%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN175-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:38:25 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.45s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 34 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 126 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 164 ( 81 ~; 69 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 71 ( 63 !; 0 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
tff(q2_type,type,
q2: ( $i * $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(n1_type,type,
n1: ( $i * $i * $i ) > $o ).
tff(q0_type,type,
q0: ( $i * $i ) > $o ).
tff(1,plain,
^ [B: $i,D: $i,C: $i] :
refl(( ( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) )
<=> ( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [B: $i,D: $i,C: $i] :
trans(monotonicity(rewrite(( ( q2(B,B,B)
| ~ q0(C,B) )
<=> ( ~ q0(C,B)
| q2(B,B,B) ) )),
( ( q2(B,B,B)
| ~ q0(C,B)
| ~ n1(C,B,D) )
<=> ( ~ q0(C,B)
| q2(B,B,B)
| ~ n1(C,B,D) ) )),
rewrite(( ( ~ q0(C,B)
| q2(B,B,B)
| ~ n1(C,B,D) )
<=> ( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ) )),
( ( q2(B,B,B)
| ~ q0(C,B)
| ~ n1(C,B,D) )
<=> ( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [B: $i,D: $i,C: $i] :
( q2(B,B,B)
| ~ q0(C,B)
| ~ n1(C,B,D) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [B: $i,D: $i,C: $i] :
( q2(B,B,B)
| ~ q0(C,B)
| ~ n1(C,B,D) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_178) ).
tff(7,plain,
! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( q0(d,d)
<=> q0(d,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
q0(d,d),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_25) ).
tff(13,plain,
q0(d,d),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( n1(d,d,d)
| ~ q0(d,d) )
<=> ( n1(d,d,d)
| ~ q0(d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
( n1(d,d,d)
| ~ q0(d,d) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_045) ).
tff(16,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[16,14]) ).
tff(18,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[17,14]) ).
tff(19,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[19,14]) ).
tff(21,plain,
n1(d,d,d),
inference(unit_resolution,[status(thm)],[20,13]) ).
tff(22,plain,
( ( ~ ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) )
| ~ q0(d,d)
| ~ n1(d,d,d)
| q2(d,d,d) )
<=> ( ~ ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) )
| ~ q0(d,d)
| ~ n1(d,d,d)
| q2(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) )
| ~ q0(d,d)
| ~ n1(d,d,d)
| q2(d,d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) )
| ~ q0(d,d)
| ~ n1(d,d,d)
| q2(d,d,d) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
q2(d,d,d),
inference(unit_resolution,[status(thm)],[24,13,21,10]) ).
tff(26,plain,
^ [Y: $i,X: $i] :
refl(( ~ q2(X,d,Y)
<=> ~ q2(X,d,Y) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [Y: $i,X: $i] : ~ q2(X,d,Y)
<=> ! [Y: $i,X: $i] : ~ q2(X,d,Y) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [Y: $i,X: $i] : ~ q2(X,d,Y)
<=> ! [Y: $i,X: $i] : ~ q2(X,d,Y) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
! [Y: $i,X: $i] : ~ q2(X,d,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(30,plain,
! [Y: $i,X: $i] : ~ q2(X,d,Y),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [Y: $i,X: $i] : ~ q2(X,d,Y),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [Y: $i,X: $i] : ~ q2(X,d,Y),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ~ ! [Y: $i,X: $i] : ~ q2(X,d,Y)
| ~ q2(d,d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
$false,
inference(unit_resolution,[status(thm)],[33,32,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN175-1 : TPTP v9.0.0. Released v1.1.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n010.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 12:30:42 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.18/0.45 % SZS status Unsatisfiable
% 0.18/0.45 % SZS output start Proof
% See solution above
% 0.18/0.46 % E exiting
%------------------------------------------------------------------------------