%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN060-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:38:06 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 19
% Syntax : Number of formulae : 42 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 140 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 145 ( 52 ~; 76 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 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; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 47 ( 42 !; 0 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
tff(big_h_type,type,
big_h: $i > $o ).
tff(a_type,type,
a: $i ).
tff(big_i_type,type,
big_i: $i > $o ).
tff(big_f_type,type,
big_f: $i > $o ).
tff(1,plain,
( ~ big_i(a)
<=> ~ big_i(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ big_i(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
tff(3,plain,
~ big_i(a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X: $i] :
refl(( ( big_h(X)
| big_i(X) )
<=> ( big_h(X)
| big_i(X) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X: $i] :
( big_h(X)
| big_i(X) )
<=> ! [X: $i] :
( big_h(X)
| big_i(X) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X: $i] :
( big_h(X)
| big_i(X) )
<=> ! [X: $i] :
( big_h(X)
| big_i(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [X: $i] :
rewrite(( ( big_i(X)
| big_h(X) )
<=> ( big_h(X)
| big_i(X) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [X: $i] :
( big_i(X)
| big_h(X) )
<=> ! [X: $i] :
( big_h(X)
| big_i(X) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [X: $i] :
( big_i(X)
| big_h(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
tff(10,plain,
! [X: $i] :
( big_h(X)
| big_i(X) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X: $i] :
( big_h(X)
| big_i(X) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [X: $i] :
( big_h(X)
| big_i(X) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [X: $i] :
( big_h(X)
| big_i(X) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [X: $i] :
( big_h(X)
| big_i(X) )
| big_h(a)
| big_i(a) )
<=> ( ~ ! [X: $i] :
( big_h(X)
| big_i(X) )
| big_h(a)
| big_i(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [X: $i] :
( big_h(X)
| big_i(X) )
| big_h(a)
| big_i(a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [X: $i] :
( big_h(X)
| big_i(X) )
| big_h(a)
| big_i(a) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
big_h(a),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
^ [X: $i] :
refl(( ( big_f(X)
| big_i(X) )
<=> ( big_f(X)
| big_i(X) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [X: $i] :
( big_f(X)
| big_i(X) )
<=> ! [X: $i] :
( big_f(X)
| big_i(X) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [X: $i] :
( big_f(X)
| big_i(X) )
<=> ! [X: $i] :
( big_f(X)
| big_i(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [X: $i] :
rewrite(( ( big_i(X)
| big_f(X) )
<=> ( big_f(X)
| big_i(X) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [X: $i] :
( big_i(X)
| big_f(X) )
<=> ! [X: $i] :
( big_f(X)
| big_i(X) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [X: $i] :
( big_i(X)
| big_f(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
tff(24,plain,
! [X: $i] :
( big_f(X)
| big_i(X) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [X: $i] :
( big_f(X)
| big_i(X) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [X: $i] :
( big_f(X)
| big_i(X) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X: $i] :
( big_f(X)
| big_i(X) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [X: $i] :
( big_f(X)
| big_i(X) )
| big_f(a)
| big_i(a) )
<=> ( ~ ! [X: $i] :
( big_f(X)
| big_i(X) )
| big_f(a)
| big_i(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [X: $i] :
( big_f(X)
| big_i(X) )
| big_f(a)
| big_i(a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [X: $i] :
( big_f(X)
| big_i(X) )
| big_f(a)
| big_i(a) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
big_f(a),
inference(unit_resolution,[status(thm)],[30,27,3]) ).
tff(32,plain,
^ [X: $i] :
refl(( ( ~ big_f(X)
| ~ big_h(X) )
<=> ( ~ big_f(X)
| ~ big_h(X) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [X: $i] :
( ~ big_f(X)
| ~ big_h(X) )
<=> ! [X: $i] :
( ~ big_f(X)
| ~ big_h(X) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X: $i] :
( ~ big_f(X)
| ~ big_h(X) )
<=> ! [X: $i] :
( ~ big_f(X)
| ~ big_h(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
! [X: $i] :
( ~ big_f(X)
| ~ big_h(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
tff(36,plain,
! [X: $i] :
( ~ big_f(X)
| ~ big_h(X) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [X: $i] :
( ~ big_f(X)
| ~ big_h(X) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [X: $i] :
( ~ big_f(X)
| ~ big_h(X) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ( ~ ! [X: $i] :
( ~ big_f(X)
| ~ big_h(X) )
| ~ big_f(a)
| ~ big_h(a) )
<=> ( ~ ! [X: $i] :
( ~ big_f(X)
| ~ big_h(X) )
| ~ big_f(a)
| ~ big_h(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [X: $i] :
( ~ big_f(X)
| ~ big_h(X) )
| ~ big_f(a)
| ~ big_h(a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [X: $i] :
( ~ big_f(X)
| ~ big_h(X) )
| ~ big_f(a)
| ~ big_h(a) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
$false,
inference(unit_resolution,[status(thm)],[41,38,31,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN060-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n008.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:27:18 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Unsatisfiable
% 0.11/0.37 % SZS output start Proof
% See solution above
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------