TSTP Solution File: GRP528-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP528-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 22:27:59 EDT 2022
% Result : Unsatisfiable 0.18s 0.57s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 45
% Syntax : Number of formulae : 151 ( 110 unt; 5 typ; 0 def)
% Number of atoms : 188 ( 184 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 72 ( 33 ~; 29 |; 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 : 153 ( 145 !; 0 ?; 153 :)
% 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(inverse_type,type,
inverse: $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(b,a) = divide(b,divide(divide(divide(b,a),divide(b,a)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
multiply(b,a) = divide(b,divide(divide(divide(b,a),divide(b,a)),a)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
divide(b,divide(divide(divide(b,a),divide(b,a)),a)) = multiply(b,a),
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(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(a,divide(divide(b,b),b))))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(a,divide(divide(b,b),b))))) = a,
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(a,divide(divide(a,divide(divide(divide(b,b),b),divide(divide(b,b),b))),divide(divide(divide(b,b),b),divide(divide(divide(b,b),b),divide(divide(b,b),b))))) = divide(divide(b,b),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
divide(a,divide(divide(a,divide(divide(divide(b,b),b),divide(divide(b,b),b))),divide(divide(divide(b,b),b),divide(divide(divide(b,b),b),divide(divide(b,b),b))))) = divide(divide(b,b),b),
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(divide(divide(b,b),b),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(b,b),b),divide(divide(b,b),b)))) = divide(divide(b,b),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(23,plain,
divide(divide(divide(b,b),b),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(b,b),b),divide(divide(b,b),b)))) = divide(divide(b,b),b),
inference(unit_resolution,[status(thm)],[22,17]) ).
tff(24,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(divide(b,b),b),divide(divide(divide(b,b),b),divide(divide(b,b),b))) = divide(divide(divide(b,b),b),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(b,b),b),divide(divide(b,b),b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
multiply(divide(divide(b,b),b),divide(divide(divide(b,b),b),divide(divide(b,b),b))) = divide(divide(divide(b,b),b),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(b,b),b),divide(divide(b,b),b)))),
inference(unit_resolution,[status(thm)],[24,7]) ).
tff(26,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(divide(b,b),b),divide(divide(divide(b,b),b),divide(divide(b,b),b))) = divide(divide(divide(b,b),b),divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(b,b),b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
multiply(divide(divide(b,b),b),divide(divide(divide(b,b),b),divide(divide(b,b),b))) = divide(divide(divide(b,b),b),divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(b,b),b)))),
inference(unit_resolution,[status(thm)],[26,7]) ).
tff(28,plain,
divide(divide(divide(b,b),b),divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(b,b),b)))) = multiply(divide(divide(b,b),b),divide(divide(divide(b,b),b),divide(divide(b,b),b))),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(divide(b,b),b),b) = divide(divide(divide(b,b),b),divide(divide(b,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
multiply(divide(divide(b,b),b),b) = divide(divide(divide(b,b),b),divide(divide(b,b),b)),
inference(unit_resolution,[status(thm)],[29,7]) ).
tff(31,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(divide(b,b),b),b) = divide(divide(divide(b,b),b),divide(divide(divide(b,a),divide(b,a)),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
multiply(divide(divide(b,b),b),b) = divide(divide(divide(b,b),b),divide(divide(divide(b,a),divide(b,a)),b)),
inference(unit_resolution,[status(thm)],[31,7]) ).
tff(33,plain,
divide(divide(divide(b,b),b),divide(divide(divide(b,a),divide(b,a)),b)) = multiply(divide(divide(b,b),b),b),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
divide(divide(divide(b,b),b),divide(divide(divide(b,a),divide(b,a)),b)) = divide(divide(divide(b,b),b),divide(divide(b,b),b)),
inference(transitivity,[status(thm)],[33,30]) ).
tff(35,plain,
divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(divide(b,a),divide(b,a)),b))) = divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(b,b),b))),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C )
| ( divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(divide(b,a),divide(b,a)),b))) = divide(divide(b,a),divide(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(divide(b,a),divide(b,a)),b))) = divide(divide(b,a),divide(b,a)),
inference(unit_resolution,[status(thm)],[36,17]) ).
tff(38,plain,
divide(divide(b,a),divide(b,a)) = divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(divide(b,a),divide(b,a)),b))),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
divide(divide(b,a),divide(b,a)) = divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(b,b),b))),
inference(transitivity,[status(thm)],[38,35]) ).
tff(40,plain,
divide(divide(divide(b,b),b),divide(divide(b,a),divide(b,a))) = divide(divide(divide(b,b),b),divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(b,b),b)))),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(b,b),b))) = divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(divide(b,a),divide(b,a)),b))),
inference(symmetry,[status(thm)],[35]) ).
