%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ROB011-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:24:18 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 24
% Syntax : Number of formulae : 70 ( 52 unt; 0 typ; 0 def)
% Number of atoms : 96 ( 91 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 34 ( 12 ~; 8 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 4 ( 4 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 88 ( 80 !; 0 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_type,type,
c: $i ).
tff(negate_type,type,
negate: $i > $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(one_type,type,
one: $i ).
tff(b_type,type,
b: $i ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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(5,plain,
! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X )
| ( negate(add(negate(add(c,add(b,a))),negate(add(c,negate(add(b,a)))))) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
negate(add(negate(add(c,add(b,a))),negate(add(c,negate(add(b,a)))))) = c,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X )
| ( negate(add(negate(add(a,b)),negate(add(a,negate(b))))) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(11,plain,
negate(add(negate(add(a,b)),negate(add(a,negate(b))))) = a,
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
( ( negate(add(a,negate(b))) = c )
<=> ( negate(add(a,negate(b))) = c ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
negate(add(a,negate(b))) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition) ).
tff(14,plain,
negate(add(a,negate(b))) = c,
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
add(negate(add(a,b)),negate(add(a,negate(b)))) = add(negate(add(a,b)),c),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
add(negate(add(a,b)),c) = add(negate(add(a,b)),negate(add(a,negate(b)))),
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
^ [Y: $i,X: $i] :
refl(( ( add(X,Y) = add(Y,X) )
<=> ( add(X,Y) = add(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(18,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)],[17]) ).
tff(19,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(20,axiom,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/ROB001-0.ax',commutativity_of_add) ).
tff(21,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(negate(add(a,b)),c) = add(c,negate(add(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
add(negate(add(a,b)),c) = add(c,negate(add(a,b))),
inference(unit_resolution,[status(thm)],[24,23]) ).
tff(26,plain,
add(c,negate(add(a,b))) = add(negate(add(a,b)),c),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(a,b) = add(b,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
add(a,b) = add(b,a),
inference(unit_resolution,[status(thm)],[27,23]) ).
tff(29,plain,
add(b,a) = add(a,b),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
negate(add(b,a)) = negate(add(a,b)),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
add(c,negate(add(b,a))) = add(c,negate(add(a,b))),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
add(c,negate(add(b,a))) = add(negate(add(a,b)),negate(add(a,negate(b)))),
inference(transitivity,[status(thm)],[31,26,16]) ).
tff(33,plain,
negate(add(c,negate(add(b,a)))) = negate(add(negate(add(a,b)),negate(add(a,negate(b))))),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
negate(add(c,negate(add(b,a)))) = a,
inference(transitivity,[status(thm)],[33,11]) ).
tff(35,plain,
^ [X: $i] :
refl(( ( multiply(one,X) = X )
<=> ( multiply(one,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [X: $i] : ( multiply(one,X) = X )
<=> ! [X: $i] : ( multiply(one,X) = X ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [X: $i] : ( multiply(one,X) = X )
<=> ! [X: $i] : ( multiply(one,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
! [X: $i] : ( multiply(one,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/ROB001-1.ax',one_times_x) ).
tff(39,plain,
! [X: $i] : ( multiply(one,X) = X ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [X: $i] : ( multiply(one,X) = X ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [X: $i] : ( multiply(one,X) = X ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ~ ! [X: $i] : ( multiply(one,X) = X )
| ( multiply(one,add(a,c)) = add(a,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
multiply(one,add(a,c)) = add(a,c),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
add(a,c) = multiply(one,add(a,c)),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
add(b,add(a,c)) = add(b,multiply(one,add(a,c))),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
<=> ( add(add(X,Y),Z) = add(X,add(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/ROB001-0.ax',associativity_of_add) ).
tff(50,plain,
! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(b,a),c) = add(b,add(a,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
add(add(b,a),c) = add(b,add(a,c)),
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(b,a),c) = add(c,add(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
add(add(b,a),c) = add(c,add(b,a)),
inference(unit_resolution,[status(thm)],[55,23]) ).
tff(57,plain,
add(c,add(b,a)) = add(add(b,a),c),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
add(c,add(b,a)) = add(b,multiply(one,add(a,c))),
inference(transitivity,[status(thm)],[57,54,45]) ).
tff(59,plain,
negate(add(c,add(b,a))) = negate(add(b,multiply(one,add(a,c)))),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
add(negate(add(c,add(b,a))),negate(add(c,negate(add(b,a))))) = add(negate(add(b,multiply(one,add(a,c)))),a),
inference(monotonicity,[status(thm)],[59,34]) ).
tff(61,plain,
add(negate(add(b,multiply(one,add(a,c)))),a) = add(negate(add(c,add(b,a))),negate(add(c,negate(add(b,a))))),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(a,negate(add(b,multiply(one,add(a,c))))) = add(negate(add(b,multiply(one,add(a,c)))),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
add(a,negate(add(b,multiply(one,add(a,c))))) = add(negate(add(b,multiply(one,add(a,c)))),a),
inference(unit_resolution,[status(thm)],[62,23]) ).
tff(64,plain,
add(a,negate(add(b,multiply(one,add(a,c))))) = add(negate(add(c,add(b,a))),negate(add(c,negate(add(b,a))))),
inference(transitivity,[status(thm)],[63,61]) ).
tff(65,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) = negate(add(negate(add(c,add(b,a))),negate(add(c,negate(add(b,a)))))),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) = c,
inference(transitivity,[status(thm)],[65,9]) ).
tff(67,plain,
( ( negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != c )
<=> ( negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != c ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,axiom,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_base_step) ).
tff(69,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != c,
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
$false,
inference(unit_resolution,[status(thm)],[69,66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ROB011-1 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.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 : Fri Jun 20 03:29:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% See solution above
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------