%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN197-1 : TPTP v9.0.0. Released v1.1.0.
% 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 05:38:28 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of formulae : 23 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 59 ( 28 ~; 23 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 23 ( 21 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(s1_type,type,
s1: $i > $o ).
tff(1,plain,
( ~ s1(b)
<=> ~ s1(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ s1(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(3,plain,
~ s1(b),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [I: $i] :
refl(( ( s1(I)
| ~ p0(I,I) )
<=> ( s1(I)
| ~ p0(I,I) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [I: $i] :
( s1(I)
| ~ p0(I,I) )
<=> ! [I: $i] :
( s1(I)
| ~ p0(I,I) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [I: $i] :
( s1(I)
| ~ p0(I,I) )
<=> ! [I: $i] :
( s1(I)
| ~ p0(I,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [I: $i] :
( s1(I)
| ~ p0(I,I) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_125) ).
tff(8,plain,
! [I: $i] :
( s1(I)
| ~ p0(I,I) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [I: $i] :
( s1(I)
| ~ p0(I,I) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [I: $i] :
( s1(I)
| ~ p0(I,I) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [I: $i] :
( s1(I)
| ~ p0(I,I) )
| s1(b)
| ~ p0(b,b) )
<=> ( ~ ! [I: $i] :
( s1(I)
| ~ p0(I,I) )
| s1(b)
| ~ p0(b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [I: $i] :
( s1(I)
| ~ p0(I,I) )
| s1(b)
| ~ p0(b,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [I: $i] :
( s1(I)
| ~ p0(I,I) )
| s1(b)
| ~ p0(b,b) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ p0(b,b),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [X: $i] :
refl(( p0(b,X)
<=> p0(b,X) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [X: $i] : p0(b,X)
<=> ! [X: $i] : p0(b,X) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [X: $i] : p0(b,X)
<=> ! [X: $i] : p0(b,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [X: $i] : p0(b,X),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_14) ).
tff(19,plain,
! [X: $i] : p0(b,X),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [X: $i] : p0(b,X),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [X: $i] : p0(b,X),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ~ ! [X: $i] : p0(b,X)
| p0(b,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,21,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN197-1 : TPTP v9.0.0. Released v1.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 12:29:18 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.48 % SZS status Unsatisfiable
% 0.20/0.48 % SZS output start Proof
% See solution above
% 0.20/0.48 % E exiting
%------------------------------------------------------------------------------