%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP206-1 : TPTP v9.0.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:07:28 AM UTC 2025
% Result : Unsatisfiable 30.42s 30.66s
% Output : Proof 30.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 41 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 54 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 8 ~; 4 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 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; 4 con; 0-2 aty)
% Number of variables : 53 ( 48 !; 0 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(identity_type,type,
identity: $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(X,multiply(multiply(Y,Z),X)) = multiply(multiply(X,Y),multiply(Z,X)) )
<=> ( multiply(X,multiply(multiply(Y,Z),X)) = multiply(multiply(X,Y),multiply(Z,X)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(Y,Z),X)) = multiply(multiply(X,Y),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(Y,Z),X)) = multiply(multiply(X,Y),multiply(Z,X)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(Y,Z),X)) = multiply(multiply(X,Y),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(Y,Z),X)) = multiply(multiply(X,Y),multiply(Z,X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(Y,Z),X)) = multiply(multiply(X,Y),multiply(Z,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',moufang4) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(Y,Z),X)) = multiply(multiply(X,Y),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(Y,Z),X)) = multiply(multiply(X,Y),multiply(Z,X)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(Y,Z),X)) = multiply(multiply(X,Y),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(Y,Z),X)) = multiply(multiply(X,Y),multiply(Z,X)) )
| ( multiply(a,multiply(multiply(b,c),a)) = multiply(multiply(a,b),multiply(c,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiply(a,multiply(multiply(b,c),a)) = multiply(multiply(a,b),multiply(c,a)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(( ( multiply(X,identity) = X )
<=> ( multiply(X,identity) = X ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] : ( multiply(X,identity) = X )
<=> ! [X: $i] : ( multiply(X,identity) = X ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( multiply(X,identity) = X )
<=> ! [X: $i] : ( multiply(X,identity) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [X: $i] : ( multiply(X,identity) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
tff(14,plain,
! [X: $i] : ( multiply(X,identity) = X ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( multiply(X,identity) = X ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( multiply(X,identity) = X ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( multiply(X,identity) = X )
| ( multiply(multiply(b,c),identity) = multiply(b,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
multiply(multiply(b,c),identity) = multiply(b,c),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
multiply(multiply(multiply(b,c),identity),a) = multiply(multiply(b,c),a),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
multiply(multiply(b,c),a) = multiply(multiply(multiply(b,c),identity),a),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
multiply(a,multiply(multiply(b,c),a)) = multiply(a,multiply(multiply(multiply(b,c),identity),a)),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
multiply(a,multiply(multiply(multiply(b,c),identity),a)) = multiply(a,multiply(multiply(b,c),a)),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,multiply(multiply(Y,Z),X)) = multiply(multiply(X,Y),multiply(Z,X)) )
| ( multiply(a,multiply(multiply(multiply(b,c),identity),a)) = multiply(multiply(a,multiply(b,c)),multiply(identity,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
multiply(a,multiply(multiply(multiply(b,c),identity),a)) = multiply(multiply(a,multiply(b,c)),multiply(identity,a)),
inference(unit_resolution,[status(thm)],[23,7]) ).
tff(25,plain,
multiply(multiply(a,multiply(b,c)),multiply(identity,a)) = multiply(a,multiply(multiply(multiply(b,c),identity),a)),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
^ [X: $i] :
refl(( ( multiply(identity,X) = X )
<=> ( multiply(identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
tff(30,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
multiply(identity,a) = a,
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
multiply(multiply(a,multiply(b,c)),multiply(identity,a)) = multiply(multiply(a,multiply(b,c)),a),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
multiply(multiply(a,multiply(b,c)),a) = multiply(multiply(a,multiply(b,c)),multiply(identity,a)),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
multiply(multiply(a,multiply(b,c)),a) = multiply(multiply(a,b),multiply(c,a)),
inference(transitivity,[status(thm)],[36,25,22,9]) ).
tff(38,plain,
( ( multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)) )
<=> ( multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_moufang1) ).
tff(40,plain,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
$false,
inference(unit_resolution,[status(thm)],[40,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : GRP206-1 : TPTP v9.0.0. Released v2.3.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 15:47:25 EDT 2025
% 0.14/0.36 % CPUTime :
% 30.42/30.66 % SZS status Unsatisfiable
% 30.42/30.66 % SZS output start Proof
% See solution above
% 30.42/30.67 % E exiting
%------------------------------------------------------------------------------