%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN005-1.010 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:37:56 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 26
% Syntax : Number of formulae : 44 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 574 ( 0 equ)
% Maximal formula atoms : 40 ( 13 avg)
% Number of connectives : 1000 ( 514 ~; 449 |; 0 &)
% ( 37 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 44 ( 44 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 170 ( 150 !; 0 ?; 170 :)
% Comments :
%------------------------------------------------------------------------------
tff(p_10_type,type,
p_10: ( $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(p_9_type,type,
p_9: ( $i * $i ) > $o ).
tff(p_8_type,type,
p_8: ( $i * $i ) > $o ).
tff(p_7_type,type,
p_7: ( $i * $i ) > $o ).
tff(p_6_type,type,
p_6: ( $i * $i ) > $o ).
tff(p_5_type,type,
p_5: ( $i * $i ) > $o ).
tff(p_4_type,type,
p_4: ( $i * $i ) > $o ).
tff(p_3_type,type,
p_3: ( $i * $i ) > $o ).
tff(p_2_type,type,
p_2: ( $i * $i ) > $o ).
tff(p_1_type,type,
p_1: ( $i * $i ) > $o ).
tff(1,plain,
( p_10(a,a)
<=> p_10(a,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
p_10(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_10) ).
tff(3,plain,
p_10(a,a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( p_9(a,a)
<=> p_9(a,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
p_9(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_9) ).
tff(6,plain,
p_9(a,a),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( p_8(a,a)
<=> p_8(a,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
p_8(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_8) ).
tff(9,plain,
p_8(a,a),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
( p_7(a,a)
<=> p_7(a,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
p_7(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_7) ).
tff(12,plain,
p_7(a,a),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( p_6(a,a)
<=> p_6(a,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
p_6(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_6) ).
tff(15,plain,
p_6(a,a),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
( p_5(a,a)
<=> p_5(a,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
p_5(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_5) ).
tff(18,plain,
p_5(a,a),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( p_4(a,a)
<=> p_4(a,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
p_4(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_4) ).
tff(21,plain,
p_4(a,a),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
( p_3(a,a)
<=> p_3(a,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
p_3(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_3) ).
tff(24,plain,
p_3(a,a),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
( p_2(a,a)
<=> p_2(a,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
p_2(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_2) ).
tff(27,plain,
p_2(a,a),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( p_1(a,a)
<=> p_1(a,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
p_1(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_1) ).
tff(30,plain,
p_1(a,a),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
^ [X9: $i,X6: $i,X4: $i,X3: $i,X10: $i,X2: $i,X7: $i,X5: $i,X8: $i,X1: $i] :
refl(( ( ~ p_10(X10,X1)
| ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) )
<=> ( ~ p_10(X10,X1)
| ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [X9: $i,X6: $i,X4: $i,X3: $i,X10: $i,X2: $i,X7: $i,X5: $i,X8: $i,X1: $i] :
( ~ p_10(X10,X1)
| ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) )
<=> ! [X9: $i,X6: $i,X4: $i,X3: $i,X10: $i,X2: $i,X7: $i,X5: $i,X8: $i,X1: $i] :
( ~ p_10(X10,X1)
| ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [X9: $i,X6: $i,X4: $i,X3: $i,X10: $i,X2: $i,X7: $i,X5: $i,X8: $i,X1: $i] :
( ~ p_10(X10,X1)
| ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) )
<=> ! [X9: $i,X6: $i,X4: $i,X3: $i,X10: $i,X2: $i,X7: $i,X5: $i,X8: $i,X1: $i] :
( ~ p_10(X10,X1)
| ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
