TSTP Solution File: GRP525-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP525-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 : Fri Sep 16 22:27:58 EDT 2022
% Result : Unsatisfiable 0.19s 0.50s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 34
% Syntax : Number of formulae : 106 ( 76 unt; 5 typ; 0 def)
% Number of atoms : 132 ( 128 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 50 ( 22 ~; 18 |; 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 : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 119 ( 111 !; 0 ?; 119 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b1_type,type,
b1: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(a1_type,type,
a1: $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
<=> ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
<=> ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
<=> ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
tff(5,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(inverse(b1),b1) = divide(inverse(b1),divide(divide(a1,a1),b1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
multiply(inverse(b1),b1) = divide(inverse(b1),divide(divide(a1,a1),b1)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
divide(inverse(b1),divide(divide(a1,a1),b1)) = multiply(inverse(b1),b1),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( divide(A,divide(divide(A,B),divide(C,B))) = C )
<=> ( divide(A,divide(divide(A,B),divide(C,B))) = C ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C )
<=> ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C )
<=> ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C )
| ( divide(a1,divide(divide(a1,a1),divide(divide(inverse(b1),divide(divide(a1,a1),b1)),a1))) = divide(inverse(b1),divide(divide(a1,a1),b1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
divide(a1,divide(divide(a1,a1),divide(divide(inverse(b1),divide(divide(a1,a1),b1)),a1))) = divide(inverse(b1),divide(divide(a1,a1),b1)),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C )
| ( divide(divide(a1,a1),divide(divide(divide(a1,a1),divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1))),divide(a1,divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1))))) = a1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
divide(divide(a1,a1),divide(divide(divide(a1,a1),divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1))),divide(a1,divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1))))) = a1,
inference(unit_resolution,[status(thm)],[20,17]) ).
tff(22,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C )
| ( divide(a1,divide(divide(a1,a1),divide(a1,a1))) = a1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(23,plain,
divide(a1,divide(divide(a1,a1),divide(a1,a1))) = a1,
inference(unit_resolution,[status(thm)],[22,17]) ).
tff(24,plain,
^ [B: $i,A: $i] :
refl(
( ( inverse(A) = divide(divide(B,B),A) )
<=> ( inverse(A) = divide(divide(B,B),A) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
<=> ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
<=> ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
tff(28,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(a1,a1)) = divide(divide(a1,a1),divide(a1,a1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
inverse(divide(a1,a1)) = divide(divide(a1,a1),divide(a1,a1)),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(a1,a1)) = divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
inverse(divide(a1,a1)) = divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1)),
inference(unit_resolution,[status(thm)],[33,30]) ).
tff(35,plain,
divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1)) = inverse(divide(a1,a1)),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1)) = divide(divide(a1,a1),divide(a1,a1)),
inference(transitivity,[status(thm)],[35,32]) ).
tff(37,plain,
divide(a1,divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1))) = divide(a1,divide(divide(a1,a1),divide(a1,a1))),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
divide(a1,divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1))) = a1,
inference(transitivity,[status(thm)],[37,23]) ).
tff(39,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C )
| ( divide(divide(a1,a1),divide(divide(divide(a1,a1),divide(inverse(b1),divide(divide(a1,a1),b1))),divide(divide(a1,a1),divide(inverse(b1),divide(divide(a1,a1),b1))))) = divide(a1,a1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
divide(divide(a1,a1),divide(divide(divide(a1,a1),divide(inverse(b1),divide(divide(a1,a1),b1))),divide(divide(a1,a1),divide(inverse(b1),divide(divide(a1,a1),b1))))) = divide(a1,a1),
inference(unit_resolution,[status(thm)],[39,17]) ).
tff(41,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C )
| ( divide(divide(a1,a1),divide(divide(divide(a1,a1),b1),divide(divide(a1,a1),b1))) = divide(a1,a1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
divide(divide(a1,a1),divide(divide(divide(a1,a1),b1),divide(divide(a1,a1),b1))) = divide(a1,a1),
inference(unit_resolution,[status(thm)],[41,17]) ).
tff(43,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(b1) = divide(divide(a1,a1),b1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
inverse(b1) = divide(divide(a1,a1),b1),
inference(unit_resolution,[status(thm)],[43,30]) ).
