%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP494-1 : 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 05:07:56 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.39s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 30
% Syntax : Number of formulae : 131 ( 106 unt; 0 typ; 0 def)
% Number of atoms : 164 ( 159 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 49 ( 20 ~; 16 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 96 ( 89 !; 0 ?; 96 :)
% Comments :
%------------------------------------------------------------------------------
tff(a2_type,type,
a2: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(double_divide_type,type,
double_divide: ( $i * $i ) > $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(1,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
<=> ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
<=> ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
<=> ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
tff(5,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,a2),double_divide(double_divide(double_divide(a2,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(a2,double_divide(a2,identity)))) = a2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
double_divide(double_divide(identity,a2),double_divide(double_divide(double_divide(a2,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(a2,double_divide(a2,identity)))) = a2,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity))) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(11,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity))) = identity,
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
identity = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity))),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
^ [A: $i] :
refl(( ( identity = double_divide(A,inverse(A)) )
<=> ( identity = double_divide(A,inverse(A)) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
<=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
<=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
tff(17,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(a2,inverse(a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
identity = double_divide(a2,inverse(a2)),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
double_divide(a2,inverse(a2)) = identity,
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
^ [A: $i] :
refl(( ( inverse(A) = double_divide(A,identity) )
<=> ( inverse(A) = double_divide(A,identity) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
<=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
<=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
tff(27,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(a2) = double_divide(a2,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
inverse(a2) = double_divide(a2,identity),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
double_divide(a2,identity) = inverse(a2),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
double_divide(a2,double_divide(a2,identity)) = double_divide(a2,inverse(a2)),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
double_divide(a2,double_divide(a2,identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity))),
inference(transitivity,[status(thm)],[33,22,12]) ).
tff(35,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity))),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[11]) ).
tff(36,plain,
double_divide(identity,double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
double_divide(a2,double_divide(a2,identity)) = identity,
inference(transitivity,[status(thm)],[33,22]) ).
tff(38,plain,
double_divide(double_divide(a2,double_divide(a2,identity)),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
double_divide(double_divide(a2,double_divide(a2,identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity))),double_divide(identity,identity)),
inference(transitivity,[status(thm)],[38,36]) ).
tff(40,plain,
double_divide(double_divide(double_divide(a2,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(a2,double_divide(a2,identity))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity)))),
inference(monotonicity,[status(thm)],[39,34]) ).
tff(41,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity)))) = double_divide(double_divide(double_divide(a2,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(a2,double_divide(a2,identity))),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
identity = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(unit_resolution,[status(thm)],[42,19]) ).
tff(44,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = identity,
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(identity) = double_divide(identity,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
inverse(identity) = double_divide(identity,identity),
inference(unit_resolution,[status(thm)],[45,29]) ).
tff(47,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
identity = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
inference(unit_resolution,[status(thm)],[47,19]) ).
tff(49,plain,
double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = identity,
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = inverse(identity),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[50,46]) ).
tff(52,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(identity,double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[49,51]) ).
tff(53,plain,
double_divide(identity,double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity))),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[35,53,44]) ).
tff(55,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity)))) = double_divide(identity,identity),
inference(monotonicity,[status(thm)],[54,11]) ).
tff(56,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity)))),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(a2,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(a2,double_divide(a2,identity))),
inference(transitivity,[status(thm)],[56,41]) ).
tff(58,plain,
double_divide(double_divide(identity,a2),double_divide(identity,identity)) = double_divide(double_divide(identity,a2),double_divide(double_divide(double_divide(a2,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(a2,double_divide(a2,identity)))),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(double_divide(identity,a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,identity)),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(identity,a2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(double_divide(identity,a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,identity)),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(identity,a2),
inference(unit_resolution,[status(thm)],[59,7]) ).
tff(61,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(identity,double_divide(a2,identity)))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(identity,double_divide(a2,identity)))))) = double_divide(identity,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(identity,double_divide(a2,identity)))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(identity,double_divide(a2,identity)))))) = double_divide(identity,identity),
inference(unit_resolution,[status(thm)],[61,7]) ).
