%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN099-1.003 : TPTP v9.0.0. Bugfixed v1.2.1.
% 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 05:38:14 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 28
% Syntax : Number of formulae : 60 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 242 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 338 ( 163 ~; 151 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 7 ( 7 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; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 61 ( 54 !; 0 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
tff(p_1_3_type,type,
p_1_3: $i > $o ).
tff(a_type,type,
a: $i ).
tff(p_2_3_type,type,
p_2_3: $i > $o ).
tff(p_3_3_type,type,
p_3_3: $i > $o ).
tff(p_2_2_type,type,
p_2_2: $i > $o ).
tff(p_1_2_type,type,
p_1_2: $i > $o ).
tff(p_1_1_type,type,
p_1_1: $i > $o ).
tff(1,plain,
( p_3_3(a)
<=> p_3_3(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
p_3_3(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_t2_5) ).
tff(3,plain,
p_3_3(a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( p_2_2(a)
<=> p_2_2(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
p_2_2(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_t2_3) ).
tff(6,plain,
p_2_2(a),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [X: $i] :
refl(( ( ~ p_2_2(X)
| p_2_3(X)
| ~ p_3_3(X) )
<=> ( ~ p_2_2(X)
| p_2_3(X)
| ~ p_3_3(X) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [X: $i] :
( ~ p_2_2(X)
| p_2_3(X)
| ~ p_3_3(X) )
<=> ! [X: $i] :
( ~ p_2_2(X)
| p_2_3(X)
| ~ p_3_3(X) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [X: $i] :
( ~ p_2_2(X)
| p_2_3(X)
| ~ p_3_3(X) )
<=> ! [X: $i] :
( ~ p_2_2(X)
| p_2_3(X)
| ~ p_3_3(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [X: $i] :
rewrite(( ( p_2_3(X)
| ~ p_3_3(X)
| ~ p_2_2(X) )
<=> ( ~ p_2_2(X)
| p_2_3(X)
| ~ p_3_3(X) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] :
( p_2_3(X)
| ~ p_3_3(X)
| ~ p_2_2(X) )
<=> ! [X: $i] :
( ~ p_2_2(X)
| p_2_3(X)
| ~ p_3_3(X) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [X: $i] :
( p_2_3(X)
| ~ p_3_3(X)
| ~ p_2_2(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s2_type11_5) ).
tff(13,plain,
! [X: $i] :
( ~ p_2_2(X)
| p_2_3(X)
| ~ p_3_3(X) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [X: $i] :
( ~ p_2_2(X)
| p_2_3(X)
| ~ p_3_3(X) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [X: $i] :
( ~ p_2_2(X)
| p_2_3(X)
| ~ p_3_3(X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] :
( ~ p_2_2(X)
| p_2_3(X)
| ~ p_3_3(X) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [X: $i] :
( ~ p_2_2(X)
| p_2_3(X)
| ~ p_3_3(X) )
| ~ p_2_2(a)
| p_2_3(a)
| ~ p_3_3(a) )
<=> ( ~ ! [X: $i] :
( ~ p_2_2(X)
| p_2_3(X)
| ~ p_3_3(X) )
| ~ p_2_2(a)
| p_2_3(a)
| ~ p_3_3(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [X: $i] :
( ~ p_2_2(X)
| p_2_3(X)
| ~ p_3_3(X) )
| ~ p_2_2(a)
| p_2_3(a)
| ~ p_3_3(a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [X: $i] :
( ~ p_2_2(X)
| p_2_3(X)
| ~ p_3_3(X) )
| ~ p_2_2(a)
| p_2_3(a)
| ~ p_3_3(a) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
p_2_3(a),
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
( p_1_1(a)
<=> p_1_1(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
p_1_1(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_t2_1) ).
tff(23,plain,
p_1_1(a),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [X: $i] :
refl(( ( ~ p_1_1(X)
| ~ p_2_2(X)
| p_1_2(X) )
<=> ( ~ p_1_1(X)
| ~ p_2_2(X)
| p_1_2(X) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [X: $i] :
( ~ p_1_1(X)
| ~ p_2_2(X)
| p_1_2(X) )
<=> ! [X: $i] :
( ~ p_1_1(X)
| ~ p_2_2(X)
| p_1_2(X) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [X: $i] :
( ~ p_1_1(X)
| ~ p_2_2(X)
| p_1_2(X) )
<=> ! [X: $i] :
( ~ p_1_1(X)
| ~ p_2_2(X)
| p_1_2(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
^ [X: $i] :
rewrite(( ( p_1_2(X)
| ~ p_2_2(X)
| ~ p_1_1(X) )
<=> ( ~ p_1_1(X)
| ~ p_2_2(X)
| p_1_2(X) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [X: $i] :
( p_1_2(X)
| ~ p_2_2(X)
| ~ p_1_1(X) )
<=> ! [X: $i] :
( ~ p_1_1(X)
| ~ p_2_2(X)
| p_1_2(X) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [X: $i] :
( p_1_2(X)
| ~ p_2_2(X)
| ~ p_1_1(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s2_type11_1) ).