tff(42,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(divide(b,b),b),b) = divide(divide(divide(b,b),b),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
multiply(divide(divide(b,b),b),b) = divide(divide(divide(b,b),b),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b)),
inference(unit_resolution,[status(thm)],[42,7]) ).
tff(44,plain,
divide(divide(divide(b,b),b),divide(divide(b,b),b)) = multiply(divide(divide(b,b),b),b),
inference(symmetry,[status(thm)],[30]) ).
tff(45,plain,
divide(divide(divide(b,b),b),divide(divide(b,b),b)) = divide(divide(divide(b,b),b),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b)),
inference(transitivity,[status(thm)],[44,43]) ).
tff(46,plain,
divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(b,b),b))) = divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b))),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b))) = divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(b,b),b))),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C )
| ( divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b))) = divide(divide(divide(b,b),b),divide(divide(b,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b))) = divide(divide(divide(b,b),b),divide(divide(b,b),b)),
inference(unit_resolution,[status(thm)],[48,17]) ).
tff(50,plain,
divide(divide(divide(b,b),b),divide(divide(b,b),b)) = divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b))),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
divide(divide(divide(b,b),b),divide(divide(b,b),b)) = divide(divide(b,a),divide(b,a)),
inference(transitivity,[status(thm)],[50,47,41,37]) ).
tff(52,plain,
divide(divide(divide(b,b),b),divide(divide(divide(b,b),b),divide(divide(b,b),b))) = divide(divide(divide(b,b),b),divide(divide(b,a),divide(b,a))),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
divide(divide(divide(b,b),b),divide(divide(divide(b,b),b),divide(divide(b,b),b))) = divide(divide(b,b),b),
inference(transitivity,[status(thm)],[52,40,28,25,23]) ).
tff(54,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C )
| ( divide(a,divide(divide(a,a),divide(a,a))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
divide(a,divide(divide(a,a),divide(a,a))) = a,
inference(unit_resolution,[status(thm)],[54,17]) ).
tff(56,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(57,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)],[56]) ).
tff(58,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(59,axiom,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
tff(60,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(b) = divide(divide(b,b),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
inverse(b) = divide(divide(b,b),b),
inference(unit_resolution,[status(thm)],[63,62]) ).
tff(65,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(b) = divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
inverse(b) = divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b),
inference(unit_resolution,[status(thm)],[65,62]) ).
tff(67,plain,
divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b) = inverse(b),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b) = divide(divide(b,b),b),
inference(transitivity,[status(thm)],[67,64]) ).
tff(69,plain,
divide(divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b),divide(divide(b,b),b)) = divide(divide(divide(b,b),b),divide(divide(b,b),b)),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
divide(divide(divide(b,b),b),divide(divide(b,b),b)) = divide(divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b),divide(divide(b,b),b)),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C )
| ( divide(b,divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(b,b),b)))) = divide(divide(divide(b,b),b),divide(divide(b,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
divide(b,divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(b,b),b)))) = divide(divide(divide(b,b),b),divide(divide(b,b),b)),
inference(unit_resolution,[status(thm)],[71,17]) ).
tff(73,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(b,divide(divide(b,b),b)),divide(divide(b,b),b)) = divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(b,b),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
multiply(divide(b,divide(divide(b,b),b)),divide(divide(b,b),b)) = divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(b,b),b))),
inference(unit_resolution,[status(thm)],[73,7]) ).
tff(75,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(b,divide(divide(b,b),b)),divide(divide(b,b),b)) = divide(divide(b,divide(divide(b,b),b)),divide(divide(a,a),divide(divide(b,b),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
multiply(divide(b,divide(divide(b,b),b)),divide(divide(b,b),b)) = divide(divide(b,divide(divide(b,b),b)),divide(divide(a,a),divide(divide(b,b),b))),
inference(unit_resolution,[status(thm)],[75,7]) ).
tff(77,plain,
divide(divide(b,divide(divide(b,b),b)),divide(divide(a,a),divide(divide(b,b),b))) = multiply(divide(b,divide(divide(b,b),b)),divide(divide(b,b),b)),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
divide(divide(b,divide(divide(b,b),b)),divide(divide(a,a),divide(divide(b,b),b))) = divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(b,b),b))),
inference(transitivity,[status(thm)],[77,74]) ).
