%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ROB002-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:24:17 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 17
% Syntax : Number of formulae : 52 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 69 ( 66 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 10 ~; 6 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 2 ( 2 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 50 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
tff(b_type,type,
b: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(negate_type,type,
negate: $i > $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
( ! [X: $i] : ( negate(negate(X)) = X )
<=> ! [X: $i] : ( negate(negate(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ! [X: $i] : ( negate(negate(X)) = X )
<=> ! [X: $i] : ( negate(negate(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
! [X: $i] : ( negate(negate(X)) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',double_negation) ).
tff(4,plain,
! [X: $i] : ( negate(negate(X)) = X ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
! [X: $i] : ( negate(negate(X)) = X ),
inference(skolemize,[status(sab)],[4]) ).
tff(6,plain,
! [X: $i] : ( negate(negate(X)) = X ),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( ~ ! [X: $i] : ( negate(negate(X)) = X )
| ( negate(negate(b)) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(8,plain,
negate(negate(b)) = b,
inference(unit_resolution,[status(thm)],[7,6]) ).
tff(9,plain,
^ [Y: $i,X: $i] :
refl(( ( add(X,Y) = add(Y,X) )
<=> ( add(X,Y) = add(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
<=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
<=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/ROB001-0.ax',commutativity_of_add) ).
tff(13,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(negate(a),negate(b)) = add(negate(b),negate(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
add(negate(a),negate(b)) = add(negate(b),negate(a)),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
add(negate(b),negate(a)) = add(negate(a),negate(b)),
inference(symmetry,[status(thm)],[17]) ).
tff(19,plain,
negate(add(negate(b),negate(a))) = negate(add(negate(a),negate(b))),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(a,negate(b)) = add(negate(b),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
add(a,negate(b)) = add(negate(b),a),
inference(unit_resolution,[status(thm)],[20,15]) ).
tff(22,plain,
add(negate(b),a) = add(a,negate(b)),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
negate(add(negate(b),a)) = negate(add(a,negate(b))),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
add(negate(add(negate(b),a)),negate(add(negate(b),negate(a)))) = add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),
inference(monotonicity,[status(thm)],[23,19]) ).
tff(25,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = add(negate(add(negate(b),a)),negate(add(negate(b),negate(a)))),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = add(negate(add(negate(a),negate(b))),negate(add(a,negate(b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = add(negate(add(negate(a),negate(b))),negate(add(a,negate(b)))),
inference(unit_resolution,[status(thm)],[26,15]) ).
tff(28,plain,
add(negate(add(negate(a),negate(b))),negate(add(a,negate(b)))) = add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
add(negate(add(negate(a),negate(b))),negate(add(a,negate(b)))) = add(negate(add(negate(b),a)),negate(add(negate(b),negate(a)))),
inference(transitivity,[status(thm)],[28,25]) ).
tff(30,plain,
negate(add(negate(add(negate(a),negate(b))),negate(add(a,negate(b))))) = negate(add(negate(add(negate(b),a)),negate(add(negate(b),negate(a))))),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
negate(add(negate(add(negate(b),a)),negate(add(negate(b),negate(a))))) = negate(add(negate(add(negate(a),negate(b))),negate(add(a,negate(b))))),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
^ [Y: $i,X: $i] :
refl(( ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X )
<=> ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X )
<=> ! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X )
<=> ! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/ROB001-0.ax',robbins_axiom) ).
tff(36,plain,
! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ~ ! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X )
| ( negate(add(negate(add(negate(b),a)),negate(add(negate(b),negate(a))))) = negate(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
negate(add(negate(add(negate(b),a)),negate(add(negate(b),negate(a))))) = negate(b),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
negate(b) = negate(add(negate(add(negate(b),a)),negate(add(negate(b),negate(a))))),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
negate(b) = negate(add(negate(add(negate(a),negate(b))),negate(add(a,negate(b))))),
inference(transitivity,[status(thm)],[41,31]) ).
tff(43,plain,
negate(negate(b)) = negate(negate(add(negate(add(negate(a),negate(b))),negate(add(a,negate(b)))))),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
negate(negate(add(negate(add(negate(a),negate(b))),negate(add(a,negate(b)))))) = negate(negate(b)),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
( ~ ! [X: $i] : ( negate(negate(X)) = X )
| ( negate(negate(add(negate(add(negate(a),negate(b))),negate(add(a,negate(b)))))) = add(negate(add(negate(a),negate(b))),negate(add(a,negate(b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
negate(negate(add(negate(add(negate(a),negate(b))),negate(add(a,negate(b)))))) = add(negate(add(negate(a),negate(b))),negate(add(a,negate(b)))),
inference(unit_resolution,[status(thm)],[45,6]) ).
tff(47,plain,
add(negate(add(negate(a),negate(b))),negate(add(a,negate(b)))) = negate(negate(add(negate(add(negate(a),negate(b))),negate(add(a,negate(b)))))),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b,
inference(transitivity,[status(thm)],[27,47,44,8]) ).
tff(49,plain,
( ( add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b )
<=> ( add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_huntingtons_axiom) ).
tff(51,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
$false,
inference(unit_resolution,[status(thm)],[51,48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ROB002-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 03:30:19 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.38 % SZS status Unsatisfiable
% 0.13/0.38 % SZS output start Proof
% See solution above
% 0.13/0.39 % E exiting
%------------------------------------------------------------------------------