%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN057-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:38:05 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 29
% Syntax : Number of formulae : 61 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 352 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 505 ( 238 ~; 232 |; 0 &)
% ( 35 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 80 ( 72 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
tff(big_h_type,type,
big_h: $i > $o ).
tff(b_type,type,
b: $i ).
tff(big_f_type,type,
big_f: $i > $o ).
tff(big_i_type,type,
big_i: $i > $o ).
tff(big_j_type,type,
big_j: $i > $o ).
tff(a_type,type,
a: $i ).
tff(big_g_type,type,
big_g: $i > $o ).
tff(1,plain,
( big_i(b)
<=> big_i(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
big_i(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
tff(3,plain,
big_i(b),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( big_j(b)
<=> big_j(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
big_j(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
tff(6,plain,
big_j(b),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [X: $i] :
refl(( ( big_f(X)
| ~ big_i(X)
| ~ big_j(X) )
<=> ( big_f(X)
| ~ big_i(X)
| ~ big_j(X) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [X: $i] :
( big_f(X)
| ~ big_i(X)
| ~ big_j(X) )
<=> ! [X: $i] :
( big_f(X)
| ~ big_i(X)
| ~ big_j(X) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [X: $i] :
( big_f(X)
| ~ big_i(X)
| ~ big_j(X) )
<=> ! [X: $i] :
( big_f(X)
| ~ big_i(X)
| ~ big_j(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ big_j(X)
| ~ big_i(X) )
<=> ( ~ big_i(X)
| ~ big_j(X) ) )),
( ( ~ big_j(X)
| ~ big_i(X)
| big_f(X) )
<=> ( ~ big_i(X)
| ~ big_j(X)
| big_f(X) ) )),
rewrite(( ( ~ big_i(X)
| ~ big_j(X)
| big_f(X) )
<=> ( big_f(X)
| ~ big_i(X)
| ~ big_j(X) ) )),
( ( ~ big_j(X)
| ~ big_i(X)
| big_f(X) )
<=> ( big_f(X)
| ~ big_i(X)
| ~ big_j(X) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] :
( ~ big_j(X)
| ~ big_i(X)
| big_f(X) )
<=> ! [X: $i] :
( big_f(X)
| ~ big_i(X)
| ~ big_j(X) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [X: $i] :
( ~ big_j(X)
| ~ big_i(X)
| big_f(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
tff(13,plain,
! [X: $i] :
( big_f(X)
| ~ big_i(X)
| ~ big_j(X) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [X: $i] :
( big_f(X)
| ~ big_i(X)
| ~ big_j(X) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [X: $i] :
( big_f(X)
| ~ big_i(X)
| ~ big_j(X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] :
( big_f(X)
| ~ big_i(X)
| ~ big_j(X) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [X: $i] :
( big_f(X)
| ~ big_i(X)
| ~ big_j(X) )
| big_f(b)
| ~ big_i(b)
| ~ big_j(b) )
<=> ( ~ ! [X: $i] :
( big_f(X)
| ~ big_i(X)
| ~ big_j(X) )
| big_f(b)
| ~ big_i(b)
| ~ big_j(b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [X: $i] :
( big_f(X)
| ~ big_i(X)
| ~ big_j(X) )
| big_f(b)
| ~ big_i(b)
| ~ big_j(b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [X: $i] :
( big_f(X)
| ~ big_i(X)
| ~ big_j(X) )
| big_f(b)
| ~ big_i(b)
| ~ big_j(b) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
big_f(b),
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
^ [X: $i] :
refl(( ( big_h(X)
| ~ big_f(X) )
<=> ( big_h(X)
| ~ big_f(X) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [X: $i] :
( big_h(X)
| ~ big_f(X) )
<=> ! [X: $i] :
( big_h(X)
