))) = divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))),
inference(monotonicity,[status(thm)],[99,93]) ).
tff(101,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,a2),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))))),divide(divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),a2)),divide(identity,a2))) = divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),a2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
divide(divide(identity,divide(divide(identity,a2),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))))),divide(divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),a2)),divide(identity,a2))) = divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),a2),
inference(unit_resolution,[status(thm)],[101,7]) ).
tff(103,plain,
divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),a2) = divide(divide(identity,divide(divide(identity,a2),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))))),divide(divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),a2)),divide(identity,a2))),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
divide(multiply(inverse(b2),b2),divide(identity,a2)) = divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),
inference(symmetry,[status(thm)],[74]) ).
tff(105,plain,
divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),a2) = divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),a2),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),a2) = divide(inverse(b2),divide(identity,b2)),
inference(transitivity,[status(thm)],[105,103,100,32,29,20]) ).
tff(107,plain,
divide(divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),a2),divide(inverse(b2),divide(identity,b2))) = divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
divide(divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),a2),divide(inverse(b2),divide(identity,b2))) = divide(inverse(b2),divide(identity,b2)),
inference(transitivity,[status(thm)],[107,32,29,20]) ).
tff(109,plain,
divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))) = divide(identity,divide(divide(identity,a2),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))))),
inference(symmetry,[status(thm)],[98]) ).
tff(110,plain,
divide(inverse(b2),divide(identity,b2)) = divide(identity,divide(divide(identity,a2),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))))),
inference(transitivity,[status(thm)],[60,59,31,109]) ).
tff(111,plain,
divide(divide(inverse(b2),divide(identity,b2)),divide(multiply(inverse(b2),b2),divide(identity,a2))) = divide(divide(identity,divide(divide(identity,a2),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))))),divide(divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(identity,a2)),divide(identity,a2))),
inference(monotonicity,[status(thm)],[110,55]) ).
tff(112,plain,
divide(divide(inverse(b2),divide(identity,b2)),divide(multiply(inverse(b2),b2),divide(identity,a2))) = divide(identity,a2),
inference(transitivity,[status(thm)],[111,37]) ).
tff(113,plain,
identity = multiply(inverse(b2),b2),
inference(transitivity,[status(thm)],[29,20,47]) ).
tff(114,plain,
divide(identity,divide(divide(inverse(b2),divide(identity,b2)),divide(multiply(inverse(b2),b2),divide(identity,a2)))) = divide(multiply(inverse(b2),b2),divide(identity,a2)),
inference(monotonicity,[status(thm)],[113,112]) ).
tff(115,plain,
divide(divide(identity,divide(divide(inverse(b2),divide(identity,b2)),divide(multiply(inverse(b2),b2),divide(identity,a2)))),divide(divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),a2),divide(inverse(b2),divide(identity,b2)))) = divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2))),
inference(monotonicity,[status(thm)],[114,108]) ).
tff(116,plain,
divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2))) = divide(divide(identity,divide(divide(inverse(b2),divide(identity,b2)),divide(multiply(inverse(b2),b2),divide(identity,a2)))),divide(divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),a2),divide(inverse(b2),divide(identity,b2)))),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
divide(divide(divide(inverse(b2),divide(identity,b2)),divide(multiply(inverse(b2),b2),divide(identity,a2))),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2))))) = divide(divide(identity,a2),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2))))),
inference(monotonicity,[status(thm)],[112]) ).
tff(118,plain,
divide(divide(identity,a2),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2))))) = divide(divide(divide(inverse(b2),divide(identity,b2)),divide(multiply(inverse(b2),b2),divide(identity,a2))),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2))))),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
divide(divide(identity,a2),divide(identity,a2)) = divide(divide(identity,divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(divide(identity,a2),divide(identity,divide(a2,divide(identity,divide(inverse(b2),divide(identity,b2))))))),divide(multiply(inverse(b2),b2),divide(identity,a2)))),
inference(symmetry,[status(thm)],[83]) ).
tff(120,plain,
divide(inverse(b2),divide(identity,b2)) = divide(divide(divide(inverse(b2),divide(identity,b2)),divide(multiply(inverse(b2),b2),divide(identity,a2))),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2))))),
inference(transitivity,[status(thm)],[60,59,34,119,95,67,118]) ).
tff(121,plain,
divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))) = divide(divide(identity,divide(divide(identity,a2),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))))),divide(divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),a2)),divide(identity,a2))),
inference(symmetry,[status(thm)],[100]) ).
tff(122,plain,
divide(inverse(b2),divide(identity,b2)) = divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),a2),
inference(transitivity,[status(thm)],[60,59,31,121,102]) ).
tff(123,plain,
divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(inverse(b2),divide(identity,b2))) = divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(identity,a2)),a2)),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(inverse(b2),divide(identity,b2))) = divide(identity,a2),
inference(transitivity,[status(thm)],[123,90]) ).
tff(125,plain,
divide(identity,divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(inverse(b2),divide(identity,b2)))) = divide(multiply(inverse(b2),b2),divide(identity,a2)),
inference(monotonicity,[status(thm)],[113,124]) ).
tff(126,plain,
divide(multiply(inverse(b2),b2),divide(identity,a2)) = divide(identity,divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(inverse(b2),divide(identity,b2)))),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2))) = divide(divide(identity,divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(multiply(inverse(b2),b2),divide(identity,a2))),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))))),
inference(monotonicity,[status(thm)],[126,120]) ).
tff(128,plain,
divide(divide(identity,divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(multiply(inverse(b2),b2),divide(identity,a2))),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))))) = divide(divide(multiply(inverse(b2),b2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2))),
inference(symmetry,[status(thm)],[127]) ).
tff(129,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,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(multiply(inverse(b2),b2),divide(identity,a2))),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))))) = divide(multiply(inverse(b2),b2),divide(identity,a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(130,plain,
divide(divide(identity,divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(multiply(inverse(b2),b2),divide(identity,a2))),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))))) = divide(multiply(inverse(b2),b2),divide(identity,a2)),
inference(unit_resolution,[status(thm)],[129,7]) ).
tff(131,plain,
divide(multiply(inverse(b2),b2),divide(identity,a2)) = divide(divide(identity,divide(divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))),divide(inverse(b2),divide(identity,b2)))),divide(divide(divide(inverse(b2),divide(identity,b2)),divide(multiply(inverse(b2),b2),divide(identity,a2))),divide(identity,divide(a2,divide(inverse(b2),divide(identity,b2)))))),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
| ( multiply(multiply(inverse(b2),b2),a2) = divide(multiply(inverse(b2),b2),divide(identity,a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(133,plain,
multiply(multiply(inverse(b2),b2),a2) = divide(multiply(inverse(b2),b2),divide(identity,a2)),
inference(unit_resolution,[status(thm)],[132,44]) ).
tff(134,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(transitivity,[status(thm)],[133,131,128,116,9]) ).
tff(135,plain,
( ( multiply(multiply(inverse(b2),b2),a2) != a2 )
<=> ( multiply(multiply(inverse(b2),b2),a2) != a2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
tff(137,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
$false,
inference(unit_resolution,[status(thm)],[137,134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP546-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 16:17:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45 % SZS output start Proof
% See solution above
% 0.20/0.48 % E exiting
%------------------------------------------------------------------------------