%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP010-4 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:06:50 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of formulae : 48 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 63 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 9 ~; 5 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 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; 3 con; 0-2 aty)
% Number of variables : 54 ( 49 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
tff(identity_type,type,
identity: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( multiply(inverse(X),X) = identity )
<=> ( multiply(inverse(X),X) = identity ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
tff(5,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(c),c) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiply(inverse(c),c) = identity,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(( ( multiply(identity,X) = X )
<=> ( multiply(identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
tff(14,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,c) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
multiply(identity,c) = c,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
multiply(inverse(c),multiply(identity,c)) = multiply(inverse(c),c),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
tff(24,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(c),identity),c) = multiply(inverse(c),multiply(identity,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
multiply(multiply(inverse(c),identity),c) = multiply(inverse(c),multiply(identity,c)),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
( ( multiply(c,b) = identity )
<=> ( multiply(c,b) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
multiply(c,b) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_b_is_e) ).
tff(31,plain,
multiply(c,b) = identity,
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
identity = multiply(c,b),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
multiply(inverse(c),identity) = multiply(inverse(c),multiply(c,b)),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
multiply(inverse(c),multiply(c,b)) = multiply(inverse(c),identity),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(c),c),b) = multiply(inverse(c),multiply(c,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
multiply(multiply(inverse(c),c),b) = multiply(inverse(c),multiply(c,b)),
inference(unit_resolution,[status(thm)],[35,26]) ).
tff(37,plain,
multiply(multiply(inverse(c),c),b) = multiply(identity,b),
inference(monotonicity,[status(thm)],[9]) ).
tff(38,plain,
multiply(identity,b) = multiply(multiply(inverse(c),c),b),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
multiply(identity,b) = b,
inference(unit_resolution,[status(thm)],[39,16]) ).
tff(41,plain,
b = multiply(identity,b),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
b = multiply(inverse(c),identity),
inference(transitivity,[status(thm)],[41,38,36,34]) ).
tff(43,plain,
multiply(b,c) = multiply(multiply(inverse(c),identity),c),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
multiply(b,c) = identity,
inference(transitivity,[status(thm)],[43,28,19,9]) ).
tff(45,plain,
( ( multiply(b,c) != identity )
<=> ( multiply(b,c) != identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
multiply(b,c) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_times_c_is_e) ).
tff(47,plain,
multiply(b,c) != identity,
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
$false,
inference(unit_resolution,[status(thm)],[47,44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP010-4 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.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 15:28:17 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% See solution above
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------