tff(30,plain,
! [X: $i] :
( ~ p_1_1(X)
| ~ p_2_2(X)
| p_1_2(X) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [X: $i] :
( ~ p_1_1(X)
| ~ p_2_2(X)
| p_1_2(X) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [X: $i] :
( ~ p_1_1(X)
| ~ p_2_2(X)
| p_1_2(X) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [X: $i] :
( ~ p_1_1(X)
| ~ p_2_2(X)
| p_1_2(X) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [X: $i] :
( ~ p_1_1(X)
| ~ p_2_2(X)
| p_1_2(X) )
| ~ p_1_1(a)
| ~ p_2_2(a)
| p_1_2(a) )
<=> ( ~ ! [X: $i] :
( ~ p_1_1(X)
| ~ p_2_2(X)
| p_1_2(X) )
| ~ p_1_1(a)
| ~ p_2_2(a)
| p_1_2(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [X: $i] :
( ~ p_1_1(X)
| ~ p_2_2(X)
| p_1_2(X) )
| ~ p_1_1(a)
| ~ p_2_2(a)
| p_1_2(a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [X: $i] :
( ~ p_1_1(X)
| ~ p_2_2(X)
| p_1_2(X) )
| ~ p_1_1(a)
| ~ p_2_2(a)
| p_1_2(a) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
p_1_2(a),
inference(unit_resolution,[status(thm)],[36,33,23,6]) ).
tff(38,plain,
^ [X: $i] :
refl(( ( p_1_3(X)
| ~ p_1_2(X)
| ~ p_2_3(X) )
<=> ( p_1_3(X)
| ~ p_1_2(X)
| ~ p_2_3(X) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [X: $i] :
( p_1_3(X)
| ~ p_1_2(X)
| ~ p_2_3(X) )
<=> ! [X: $i] :
( p_1_3(X)
| ~ p_1_2(X)
| ~ p_2_3(X) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [X: $i] :
( p_1_3(X)
| ~ p_1_2(X)
| ~ p_2_3(X) )
<=> ! [X: $i] :
( p_1_3(X)
| ~ p_1_2(X)
| ~ p_2_3(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
^ [X: $i] :
rewrite(( ( p_1_3(X)
| ~ p_2_3(X)
| ~ p_1_2(X) )
<=> ( p_1_3(X)
| ~ p_1_2(X)
| ~ p_2_3(X) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [X: $i] :
( p_1_3(X)
| ~ p_2_3(X)
| ~ p_1_2(X) )
<=> ! [X: $i] :
( p_1_3(X)
| ~ p_1_2(X)
| ~ p_2_3(X) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,axiom,
! [X: $i] :
( p_1_3(X)
| ~ p_2_3(X)
| ~ p_1_2(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s2_type11_3) ).
tff(44,plain,
! [X: $i] :
( p_1_3(X)
| ~ p_1_2(X)
| ~ p_2_3(X) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [X: $i] :
( p_1_3(X)
| ~ p_1_2(X)
| ~ p_2_3(X) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [X: $i] :
( p_1_3(X)
| ~ p_1_2(X)
| ~ p_2_3(X) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [X: $i] :
( p_1_3(X)
| ~ p_1_2(X)
| ~ p_2_3(X) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( ( ~ ! [X: $i] :
( p_1_3(X)
| ~ p_1_2(X)
| ~ p_2_3(X) )
| p_1_3(a)
| ~ p_1_2(a)
| ~ p_2_3(a) )
<=> ( ~ ! [X: $i] :
( p_1_3(X)
| ~ p_1_2(X)
| ~ p_2_3(X) )
| p_1_3(a)
| ~ p_1_2(a)
| ~ p_2_3(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [X: $i] :
( p_1_3(X)
| ~ p_1_2(X)
| ~ p_2_3(X) )
| p_1_3(a)
| ~ p_1_2(a)
| ~ p_2_3(a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [X: $i] :
( p_1_3(X)
| ~ p_1_2(X)
| ~ p_2_3(X) )
| p_1_3(a)
| ~ p_1_2(a)
| ~ p_2_3(a) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
p_1_3(a),
inference(unit_resolution,[status(thm)],[50,47,37,20]) ).
tff(52,plain,
^ [X: $i] :
refl(( ~ p_1_3(X)
<=> ~ p_1_3(X) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [X: $i] : ~ p_1_3(X)
<=> ! [X: $i] : ~ p_1_3(X) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [X: $i] : ~ p_1_3(X)
<=> ! [X: $i] : ~ p_1_3(X) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,axiom,
! [X: $i] : ~ p_1_3(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s2_goal_1) ).
tff(56,plain,
! [X: $i] : ~ p_1_3(X),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [X: $i] : ~ p_1_3(X),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [X: $i] : ~ p_1_3(X),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
( ~ ! [X: $i] : ~ p_1_3(X)
| ~ p_1_3(a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
$false,
inference(unit_resolution,[status(thm)],[59,58,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN099-1.003 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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 12:28:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------