%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP012-4 : TPTP v9.0.0. Released v1.0.0.
% 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 05:06:50 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 33
% Syntax : Number of formulae : 107 ( 80 unt; 0 typ; 0 def)
% Number of atoms : 144 ( 138 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 52 ( 20 ~; 16 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 5 ( 5 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 : 91 ( 84 !; 0 ?; 91 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(identity_type,type,
identity: $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( multiply(X,identity) = X )
<=> ( multiply(X,identity) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( multiply(X,identity) = X )
<=> ! [X: $i] : ( multiply(X,identity) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( multiply(X,identity) = X )
<=> ! [X: $i] : ( multiply(X,identity) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( multiply(X,identity) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
tff(5,plain,
! [X: $i] : ( multiply(X,identity) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( multiply(X,identity) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( multiply(X,identity) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( multiply(X,identity) = X )
| ( multiply(inverse(multiply(a,b)),identity) = inverse(multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiply(inverse(multiply(a,b)),identity) = inverse(multiply(a,b)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(( ( multiply(X,inverse(X)) = identity )
<=> ( multiply(X,inverse(X)) = identity ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] : ( multiply(X,inverse(X)) = identity )
<=> ! [X: $i] : ( multiply(X,inverse(X)) = identity ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( multiply(X,inverse(X)) = identity )
<=> ! [X: $i] : ( multiply(X,inverse(X)) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [X: $i] : ( multiply(X,inverse(X)) = identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
tff(14,plain,
! [X: $i] : ( multiply(X,inverse(X)) = identity ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( multiply(X,inverse(X)) = identity ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( multiply(X,inverse(X)) = identity ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( multiply(X,inverse(X)) = identity )
| ( multiply(multiply(a,b),inverse(multiply(a,b))) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
multiply(multiply(a,b),inverse(multiply(a,b))) = identity,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
identity = multiply(multiply(a,b),inverse(multiply(a,b))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
multiply(inverse(multiply(a,b)),identity) = multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b)))),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b)))) = multiply(inverse(multiply(a,b)),identity),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b)))) = inverse(multiply(a,b)),
inference(transitivity,[status(thm)],[21,9]) ).
tff(23,plain,
multiply(b,multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b))))) = multiply(b,inverse(multiply(a,b))),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
multiply(b,inverse(multiply(a,b))) = multiply(b,multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b))))),
inference(symmetry,[status(thm)],[23]) ).
tff(25,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(26,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)],[25]) ).
tff(27,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(28,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
tff(29,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(multiply(a,b)),multiply(a,b)),inverse(multiply(a,b))) = multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
multiply(multiply(inverse(multiply(a,b)),multiply(a,b)),inverse(multiply(a,b))) = multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b)))),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
^ [X: $i] :
refl(( ( multiply(inverse(X),X) = identity )
<=> ( multiply(inverse(X),X) = identity ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
tff(38,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(multiply(a,b)),multiply(a,b)) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
multiply(inverse(multiply(a,b)),multiply(a,b)) = identity,
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
identity = multiply(inverse(multiply(a,b)),multiply(a,b)),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
multiply(identity,multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b))))) = multiply(multiply(inverse(multiply(a,b)),multiply(a,b)),inverse(multiply(a,b))),
inference(monotonicity,[status(thm)],[43,22]) ).
tff(45,plain,
multiply(identity,multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b))))) = inverse(multiply(a,b)),
inference(transitivity,[status(thm)],[44,33,21,9]) ).
tff(46,plain,
multiply(b,multiply(identity,multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b)))))) = multiply(b,inverse(multiply(a,b))),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,identity),multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b))))) = multiply(b,multiply(identity,multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
multiply(multiply(b,identity),multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b))))) = multiply(b,multiply(identity,multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b)))))),
inference(unit_resolution,[status(thm)],[47,31]) ).
tff(49,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(b),b) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
multiply(inverse(b),b) = identity,
inference(unit_resolution,[status(thm)],[49,40]) ).
tff(51,plain,
multiply(inverse(b),b) = multiply(inverse(multiply(a,b)),multiply(a,b)),
inference(transitivity,[status(thm)],[50,43]) ).
tff(52,plain,
multiply(multiply(inverse(b),b),multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b))))) = multiply(multiply(inverse(multiply(a,b)),multiply(a,b)),inverse(multiply(a,b))),
inference(monotonicity,[status(thm)],[51,22]) ).
tff(53,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(b),b),multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b))))) = multiply(inverse(b),multiply(b,multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
multiply(multiply(inverse(b),b),multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b))))) = multiply(inverse(b),multiply(b,multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b)))))),
inference(unit_resolution,[status(thm)],[53,31]) ).
tff(55,plain,
multiply(inverse(b),multiply(b,multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b)))))) = multiply(multiply(inverse(b),b),multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b))))),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
multiply(inverse(b),multiply(b,inverse(multiply(a,b)))) = multiply(inverse(b),multiply(b,multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b)))))),
inference(monotonicity,[status(thm)],[24]) ).
tff(57,plain,
multiply(inverse(b),multiply(b,inverse(multiply(a,b)))) = multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b)))),
inference(transitivity,[status(thm)],[56,55,52,33]) ).
tff(58,plain,
multiply(multiply(b,identity),multiply(inverse(b),multiply(b,inverse(multiply(a,b))))) = multiply(multiply(b,identity),multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b))))),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( ~ ! [X: $i] : ( multiply(X,identity) = X )
| ( multiply(b,identity) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
multiply(b,identity) = b,
inference(unit_resolution,[status(thm)],[59,7]) ).
