%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN136-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:38:19 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.48s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 23
% Syntax : Number of formulae : 52 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 165 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 211 ( 101 ~; 89 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 3 ( 3 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 : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 53 ( 49 !; 0 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
tff(m3_type,type,
m3: ( $i * $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(l0_type,type,
l0: $i > $o ).
tff(s0_type,type,
s0: $i > $o ).
tff(d_type,type,
d: $i ).
tff(1,plain,
^ [I: $i] :
refl(( ( m3(I,I,I)
| ~ p2(I,I,I) )
<=> ( m3(I,I,I)
| ~ p2(I,I,I) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
<=> ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
<=> ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_238) ).
tff(5,plain,
! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,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(9,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)],[8]) ).
tff(10,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(11,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(12,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( l0(a)
<=> l0(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
l0(a),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_20) ).
tff(17,plain,
l0(a),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( s0(d)
<=> s0(d) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
s0(d),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_1) ).
tff(20,plain,
s0(d),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) )
<=> ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) )
<=> ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ( m1(a,a,a)
| ~ l0(a) )
<=> ( m1(a,a,a)
| ~ l0(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) )
<=> ( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) ) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) )
<=> ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ) ),
inference(transitivity,[status(thm)],[24,22]) ).
tff(26,axiom,
( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_023) ).
tff(27,plain,
( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ),
inference(modus_ponens,[status(thm)],[27,21]) ).
tff(29,plain,
( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ),
inference(modus_ponens,[status(thm)],[28,21]) ).
tff(30,plain,
( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ),
inference(modus_ponens,[status(thm)],[29,21]) ).
tff(31,plain,
( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ),
inference(modus_ponens,[status(thm)],[30,21]) ).
tff(32,plain,
m1(a,a,a),
inference(unit_resolution,[status(thm)],[31,20,17]) ).
tff(33,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(a,a,a)
| ~ m1(a,a,a) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(a,a,a)
| ~ m1(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(a,a,a)
| ~ m1(a,a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(a,a,a)
| ~ m1(a,a,a) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
p2(a,a,a),
inference(unit_resolution,[status(thm)],[35,32,14]) ).
tff(37,plain,
( ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(a,a,a)
| m3(a,a,a) )
<=> ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(a,a,a)
| m3(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ( m3(a,a,a)
| ~ p2(a,a,a) )
<=> ( ~ p2(a,a,a)
| m3(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| m3(a,a,a)
| ~ p2(a,a,a) )
<=> ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(a,a,a)
| m3(a,a,a) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| m3(a,a,a)
| ~ p2(a,a,a) )
<=> ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(a,a,a)
| m3(a,a,a) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
tff(41,plain,
( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| m3(a,a,a)
| ~ p2(a,a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(a,a,a)
| m3(a,a,a) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
m3(a,a,a),
inference(unit_resolution,[status(thm)],[42,36,7]) ).
tff(44,plain,
^ [X: $i] :
refl(( ~ m3(X,a,a)
<=> ~ m3(X,a,a) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [X: $i] : ~ m3(X,a,a)
<=> ! [X: $i] : ~ m3(X,a,a) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [X: $i] : ~ m3(X,a,a)
<=> ! [X: $i] : ~ m3(X,a,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
! [X: $i] : ~ m3(X,a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(48,plain,
! [X: $i] : ~ m3(X,a,a),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [X: $i] : ~ m3(X,a,a),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [X: $i] : ~ m3(X,a,a),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
( ~ ! [X: $i] : ~ m3(X,a,a)
| ~ m3(a,a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
$false,
inference(unit_resolution,[status(thm)],[51,50,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYN136-1 : TPTP v9.0.0. Released v1.1.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 12:28:23 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.48 % SZS status Unsatisfiable
% 0.21/0.48 % SZS output start Proof
% See solution above
% 0.21/0.49 % E exiting
%------------------------------------------------------------------------------