%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP461-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:07:49 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 63 ( 50 unt; 0 typ; 0 def)
% Number of atoms : 82 ( 78 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 26 ( 10 ~; 6 |; 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 : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 65 ( 59 !; 0 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
tff(a2_type,type,
a2: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( divide(A,divide(divide(divide(identity,B),C),divide(divide(divide(A,A),A),C))) = B )
<=> ( divide(A,divide(divide(divide(identity,B),C),divide(divide(divide(A,A),A),C))) = B ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(divide(identity,B),C),divide(divide(divide(A,A),A),C))) = B )
<=> ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(divide(identity,B),C),divide(divide(divide(A,A),A),C))) = B ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(divide(identity,B),C),divide(divide(divide(A,A),A),C))) = B )
<=> ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(divide(identity,B),C),divide(divide(divide(A,A),A),C))) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(divide(identity,B),C),divide(divide(divide(A,A),A),C))) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
tff(5,plain,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(divide(identity,B),C),divide(divide(divide(A,A),A),C))) = B ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(divide(identity,B),C),divide(divide(divide(A,A),A),C))) = B ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(divide(identity,B),C),divide(divide(divide(A,A),A),C))) = B ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(divide(identity,B),C),divide(divide(divide(A,A),A),C))) = B )
| ( divide(identity,divide(divide(divide(identity,a2),identity),divide(divide(divide(identity,identity),identity),identity))) = a2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
divide(identity,divide(divide(divide(identity,a2),identity),divide(divide(divide(identity,identity),identity),identity))) = a2,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(divide(divide(identity,B),C),divide(divide(divide(A,A),A),C))) = B )
| ( divide(divide(identity,a2),divide(divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(identity,a2)),divide(identity,divide(identity,a2))))) = divide(identity,a2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(11,plain,
divide(divide(identity,a2),divide(divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(identity,a2)),divide(identity,divide(identity,a2))))) = divide(identity,a2),
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
^ [A: $i] :
refl(( ( identity = divide(A,A) )
<=> ( identity = divide(A,A) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [A: $i] : ( identity = divide(A,A) )
<=> ! [A: $i] : ( identity = divide(A,A) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [A: $i] : ( identity = divide(A,A) )
<=> ! [A: $i] : ( identity = divide(A,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
! [A: $i] : ( identity = divide(A,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
tff(16,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
identity = divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))) = identity,
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(identity,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
identity = divide(identity,identity),
inference(unit_resolution,[status(thm)],[22,18]) ).
tff(24,plain,
divide(identity,identity) = identity,
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
divide(divide(identity,identity),identity) = divide(identity,identity),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
divide(divide(identity,identity),identity) = identity,
inference(transitivity,[status(thm)],[25,24]) ).
tff(27,plain,
divide(divide(divide(identity,identity),identity),divide(identity,a2)) = divide(identity,divide(identity,a2)),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
divide(divide(identity,identity),divide(identity,a2)) = divide(identity,divide(identity,a2)),
inference(monotonicity,[status(thm)],[24]) ).
tff(29,plain,
divide(divide(divide(identity,identity),divide(identity,a2)),divide(divide(divide(identity,identity),identity),divide(identity,a2))) = divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))),
inference(monotonicity,[status(thm)],[28,27]) ).
tff(30,plain,
divide(identity,divide(identity,a2)) = divide(divide(divide(identity,identity),identity),divide(identity,a2)),
inference(symmetry,[status(thm)],[27]) ).
tff(31,plain,
divide(identity,divide(identity,a2)) = divide(divide(identity,identity),divide(identity,a2)),
inference(symmetry,[status(thm)],[28]) ).
tff(32,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(divide(identity,a2),divide(identity,a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
identity = divide(divide(identity,a2),divide(identity,a2)),
inference(unit_resolution,[status(thm)],[32,18]) ).
tff(34,plain,
divide(divide(identity,a2),divide(identity,a2)) = identity,
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
divide(divide(divide(identity,a2),divide(identity,a2)),divide(identity,a2)) = divide(identity,divide(identity,a2)),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
divide(divide(divide(identity,a2),divide(identity,a2)),divide(identity,a2)) = divide(divide(identity,identity),divide(identity,a2)),
inference(transitivity,[status(thm)],[35,31]) ).
tff(37,plain,
divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(identity,a2)),divide(identity,divide(identity,a2))) = divide(divide(divide(identity,identity),divide(identity,a2)),divide(divide(divide(identity,identity),identity),divide(identity,a2))),
inference(monotonicity,[status(thm)],[36,30]) ).
tff(38,plain,
divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(identity,a2)),divide(identity,divide(identity,a2))) = identity,
inference(transitivity,[status(thm)],[37,29,21]) ).
tff(39,plain,
divide(divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(identity,a2)),divide(identity,divide(identity,a2)))) = divide(identity,identity),
inference(monotonicity,[status(thm)],[21,38]) ).
tff(40,plain,
divide(identity,identity) = divide(divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(identity,a2)),divide(identity,divide(identity,a2)))),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
divide(divide(divide(identity,identity),identity),identity) = divide(identity,identity),
inference(monotonicity,[status(thm)],[26]) ).
tff(42,plain,
divide(divide(divide(identity,identity),identity),identity) = divide(divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(identity,a2)),divide(identity,divide(identity,a2)))),
inference(transitivity,[status(thm)],[41,40]) ).
tff(43,plain,
identity = divide(divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(identity,a2)),divide(identity,divide(identity,a2)))),
inference(transitivity,[status(thm)],[23,40]) ).
tff(44,plain,
divide(divide(identity,a2),identity) = divide(divide(identity,a2),divide(divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(identity,a2)),divide(identity,divide(identity,a2))))),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
divide(divide(identity,a2),identity) = divide(identity,a2),
inference(transitivity,[status(thm)],[44,11]) ).
tff(46,plain,
divide(divide(divide(identity,a2),identity),divide(divide(divide(identity,identity),identity),identity)) = divide(divide(identity,a2),divide(divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))),divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(identity,a2)),divide(identity,divide(identity,a2))))),
inference(monotonicity,[status(thm)],[45,42]) ).
tff(47,plain,
divide(divide(divide(identity,a2),identity),divide(divide(divide(identity,identity),identity),identity)) = divide(identity,a2),
inference(transitivity,[status(thm)],[46,11]) ).
tff(48,plain,
divide(identity,divide(divide(divide(identity,a2),identity),divide(divide(divide(identity,identity),identity),identity))) = divide(identity,divide(identity,a2)),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
divide(identity,divide(identity,a2)) = divide(identity,divide(divide(divide(identity,a2),identity),divide(divide(divide(identity,identity),identity),identity))),
inference(symmetry,[status(thm)],[48]) ).
tff(50,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(51,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)],[50]) ).
tff(52,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(53,axiom,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
tff(54,plain,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
| ( multiply(identity,a2) = divide(identity,divide(identity,a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
multiply(identity,a2) = divide(identity,divide(identity,a2)),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
multiply(identity,a2) = a2,
inference(transitivity,[status(thm)],[58,49,9]) ).
tff(60,plain,
( ( multiply(identity,a2) != a2 )
<=> ( multiply(identity,a2) != a2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
multiply(identity,a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
tff(62,plain,
multiply(identity,a2) != a2,
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
$false,
inference(unit_resolution,[status(thm)],[62,59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP461-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 16:09:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Unsatisfiable
% 0.19/0.37 % SZS output start Proof
% See solution above
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------