| ~ big_f(X) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X: $i] :
( big_h(X)
| ~ big_f(X) )
<=> ! [X: $i] :
( big_h(X)
| ~ big_f(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [X: $i] :
rewrite(( ( ~ big_f(X)
| big_h(X) )
<=> ( big_h(X)
| ~ big_f(X) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [X: $i] :
( ~ big_f(X)
| big_h(X) )
<=> ! [X: $i] :
( big_h(X)
| ~ big_f(X) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [X: $i] :
( ~ big_f(X)
| big_h(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
tff(27,plain,
! [X: $i] :
( big_h(X)
| ~ big_f(X) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [X: $i] :
( big_h(X)
| ~ big_f(X) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [X: $i] :
( big_h(X)
| ~ big_f(X) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [X: $i] :
( big_h(X)
| ~ big_f(X) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [X: $i] :
( big_h(X)
| ~ big_f(X) )
| big_h(b)
| ~ big_f(b) )
<=> ( ~ ! [X: $i] :
( big_h(X)
| ~ big_f(X) )
| big_h(b)
| ~ big_f(b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [X: $i] :
( big_h(X)
| ~ big_f(X) )
| big_h(b)
| ~ big_f(b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [X: $i] :
( big_h(X)
| ~ big_f(X) )
| big_h(b)
| ~ big_f(b) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
big_h(b),
inference(unit_resolution,[status(thm)],[33,30,20]) ).
tff(35,plain,
( big_f(a)
<=> big_f(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
big_f(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
tff(37,plain,
big_f(a),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( ( ~ ! [X: $i] :
( big_h(X)
| ~ big_f(X) )
| big_h(a)
| ~ big_f(a) )
<=> ( ~ ! [X: $i] :
( big_h(X)
| ~ big_f(X) )
| big_h(a)
| ~ big_f(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [X: $i] :
( big_h(X)
| ~ big_f(X) )
| big_h(a)
| ~ big_f(a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [X: $i] :
( big_h(X)
| ~ big_f(X) )
| big_h(a)
| ~ big_f(a) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
big_h(a),
inference(unit_resolution,[status(thm)],[40,37,30]) ).
tff(42,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ big_h(Y)
| ~ big_i(Y)
| big_g(X)
| ~ big_h(X) )
<=> ( ~ big_h(Y)
| ~ big_i(Y)
| big_g(X)
| ~ big_h(X) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [Y: $i,X: $i] :
( ~ big_h(Y)
| ~ big_i(Y)
| big_g(X)
| ~ big_h(X) )
<=> ! [Y: $i,X: $i] :
( ~ big_h(Y)
| ~ big_i(Y)
| big_g(X)
| ~ big_h(X) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [Y: $i,X: $i] :
( ~ big_h(Y)
| ~ big_i(Y)
| big_g(X)
| ~ big_h(X) )
<=> ! [Y: $i,X: $i] :
( ~ big_h(Y)
| ~ big_i(Y)
| big_g(X)
| ~ big_h(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
^ [Y: $i,X: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ big_h(X)
| big_g(X) )
<=> ( big_g(X)
| ~ big_h(X) ) )),
( ( ~ big_h(X)
| big_g(X)
| ~ big_i(Y) )
<=> ( big_g(X)
| ~ big_h(X)
| ~ big_i(Y) ) )),
rewrite(( ( big_g(X)
| ~ big_h(X)
| ~ big_i(Y) )
<=> ( ~ big_i(Y)
| big_g(X)
| ~ big_h(X) ) )),
( ( ~ big_h(X)
| big_g(X)
| ~ big_i(Y) )
<=> ( ~ big_i(Y)
| big_g(X)
| ~ big_h(X) ) )),
( ( ~ big_h(X)
| big_g(X)
| ~ big_i(Y)
| ~ big_h(Y) )
<=> ( ~ big_i(Y)
| big_g(X)
| ~ big_h(X)
| ~ big_h(Y) ) )),
rewrite(( ( ~ big_i(Y)
| big_g(X)
| ~ big_h(X)
| ~ big_h(Y) )
<=> ( ~ big_h(Y)
| ~ big_i(Y)
| big_g(X)
| ~ big_h(X) ) )),
( ( ~ big_h(X)
| big_g(X)
| ~ big_i(Y)
| ~ big_h(Y) )
<=> ( ~ big_h(Y)
| ~ big_i(Y)
| big_g(X)
| ~ big_h(X) ) )),
inference(bind,[status(th)],[]) ).
