%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN125-1 : 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 05:38:18 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 26
% Syntax : Number of formulae : 54 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 266 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 367 ( 172 ~; 166 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 17 ( 17 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 102 ( 92 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(e_type,type,
e: $i ).
tff(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(l3_type,type,
l3: ( $i * $i ) > $o ).
tff(r0_type,type,
r0: $i > $o ).
tff(k0_type,type,
k0: $i > $o ).
tff(l0_type,type,
l0: $i > $o ).
tff(1,plain,
( ~ l3(e,c)
<=> ~ l3(e,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ l3(e,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(3,plain,
~ l3(e,c),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [H: $i,G: $i] :
refl(( ( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) )
<=> ( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [H: $i,G: $i] :
( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) )
<=> ! [H: $i,G: $i] :
( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [H: $i,G: $i] :
( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) )
<=> ! [H: $i,G: $i] :
( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [H: $i,G: $i] :
trans(monotonicity(rewrite(( ( l3(G,H)
| ~ r0(G) )
<=> ( ~ r0(G)
| l3(G,H) ) )),
( ( l3(G,H)
| ~ r0(G)
| ~ p2(G,H,G) )
<=> ( ~ r0(G)
| l3(G,H)
| ~ p2(G,H,G) ) )),
rewrite(( ( ~ r0(G)
| l3(G,H)
| ~ p2(G,H,G) )
<=> ( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) ) )),
( ( l3(G,H)
| ~ r0(G)
| ~ p2(G,H,G) )
<=> ( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [H: $i,G: $i] :
( l3(G,H)
| ~ r0(G)
| ~ p2(G,H,G) )
<=> ! [H: $i,G: $i] :
( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [H: $i,G: $i] :
( l3(G,H)
| ~ r0(G)
| ~ p2(G,H,G) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_215) ).
tff(10,plain,
! [H: $i,G: $i] :
( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [H: $i,G: $i] :
( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [H: $i,G: $i] :
( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [H: $i,G: $i] :
( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( r0(e)
<=> r0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
r0(e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_13) ).
tff(16,plain,
r0(e),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [H: $i,G: $i] :
( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) )
| ~ r0(e)
| ~ p2(e,c,e)
| l3(e,c) )
<=> ( ~ ! [H: $i,G: $i] :
( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) )
| ~ r0(e)
| ~ p2(e,c,e)
| l3(e,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [H: $i,G: $i] :
( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) )
| ~ r0(e)
| ~ p2(e,c,e)
| l3(e,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [H: $i,G: $i] :
( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) )
| ~ r0(e)
| ~ p2(e,c,e)
| l3(e,c) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ p2(e,c,e),
inference(unit_resolution,[status(thm)],[19,16,13,3]) ).
tff(21,plain,
^ [D: $i,E: $i] :
refl(( ( p2(D,E,D)
| ~ m1(E,D,E) )
<=> ( p2(D,E,D)
| ~ m1(E,D,E) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
<=> ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
<=> ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_176) ).
tff(25,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,c,e)
| ~ m1(c,e,c) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,c,e)
| ~ m1(c,e,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,c,e)
| ~ m1(c,e,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,c,e)
| ~ m1(c,e,c) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
~ m1(c,e,c),
inference(unit_resolution,[status(thm)],[30,27,20]) ).
tff(32,plain,
^ [I: $i,J: $i] :
refl(( ( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) )
<=> ( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [I: $i,J: $i] :
( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) )
<=> ! [I: $i,J: $i] :
( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [I: $i,J: $i] :
( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) )
<=> ! [I: $i,J: $i] :
( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [I: $i,J: $i] :
trans(monotonicity(rewrite(( ( m1(I,J,I)
| ~ l0(I) )
<=> ( m1(I,J,I)
| ~ l0(I) ) )),
( ( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) )
<=> ( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) ) )),
rewrite(( ( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) )
<=> ( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) ) )),
( ( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) )
<=> ( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [I: $i,J: $i] :
( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) )
<=> ! [I: $i,J: $i] :
( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [I: $i,J: $i] :
( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_021) ).
tff(38,plain,
! [I: $i,J: $i] :
( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [I: $i,J: $i] :
( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [I: $i,J: $i] :
( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [I: $i,J: $i] :
( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( k0(e)
<=> k0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
k0(e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_28) ).
tff(44,plain,
k0(e),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
( l0(c)
<=> l0(c) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
l0(c),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_24) ).
tff(47,plain,
l0(c),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
( ( ~ ! [I: $i,J: $i] :
( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) )
| ~ l0(c)
| ~ k0(e)
| m1(c,e,c) )
<=> ( ~ ! [I: $i,J: $i] :
( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) )
| ~ l0(c)
| ~ k0(e)
| m1(c,e,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ( m1(c,e,c)
| ~ l0(c)
| ~ k0(e) )
<=> ( ~ l0(c)
| ~ k0(e)
| m1(c,e,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ( ~ ! [I: $i,J: $i] :
( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) )
| m1(c,e,c)
| ~ l0(c)
| ~ k0(e) )
<=> ( ~ ! [I: $i,J: $i] :
( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) )
| ~ l0(c)
| ~ k0(e)
| m1(c,e,c) ) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ( ~ ! [I: $i,J: $i] :
( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) )
| m1(c,e,c)
| ~ l0(c)
| ~ k0(e) )
<=> ( ~ ! [I: $i,J: $i] :
( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) )
| ~ l0(c)
| ~ k0(e)
| m1(c,e,c) ) ),
inference(transitivity,[status(thm)],[50,48]) ).
tff(52,plain,
( ~ ! [I: $i,J: $i] :
( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) )
| m1(c,e,c)
| ~ l0(c)
| ~ k0(e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [I: $i,J: $i] :
( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) )
| ~ l0(c)
| ~ k0(e)
| m1(c,e,c) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
$false,
inference(unit_resolution,[status(thm)],[53,47,44,41,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN125-1 : TPTP v9.0.0. Released v1.1.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 12:28:48 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
% 0.19/0.48 % E exiting
%------------------------------------------------------------------------------