%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP530-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:08:01 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 23
% Syntax : Number of formulae : 96 ( 77 unt; 0 typ; 0 def)
% Number of atoms : 121 ( 117 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 38 ( 16 ~; 12 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 10 ( 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; 2 con; 0-2 aty)
% Number of variables : 103 ( 95 !; 0 ?; 103 :)
% 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(1,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
<=> ( divide(divide(A,divide(B,C)),divide(A,B)) = C ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
<=> ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
<=> ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
tff(5,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(multiply(inverse(b2),b2),divide(a2,a2)),divide(multiply(inverse(b2),b2),a2)) = a2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
divide(divide(multiply(inverse(b2),b2),divide(a2,a2)),divide(multiply(inverse(b2),b2),a2)) = a2,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,axiom,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
tff(14,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = divide(divide(inverse(b2),inverse(b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
inverse(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = divide(divide(inverse(b2),inverse(b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
inverse(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),
inference(unit_resolution,[status(thm)],[19,16]) ).
tff(21,plain,
divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = inverse(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = divide(divide(inverse(b2),inverse(b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),
inference(transitivity,[status(thm)],[21,18]) ).
tff(23,plain,
divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2))) = divide(divide(divide(inverse(b2),inverse(b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2))),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
divide(divide(divide(inverse(b2),inverse(b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2))) = divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2))),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(inverse(b2),inverse(b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2))) = multiply(inverse(b2),b2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
divide(divide(divide(inverse(b2),inverse(b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2))) = multiply(inverse(b2),b2),
inference(unit_resolution,[status(thm)],[25,7]) ).
tff(27,plain,
multiply(inverse(b2),b2) = divide(divide(divide(inverse(b2),inverse(b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2))),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
multiply(inverse(b2),b2) = divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2))),
inference(transitivity,[status(thm)],[27,24]) ).
tff(29,plain,
divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)) = divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2)))),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2)))) = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2)))))),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
divide(divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2)))))),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2)))),
inference(unit_resolution,[status(thm)],[31,7]) ).
tff(33,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2))) = divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
inverse(divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2))) = divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2))),
inference(unit_resolution,[status(thm)],[33,16]) ).
tff(35,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(b2) = divide(divide(inverse(b2),inverse(b2)),b2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
inverse(b2) = divide(divide(inverse(b2),inverse(b2)),b2),
inference(unit_resolution,[status(thm)],[35,16]) ).
tff(37,plain,
divide(divide(inverse(b2),inverse(b2)),b2) = inverse(b2),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
multiply(divide(divide(inverse(b2),inverse(b2)),b2),b2) = multiply(inverse(b2),b2),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,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(40,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)],[39]) ).
tff(41,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(42,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(43,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(divide(inverse(b2),inverse(b2)),b2),b2) = divide(divide(divide(inverse(b2),inverse(b2)),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),b2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
multiply(divide(divide(inverse(b2),inverse(b2)),b2),b2) = divide(divide(divide(inverse(b2),inverse(b2)),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),b2)),
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
divide(divide(divide(inverse(b2),inverse(b2)),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),b2)) = multiply(divide(divide(inverse(b2),inverse(b2)),b2),b2),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(b2) = divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),b2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
inverse(b2) = divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),b2),
inference(unit_resolution,[status(thm)],[49,16]) ).
tff(51,plain,
divide(inverse(b2),inverse(b2)) = divide(divide(divide(inverse(b2),inverse(b2)),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),b2)),
inference(monotonicity,[status(thm)],[36,50]) ).
tff(52,plain,
divide(inverse(b2),inverse(b2)) = multiply(inverse(b2),b2),
inference(transitivity,[status(thm)],[51,48,38]) ).
tff(53,plain,
divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2)) = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)) = divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2)),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
inverse(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = inverse(divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2))),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
divide(divide(inverse(b2),inverse(b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = inverse(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),
inference(symmetry,[status(thm)],[18]) ).
tff(57,plain,
divide(divide(divide(inverse(b2),inverse(b2)),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),b2)) = divide(inverse(b2),inverse(b2)),
inference(symmetry,[status(thm)],[51]) ).
tff(58,plain,
multiply(inverse(b2),b2) = multiply(divide(divide(inverse(b2),inverse(b2)),b2),b2),
inference(symmetry,[status(thm)],[38]) ).
tff(59,plain,
multiply(inverse(b2),b2) = divide(inverse(b2),inverse(b2)),
inference(transitivity,[status(thm)],[58,47,57]) ).
tff(60,plain,
divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = divide(divide(inverse(b2),inverse(b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2))))) = divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),
inference(monotonicity,[status(thm)],[30]) ).
tff(62,plain,
divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2))))) = multiply(inverse(b2),b2),
inference(transitivity,[status(thm)],[61,60,56,55,34,23,26]) ).
tff(63,plain,
divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2)))))) = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
divide(divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2)))))),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = divide(divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2)))))),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
inverse(divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2))) = inverse(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),
inference(symmetry,[status(thm)],[55]) ).
