%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN236-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:38:33 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 19
% Syntax : Number of formulae : 40 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 172 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 230 ( 107 ~; 103 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 68 ( 62 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
tff(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(r0_type,type,
r0: $i > $o ).
tff(l3_type,type,
l3: ( $i * $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/sandbox2/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/sandbox2/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/sandbox2/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,
( ~ l3(e,e)
<=> ~ l3(e,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
~ l3(e,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(26,plain,
~ l3(e,e),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,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(28,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)],[27]) ).
tff(29,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(30,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(31,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)],[30]) ).
tff(32,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(33,plain,
! [H: $i,G: $i] :
( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [H: $i,G: $i] :
( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [H: $i,G: $i] :
( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [H: $i,G: $i] :
( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
( ( ~ ! [H: $i,G: $i] :
( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) )
| ~ r0(e)
| ~ p2(e,e,e)
| l3(e,e) )
<=> ( ~ ! [H: $i,G: $i] :
( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) )
| ~ r0(e)
| ~ p2(e,e,e)
| l3(e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [H: $i,G: $i] :
( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) )
| ~ r0(e)
| ~ p2(e,e,e)
| l3(e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [H: $i,G: $i] :
( ~ r0(G)
| ~ p2(G,H,G)
| l3(G,H) )
| ~ r0(e)
| ~ p2(e,e,e)
| l3(e,e) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
$false,
inference(unit_resolution,[status(thm)],[39,10,36,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SYN236-1 : TPTP v9.0.0. Released v1.1.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n005.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Jun 20 12:29:35 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.19/0.44 % SZS status Unsatisfiable
% 0.19/0.44 % SZS output start Proof
% See solution above
% 0.19/0.46 % E exiting
%------------------------------------------------------------------------------