%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP581-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:08:07 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 21
% Syntax : Number of formulae : 70 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 94 ( 89 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 31 ( 11 ~; 7 |; 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 : 73 ( 66 !; 0 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
tff(identity_type,type,
identity: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(a1_type,type,
a1: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(double_divide_type,type,
double_divide: ( $i * $i ) > $i ).
tff(1,plain,
^ [A: $i] :
refl(( ( identity = double_divide(A,inverse(A)) )
<=> ( identity = double_divide(A,inverse(A)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
<=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
<=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
tff(5,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
identity = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1)))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1)))) = identity,
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [A: $i] :
refl(( ( inverse(A) = double_divide(A,identity) )
<=> ( inverse(A) = double_divide(A,identity) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
<=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
<=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
tff(15,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(a1,inverse(a1))) = double_divide(double_divide(a1,inverse(a1)),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
inverse(double_divide(a1,inverse(a1))) = double_divide(double_divide(a1,inverse(a1)),identity),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
double_divide(double_divide(a1,inverse(a1)),identity) = inverse(double_divide(a1,inverse(a1))),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(a1,inverse(a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
identity = double_divide(a1,inverse(a1)),
inference(unit_resolution,[status(thm)],[21,7]) ).
tff(23,plain,
double_divide(identity,identity) = double_divide(double_divide(a1,inverse(a1)),identity),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
double_divide(identity,identity) = inverse(double_divide(a1,inverse(a1))),
inference(transitivity,[status(thm)],[23,20]) ).
tff(25,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),inverse(double_divide(double_divide(a1,inverse(a1)),identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
identity = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),inverse(double_divide(double_divide(a1,inverse(a1)),identity))),
inference(unit_resolution,[status(thm)],[25,7]) ).
tff(27,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),inverse(double_divide(double_divide(a1,inverse(a1)),identity))) = identity,
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(a1,inverse(a1)),identity)) = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
inverse(double_divide(double_divide(a1,inverse(a1)),identity)) = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity),
inference(unit_resolution,[status(thm)],[28,17]) ).
tff(30,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity) = inverse(double_divide(double_divide(a1,inverse(a1)),identity)),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
double_divide(a1,inverse(a1)) = identity,
inference(symmetry,[status(thm)],[22]) ).
tff(32,plain,
double_divide(double_divide(a1,inverse(a1)),double_divide(a1,inverse(a1))) = double_divide(double_divide(a1,inverse(a1)),identity),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
double_divide(double_divide(a1,inverse(a1)),identity) = double_divide(double_divide(a1,inverse(a1)),double_divide(a1,inverse(a1))),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity) = double_divide(double_divide(double_divide(a1,inverse(a1)),double_divide(a1,inverse(a1))),identity),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),double_divide(a1,inverse(a1))),identity) = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))) = double_divide(double_divide(double_divide(a1,inverse(a1)),double_divide(a1,inverse(a1))),identity),
inference(monotonicity,[status(thm)],[33,31]) ).
tff(37,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))) = inverse(double_divide(double_divide(a1,inverse(a1)),identity)),
inference(transitivity,[status(thm)],[36,35,30]) ).
tff(38,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1)))) = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),inverse(double_divide(double_divide(a1,inverse(a1)),identity))),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1)))) = identity,
inference(transitivity,[status(thm)],[38,27]) ).
tff(40,plain,
double_divide(identity,double_divide(double_divide(a1,inverse(a1)),identity)) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1)))),
inference(monotonicity,[status(thm)],[22,20]) ).
tff(41,plain,
double_divide(identity,double_divide(double_divide(a1,inverse(a1)),identity)) = double_divide(a1,inverse(a1)),
inference(transitivity,[status(thm)],[40,10,22]) ).
tff(42,plain,
double_divide(double_divide(identity,double_divide(double_divide(a1,inverse(a1)),identity)),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))) = double_divide(double_divide(a1,inverse(a1)),identity),
inference(monotonicity,[status(thm)],[41,39]) ).
tff(43,plain,
double_divide(double_divide(identity,double_divide(double_divide(a1,inverse(a1)),identity)),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))) = inverse(double_divide(a1,inverse(a1))),
inference(transitivity,[status(thm)],[42,20]) ).
tff(44,plain,
double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(identity,double_divide(double_divide(a1,inverse(a1)),identity)),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1)))))) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1)))),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(identity,double_divide(double_divide(a1,inverse(a1)),identity)),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1)))))) = double_divide(a1,inverse(a1)),
inference(transitivity,[status(thm)],[44,10,22]) ).
tff(46,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(identity,double_divide(double_divide(a1,inverse(a1)),identity)),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1)))))),double_divide(identity,identity)) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1)))),
inference(monotonicity,[status(thm)],[45,24]) ).
tff(47,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
<=> ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
<=> ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
<=> ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
tff(51,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C )
| ( double_divide(double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(identity,double_divide(double_divide(a1,inverse(a1)),identity)),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1)))))),double_divide(identity,identity)) = double_divide(double_divide(a1,inverse(a1)),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(identity,double_divide(double_divide(a1,inverse(a1)),identity)),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1)))))),double_divide(identity,identity)) = double_divide(double_divide(a1,inverse(a1)),identity),
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
double_divide(double_divide(a1,inverse(a1)),identity) = double_divide(double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(identity,double_divide(double_divide(a1,inverse(a1)),identity)),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1)))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[55]) ).
tff(57,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(58,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)],[57]) ).
tff(59,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(60,axiom,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
tff(61,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(inverse(a1),a1) = double_divide(double_divide(a1,inverse(a1)),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
multiply(inverse(a1),a1) = double_divide(double_divide(a1,inverse(a1)),identity),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
multiply(inverse(a1),a1) = identity,
inference(transitivity,[status(thm)],[65,56,46,10]) ).
tff(67,plain,
( ( multiply(inverse(a1),a1) != identity )
<=> ( multiply(inverse(a1),a1) != identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,axiom,
multiply(inverse(a1),a1) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
tff(69,plain,
multiply(inverse(a1),a1) != identity,
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
$false,
inference(unit_resolution,[status(thm)],[69,66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP581-1 : TPTP v9.0.0. Released v2.6.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n006.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 16:18:50 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38 % SZS output start Proof
% See solution above
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------