%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP004-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:06:49 AM UTC 2025
% Result : Unsatisfiable 0.47s 0.66s
% Output : Proof 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 28
% Syntax : Number of formulae : 65 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 368 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 551 ( 267 ~; 251 |; 0 &)
% ( 33 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 19 ( 19 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 284 ( 257 !; 0 ?; 284 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(identity_type,type,
identity: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
^ [X: $i] :
refl(( product(inverse(X),X,identity)
<=> product(inverse(X),X,identity) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : product(inverse(X),X,identity)
<=> ! [X: $i] : product(inverse(X),X,identity) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : product(inverse(X),X,identity)
<=> ! [X: $i] : product(inverse(X),X,identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : product(inverse(X),X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
tff(5,plain,
! [X: $i] : product(inverse(X),X,identity),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : product(inverse(X),X,identity),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : product(inverse(X),X,identity),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : product(inverse(X),X,identity)
| product(inverse(inverse(a)),inverse(a),identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
product(inverse(inverse(a)),inverse(a),identity),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(( product(identity,X,X)
<=> product(identity,X,X) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] : product(identity,X,X)
<=> ! [X: $i] : product(identity,X,X) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : product(identity,X,X)
<=> ! [X: $i] : product(identity,X,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [X: $i] : product(identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
tff(14,plain,
! [X: $i] : product(identity,X,X),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : product(identity,X,X),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : product(identity,X,X),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : product(identity,X,X)
| product(identity,a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
product(identity,a,a),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ ! [X: $i] : product(inverse(X),X,identity)
| product(inverse(a),a,identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
product(inverse(a),a,identity),
inference(unit_resolution,[status(thm)],[19,7]) ).
tff(21,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(( ( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
<=> ( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
trans(monotonicity(rewrite(( ( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W) )
<=> ( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ) )),
( ( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W)
| product(X,V,W) )
<=> ( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ) )),
rewrite(( ( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) )
<=> ( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ) )),
( ( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W)
| product(X,V,W) )
<=> ( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W)
| product(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W)
| product(X,V,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
tff(27,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| ~ product(inverse(a),a,identity)
| ~ product(identity,a,a)
| product(inverse(inverse(a)),identity,a)
| ~ product(inverse(inverse(a)),inverse(a),identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| ~ product(inverse(a),a,identity)
| ~ product(identity,a,a)
| product(inverse(inverse(a)),identity,a)
| ~ product(inverse(inverse(a)),inverse(a),identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ( product(inverse(inverse(a)),identity,a)
| ~ product(identity,a,a)
| ~ product(inverse(a),a,identity)
| ~ product(inverse(inverse(a)),inverse(a),identity) )
<=> ( ~ product(inverse(a),a,identity)
| ~ product(identity,a,a)
| product(inverse(inverse(a)),identity,a)
| ~ product(inverse(inverse(a)),inverse(a),identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| product(inverse(inverse(a)),identity,a)
| ~ product(identity,a,a)
| ~ product(inverse(a),a,identity)
| ~ product(inverse(inverse(a)),inverse(a),identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| ~ product(inverse(a),a,identity)
| ~ product(identity,a,a)
| product(inverse(inverse(a)),identity,a)
| ~ product(inverse(inverse(a)),inverse(a),identity) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| product(inverse(inverse(a)),identity,a)
| ~ product(identity,a,a)
| ~ product(inverse(a),a,identity)
| ~ product(inverse(inverse(a)),inverse(a),identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| ~ product(inverse(a),a,identity)
| ~ product(identity,a,a)
| product(inverse(inverse(a)),identity,a)
| ~ product(inverse(inverse(a)),inverse(a),identity) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| product(inverse(inverse(a)),identity,a)
| ~ product(identity,a,a)
| ~ product(inverse(a),a,identity)
| ~ product(inverse(inverse(a)),inverse(a),identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
| ~ product(inverse(a),a,identity)
| ~ product(identity,a,a)
| product(inverse(inverse(a)),identity,a)
| ~ product(inverse(inverse(a)),inverse(a),identity) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
product(inverse(inverse(a)),identity,a),
inference(unit_resolution,[status(thm)],[36,30,20,18,9]) ).