tff(45,plain,
divide(divide(a1,a1),b1) = inverse(b1),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
divide(divide(divide(a1,a1),b1),divide(divide(a1,a1),b1)) = divide(inverse(b1),divide(divide(a1,a1),b1)),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
divide(inverse(b1),divide(divide(a1,a1),b1)) = divide(divide(divide(a1,a1),b1),divide(divide(a1,a1),b1)),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
divide(divide(a1,a1),divide(inverse(b1),divide(divide(a1,a1),b1))) = divide(divide(a1,a1),divide(divide(divide(a1,a1),b1),divide(divide(a1,a1),b1))),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
divide(divide(a1,a1),divide(inverse(b1),divide(divide(a1,a1),b1))) = divide(a1,a1),
inference(transitivity,[status(thm)],[48,42]) ).
tff(50,plain,
divide(divide(divide(a1,a1),divide(inverse(b1),divide(divide(a1,a1),b1))),divide(divide(a1,a1),divide(inverse(b1),divide(divide(a1,a1),b1)))) = divide(divide(a1,a1),divide(a1,a1)),
inference(monotonicity,[status(thm)],[49,49]) ).
tff(51,plain,
divide(divide(a1,a1),divide(a1,a1)) = divide(divide(divide(a1,a1),divide(inverse(b1),divide(divide(a1,a1),b1))),divide(divide(a1,a1),divide(inverse(b1),divide(divide(a1,a1),b1)))),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
divide(divide(a1,a1),divide(divide(a1,a1),divide(a1,a1))) = divide(divide(a1,a1),divide(divide(divide(a1,a1),divide(inverse(b1),divide(divide(a1,a1),b1))),divide(divide(a1,a1),divide(inverse(b1),divide(divide(a1,a1),b1))))),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(a1,a1),divide(a1,a1)) = divide(divide(a1,a1),divide(divide(a1,a1),divide(a1,a1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
multiply(divide(a1,a1),divide(a1,a1)) = divide(divide(a1,a1),divide(divide(a1,a1),divide(a1,a1))),
inference(unit_resolution,[status(thm)],[53,7]) ).
tff(55,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(a1,a1),divide(a1,a1)) = divide(divide(a1,a1),divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
multiply(divide(a1,a1),divide(a1,a1)) = divide(divide(a1,a1),divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1))),
inference(unit_resolution,[status(thm)],[55,7]) ).
tff(57,plain,
divide(divide(a1,a1),divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1))) = multiply(divide(a1,a1),divide(a1,a1)),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
divide(divide(a1,a1),divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1))) = divide(a1,a1),
inference(transitivity,[status(thm)],[57,54,52,40]) ).
tff(59,plain,
divide(divide(divide(a1,a1),divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1))),divide(a1,divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1)))) = divide(divide(a1,a1),a1),
inference(monotonicity,[status(thm)],[58,38]) ).
tff(60,plain,
divide(divide(a1,a1),a1) = divide(divide(divide(a1,a1),divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1))),divide(a1,divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1)))),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(a1) = divide(divide(a1,a1),a1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
inverse(a1) = divide(divide(a1,a1),a1),
inference(unit_resolution,[status(thm)],[61,30]) ).
tff(63,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(a1) = divide(divide(inverse(b1),inverse(b1)),a1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
inverse(a1) = divide(divide(inverse(b1),inverse(b1)),a1),
inference(unit_resolution,[status(thm)],[63,30]) ).
tff(65,plain,
divide(divide(inverse(b1),inverse(b1)),a1) = inverse(a1),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
divide(inverse(b1),inverse(b1)) = divide(inverse(b1),divide(divide(a1,a1),b1)),
inference(monotonicity,[status(thm)],[44]) ).
tff(67,plain,
divide(inverse(b1),divide(divide(a1,a1),b1)) = divide(inverse(b1),inverse(b1)),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
divide(divide(inverse(b1),divide(divide(a1,a1),b1)),a1) = divide(divide(inverse(b1),inverse(b1)),a1),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
divide(divide(inverse(b1),divide(divide(a1,a1),b1)),a1) = divide(divide(divide(a1,a1),divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1))),divide(a1,divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1)))),
inference(transitivity,[status(thm)],[68,65,62,60]) ).
tff(70,plain,
divide(divide(a1,a1),divide(divide(inverse(b1),divide(divide(a1,a1),b1)),a1)) = divide(divide(a1,a1),divide(divide(divide(a1,a1),divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1))),divide(a1,divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1))))),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
divide(divide(a1,a1),divide(divide(inverse(b1),divide(divide(a1,a1),b1)),a1)) = a1,
inference(transitivity,[status(thm)],[70,21]) ).