tff(46,plain,
( ! [Y: $i,X: $i] :
( ~ big_h(X)
| big_g(X)
| ~ big_i(Y)
| ~ big_h(Y) )
<=> ! [Y: $i,X: $i] :
( ~ big_h(Y)
| ~ big_i(Y)
| big_g(X)
| ~ big_h(X) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,axiom,
! [Y: $i,X: $i] :
( ~ big_h(X)
| big_g(X)
| ~ big_i(Y)
| ~ big_h(Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
tff(48,plain,
! [Y: $i,X: $i] :
( ~ big_h(Y)
| ~ big_i(Y)
| big_g(X)
| ~ big_h(X) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [Y: $i,X: $i] :
( ~ big_h(Y)
| ~ big_i(Y)
| big_g(X)
| ~ big_h(X) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
! [Y: $i,X: $i] :
( ~ big_h(Y)
| ~ big_i(Y)
| big_g(X)
| ~ big_h(X) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [Y: $i,X: $i] :
( ~ big_h(Y)
| ~ big_i(Y)
| big_g(X)
| ~ big_h(X) ),
inference(modus_ponens,[status(thm)],[50,43]) ).
tff(52,plain,
( ~ big_g(a)
<=> ~ big_g(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
~ big_g(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
tff(54,plain,
~ big_g(a),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ big_h(Y)
| ~ big_i(Y)
| big_g(X)
| ~ big_h(X) )
| big_g(a)
| ~ big_i(b)
| ~ big_h(a)
| ~ big_h(b) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ big_h(Y)
| ~ big_i(Y)
| big_g(X)
| ~ big_h(X) )
| big_g(a)
| ~ big_i(b)
| ~ big_h(a)
| ~ big_h(b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
( ( ~ big_h(b)
| ~ big_i(b)
| big_g(a)
| ~ big_h(a) )
<=> ( big_g(a)
| ~ big_i(b)
| ~ big_h(a)
| ~ big_h(b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ big_h(Y)
| ~ big_i(Y)
| big_g(X)
| ~ big_h(X) )
| ~ big_h(b)
| ~ big_i(b)
| big_g(a)
| ~ big_h(a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ big_h(Y)
| ~ big_i(Y)
| big_g(X)
| ~ big_h(X) )
| big_g(a)
| ~ big_i(b)
| ~ big_h(a)
| ~ big_h(b) ) ),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ big_h(Y)
| ~ big_i(Y)
| big_g(X)
| ~ big_h(X) )
| ~ big_h(b)
| ~ big_i(b)
| big_g(a)
| ~ big_h(a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ big_h(Y)
| ~ big_i(Y)
| big_g(X)
| ~ big_h(X) )
| big_g(a)
| ~ big_i(b)
| ~ big_h(a)
| ~ big_h(b) ) ),
inference(transitivity,[status(thm)],[57,55]) ).
tff(59,plain,
( ~ ! [Y: $i,X: $i] :
( ~ big_h(Y)
| ~ big_i(Y)
| big_g(X)
| ~ big_h(X) )
| ~ big_h(b)
| ~ big_i(b)
| big_g(a)
| ~ big_h(a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
( ~ ! [Y: $i,X: $i] :
( ~ big_h(Y)
| ~ big_i(Y)
| big_g(X)
| ~ big_h(X) )
| big_g(a)
| ~ big_i(b)
| ~ big_h(a)
| ~ big_h(b) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
$false,
inference(unit_resolution,[status(thm)],[60,54,51,3,41,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN057-1 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:27:24 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Unsatisfiable
% 0.11/0.36 % SZS output start Proof
% See solution above
% 0.11/0.36 % E exiting
%------------------------------------------------------------------------------