%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN243-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:38:34 AM UTC 2025
% Result : Unsatisfiable 0.42s 0.58s
% Output : Proof 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 29 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 141 ( 66 ~; 61 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 71 ( 63 !; 0 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(d_type,type,
d: $i ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(l0_type,type,
l0: $i > $o ).
tff(c_type,type,
c: $i ).
tff(1,plain,
( ~ m1(a,d,d)
<=> ~ m1(a,d,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ m1(a,d,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(3,plain,
~ m1(a,d,d),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [B: $i,D: $i,C: $i] :
refl(( ( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
<=> ( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [B: $i,D: $i,C: $i] :
trans(monotonicity(rewrite(( ( m1(B,C,C)
| ~ l0(D) )
<=> ( ~ l0(D)
| m1(B,C,C) ) )),
( ( m1(B,C,C)
| ~ l0(D)
| ~ m0(C,C,B) )
<=> ( ~ l0(D)
| m1(B,C,C)
| ~ m0(C,C,B) ) )),
rewrite(( ( ~ l0(D)
| m1(B,C,C)
| ~ m0(C,C,B) )
<=> ( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ) )),
( ( m1(B,C,C)
| ~ l0(D)
| ~ m0(C,C,B) )
<=> ( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [B: $i,D: $i,C: $i] :
( m1(B,C,C)
| ~ l0(D)
| ~ m0(C,C,B) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [B: $i,D: $i,C: $i] :
( m1(B,C,C)
| ~ l0(D)
| ~ m0(C,C,B) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_015) ).
tff(10,plain,
! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( l0(c)
<=> l0(c) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
l0(c),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_24) ).
tff(16,plain,
l0(c),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
| ~ l0(c)
| ~ m0(d,d,a)
| m1(a,d,d) )
<=> ( ~ ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
| ~ l0(c)
| ~ m0(d,d,a)
| m1(a,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
| ~ l0(c)
| ~ m0(d,d,a)
| m1(a,d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
| ~ l0(c)
| ~ m0(d,d,a)
| m1(a,d,d) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ m0(d,d,a),
inference(unit_resolution,[status(thm)],[19,16,13,3]) ).
tff(21,plain,
^ [Y: $i,X: $i] :
refl(( m0(X,d,Y)
<=> m0(X,d,Y) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [Y: $i,X: $i] : m0(X,d,Y)
<=> ! [Y: $i,X: $i] : m0(X,d,Y) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Y: $i,X: $i] : m0(X,d,Y)
<=> ! [Y: $i,X: $i] : m0(X,d,Y) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [Y: $i,X: $i] : m0(X,d,Y),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_19) ).
tff(25,plain,
! [Y: $i,X: $i] : m0(X,d,Y),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Y: $i,X: $i] : m0(X,d,Y),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Y: $i,X: $i] : m0(X,d,Y),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [Y: $i,X: $i] : m0(X,d,Y)
| m0(d,d,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,27,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN243-1 : TPTP v9.0.0. Released v1.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.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 12:29:56 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.42/0.58 % SZS status Unsatisfiable
% 0.42/0.58 % SZS output start Proof
% See solution above
% 0.42/0.59 % E exiting
%------------------------------------------------------------------------------