tff(61,plain,
b = multiply(b,identity),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
multiply(b,multiply(inverse(b),multiply(b,inverse(multiply(a,b))))) = multiply(multiply(b,identity),multiply(inverse(b),multiply(b,inverse(multiply(a,b))))),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,inverse(b)),multiply(b,inverse(multiply(a,b)))) = multiply(b,multiply(inverse(b),multiply(b,inverse(multiply(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
multiply(multiply(b,inverse(b)),multiply(b,inverse(multiply(a,b)))) = multiply(b,multiply(inverse(b),multiply(b,inverse(multiply(a,b))))),
inference(unit_resolution,[status(thm)],[63,31]) ).
tff(65,plain,
( ~ ! [X: $i] : ( multiply(X,inverse(X)) = identity )
| ( multiply(b,inverse(b)) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
multiply(b,inverse(b)) = identity,
inference(unit_resolution,[status(thm)],[65,16]) ).
tff(67,plain,
identity = multiply(b,inverse(b)),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(a),a) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
multiply(inverse(a),a) = identity,
inference(unit_resolution,[status(thm)],[68,40]) ).
tff(70,plain,
multiply(inverse(a),a) = multiply(b,inverse(b)),
inference(transitivity,[status(thm)],[69,67]) ).
tff(71,plain,
multiply(multiply(inverse(a),a),multiply(b,inverse(multiply(a,b)))) = multiply(multiply(b,inverse(b)),multiply(b,inverse(multiply(a,b)))),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(a),a),multiply(b,inverse(multiply(a,b)))) = multiply(inverse(a),multiply(a,multiply(b,inverse(multiply(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
multiply(multiply(inverse(a),a),multiply(b,inverse(multiply(a,b)))) = multiply(inverse(a),multiply(a,multiply(b,inverse(multiply(a,b))))),
inference(unit_resolution,[status(thm)],[72,31]) ).
tff(74,plain,
multiply(inverse(a),multiply(a,multiply(b,inverse(multiply(a,b))))) = multiply(multiply(inverse(a),a),multiply(b,inverse(multiply(a,b)))),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),inverse(multiply(a,b))) = multiply(a,multiply(b,inverse(multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
multiply(multiply(a,b),inverse(multiply(a,b))) = multiply(a,multiply(b,inverse(multiply(a,b)))),
inference(unit_resolution,[status(thm)],[75,31]) ).
tff(77,plain,
( ~ ! [X: $i] : ( multiply(X,inverse(X)) = identity )
| ( multiply(identity,inverse(identity)) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
multiply(identity,inverse(identity)) = identity,
inference(unit_resolution,[status(thm)],[77,16]) ).
tff(79,plain,
^ [X: $i] :
refl(( ( multiply(identity,X) = X )
<=> ( multiply(identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(80,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
tff(83,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,inverse(identity)) = inverse(identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
multiply(identity,inverse(identity)) = inverse(identity),
inference(unit_resolution,[status(thm)],[86,85]) ).
tff(88,plain,
inverse(identity) = multiply(identity,inverse(identity)),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
inverse(identity) = multiply(a,multiply(b,inverse(multiply(a,b)))),
inference(transitivity,[status(thm)],[88,78,19,76]) ).
tff(90,plain,
multiply(inverse(a),inverse(identity)) = multiply(inverse(a),multiply(a,multiply(b,inverse(multiply(a,b))))),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
identity = multiply(identity,inverse(identity)),
inference(symmetry,[status(thm)],[78]) ).
tff(92,plain,
identity = inverse(identity),
inference(transitivity,[status(thm)],[91,87]) ).
tff(93,plain,
multiply(inverse(a),identity) = multiply(inverse(a),inverse(identity)),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
( ~ ! [X: $i] : ( multiply(X,identity) = X )
| ( multiply(inverse(a),identity) = inverse(a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
multiply(inverse(a),identity) = inverse(a),
inference(unit_resolution,[status(thm)],[94,7]) ).
tff(96,plain,
inverse(a) = multiply(inverse(a),identity),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
inverse(a) = multiply(b,multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b))))),
inference(transitivity,[status(thm)],[96,93,90,74,71,64,62,58,48,46,24]) ).
tff(98,plain,
multiply(inverse(b),inverse(a)) = multiply(inverse(b),multiply(b,multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b)))))),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
multiply(inverse(b),multiply(b,multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b)))))) = multiply(inverse(b),inverse(a)),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
multiply(multiply(inverse(multiply(a,b)),multiply(a,b)),inverse(multiply(a,b))) = multiply(multiply(inverse(b),b),multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b))))),
inference(symmetry,[status(thm)],[52]) ).
tff(101,plain,
multiply(inverse(multiply(a,b)),multiply(multiply(a,b),inverse(multiply(a,b)))) = multiply(multiply(inverse(multiply(a,b)),multiply(a,b)),inverse(multiply(a,b))),
inference(symmetry,[status(thm)],[33]) ).
tff(102,plain,
inverse(multiply(a,b)) = multiply(inverse(multiply(a,b)),identity),
inference(symmetry,[status(thm)],[9]) ).
tff(103,plain,
inverse(multiply(a,b)) = multiply(inverse(b),inverse(a)),
inference(transitivity,[status(thm)],[102,20,101,100,54,99]) ).
tff(104,plain,
( ( inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)) )
<=> ( inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,axiom,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_of_product_is_product_of_inverses) ).
tff(106,plain,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
$false,
inference(unit_resolution,[status(thm)],[106,103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP012-4 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n007.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Thu Jun 19 15:29:20 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40 % SZS output start Proof
% See solution above
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------