%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN229-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 30
% Syntax : Number of formulae : 66 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 307 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 423 ( 200 ~; 188 |; 0 &)
% ( 35 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 18 ( 18 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 : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 158 ( 143 !; 0 ?; 158 :)
% Comments :
%------------------------------------------------------------------------------
tff(l3_type,type,
l3: ( $i * $i ) > $o ).
tff(c_type,type,
c: $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(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(e_type,type,
e: $i ).
tff(1,plain,
^ [X: $i] :
refl(( ~ l3(c,X)
<=> ~ l3(c,X) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ~ l3(c,X)
<=> ! [X: $i] : ~ l3(c,X) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ~ l3(c,X)
<=> ! [X: $i] : ~ l3(c,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ~ l3(c,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(5,plain,
! [X: $i] : ~ l3(c,X),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ~ l3(c,X),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ~ l3(c,X),
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/sandbox/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(c)
<=> l0(c) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
l0(c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_24) ).
tff(17,plain,
l0(c),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( ( ~ l0(c)
| m1(c,c,c) )
<=> ( ~ l0(c)
| m1(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( m1(c,c,c)
| ~ l0(c) )
<=> ( ~ l0(c)
| m1(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
( m1(c,c,c)
| ~ l0(c) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_020) ).
tff(21,plain,
( ~ l0(c)
| m1(c,c,c) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
( ~ l0(c)
| m1(c,c,c) ),
inference(modus_ponens,[status(thm)],[21,18]) ).
tff(23,plain,
m1(c,c,c),
inference(unit_resolution,[status(thm)],[22,17]) ).
tff(24,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(c,c,c)
| p2(c,c,c) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(c,c,c)
| p2(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( p2(c,c,c)
| ~ m1(c,c,c) )
<=> ( ~ m1(c,c,c)
| p2(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(c,c,c)
| ~ m1(c,c,c) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(c,c,c)
| p2(c,c,c) ) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(c,c,c)
| ~ m1(c,c,c) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(c,c,c)
| p2(c,c,c) ) ),
inference(transitivity,[status(thm)],[26,24]) ).
tff(28,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(c,c,c)
| ~ m1(c,c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(c,c,c)
| p2(c,c,c) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
p2(c,c,c),
inference(unit_resolution,[status(thm)],[29,23,14]) ).
tff(31,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(32,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)],[31]) ).
tff(33,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(34,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(35,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)],[34]) ).
tff(36,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(37,plain,
! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
^ [I: $i,A: $i,J: $i] :
refl(( ( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
<=> ( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
^ [I: $i,A: $i,J: $i] :
trans(monotonicity(rewrite(( ( p1(I,I,I)
| ~ l0(I) )
<=> ( ~ l0(I)
| p1(I,I,I) ) )),
( ( p1(I,I,I)
| ~ l0(I)
| ~ m0(J,A,I) )
<=> ( ~ l0(I)
| p1(I,I,I)
| ~ m0(J,A,I) ) )),
rewrite(( ( ~ l0(I)
| p1(I,I,I)
| ~ m0(J,A,I) )
<=> ( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) )),
( ( p1(I,I,I)
| ~ l0(I)
| ~ m0(J,A,I) )
<=> ( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [I: $i,A: $i,J: $i] :
( p1(I,I,I)
| ~ l0(I)
| ~ m0(J,A,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [I: $i,A: $i,J: $i] :
( p1(I,I,I)
| ~ l0(I)
| ~ m0(J,A,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_086) ).
tff(47,plain,
! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( m0(e,b,c)
<=> m0(e,b,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
m0(e,b,c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_27) ).
tff(53,plain,
m0(e,b,c),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
( ( ~ ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
| ~ l0(c)
| ~ m0(e,b,c)
| p1(c,c,c) )
<=> ( ~ ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
| ~ l0(c)
| ~ m0(e,b,c)
| p1(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
| ~ l0(c)
| ~ m0(e,b,c)
| p1(c,c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
| ~ l0(c)
| ~ m0(e,b,c)
| p1(c,c,c) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
p1(c,c,c),
inference(unit_resolution,[status(thm)],[56,17,53,50]) ).
tff(58,plain,
( ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| l3(c,c)
| ~ p2(c,c,c)
| ~ p1(c,c,c) )
<=> ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| l3(c,c)
| ~ p2(c,c,c)
| ~ p1(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ( ~ p2(c,c,c)
| ~ p1(c,c,c)
| l3(c,c) )
<=> ( l3(c,c)
| ~ p2(c,c,c)
| ~ p1(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
( ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| ~ p2(c,c,c)
| ~ p1(c,c,c)
| l3(c,c) )
<=> ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| l3(c,c)
| ~ p2(c,c,c)
| ~ p1(c,c,c) ) ),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| ~ p2(c,c,c)
| ~ p1(c,c,c)
| l3(c,c) )
<=> ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| l3(c,c)
| ~ p2(c,c,c)
| ~ p1(c,c,c) ) ),
inference(transitivity,[status(thm)],[60,58]) ).
tff(62,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| ~ p2(c,c,c)
| ~ p1(c,c,c)
| l3(c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| l3(c,c)
| ~ p2(c,c,c)
| ~ p1(c,c,c) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
l3(c,c),
inference(unit_resolution,[status(thm)],[63,57,40,30]) ).
tff(65,plain,
( ~ ! [X: $i] : ~ l3(c,X)
| ~ l3(c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
$false,
inference(unit_resolution,[status(thm)],[65,64,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN229-1 : TPTP v9.0.0. Released v1.1.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.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 12:29:39 EDT 2025
% 0.19/0.34 % CPUTime :
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46 % SZS output start Proof
% See solution above
% 0.19/0.48 % E exiting
%------------------------------------------------------------------------------