%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN231-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.18s 0.45s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 28
% Syntax : Number of formulae : 65 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 247 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 324 ( 154 ~; 142 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 12 ( 12 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 : 120 ( 108 !; 0 ?; 120 :)
% Comments :
%------------------------------------------------------------------------------
tff(l3_type,type,
l3: ( $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(n1_type,type,
n1: ( $i * $i * $i ) > $o ).
tff(q0_type,type,
q0: ( $i * $i ) > $o ).
tff(1,plain,
^ [X: $i] :
refl(( ~ l3(d,X)
<=> ~ l3(d,X) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ~ l3(d,X)
<=> ! [X: $i] : ~ l3(d,X) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ~ l3(d,X)
<=> ! [X: $i] : ~ l3(d,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ~ l3(d,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(5,plain,
! [X: $i] : ~ l3(d,X),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ~ l3(d,X),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ~ l3(d,X),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
^ [B: $i,C: $i] :
refl(( ( ~ p0(C,B)
| p1(B,B,B) )
<=> ( ~ p0(C,B)
| p1(B,B,B) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
<=> ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
<=> ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
^ [B: $i,C: $i] :
rewrite(( ( p1(B,B,B)
| ~ p0(C,B) )
<=> ( ~ p0(C,B)
| p1(B,B,B) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [B: $i,C: $i] :
( p1(B,B,B)
| ~ p0(C,B) )
<=> ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,axiom,
! [B: $i,C: $i] :
( p1(B,B,B)
| ~ p0(C,B) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_085) ).
tff(14,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(modus_ponens,[status(thm)],[16,9]) ).
tff(18,plain,
( p0(b,d)
<=> p0(b,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
p0(b,d),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_10) ).
tff(20,plain,
p0(b,d),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(b,d)
| p1(d,d,d) )
<=> ( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(b,d)
| p1(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(b,d)
| p1(d,d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(b,d)
| p1(d,d,d) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
p1(d,d,d),
inference(unit_resolution,[status(thm)],[23,20,17]) ).
tff(25,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(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(quant_intro,[status(thm)],[25]) ).
tff(27,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(28,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(29,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)],[28]) ).
tff(30,axiom,
! [D: $i,E: $i,F: $i] :
( l3(D,D)
| ~ p1(D,D,E)
| ~ p2(E,F,D) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_216) ).
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)],[30,29]) ).
tff(32,plain,
! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ),
inference(modus_ponens,[status(thm)],[33,26]) ).
tff(35,plain,
^ [B: $i] :
refl(( ( p2(B,B,B)
| ~ n1(d,d,B) )
<=> ( p2(B,B,B)
| ~ n1(d,d,B) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
<=> ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
<=> ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_153) ).
tff(39,plain,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( q0(d,d)
<=> q0(d,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
q0(d,d),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_25) ).
tff(44,plain,
q0(d,d),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
( ( n1(d,d,d)
| ~ q0(d,d) )
<=> ( n1(d,d,d)
| ~ q0(d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
( n1(d,d,d)
| ~ q0(d,d) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_045) ).
tff(47,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[47,45]) ).
tff(49,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[48,45]) ).
tff(50,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[50,45]) ).
tff(52,plain,
n1(d,d,d),
inference(unit_resolution,[status(thm)],[51,44]) ).
tff(53,plain,
( ( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) )
<=> ( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
p2(d,d,d),
inference(unit_resolution,[status(thm)],[55,52,41]) ).
tff(57,plain,
( ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| l3(d,d)
| ~ p1(d,d,d)
| ~ p2(d,d,d) )
<=> ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| l3(d,d)
| ~ p1(d,d,d)
| ~ p2(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ( ~ p2(d,d,d)
| ~ p1(d,d,d)
| l3(d,d) )
<=> ( l3(d,d)
| ~ p1(d,d,d)
| ~ p2(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| ~ p2(d,d,d)
| ~ p1(d,d,d)
| l3(d,d) )
<=> ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| l3(d,d)
| ~ p1(d,d,d)
| ~ p2(d,d,d) ) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| ~ p2(d,d,d)
| ~ p1(d,d,d)
| l3(d,d) )
<=> ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| l3(d,d)
| ~ p1(d,d,d)
| ~ p2(d,d,d) ) ),
inference(transitivity,[status(thm)],[59,57]) ).
tff(61,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| ~ p2(d,d,d)
| ~ p1(d,d,d)
| l3(d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| l3(d,d)
| ~ p1(d,d,d)
| ~ p2(d,d,d) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
l3(d,d),
inference(unit_resolution,[status(thm)],[62,56,34,24]) ).
tff(64,plain,
( ~ ! [X: $i] : ~ l3(d,X)
| ~ l3(d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
$false,
inference(unit_resolution,[status(thm)],[64,63,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN231-1 : TPTP v9.0.0. Released v1.1.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n002.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:31:02 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.45 % SZS status Unsatisfiable
% 0.18/0.45 % SZS output start Proof
% See solution above
% 0.18/0.47 % E exiting
%------------------------------------------------------------------------------