%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN166-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:38:24 AM UTC 2025
% Result : Unsatisfiable 0.61s 0.85s
% Output : Proof 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 29
% Syntax : Number of formulae : 64 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 270 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 369 ( 172 ~; 167 |; 0 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 126 ( 117 !; 0 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(l0_type,type,
l0: $i > $o ).
tff(r0_type,type,
r0: $i > $o ).
tff(1,plain,
^ [X: $i] :
refl(( m0(a,X,a)
<=> m0(a,X,a) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : m0(a,X,a)
<=> ! [X: $i] : m0(a,X,a) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : m0(a,X,a)
<=> ! [X: $i] : m0(a,X,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : m0(a,X,a),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_12) ).
tff(5,plain,
! [X: $i] : m0(a,X,a),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : m0(a,X,a),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : m0(a,X,a),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : m0(a,X,a)
| m0(a,b,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
m0(a,b,a),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ p1(a,b,b)
<=> ~ p1(a,b,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
~ p1(a,b,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(12,plain,
~ p1(a,b,b),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [I: $i,A: $i,J: $i,H: $i] :
refl(( ( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
<=> ( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
^ [I: $i,A: $i,J: $i,H: $i] :
trans(monotonicity(rewrite(( ( p1(H,I,J)
| ~ m0(J,H,A) )
<=> ( ~ m0(J,H,A)
| p1(H,I,J) ) )),
( ( p1(H,I,J)
| ~ m0(J,H,A)
| ~ p1(J,H,A) )
<=> ( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ) )),
rewrite(( ( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
<=> ( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ) )),
( ( p1(H,I,J)
| ~ m0(J,H,A)
| ~ p1(J,H,A) )
<=> ( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( p1(H,I,J)
| ~ m0(J,H,A)
| ~ p1(J,H,A) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [I: $i,A: $i,J: $i,H: $i] :
( p1(H,I,J)
| ~ m0(J,H,A)
| ~ p1(J,H,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_082) ).
tff(19,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( m0(b,a,a)
<=> m0(b,a,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
m0(b,a,a),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_38) ).
tff(25,plain,
m0(b,a,a),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(a,b,b)
| ~ m0(b,a,a)
| ~ p1(b,a,a) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(a,b,b)
| ~ m0(b,a,a)
| ~ p1(b,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ( ~ m0(b,a,a)
| p1(a,b,b)
| ~ p1(b,a,a) )
<=> ( p1(a,b,b)
| ~ m0(b,a,a)
| ~ p1(b,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| ~ m0(b,a,a)
| p1(a,b,b)
| ~ p1(b,a,a) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(a,b,b)
| ~ m0(b,a,a)
| ~ p1(b,a,a) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| ~ m0(b,a,a)
| p1(a,b,b)
| ~ p1(b,a,a) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(a,b,b)
| ~ m0(b,a,a)
| ~ p1(b,a,a) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| ~ m0(b,a,a)
| p1(a,b,b)
| ~ p1(b,a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(a,b,b)
| ~ m0(b,a,a)
| ~ p1(b,a,a) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
~ p1(b,a,a),
inference(unit_resolution,[status(thm)],[31,25,22,12]) ).
tff(33,plain,
( l0(a)
<=> l0(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
l0(a),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_20) ).
tff(35,plain,
l0(a),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
( ( ~ l0(a)
| p1(a,a,a) )
<=> ( ~ l0(a)
| p1(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
( ( p1(a,a,a)
| ~ l0(a) )
<=> ( ~ l0(a)
| p1(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
( p1(a,a,a)
| ~ l0(a) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_088) ).
tff(39,plain,
( ~ l0(a)
| p1(a,a,a) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ l0(a)
| p1(a,a,a) ),
inference(modus_ponens,[status(thm)],[39,36]) ).
tff(41,plain,
p1(a,a,a),
inference(unit_resolution,[status(thm)],[40,35]) ).
tff(42,plain,
( r0(b)
<=> r0(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
r0(b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_9) ).
tff(44,plain,
r0(b),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
( ( ~ r0(b)
| p1(a,b,a)
| ~ p1(a,a,a) )
<=> ( ~ r0(b)
| p1(a,b,a)
| ~ p1(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ( ~ r0(b)
| p1(a,b,a)
| ~ p1(a,a,a) )
<=> ( ~ r0(b)
| p1(a,b,a)
| ~ p1(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ( p1(a,b,a)
| ~ r0(b) )
<=> ( ~ r0(b)
| p1(a,b,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ( p1(a,b,a)
| ~ r0(b)
| ~ p1(a,a,a) )
<=> ( ~ r0(b)
| p1(a,b,a)
| ~ p1(a,a,a) ) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ( p1(a,b,a)
| ~ r0(b)
| ~ p1(a,a,a) )
<=> ( ~ r0(b)
| p1(a,b,a)
| ~ p1(a,a,a) ) ),
inference(transitivity,[status(thm)],[48,46]) ).
tff(50,axiom,
( p1(a,b,a)
| ~ r0(b)
| ~ p1(a,a,a) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_087) ).
tff(51,plain,
( ~ r0(b)
| p1(a,b,a)
| ~ p1(a,a,a) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( ~ r0(b)
| p1(a,b,a)
| ~ p1(a,a,a) ),
inference(modus_ponens,[status(thm)],[51,45]) ).
tff(53,plain,
( ~ r0(b)
| p1(a,b,a)
| ~ p1(a,a,a) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,plain,
( ~ r0(b)
| p1(a,b,a)
| ~ p1(a,a,a) ),
inference(modus_ponens,[status(thm)],[53,45]) ).
tff(55,plain,
( ~ r0(b)
| p1(a,b,a)
| ~ p1(a,a,a) ),
inference(modus_ponens,[status(thm)],[54,45]) ).
tff(56,plain,
( p1(a,b,a)
| ~ p1(a,a,a) ),
inference(unit_resolution,[status(thm)],[55,44]) ).
tff(57,plain,
p1(a,b,a),
inference(unit_resolution,[status(thm)],[56,41]) ).
tff(58,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(b,a,a)
| ~ p1(a,b,a)
| ~ m0(a,b,a) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(b,a,a)
| ~ p1(a,b,a)
| ~ m0(a,b,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ( ~ m0(a,b,a)
| p1(b,a,a)
| ~ p1(a,b,a) )
<=> ( p1(b,a,a)
| ~ p1(a,b,a)
| ~ m0(a,b,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| ~ m0(a,b,a)
| p1(b,a,a)
| ~ p1(a,b,a) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(b,a,a)
| ~ p1(a,b,a)
| ~ m0(a,b,a) ) ),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| ~ m0(a,b,a)
| p1(b,a,a)
| ~ p1(a,b,a) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(b,a,a)
| ~ p1(a,b,a)
| ~ m0(a,b,a) ) ),
inference(transitivity,[status(thm)],[60,58]) ).
tff(62,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| ~ m0(a,b,a)
| p1(b,a,a)
| ~ p1(a,b,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(b,a,a)
| ~ p1(a,b,a)
| ~ m0(a,b,a) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
$false,
inference(unit_resolution,[status(thm)],[63,22,57,32,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN166-1 : TPTP v9.0.0. Released v1.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n015.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 12:29:11 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.61/0.85 % SZS status Unsatisfiable
% 0.61/0.85 % SZS output start Proof
% See solution above
% 0.61/0.86 % E exiting
%------------------------------------------------------------------------------