%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN063-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 33 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 214 ( 0 equ)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 246 ( 79 ~; 148 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 14 ( 14 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; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 42 ( 38 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
tff(big_p_type,type,
big_p: $i > $o ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
( ~ big_p(c)
<=> ~ big_p(c) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ big_p(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
tff(3,plain,
~ big_p(c),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( big_p(a)
<=> big_p(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
big_p(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
tff(6,plain,
big_p(a),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) )
<=> ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,plain,
( ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) )
<=> ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
tff(10,plain,
( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ),
inference(modus_ponens,[status(thm)],[10,7]) ).
tff(12,plain,
( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ),
inference(modus_ponens,[status(thm)],[12,7]) ).
tff(14,plain,
( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ),
inference(modus_ponens,[status(thm)],[13,7]) ).
tff(15,plain,
( ~ big_p(b)
| big_p(c) ),
inference(unit_resolution,[status(thm)],[14,6]) ).
tff(16,plain,
~ big_p(b),
inference(unit_resolution,[status(thm)],[15,3]) ).
tff(17,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) )
<=> ( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) )
<=> ! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) )
<=> ! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
^ [Y: $i,X: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ big_p(a)
| big_p(X) )
<=> ( ~ big_p(a)
| big_p(X) ) )),
( ( ~ big_p(a)
| big_p(X)
| big_p(c) )
<=> ( ~ big_p(a)
| big_p(X)
| big_p(c) ) )),
rewrite(( ( ~ big_p(a)
| big_p(X)
| big_p(c) )
<=> ( ~ big_p(a)
| big_p(c)
| big_p(X) ) )),
( ( ~ big_p(a)
| big_p(X)
| big_p(c) )
<=> ( ~ big_p(a)
| big_p(c)
| big_p(X) ) )),
( ( ~ big_p(a)
| big_p(X)
| big_p(c)
| big_p(Y) )
<=> ( ~ big_p(a)
| big_p(c)
| big_p(X)
| big_p(Y) ) )),
rewrite(( ( ~ big_p(a)
| big_p(c)
| big_p(X)
| big_p(Y) )
<=> ( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) ) )),
( ( ~ big_p(a)
| big_p(X)
| big_p(c)
| big_p(Y) )
<=> ( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(X)
| big_p(c)
| big_p(Y) )
<=> ! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,axiom,
! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(X)
| big_p(c)
| big_p(Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
tff(23,plain,
! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) ),
inference(modus_ponens,[status(thm)],[25,18]) ).
tff(27,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) )
| big_p(b)
| ~ big_p(a)
| big_p(c) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) )
| big_p(b)
| ~ big_p(a)
| big_p(c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ( ~ big_p(a)
| big_p(c)
| big_p(b)
| big_p(b) )
<=> ( big_p(b)
| ~ big_p(a)
| big_p(c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) )
| ~ big_p(a)
| big_p(c)
| big_p(b)
| big_p(b) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) )
| big_p(b)
| ~ big_p(a)
| big_p(c) ) ),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) )
| ~ big_p(a)
| big_p(c)
| big_p(b)
| big_p(b) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) )
| big_p(b)
| ~ big_p(a)
| big_p(c) ) ),
inference(transitivity,[status(thm)],[29,27]) ).
tff(31,plain,
( ~ ! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) )
| ~ big_p(a)
| big_p(c)
| big_p(b)
| big_p(b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) )
| big_p(b)
| ~ big_p(a)
| big_p(c) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
$false,
inference(unit_resolution,[status(thm)],[32,6,26,16,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN063-1 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:27:42 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------