%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET838-2 : TPTP v9.0.0. Released v3.2.0.
% 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 05:26:28 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.35s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 50 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 150 ( 144 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 193 ( 98 ~; 78 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 47 ( 42 !; 0 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
tff(v_g_type,type,
v_g: $i > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_xa_type,type,
v_xa: $i > $i ).
tff(v_f_type,type,
v_f: $i > $i ).
tff(1,plain,
( ( v_f(v_g(v_x)) = v_x )
<=> ( v_f(v_g(v_x)) = v_x ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
v_f(v_g(v_x)) = v_x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(3,plain,
v_f(v_g(v_x)) = v_x,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
v_g(v_f(v_g(v_x))) = v_g(v_x),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
^ [V_U: $i] :
refl(( ( ( v_g(v_f(V_U)) != V_U )
| ( v_g(v_f(v_xa(V_U))) = v_xa(V_U) ) )
<=> ( ( v_g(v_f(V_U)) != V_U )
| ( v_g(v_f(v_xa(V_U))) = v_xa(V_U) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [V_U: $i] :
( ( v_g(v_f(V_U)) != V_U )
| ( v_g(v_f(v_xa(V_U))) = v_xa(V_U) ) )
<=> ! [V_U: $i] :
( ( v_g(v_f(V_U)) != V_U )
| ( v_g(v_f(v_xa(V_U))) = v_xa(V_U) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [V_U: $i] :
( ( v_g(v_f(V_U)) != V_U )
| ( v_g(v_f(v_xa(V_U))) = v_xa(V_U) ) )
<=> ! [V_U: $i] :
( ( v_g(v_f(V_U)) != V_U )
| ( v_g(v_f(v_xa(V_U))) = v_xa(V_U) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,plain,
^ [V_U: $i] :
rewrite(( ( ( v_g(v_f(v_xa(V_U))) = v_xa(V_U) )
| ( v_g(v_f(V_U)) != V_U ) )
<=> ( ( v_g(v_f(V_U)) != V_U )
| ( v_g(v_f(v_xa(V_U))) = v_xa(V_U) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [V_U: $i] :
( ( v_g(v_f(v_xa(V_U))) = v_xa(V_U) )
| ( v_g(v_f(V_U)) != V_U ) )
<=> ! [V_U: $i] :
( ( v_g(v_f(V_U)) != V_U )
| ( v_g(v_f(v_xa(V_U))) = v_xa(V_U) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,axiom,
! [V_U: $i] :
( ( v_g(v_f(v_xa(V_U))) = v_xa(V_U) )
| ( v_g(v_f(V_U)) != V_U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(11,plain,
! [V_U: $i] :
( ( v_g(v_f(V_U)) != V_U )
| ( v_g(v_f(v_xa(V_U))) = v_xa(V_U) ) ),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [V_U: $i] :
( ( v_g(v_f(V_U)) != V_U )
| ( v_g(v_f(v_xa(V_U))) = v_xa(V_U) ) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
! [V_U: $i] :
( ( v_g(v_f(V_U)) != V_U )
| ( v_g(v_f(v_xa(V_U))) = v_xa(V_U) ) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [V_U: $i] :
( ( v_g(v_f(V_U)) != V_U )
| ( v_g(v_f(v_xa(V_U))) = v_xa(V_U) ) ),
inference(modus_ponens,[status(thm)],[13,6]) ).