tff(72,plain,
divide(a1,divide(divide(a1,a1),divide(divide(inverse(b1),divide(divide(a1,a1),b1)),a1))) = divide(a1,a1),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
divide(a1,a1) = divide(a1,divide(divide(a1,a1),divide(divide(inverse(b1),divide(divide(a1,a1),b1)),a1))),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C )
| ( divide(divide(a1,a1),divide(divide(divide(a1,a1),inverse(a1)),divide(divide(a1,a1),inverse(a1)))) = divide(a1,a1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
divide(divide(a1,a1),divide(divide(divide(a1,a1),inverse(a1)),divide(divide(a1,a1),inverse(a1)))) = divide(a1,a1),
inference(unit_resolution,[status(thm)],[74,17]) ).
tff(76,plain,
inverse(a1) = divide(divide(divide(a1,a1),divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1))),divide(a1,divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1)))),
inference(transitivity,[status(thm)],[62,60]) ).
tff(77,plain,
divide(divide(a1,a1),inverse(a1)) = divide(divide(a1,a1),divide(divide(divide(a1,a1),divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1))),divide(a1,divide(divide(divide(a1,a1),divide(a1,a1)),divide(a1,a1))))),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
divide(divide(a1,a1),inverse(a1)) = a1,
inference(transitivity,[status(thm)],[77,21]) ).
tff(79,plain,
divide(divide(divide(a1,a1),inverse(a1)),divide(divide(a1,a1),inverse(a1))) = divide(a1,a1),
inference(monotonicity,[status(thm)],[78,78]) ).
tff(80,plain,
divide(a1,a1) = divide(divide(divide(a1,a1),inverse(a1)),divide(divide(a1,a1),inverse(a1))),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
divide(divide(a1,a1),divide(a1,a1)) = divide(divide(a1,a1),divide(divide(divide(a1,a1),inverse(a1)),divide(divide(a1,a1),inverse(a1)))),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(inverse(a1)) = divide(divide(a1,a1),inverse(a1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
inverse(inverse(a1)) = divide(divide(a1,a1),inverse(a1)),
inference(unit_resolution,[status(thm)],[82,30]) ).
tff(84,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(inverse(a1)) = divide(divide(inverse(a1),inverse(a1)),inverse(a1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
inverse(inverse(a1)) = divide(divide(inverse(a1),inverse(a1)),inverse(a1)),
inference(unit_resolution,[status(thm)],[84,30]) ).
tff(86,plain,
divide(divide(inverse(a1),inverse(a1)),inverse(a1)) = inverse(inverse(a1)),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
divide(divide(inverse(a1),inverse(a1)),inverse(a1)) = a1,
inference(transitivity,[status(thm)],[86,83,77,21]) ).
tff(88,plain,
divide(divide(divide(a1,a1),inverse(a1)),divide(divide(inverse(a1),inverse(a1)),inverse(a1))) = divide(a1,a1),
inference(monotonicity,[status(thm)],[78,87]) ).
tff(89,plain,
divide(divide(a1,a1),divide(divide(divide(a1,a1),inverse(a1)),divide(divide(inverse(a1),inverse(a1)),inverse(a1)))) = divide(divide(a1,a1),divide(a1,a1)),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C )
| ( divide(divide(a1,a1),divide(divide(divide(a1,a1),inverse(a1)),divide(divide(inverse(a1),inverse(a1)),inverse(a1)))) = divide(inverse(a1),inverse(a1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
divide(divide(a1,a1),divide(divide(divide(a1,a1),inverse(a1)),divide(divide(inverse(a1),inverse(a1)),inverse(a1)))) = divide(inverse(a1),inverse(a1)),
inference(unit_resolution,[status(thm)],[90,17]) ).
tff(92,plain,
divide(inverse(a1),inverse(a1)) = divide(divide(a1,a1),divide(divide(divide(a1,a1),inverse(a1)),divide(divide(inverse(a1),inverse(a1)),inverse(a1)))),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
divide(divide(a1,a1),a1) = inverse(a1),
inference(symmetry,[status(thm)],[62]) ).
tff(94,plain,
divide(inverse(a1),divide(divide(a1,a1),a1)) = divide(inverse(a1),inverse(a1)),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(inverse(a1),a1) = divide(inverse(a1),divide(divide(a1,a1),a1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,plain,
multiply(inverse(a1),a1) = divide(inverse(a1),divide(divide(a1,a1),a1)),
inference(unit_resolution,[status(thm)],[95,7]) ).
tff(97,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(transitivity,[status(thm)],[96,94,92,89,81,75,73,19,10]) ).
tff(98,plain,
( ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1) )
<=> ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
tff(100,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
$false,
inference(unit_resolution,[status(thm)],[100,97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP525-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n002.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 17:42:15 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.50 % SZS status Unsatisfiable
% 0.19/0.50 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------