%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN223-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:38:32 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.47s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 27
% Syntax : Number of formulae : 61 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 233 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 308 ( 146 ~; 134 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 10 ( 10 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 : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 95 ( 86 !; 0 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
tff(l3_type,type,
l3: ( $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(r0_type,type,
r0: $i > $o ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(k0_type,type,
k0: $i > $o ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,axiom,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_176) ).
tff(5,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( r0(e)
<=> r0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
r0(e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_13) ).
tff(10,plain,
r0(e),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ r0(e)
| m1(e,e,e) )
<=> ( ~ r0(e)
| m1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ( m1(e,e,e)
| ~ r0(e) )
<=> ( ~ r0(e)
| m1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
( m1(e,e,e)
| ~ r0(e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_012) ).
tff(14,plain,
( ~ r0(e)
| m1(e,e,e) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
( ~ r0(e)
| m1(e,e,e) ),
inference(modus_ponens,[status(thm)],[14,11]) ).
tff(16,plain,
m1(e,e,e),
inference(unit_resolution,[status(thm)],[15,10]) ).
tff(17,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,e,e)
| ~ m1(e,e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
p2(e,e,e),
inference(unit_resolution,[status(thm)],[22,16,7]) ).
tff(24,plain,
^ [D: $i,E: $i,F: $i] :
refl(( ( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
<=> ( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
<=> ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
<=> ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
^ [D: $i,E: $i,F: $i] :
trans(monotonicity(rewrite(( ( l3(D,D)
| ~ p1(D,D,E) )
<=> ( ~ p1(D,D,E)
| l3(D,D) ) )),
( ( l3(D,D)
| ~ p1(D,D,E)
| ~ p2(E,F,D) )
<=> ( ~ p1(D,D,E)
| l3(D,D)
| ~ p2(E,F,D) ) )),
rewrite(( ( ~ p1(D,D,E)
| l3(D,D)
| ~ p2(E,F,D) )
<=> ( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ) )),
( ( l3(D,D)
| ~ p1(D,D,E)
| ~ p2(E,F,D) )
<=> ( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [D: $i,E: $i,F: $i] :
( l3(D,D)
| ~ p1(D,D,E)
| ~ p2(E,F,D) )
<=> ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [D: $i,E: $i,F: $i] :
( l3(D,D)
| ~ p1(D,D,E)
| ~ p2(E,F,D) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_216) ).
tff(30,plain,
! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( k0(e)
<=> k0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
k0(e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_28) ).
tff(36,plain,
k0(e),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
( ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ( p1(e,e,e)
| ~ r0(e) )
<=> ( ~ r0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) ) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(transitivity,[status(thm)],[40,38]) ).
tff(42,axiom,
( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_090) ).
tff(43,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[43,37]) ).
tff(45,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[45,37]) ).
tff(47,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[46,37]) ).
tff(48,plain,
p1(e,e,e),
inference(unit_resolution,[status(thm)],[47,10,36]) ).
tff(49,plain,
( ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| ~ p2(e,e,e)
| ~ p1(e,e,e)
| l3(e,e) )
<=> ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| ~ p2(e,e,e)
| ~ p1(e,e,e)
| l3(e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| ~ p2(e,e,e)
| ~ p1(e,e,e)
| l3(e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| ~ p2(e,e,e)
| ~ p1(e,e,e)
| l3(e,e) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
l3(e,e),
inference(unit_resolution,[status(thm)],[51,48,33,23]) ).
tff(53,plain,
^ [X: $i] :
refl(( ~ l3(X,e)
<=> ~ l3(X,e) )),
inference(bind,[status(th)],[]) ).
tff(54,plain,
( ! [X: $i] : ~ l3(X,e)
<=> ! [X: $i] : ~ l3(X,e) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [X: $i] : ~ l3(X,e)
<=> ! [X: $i] : ~ l3(X,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
! [X: $i] : ~ l3(X,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(57,plain,
! [X: $i] : ~ l3(X,e),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [X: $i] : ~ l3(X,e),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [X: $i] : ~ l3(X,e),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
( ~ ! [X: $i] : ~ l3(X,e)
| ~ l3(e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
$false,
inference(unit_resolution,[status(thm)],[60,59,52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN223-1 : TPTP v9.0.0. Released v1.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 12:29:23 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.47 % SZS status Unsatisfiable
% 0.19/0.47 % SZS output start Proof
% See solution above
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------