tff(15,plain,
( ( ~ ! [V_U: $i] :
( ( v_g(v_f(V_U)) != V_U )
| ( v_g(v_f(v_xa(V_U))) = v_xa(V_U) ) )
| ( v_g(v_f(v_g(v_x))) != v_g(v_x) )
| ( v_g(v_f(v_xa(v_g(v_x)))) = v_xa(v_g(v_x)) ) )
<=> ( ~ ! [V_U: $i] :
( ( v_g(v_f(V_U)) != V_U )
| ( v_g(v_f(v_xa(V_U))) = v_xa(V_U) ) )
| ( v_g(v_f(v_g(v_x))) != v_g(v_x) )
| ( v_g(v_f(v_xa(v_g(v_x)))) = v_xa(v_g(v_x)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [V_U: $i] :
( ( v_g(v_f(V_U)) != V_U )
| ( v_g(v_f(v_xa(V_U))) = v_xa(V_U) ) )
| ( v_g(v_f(v_g(v_x))) != v_g(v_x) )
| ( v_g(v_f(v_xa(v_g(v_x)))) = v_xa(v_g(v_x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
( ~ ! [V_U: $i] :
( ( v_g(v_f(V_U)) != V_U )
| ( v_g(v_f(v_xa(V_U))) = v_xa(V_U) ) )
| ( v_g(v_f(v_g(v_x))) != v_g(v_x) )
| ( v_g(v_f(v_xa(v_g(v_x)))) = v_xa(v_g(v_x)) ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
v_g(v_f(v_xa(v_g(v_x)))) = v_xa(v_g(v_x)),
inference(unit_resolution,[status(thm)],[17,14,4]) ).
tff(19,plain,
v_f(v_g(v_f(v_xa(v_g(v_x))))) = v_f(v_xa(v_g(v_x))),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
^ [V_U: $i] :
refl(( ( ( v_f(v_g(V_U)) != V_U )
| ( V_U = v_x ) )
<=> ( ( v_f(v_g(V_U)) != V_U )
| ( V_U = v_x ) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [V_U: $i] :
( ( v_f(v_g(V_U)) != V_U )
| ( V_U = v_x ) )
<=> ! [V_U: $i] :
( ( v_f(v_g(V_U)) != V_U )
| ( V_U = v_x ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [V_U: $i] :
( ( v_f(v_g(V_U)) != V_U )
| ( V_U = v_x ) )
<=> ! [V_U: $i] :
( ( v_f(v_g(V_U)) != V_U )
| ( V_U = v_x ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
^ [V_U: $i] :
rewrite(( ( ( V_U = v_x )
| ( v_f(v_g(V_U)) != V_U ) )
<=> ( ( v_f(v_g(V_U)) != V_U )
| ( V_U = v_x ) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [V_U: $i] :
( ( V_U = v_x )
| ( v_f(v_g(V_U)) != V_U ) )
<=> ! [V_U: $i] :
( ( v_f(v_g(V_U)) != V_U )
| ( V_U = v_x ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,axiom,
! [V_U: $i] :
( ( V_U = v_x )
| ( v_f(v_g(V_U)) != V_U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(26,plain,
! [V_U: $i] :
( ( v_f(v_g(V_U)) != V_U )
| ( V_U = v_x ) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [V_U: $i] :
( ( v_f(v_g(V_U)) != V_U )
| ( V_U = v_x ) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
! [V_U: $i] :
( ( v_f(v_g(V_U)) != V_U )
| ( V_U = v_x ) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [V_U: $i] :
( ( v_f(v_g(V_U)) != V_U )
| ( V_U = v_x ) ),
inference(modus_ponens,[status(thm)],[28,21]) ).
tff(30,plain,
( ( ~ ! [V_U: $i] :
( ( v_f(v_g(V_U)) != V_U )
| ( V_U = v_x ) )
| ( v_f(v_g(v_f(v_xa(v_g(v_x))))) != v_f(v_xa(v_g(v_x))) )
| ( v_f(v_xa(v_g(v_x))) = v_x ) )
<=> ( ~ ! [V_U: $i] :
( ( v_f(v_g(V_U)) != V_U )
| ( V_U = v_x ) )
| ( v_f(v_g(v_f(v_xa(v_g(v_x))))) != v_f(v_xa(v_g(v_x))) )
| ( v_f(v_xa(v_g(v_x))) = v_x ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
( ~ ! [V_U: $i] :
( ( v_f(v_g(V_U)) != V_U )
| ( V_U = v_x ) )
| ( v_f(v_g(v_f(v_xa(v_g(v_x))))) != v_f(v_xa(v_g(v_x))) )
| ( v_f(v_xa(v_g(v_x))) = v_x ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [V_U: $i] :
( ( v_f(v_g(V_U)) != V_U )
| ( V_U = v_x ) )
| ( v_f(v_g(v_f(v_xa(v_g(v_x))))) != v_f(v_xa(v_g(v_x))) )
| ( v_f(v_xa(v_g(v_x))) = v_x ) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
( ( v_f(v_g(v_f(v_xa(v_g(v_x))))) != v_f(v_xa(v_g(v_x))) )
| ( v_f(v_xa(v_g(v_x))) = v_x ) ),
inference(unit_resolution,[status(thm)],[32,29]) ).