tff(79,plain,
divide(b,divide(divide(b,divide(divide(b,b),b)),divide(divide(a,a),divide(divide(b,b),b)))) = divide(b,divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(b,b),b)))),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C )
| ( divide(b,divide(divide(b,divide(divide(b,b),b)),divide(divide(a,a),divide(divide(b,b),b)))) = divide(a,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
divide(b,divide(divide(b,divide(divide(b,b),b)),divide(divide(a,a),divide(divide(b,b),b)))) = divide(a,a),
inference(unit_resolution,[status(thm)],[80,17]) ).
tff(82,plain,
divide(a,a) = divide(b,divide(divide(b,divide(divide(b,b),b)),divide(divide(a,a),divide(divide(b,b),b)))),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
divide(a,a) = divide(divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b),divide(divide(b,b),b)),
inference(transitivity,[status(thm)],[82,79,72,70]) ).
tff(84,plain,
divide(a,a) = divide(divide(divide(b,b),b),divide(divide(b,b),b)),
inference(transitivity,[status(thm)],[82,79,72]) ).
tff(85,plain,
divide(divide(a,a),divide(a,a)) = divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b),divide(divide(b,b),b))),
inference(monotonicity,[status(thm)],[84,83]) ).
tff(86,plain,
divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b),divide(divide(b,b),b))) = divide(divide(a,a),divide(a,a)),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C )
| ( divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b),divide(divide(b,b),b))) = divide(b,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b),divide(divide(b,b),b))) = divide(b,b),
inference(unit_resolution,[status(thm)],[87,17]) ).
tff(89,plain,
divide(b,b) = divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b),divide(divide(b,b),b))),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C )
| ( divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(b,b),b))) = divide(b,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(b,b),b))) = divide(b,b),
inference(unit_resolution,[status(thm)],[90,17]) ).
tff(92,plain,
divide(divide(divide(b,b),b),divide(divide(b,b),b)) = divide(divide(a,a),divide(a,a)),
inference(transitivity,[status(thm)],[50,47,91,89,86]) ).
tff(93,plain,
divide(a,divide(divide(divide(b,b),b),divide(divide(b,b),b))) = divide(a,divide(divide(a,a),divide(a,a))),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
divide(a,divide(divide(divide(b,b),b),divide(divide(b,b),b))) = a,
inference(transitivity,[status(thm)],[93,55]) ).
tff(95,plain,
divide(divide(a,divide(divide(divide(b,b),b),divide(divide(b,b),b))),divide(divide(divide(b,b),b),divide(divide(divide(b,b),b),divide(divide(b,b),b)))) = divide(a,divide(divide(b,b),b)),
inference(monotonicity,[status(thm)],[94,53]) ).
tff(96,plain,
divide(a,divide(divide(b,b),b)) = divide(divide(a,divide(divide(divide(b,b),b),divide(divide(b,b),b))),divide(divide(divide(b,b),b),divide(divide(divide(b,b),b),divide(divide(b,b),b)))),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
divide(a,divide(a,divide(divide(b,b),b))) = divide(a,divide(divide(a,divide(divide(divide(b,b),b),divide(divide(b,b),b))),divide(divide(divide(b,b),b),divide(divide(divide(b,b),b),divide(divide(b,b),b))))),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
divide(a,divide(a,divide(divide(b,b),b))) = divide(divide(b,b),b),
inference(transitivity,[status(thm)],[97,21]) ).
tff(99,plain,
divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(a,divide(divide(b,b),b)))) = divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(b,b),b)),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(b,b),b)) = divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(a,divide(divide(b,b),b)))),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(divide(b,b),b)) = divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(b,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(102,plain,
inverse(divide(divide(b,b),b)) = divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(b,b),b)),
inference(unit_resolution,[status(thm)],[101,62]) ).
tff(103,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(divide(b,b),b)) = divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(b,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
inverse(divide(divide(b,b),b)) = divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(b,b),b)),
inference(unit_resolution,[status(thm)],[103,62]) ).
tff(105,plain,
divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(b,b),b)) = inverse(divide(divide(b,b),b)),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b) = divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(b,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
multiply(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b) = divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(b,b),b)),
inference(unit_resolution,[status(thm)],[106,7]) ).
tff(108,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b) = divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(109,plain,
multiply(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b) = divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b)),
inference(unit_resolution,[status(thm)],[108,7]) ).
tff(110,plain,
divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b)) = multiply(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
divide(b,b) = divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(b,b),b))),
inference(symmetry,[status(thm)],[91]) ).
tff(112,plain,
divide(b,b) = divide(divide(b,a),divide(b,a)),
inference(transitivity,[status(thm)],[111,41,37]) ).
tff(113,plain,
divide(divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b),divide(b,b)) = divide(divide(divide(b,b),b),divide(divide(b,a),divide(b,a))),
inference(monotonicity,[status(thm)],[68,112]) ).
