%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN251-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:38:35 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 23 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 103 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 136 ( 64 ~; 60 |; 0 &)
% ( 12 <=>; 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 : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 51 ( 45 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
tff(m1_type,type,
m1: ( $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(l0_type,type,
l0: $i > $o ).
tff(a_type,type,
a: $i ).
tff(1,plain,
( ~ m1(e,b,b)
<=> ~ m1(e,b,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ m1(e,b,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(3,plain,
~ m1(e,b,b),
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/sandbox/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,
( m0(b,b,e)
<=> m0(b,b,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
m0(b,b,e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_31) ).
tff(16,plain,
m0(b,b,e),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( l0(a)
<=> l0(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
l0(a),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_20) ).
tff(19,plain,
l0(a),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( ( ~ ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
| ~ l0(a)
| ~ m0(b,b,e)
| m1(e,b,b) )
<=> ( ~ ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
| ~ l0(a)
| ~ m0(b,b,e)
| m1(e,b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
| ~ l0(a)
| ~ m0(b,b,e)
| m1(e,b,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
| ~ l0(a)
| ~ m0(b,b,e)
| m1(e,b,b) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,19,16,13,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN251-1 : TPTP v9.0.0. Released v1.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.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 12:31:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46 % SZS output start Proof
% See solution above
% 0.19/0.47 % E exiting
%------------------------------------------------------------------------------