tff(38,plain,
( ~ ! [X: $i] : product(identity,X,X)
| product(identity,inverse(a),inverse(a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
product(identity,inverse(a),inverse(a)),
inference(unit_resolution,[status(thm)],[38,16]) ).
tff(40,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(( ( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
<=> ( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
trans(monotonicity(rewrite(( ( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W) )
<=> ( ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) )),
( ( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) )
<=> ( ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W)
| product(U,Z,W) ) )),
rewrite(( ( ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W)
| product(U,Z,W) )
<=> ( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) )),
( ( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) )
<=> ( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
tff(46,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(identity,inverse(a),inverse(a))
| ~ product(inverse(inverse(a)),inverse(a),identity)
| ~ product(inverse(inverse(a)),identity,a)
| product(a,inverse(a),identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(identity,inverse(a),inverse(a))
| ~ product(inverse(inverse(a)),inverse(a),identity)
| ~ product(inverse(inverse(a)),identity,a)
| product(a,inverse(a),identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ( product(a,inverse(a),identity)
| ~ product(identity,inverse(a),inverse(a))
| ~ product(inverse(inverse(a)),identity,a)
| ~ product(inverse(inverse(a)),inverse(a),identity) )
<=> ( ~ product(identity,inverse(a),inverse(a))
| ~ product(inverse(inverse(a)),inverse(a),identity)
| ~ product(inverse(inverse(a)),identity,a)
| product(a,inverse(a),identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(a,inverse(a),identity)
| ~ product(identity,inverse(a),inverse(a))
| ~ product(inverse(inverse(a)),identity,a)
| ~ product(inverse(inverse(a)),inverse(a),identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(identity,inverse(a),inverse(a))
| ~ product(inverse(inverse(a)),inverse(a),identity)
| ~ product(inverse(inverse(a)),identity,a)
| product(a,inverse(a),identity) ) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(a,inverse(a),identity)
| ~ product(identity,inverse(a),inverse(a))
| ~ product(inverse(inverse(a)),identity,a)
| ~ product(inverse(inverse(a)),inverse(a),identity) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(identity,inverse(a),inverse(a))
| ~ product(inverse(inverse(a)),inverse(a),identity)
| ~ product(inverse(inverse(a)),identity,a)
| product(a,inverse(a),identity) ) ),
inference(transitivity,[status(thm)],[52,50]) ).
tff(54,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(a,inverse(a),identity)
| ~ product(identity,inverse(a),inverse(a))
| ~ product(inverse(inverse(a)),identity,a)
| ~ product(inverse(inverse(a)),inverse(a),identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(identity,inverse(a),inverse(a))
| ~ product(inverse(inverse(a)),inverse(a),identity)
| ~ product(inverse(inverse(a)),identity,a)
| product(a,inverse(a),identity) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
product(a,inverse(a),identity),
inference(unit_resolution,[status(thm)],[55,49,9,39,37]) ).
tff(57,plain,
^ [X: $i] :
refl(( ~ product(a,X,identity)
<=> ~ product(a,X,identity) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [X: $i] : ~ product(a,X,identity)
<=> ! [X: $i] : ~ product(a,X,identity) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [X: $i] : ~ product(a,X,identity)
<=> ! [X: $i] : ~ product(a,X,identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,axiom,
! [X: $i] : ~ product(a,X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_a_right_inverse) ).
tff(61,plain,
! [X: $i] : ~ product(a,X,identity),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [X: $i] : ~ product(a,X,identity),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [X: $i] : ~ product(a,X,identity),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
( ~ ! [X: $i] : ~ product(a,X,identity)
| ~ product(a,inverse(a),identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
$false,
inference(unit_resolution,[status(thm)],[64,63,56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP004-1 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 15:27:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.47/0.66 % SZS status Unsatisfiable
% 0.47/0.66 % SZS output start Proof
% See solution above
% 0.47/0.66 % E exiting
%------------------------------------------------------------------------------