tff(67,plain,
divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2))) = inverse(divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2))),
inference(symmetry,[status(thm)],[34]) ).
tff(68,plain,
multiply(inverse(b2),b2) = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),
inference(transitivity,[status(thm)],[27,24,67,66,20,65,32,30]) ).
tff(69,plain,
divide(multiply(inverse(b2),b2),a2) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2) = divide(multiply(inverse(b2),b2),a2),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2)))) = divide(divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2)))))),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),
inference(symmetry,[status(thm)],[32]) ).
tff(72,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(inverse(b2),divide(inverse(b2),a2)),divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2)))))),divide(divide(inverse(b2),divide(inverse(b2),a2)),multiply(inverse(b2),b2))) = divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
divide(divide(divide(inverse(b2),divide(inverse(b2),a2)),divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2)))))),divide(divide(inverse(b2),divide(inverse(b2),a2)),multiply(inverse(b2),b2))) = divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2)))),
inference(unit_resolution,[status(thm)],[72,7]) ).
tff(74,plain,
divide(divide(inverse(b2),divide(inverse(b2),a2)),multiply(inverse(b2),b2)) = divide(divide(inverse(b2),divide(inverse(b2),a2)),divide(inverse(b2),inverse(b2))),
inference(monotonicity,[status(thm)],[59]) ).
tff(75,plain,
divide(divide(inverse(b2),divide(inverse(b2),a2)),divide(inverse(b2),inverse(b2))) = divide(divide(inverse(b2),divide(inverse(b2),a2)),multiply(inverse(b2),b2)),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(inverse(b2),divide(inverse(b2),a2)),divide(inverse(b2),inverse(b2))) = a2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
divide(divide(inverse(b2),divide(inverse(b2),a2)),divide(inverse(b2),inverse(b2))) = a2,
inference(unit_resolution,[status(thm)],[76,7]) ).
tff(78,plain,
a2 = divide(divide(inverse(b2),divide(inverse(b2),a2)),divide(inverse(b2),inverse(b2))),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
a2 = divide(divide(inverse(b2),divide(inverse(b2),a2)),multiply(inverse(b2),b2)),
inference(transitivity,[status(thm)],[78,75]) ).
tff(80,plain,
divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2))))) = divide(inverse(b2),inverse(b2)),
inference(transitivity,[status(thm)],[61,60,56,55,34,23,26,58,47,57]) ).
tff(81,plain,
divide(divide(inverse(b2),divide(inverse(b2),a2)),divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2)))))) = divide(divide(inverse(b2),divide(inverse(b2),a2)),divide(inverse(b2),inverse(b2))),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
divide(divide(inverse(b2),divide(inverse(b2),a2)),divide(inverse(b2),inverse(b2))) = divide(divide(inverse(b2),divide(inverse(b2),a2)),divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2)))))),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
a2 = divide(divide(inverse(b2),divide(inverse(b2),a2)),divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2)))))),
inference(transitivity,[status(thm)],[78,82]) ).
tff(84,plain,
divide(a2,a2) = divide(divide(divide(inverse(b2),divide(inverse(b2),a2)),divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),divide(divide(inverse(b2),inverse(b2)),multiply(inverse(b2),b2)))))),divide(divide(inverse(b2),divide(inverse(b2),a2)),multiply(inverse(b2),b2))),
inference(monotonicity,[status(thm)],[83,79]) ).
tff(85,plain,
divide(a2,a2) = multiply(inverse(b2),b2),
inference(transitivity,[status(thm)],[84,73,71,64,21,55,34,23,26]) ).
tff(86,plain,
divide(multiply(inverse(b2),b2),divide(a2,a2)) = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)) = divide(multiply(inverse(b2),b2),divide(a2,a2)),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
multiply(inverse(b2),b2) = divide(multiply(inverse(b2),b2),divide(a2,a2)),
inference(transitivity,[status(thm)],[27,24,67,66,20,65,32,30,87]) ).
tff(89,plain,
divide(multiply(inverse(b2),b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2)) = divide(divide(multiply(inverse(b2),b2),divide(a2,a2)),divide(multiply(inverse(b2),b2),a2)),
inference(monotonicity,[status(thm)],[88,70]) ).
tff(90,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(multiply(inverse(b2),b2),a2) = divide(multiply(inverse(b2),b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
multiply(multiply(inverse(b2),b2),a2) = divide(multiply(inverse(b2),b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2)),
inference(unit_resolution,[status(thm)],[90,45]) ).
tff(92,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(transitivity,[status(thm)],[91,89,9]) ).
tff(93,plain,
( ( multiply(multiply(inverse(b2),b2),a2) != a2 )
<=> ( multiply(multiply(inverse(b2),b2),a2) != a2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
tff(95,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
$false,
inference(unit_resolution,[status(thm)],[95,92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP530-1 : TPTP v9.0.0. Released v2.6.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n010.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 16:17:26 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.41 % SZS status Unsatisfiable
% 0.12/0.41 % SZS output start Proof
% See solution above
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------