tff(63,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(identity,double_divide(a2,identity)))) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(identity,double_divide(a2,identity)))) = identity,
inference(unit_resolution,[status(thm)],[63,7]) ).
tff(65,plain,
double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(identity,double_divide(a2,identity)))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity))),
inference(transitivity,[status(thm)],[64,12]) ).
tff(66,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(identity,double_divide(a2,identity)))),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[64]) ).
tff(67,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(identity,double_divide(a2,identity)))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity))),double_divide(identity,identity)),
inference(transitivity,[status(thm)],[66,36]) ).
tff(68,plain,
double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(identity,double_divide(a2,identity)))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(identity,double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity)))),
inference(monotonicity,[status(thm)],[67,65]) ).
tff(69,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity)))) = double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(identity,double_divide(a2,identity)))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(identity,double_divide(a2,identity))))),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(identity,double_divide(a2,identity)))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(identity,double_divide(a2,identity))))),
inference(transitivity,[status(thm)],[56,69]) ).
tff(71,plain,
identity = double_divide(identity,double_divide(identity,identity)),
inference(transitivity,[status(thm)],[43,52]) ).
tff(72,plain,
double_divide(identity,double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(identity,double_divide(a2,identity)))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(identity,double_divide(a2,identity)))))),
inference(monotonicity,[status(thm)],[71,70]) ).
tff(73,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(a2,identity)) = double_divide(double_divide(a2,identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
inverse(double_divide(a2,identity)) = double_divide(double_divide(a2,identity),identity),
inference(unit_resolution,[status(thm)],[73,29]) ).
tff(75,plain,
double_divide(double_divide(a2,identity),identity) = inverse(double_divide(a2,identity)),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(a2,identity),identity),
inference(monotonicity,[status(thm)],[49]) ).
tff(77,plain,
double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = inverse(double_divide(a2,identity)),
inference(transitivity,[status(thm)],[76,75]) ).
tff(78,plain,
double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(identity,double_divide(a2,identity)))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(identity,double_divide(a2,identity)))))) = double_divide(identity,double_divide(identity,identity)),
inference(symmetry,[status(thm)],[72]) ).
tff(79,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(identity,double_divide(a2,identity)))),double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),double_divide(identity,double_divide(a2,identity)))))),
inference(symmetry,[status(thm)],[62]) ).
tff(80,plain,
double_divide(identity,identity) = identity,
inference(transitivity,[status(thm)],[79,78,53,44]) ).
tff(81,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),double_divide(identity,identity)),double_divide(double_divide(a2,identity),identity))) = a2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),double_divide(identity,identity)),double_divide(double_divide(a2,identity),identity))) = a2,
inference(unit_resolution,[status(thm)],[81,7]) ).
tff(83,plain,
double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),double_divide(identity,identity)),double_divide(double_divide(a2,identity),identity))),double_divide(identity,identity)) = double_divide(a2,identity),
inference(monotonicity,[status(thm)],[82,80]) ).
tff(84,plain,
a2 = double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),double_divide(identity,identity)),double_divide(double_divide(a2,identity),identity))),
inference(symmetry,[status(thm)],[82]) ).
tff(85,plain,
double_divide(double_divide(identity,a2),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),double_divide(identity,identity)),double_divide(double_divide(a2,identity),identity))),
inference(transitivity,[status(thm)],[58,9,84]) ).
tff(86,plain,
double_divide(double_divide(double_divide(identity,a2),double_divide(identity,identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(a2,identity),double_divide(identity,identity)),double_divide(double_divide(a2,identity),identity))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
identity = double_divide(identity,identity),
inference(transitivity,[status(thm)],[43,52,72,62]) ).
tff(88,plain,
double_divide(double_divide(double_divide(identity,a2),double_divide(identity,identity)),identity) = double_divide(double_divide(double_divide(identity,a2),double_divide(identity,identity)),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
^ [B: $i,A: $i] :
refl(( ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
<=> ( multiply(A,B) = double_divide(double_divide(B,A),identity) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
<=> ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
<=> ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,axiom,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
tff(93,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(identity,identity),double_divide(identity,a2)) = double_divide(double_divide(double_divide(identity,a2),double_divide(identity,identity)),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
multiply(double_divide(identity,identity),double_divide(identity,a2)) = double_divide(double_divide(double_divide(identity,a2),double_divide(identity,identity)),identity),
inference(unit_resolution,[status(thm)],[96,95]) ).