tff(114,plain,
divide(divide(divide(b,b),b),divide(divide(b,a),divide(b,a))) = divide(divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b),divide(b,b)),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
divide(divide(divide(b,b),b),divide(divide(b,b),divide(divide(divide(b,b),b),divide(divide(b,b),b)))) = divide(divide(divide(b,b),b),divide(divide(b,a),divide(b,a))),
inference(symmetry,[status(thm)],[40]) ).
tff(116,plain,
divide(divide(divide(b,b),b),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(b,b),b),divide(divide(b,b),b)))) = multiply(divide(divide(b,b),b),divide(divide(divide(b,b),b),divide(divide(b,b),b))),
inference(symmetry,[status(thm)],[25]) ).
tff(117,plain,
divide(divide(b,b),b) = divide(divide(divide(b,b),b),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(b,b),b),divide(divide(b,b),b)))),
inference(symmetry,[status(thm)],[23]) ).
tff(118,plain,
divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b) = divide(divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b),divide(b,b)),
inference(transitivity,[status(thm)],[67,64,117,116,27,115,114]) ).
tff(119,plain,
divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b)) = divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b),divide(b,b))),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b),divide(b,b))) = divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b)),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C )
| ( divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b),divide(b,b))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b),divide(b,b))) = b,
inference(unit_resolution,[status(thm)],[121,17]) ).
tff(123,plain,
b = divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),b),divide(b,b))),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
b = divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(a,divide(divide(b,b),b)))),
inference(transitivity,[status(thm)],[123,120,110,107,105,102,100]) ).
tff(125,plain,
divide(divide(a,divide(divide(b,b),b)),b) = divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(a,divide(divide(b,b),b))))),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
divide(divide(a,divide(divide(b,b),b)),b) = a,
inference(transitivity,[status(thm)],[125,19]) ).
tff(127,plain,
divide(divide(b,b),divide(divide(a,divide(divide(b,b),b)),b)) = divide(divide(b,b),a),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
divide(divide(b,b),a) = divide(divide(b,b),divide(divide(a,divide(divide(b,b),b)),b)),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(a) = divide(divide(b,b),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,plain,
inverse(a) = divide(divide(b,b),a),
inference(unit_resolution,[status(thm)],[129,62]) ).
tff(131,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(a) = divide(divide(divide(b,a),divide(b,a)),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(132,plain,
inverse(a) = divide(divide(divide(b,a),divide(b,a)),a),
inference(unit_resolution,[status(thm)],[131,62]) ).
tff(133,plain,
divide(divide(divide(b,a),divide(b,a)),a) = inverse(a),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
divide(divide(divide(b,a),divide(b,a)),a) = divide(divide(b,b),divide(divide(a,divide(divide(b,b),b)),b)),
inference(transitivity,[status(thm)],[133,130,128]) ).
tff(135,plain,
divide(b,divide(divide(divide(b,a),divide(b,a)),a)) = divide(b,divide(divide(b,b),divide(divide(a,divide(divide(b,b),b)),b))),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
divide(b,divide(divide(b,b),divide(divide(a,divide(divide(b,b),b)),b))) = divide(b,divide(divide(divide(b,a),divide(b,a)),a)),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(A,B),divide(C,B))) = C )
| ( divide(b,divide(divide(b,b),divide(divide(a,divide(divide(b,b),b)),b))) = divide(a,divide(divide(b,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
divide(b,divide(divide(b,b),divide(divide(a,divide(divide(b,b),b)),b))) = divide(a,divide(divide(b,b),b)),
inference(unit_resolution,[status(thm)],[137,17]) ).
tff(139,plain,
divide(a,divide(divide(b,b),b)) = divide(b,divide(divide(b,b),divide(divide(a,divide(divide(b,b),b)),b))),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(a,b) = divide(a,divide(divide(b,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(141,plain,
multiply(a,b) = divide(a,divide(divide(b,b),b)),
inference(unit_resolution,[status(thm)],[140,7]) ).
tff(142,plain,
multiply(a,b) = multiply(b,a),
inference(transitivity,[status(thm)],[141,139,136,10]) ).
tff(143,plain,
( ( multiply(a,b) != multiply(b,a) )
<=> ( multiply(a,b) != multiply(b,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(144,axiom,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_4) ).
tff(145,plain,
multiply(a,b) != multiply(b,a),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
$false,
inference(unit_resolution,[status(thm)],[145,142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP528-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n015.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 : Wed Aug 31 17:42:22 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.18/0.57 % SZS status Unsatisfiable
% 0.18/0.57 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------