%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN149-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:38:21 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 32 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 143 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 199 ( 97 ~; 85 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 94 ( 85 !; 0 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
tff(n1_type,type,
n1: ( $i * $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(e_type,type,
e: $i ).
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(1,plain,
^ [I: $i,A: $i,J: $i,H: $i] :
refl(( ( ~ m0(I,J,H)
| ~ m0(J,A,A)
| n1(H,H,I) )
<=> ( ~ m0(I,J,H)
| ~ m0(J,A,A)
| n1(H,H,I) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(I,J,H)
| ~ m0(J,A,A)
| n1(H,H,I) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(I,J,H)
| ~ m0(J,A,A)
| n1(H,H,I) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(I,J,H)
| ~ m0(J,A,A)
| n1(H,H,I) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(I,J,H)
| ~ m0(J,A,A)
| n1(H,H,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [I: $i,A: $i,J: $i,H: $i] :
trans(monotonicity(rewrite(( ( n1(H,H,I)
| ~ m0(J,A,A) )
<=> ( ~ m0(J,A,A)
| n1(H,H,I) ) )),
( ( n1(H,H,I)
| ~ m0(J,A,A)
| ~ m0(I,J,H) )
<=> ( ~ m0(J,A,A)
| n1(H,H,I)
| ~ m0(I,J,H) ) )),
rewrite(( ( ~ m0(J,A,A)
| n1(H,H,I)
| ~ m0(I,J,H) )
<=> ( ~ m0(I,J,H)
| ~ m0(J,A,A)
| n1(H,H,I) ) )),
( ( n1(H,H,I)
| ~ m0(J,A,A)
| ~ m0(I,J,H) )
<=> ( ~ m0(I,J,H)
| ~ m0(J,A,A)
| n1(H,H,I) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( n1(H,H,I)
| ~ m0(J,A,A)
| ~ m0(I,J,H) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(I,J,H)
| ~ m0(J,A,A)
| n1(H,H,I) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [I: $i,A: $i,J: $i,H: $i] :
( n1(H,H,I)
| ~ m0(J,A,A)
| ~ m0(I,J,H) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_059) ).
tff(7,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(I,J,H)
| ~ m0(J,A,A)
| n1(H,H,I) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(I,J,H)
| ~ m0(J,A,A)
| n1(H,H,I) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(I,J,H)
| ~ m0(J,A,A)
| n1(H,H,I) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(I,J,H)
| ~ m0(J,A,A)
| n1(H,H,I) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( m0(b,a,a)
<=> m0(b,a,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
m0(b,a,a),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_38) ).
tff(13,plain,
m0(b,a,a),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( m0(b,b,e)
<=> m0(b,b,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
m0(b,b,e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_31) ).
tff(16,plain,
m0(b,b,e),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(I,J,H)
| ~ m0(J,A,A)
| n1(H,H,I) )
| ~ m0(b,a,a)
| ~ m0(b,b,e)
| n1(e,e,b) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(I,J,H)
| ~ m0(J,A,A)
| n1(H,H,I) )
| ~ m0(b,a,a)
| ~ m0(b,b,e)
| n1(e,e,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( ~ m0(b,b,e)
| ~ m0(b,a,a)
| n1(e,e,b) )
<=> ( ~ m0(b,a,a)
| ~ m0(b,b,e)
| n1(e,e,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(I,J,H)
| ~ m0(J,A,A)
| n1(H,H,I) )
| ~ m0(b,b,e)
| ~ m0(b,a,a)
| n1(e,e,b) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(I,J,H)
| ~ m0(J,A,A)
| n1(H,H,I) )
| ~ m0(b,a,a)
| ~ m0(b,b,e)
| n1(e,e,b) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(I,J,H)
| ~ m0(J,A,A)
| n1(H,H,I) )
| ~ m0(b,b,e)
| ~ m0(b,a,a)
| n1(e,e,b) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(I,J,H)
| ~ m0(J,A,A)
| n1(H,H,I) )
| ~ m0(b,a,a)
| ~ m0(b,b,e)
| n1(e,e,b) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(I,J,H)
| ~ m0(J,A,A)
| n1(H,H,I) )
| ~ m0(b,b,e)
| ~ m0(b,a,a)
| n1(e,e,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(I,J,H)
| ~ m0(J,A,A)
| n1(H,H,I) )
| ~ m0(b,a,a)
| ~ m0(b,b,e)
| n1(e,e,b) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
n1(e,e,b),
inference(unit_resolution,[status(thm)],[22,16,13,10]) ).
tff(24,plain,
^ [X: $i] :
refl(( ~ n1(e,e,X)
<=> ~ n1(e,e,X) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [X: $i] : ~ n1(e,e,X)
<=> ! [X: $i] : ~ n1(e,e,X) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [X: $i] : ~ n1(e,e,X)
<=> ! [X: $i] : ~ n1(e,e,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
! [X: $i] : ~ n1(e,e,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(28,plain,
! [X: $i] : ~ n1(e,e,X),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [X: $i] : ~ n1(e,e,X),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [X: $i] : ~ n1(e,e,X),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ~ ! [X: $i] : ~ n1(e,e,X)
| ~ n1(e,e,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
$false,
inference(unit_resolution,[status(thm)],[31,30,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN149-1 : TPTP v9.0.0. Released v1.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n016.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 12:29:17 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46 % SZS output start Proof
% See solution above
% 0.19/0.48 % E exiting
%------------------------------------------------------------------------------