tff(98,plain,
double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[49,43,52,72,62]) ).
tff(99,plain,
multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(identity,a2)) = multiply(double_divide(identity,identity),double_divide(identity,a2)),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(identity,a2)) = double_divide(double_divide(double_divide(identity,a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(identity,a2)) = double_divide(double_divide(double_divide(identity,a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(unit_resolution,[status(thm)],[100,95]) ).
tff(102,plain,
double_divide(double_divide(double_divide(identity,a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(identity,a2)),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
double_divide(double_divide(double_divide(identity,a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
inference(monotonicity,[status(thm)],[80]) ).
tff(104,plain,
double_divide(double_divide(double_divide(identity,a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,identity)) = double_divide(a2,identity),
inference(transitivity,[status(thm)],[103,102,99,97,88,86,83]) ).
tff(105,plain,
double_divide(double_divide(double_divide(double_divide(identity,a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,identity)),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
inference(monotonicity,[status(thm)],[104,77]) ).
tff(106,plain,
double_divide(double_divide(double_divide(double_divide(identity,a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,identity)),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[105,49,43,52,72,62]) ).
tff(107,plain,
double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(double_divide(identity,a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,identity)),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(double_divide(identity,a2),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,identity)),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
inference(monotonicity,[status(thm)],[75]) ).
tff(110,plain,
double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity))),
inference(transitivity,[status(thm)],[109,49,12]) ).
tff(111,plain,
double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)) = identity,
inference(transitivity,[status(thm)],[109,49]) ).
tff(112,plain,
double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity))),double_divide(identity,identity)),
inference(transitivity,[status(thm)],[112,36]) ).
tff(114,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),double_divide(identity,identity)),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity)))),
inference(monotonicity,[status(thm)],[113,110]) ).
tff(115,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity))),double_divide(identity,identity)),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(double_divide(double_divide(a2,identity),identity),identity)))) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),double_divide(identity,identity)),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),double_divide(identity,identity)),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),
inference(transitivity,[status(thm)],[56,115]) ).
tff(117,plain,
double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),double_divide(identity,identity)),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),double_divide(identity,identity)),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B )
| ( double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),double_divide(identity,identity)),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(a2,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(120,plain,
double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),double_divide(identity,identity)),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(a2,identity),
inference(unit_resolution,[status(thm)],[119,7]) ).
tff(121,plain,
double_divide(a2,identity) = double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),double_divide(identity,identity)),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
double_divide(a2,identity) = double_divide(identity,a2),
inference(transitivity,[status(thm)],[121,118,108,60]) ).
tff(123,plain,
double_divide(double_divide(a2,identity),double_divide(identity,identity)) = double_divide(double_divide(identity,a2),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
double_divide(double_divide(a2,identity),identity) = double_divide(double_divide(a2,identity),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[87]) ).
tff(125,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(identity,a2) = double_divide(double_divide(a2,identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
multiply(identity,a2) = double_divide(double_divide(a2,identity),identity),
inference(unit_resolution,[status(thm)],[125,95]) ).
tff(127,plain,
multiply(identity,a2) = a2,
inference(transitivity,[status(thm)],[126,124,123,58,9]) ).
tff(128,plain,
( ( multiply(identity,a2) != a2 )
<=> ( multiply(identity,a2) != a2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,axiom,
multiply(identity,a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
tff(130,plain,
multiply(identity,a2) != a2,
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
$false,
inference(unit_resolution,[status(thm)],[130,127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP494-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n007.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 16:13:19 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.22/0.39 % SZS status Unsatisfiable
% 0.22/0.39 % SZS output start Proof
% See solution above
% 0.22/0.43 % E exiting
%------------------------------------------------------------------------------