tff(34,plain,
v_f(v_xa(v_g(v_x))) = v_x,
inference(unit_resolution,[status(thm)],[33,19]) ).
tff(35,plain,
v_g(v_f(v_xa(v_g(v_x)))) = v_g(v_x),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
v_xa(v_g(v_x)) = v_g(v_f(v_xa(v_g(v_x)))),
inference(symmetry,[status(thm)],[18]) ).
tff(37,plain,
v_xa(v_g(v_x)) = v_g(v_x),
inference(transitivity,[status(thm)],[36,35]) ).
tff(38,plain,
^ [V_U: $i] :
refl(( ( ( v_xa(V_U) != V_U )
| ( v_g(v_f(V_U)) != V_U ) )
<=> ( ( v_xa(V_U) != V_U )
| ( v_g(v_f(V_U)) != V_U ) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [V_U: $i] :
( ( v_xa(V_U) != V_U )
| ( v_g(v_f(V_U)) != V_U ) )
<=> ! [V_U: $i] :
( ( v_xa(V_U) != V_U )
| ( v_g(v_f(V_U)) != V_U ) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [V_U: $i] :
( ( v_xa(V_U) != V_U )
| ( v_g(v_f(V_U)) != V_U ) )
<=> ! [V_U: $i] :
( ( v_xa(V_U) != V_U )
| ( v_g(v_f(V_U)) != V_U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
! [V_U: $i] :
( ( v_xa(V_U) != V_U )
| ( v_g(v_f(V_U)) != V_U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(42,plain,
! [V_U: $i] :
( ( v_xa(V_U) != V_U )
| ( v_g(v_f(V_U)) != V_U ) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [V_U: $i] :
( ( v_xa(V_U) != V_U )
| ( v_g(v_f(V_U)) != V_U ) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [V_U: $i] :
( ( v_xa(V_U) != V_U )
| ( v_g(v_f(V_U)) != V_U ) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ( ~ ! [V_U: $i] :
( ( v_xa(V_U) != V_U )
| ( v_g(v_f(V_U)) != V_U ) )
| ( v_xa(v_g(v_x)) != v_g(v_x) )
| ( v_g(v_f(v_g(v_x))) != v_g(v_x) ) )
<=> ( ~ ! [V_U: $i] :
( ( v_xa(V_U) != V_U )
| ( v_g(v_f(V_U)) != V_U ) )
| ( v_xa(v_g(v_x)) != v_g(v_x) )
| ( v_g(v_f(v_g(v_x))) != v_g(v_x) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [V_U: $i] :
( ( v_xa(V_U) != V_U )
| ( v_g(v_f(V_U)) != V_U ) )
| ( v_xa(v_g(v_x)) != v_g(v_x) )
| ( v_g(v_f(v_g(v_x))) != v_g(v_x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [V_U: $i] :
( ( v_xa(V_U) != V_U )
| ( v_g(v_f(V_U)) != V_U ) )
| ( v_xa(v_g(v_x)) != v_g(v_x) )
| ( v_g(v_f(v_g(v_x))) != v_g(v_x) ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
( ( v_xa(v_g(v_x)) != v_g(v_x) )
| ( v_g(v_f(v_g(v_x))) != v_g(v_x) ) ),
inference(unit_resolution,[status(thm)],[47,44]) ).
tff(49,plain,
v_xa(v_g(v_x)) != v_g(v_x),
inference(unit_resolution,[status(thm)],[48,4]) ).
tff(50,plain,
$false,
inference(unit_resolution,[status(thm)],[49,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SET838-2 : TPTP v9.0.0. Released v3.2.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n009.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Jun 20 05:44:33 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.35 % SZS status Unsatisfiable
% 0.18/0.35 % SZS output start Proof
% See solution above
% 0.18/0.36 % E exiting
%------------------------------------------------------------------------------