%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM025-1 : TPTP v9.0.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:18:42 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 28 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 141 ( 71 ~; 57 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 8 ( 8 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 : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 58 ( 54 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
tff(less_type,type,
less: ( $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(1,plain,
( less(b,a)
<=> less(b,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
less(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_not_less_than_a) ).
tff(3,plain,
less(b,a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( less(a,b)
<=> less(a,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
less(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_less_than_b) ).
tff(6,plain,
less(a,b),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) )
<=> ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,plain,
( ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) )
<=> ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,plain,
^ [B: $i,A: $i,C: $i] :
trans(monotonicity(rewrite(( ( ~ less(A,B)
| ~ less(C,A) )
<=> ( ~ less(C,A)
| ~ less(A,B) ) )),
( ( ~ less(A,B)
| ~ less(C,A)
| less(C,B) )
<=> ( ~ less(C,A)
| ~ less(A,B)
| less(C,B) ) )),
rewrite(( ( ~ less(C,A)
| ~ less(A,B)
| less(C,B) )
<=> ( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ) )),
( ( ~ less(A,B)
| ~ less(C,A)
| less(C,B) )
<=> ( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| ~ less(C,A)
| less(C,B) )
<=> ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,axiom,
! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| ~ less(C,A)
| less(C,B) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-1.ax',transitivity_of_less) ).
tff(12,plain,
! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
inference(modus_ponens,[status(thm)],[14,7]) ).
tff(16,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) )
| less(a,a)
| ~ less(a,b)
| ~ less(b,a) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) )
| less(a,a)
| ~ less(a,b)
| ~ less(b,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) )
| less(a,a)
| ~ less(a,b)
| ~ less(b,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) )
| less(a,a)
| ~ less(a,b)
| ~ less(b,a) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
less(a,a),
inference(unit_resolution,[status(thm)],[18,15,6,3]) ).
tff(20,plain,
^ [A: $i] :
refl(( ~ less(A,A)
<=> ~ less(A,A) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [A: $i] : ~ less(A,A)
<=> ! [A: $i] : ~ less(A,A) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [A: $i] : ~ less(A,A)
<=> ! [A: $i] : ~ less(A,A) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [A: $i] : ~ less(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_number_less_than_itself) ).
tff(24,plain,
! [A: $i] : ~ less(A,A),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [A: $i] : ~ less(A,A),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [A: $i] : ~ less(A,A),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [A: $i] : ~ less(A,A)
| ~ less(a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
$false,
inference(unit_resolution,[status(thm)],[27,26,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM025-1 : TPTP v9.0.0. Bugfixed v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 00:00:18 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
%------------------------------------------------------------------------------