%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN065-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:38:07 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 19
% Syntax : Number of formulae : 44 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 144 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 185 ( 90 ~; 77 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 5 ( 5 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; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 93 ( 84 !; 0 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
tff(big_h_type,type,
big_h: ( $i * $i ) > $o ).
tff(g_type,type,
g: $i > $i ).
tff(f_type,type,
f: $i > $i ).
tff(a_type,type,
a: $i ).
tff(big_g_type,type,
big_g: ( $i * $i ) > $o ).
tff(big_f_type,type,
big_f: ( $i * $i ) > $o ).
tff(1,plain,
^ [X: $i] :
refl(( ~ big_h(a,X)
<=> ~ big_h(a,X) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ~ big_h(a,X)
<=> ! [X: $i] : ~ big_h(a,X) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ~ big_h(a,X)
<=> ! [X: $i] : ~ big_h(a,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ~ big_h(a,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).
tff(5,plain,
! [X: $i] : ~ big_h(a,X),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ~ big_h(a,X),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ~ big_h(a,X),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ~ big_h(a,X)
| ~ big_h(a,g(f(a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
~ big_h(a,g(f(a))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(( big_g(X,g(X))
<=> big_g(X,g(X)) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] : big_g(X,g(X))
<=> ! [X: $i] : big_g(X,g(X)) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : big_g(X,g(X))
<=> ! [X: $i] : big_g(X,g(X)) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [X: $i] : big_g(X,g(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
tff(14,plain,
! [X: $i] : big_g(X,g(X)),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : big_g(X,g(X)),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : big_g(X,g(X)),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : big_g(X,g(X))
| big_g(f(a),g(f(a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
big_g(f(a),g(f(a))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [X: $i] :
refl(( big_f(X,f(X))
<=> big_f(X,f(X)) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [X: $i] : big_f(X,f(X))
<=> ! [X: $i] : big_f(X,f(X)) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X: $i] : big_f(X,f(X))
<=> ! [X: $i] : big_f(X,f(X)) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
! [X: $i] : big_f(X,f(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
tff(23,plain,
! [X: $i] : big_f(X,f(X)),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [X: $i] : big_f(X,f(X)),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [X: $i] : big_f(X,f(X)),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [X: $i] : big_f(X,f(X))
| big_f(a,f(a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
big_f(a,f(a)),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( big_h(X,Z)
| ~ big_f(X,Y)
| ~ big_g(Y,Z) )
<=> ( big_h(X,Z)
| ~ big_f(X,Y)
| ~ big_g(Y,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(X,Y)
| ~ big_g(Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(X,Y)
| ~ big_g(Y,Z) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(X,Y)
| ~ big_g(Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(X,Y)
| ~ big_g(Y,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(( ( ~ big_f(X,Y)
| ~ big_g(Y,Z)
| big_h(X,Z) )
<=> ( big_h(X,Z)
| ~ big_f(X,Y)
| ~ big_g(Y,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ big_f(X,Y)
| ~ big_g(Y,Z)
| big_h(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(X,Y)
| ~ big_g(Y,Z) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ big_f(X,Y)
| ~ big_g(Y,Z)
| big_h(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
tff(34,plain,
! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(X,Y)
| ~ big_g(Y,Z) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(X,Y)
| ~ big_g(Y,Z) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(X,Y)
| ~ big_g(Y,Z) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(X,Y)
| ~ big_g(Y,Z) ),
inference(modus_ponens,[status(thm)],[36,29]) ).
tff(38,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(X,Y)
| ~ big_g(Y,Z) )
| ~ big_f(a,f(a))
| big_h(a,g(f(a)))
| ~ big_g(f(a),g(f(a))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(X,Y)
| ~ big_g(Y,Z) )
| ~ big_f(a,f(a))
| big_h(a,g(f(a)))
| ~ big_g(f(a),g(f(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ( big_h(a,g(f(a)))
| ~ big_f(a,f(a))
| ~ big_g(f(a),g(f(a))) )
<=> ( ~ big_f(a,f(a))
| big_h(a,g(f(a)))
| ~ big_g(f(a),g(f(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(X,Y)
| ~ big_g(Y,Z) )
| big_h(a,g(f(a)))
| ~ big_f(a,f(a))
| ~ big_g(f(a),g(f(a))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(X,Y)
| ~ big_g(Y,Z) )
| ~ big_f(a,f(a))
| big_h(a,g(f(a)))
| ~ big_g(f(a),g(f(a))) ) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(X,Y)
| ~ big_g(Y,Z) )
| big_h(a,g(f(a)))
| ~ big_f(a,f(a))
| ~ big_g(f(a),g(f(a))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(X,Y)
| ~ big_g(Y,Z) )
| ~ big_f(a,f(a))
| big_h(a,g(f(a)))
| ~ big_g(f(a),g(f(a))) ) ),
inference(transitivity,[status(thm)],[40,38]) ).
tff(42,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(X,Y)
| ~ big_g(Y,Z) )
| big_h(a,g(f(a)))
| ~ big_f(a,f(a))
| ~ big_g(f(a),g(f(a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(X,Y)
| ~ big_g(Y,Z) )
| ~ big_f(a,f(a))
| big_h(a,g(f(a)))
| ~ big_g(f(a),g(f(a))) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
$false,
inference(unit_resolution,[status(thm)],[43,37,27,18,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN065-1 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.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 12:28:46 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.45 % SZS status Unsatisfiable
% 0.21/0.45 % SZS output start Proof
% See solution above
% 0.21/0.46 % E exiting
%------------------------------------------------------------------------------