^ [X9: $i,X6: $i,X4: $i,X3: $i,X10: $i,X2: $i,X7: $i,X5: $i,X8: $i,X1: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ p_1(X1,X2)
| ~ p_2(X2,X3)
| ~ p_3(X3,X4) )
<=> ( ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ) )),
( ( ~ p_1(X1,X2)
| ~ p_2(X2,X3)
| ~ p_3(X3,X4)
| ~ p_4(X4,X5) )
<=> ( ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2)
| ~ p_4(X4,X5) ) )),
rewrite(( ( ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2)
| ~ p_4(X4,X5) )
<=> ( ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ) )),
( ( ~ p_1(X1,X2)
| ~ p_2(X2,X3)
| ~ p_3(X3,X4)
| ~ p_4(X4,X5) )
<=> ( ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ) )),
( ( ~ p_1(X1,X2)
| ~ p_2(X2,X3)
| ~ p_3(X3,X4)
| ~ p_4(X4,X5)
| ~ p_5(X5,X6) )
<=> ( ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2)
| ~ p_5(X5,X6) ) )),
rewrite(( ( ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2)
| ~ p_5(X5,X6) )
<=> ( ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ) )),
( ( ~ p_1(X1,X2)
| ~ p_2(X2,X3)
| ~ p_3(X3,X4)
| ~ p_4(X4,X5)
| ~ p_5(X5,X6) )
<=> ( ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ) )),
( ( ~ p_1(X1,X2)
| ~ p_2(X2,X3)
| ~ p_3(X3,X4)
| ~ p_4(X4,X5)
| ~ p_5(X5,X6)
| ~ p_6(X6,X7) )
<=> ( ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2)
| ~ p_6(X6,X7) ) )),
rewrite(( ( ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2)
| ~ p_6(X6,X7) )
<=> ( ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ) )),
( ( ~ p_1(X1,X2)
| ~ p_2(X2,X3)
| ~ p_3(X3,X4)
| ~ p_4(X4,X5)
| ~ p_5(X5,X6)
| ~ p_6(X6,X7) )
<=> ( ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ) )),
( ( ~ p_1(X1,X2)
| ~ p_2(X2,X3)
| ~ p_3(X3,X4)
| ~ p_4(X4,X5)
| ~ p_5(X5,X6)
| ~ p_6(X6,X7)
| ~ p_7(X7,X8) )
<=> ( ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2)
| ~ p_7(X7,X8) ) )),
rewrite(( ( ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2)
| ~ p_7(X7,X8) )
<=> ( ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ) )),
( ( ~ p_1(X1,X2)
| ~ p_2(X2,X3)
| ~ p_3(X3,X4)
| ~ p_4(X4,X5)
| ~ p_5(X5,X6)
| ~ p_6(X6,X7)
| ~ p_7(X7,X8) )
<=> ( ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ) )),
( ( ~ p_1(X1,X2)
| ~ p_2(X2,X3)
| ~ p_3(X3,X4)
| ~ p_4(X4,X5)
| ~ p_5(X5,X6)
| ~ p_6(X6,X7)
| ~ p_7(X7,X8)
| ~ p_8(X8,X9) )
<=> ( ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2)
| ~ p_8(X8,X9) ) )),
rewrite(( ( ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2)
| ~ p_8(X8,X9) )
<=> ( ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ) )),
( ( ~ p_1(X1,X2)
| ~ p_2(X2,X3)
| ~ p_3(X3,X4)
| ~ p_4(X4,X5)
| ~ p_5(X5,X6)
| ~ p_6(X6,X7)
| ~ p_7(X7,X8)
| ~ p_8(X8,X9) )
<=> ( ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ) )),
( ( ~ p_1(X1,X2)
| ~ p_2(X2,X3)
| ~ p_3(X3,X4)
| ~ p_4(X4,X5)
| ~ p_5(X5,X6)
| ~ p_6(X6,X7)
| ~ p_7(X7,X8)
| ~ p_8(X8,X9)
| ~ p_9(X9,X10) )
<=> ( ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2)
| ~ p_9(X9,X10) ) )),
rewrite(( ( ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2)
| ~ p_9(X9,X10) )
<=> ( ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ) )),
( ( ~ p_1(X1,X2)
| ~ p_2(X2,X3)
| ~ p_3(X3,X4)
| ~ p_4(X4,X5)
| ~ p_5(X5,X6)
| ~ p_6(X6,X7)
| ~ p_7(X7,X8)
| ~ p_8(X8,X9)
| ~ p_9(X9,X10) )
<=> ( ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ) )),
( ( ~ p_1(X1,X2)
| ~ p_2(X2,X3)
| ~ p_3(X3,X4)
| ~ p_4(X4,X5)
| ~ p_5(X5,X6)
| ~ p_6(X6,X7)
| ~ p_7(X7,X8)
| ~ p_8(X8,X9)
| ~ p_9(X9,X10)
| ~ p_10(X10,X1) )
<=> ( ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2)
| ~ p_10(X10,X1) ) )),
rewrite(( ( ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2)
| ~ p_10(X10,X1) )
<=> ( ~ p_10(X10,X1)
| ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ) )),
( ( ~ p_1(X1,X2)
| ~ p_2(X2,X3)
| ~ p_3(X3,X4)
| ~ p_4(X4,X5)
| ~ p_5(X5,X6)
| ~ p_6(X6,X7)
| ~ p_7(X7,X8)
| ~ p_8(X8,X9)
| ~ p_9(X9,X10)
| ~ p_10(X10,X1) )
<=> ( ~ p_10(X10,X1)
| ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [X9: $i,X6: $i,X4: $i,X3: $i,X10: $i,X2: $i,X7: $i,X5: $i,X8: $i,X1: $i] :
( ~ p_1(X1,X2)
| ~ p_2(X2,X3)
| ~ p_3(X3,X4)
| ~ p_4(X4,X5)
| ~ p_5(X5,X6)
| ~ p_6(X6,X7)
| ~ p_7(X7,X8)
| ~ p_8(X8,X9)
| ~ p_9(X9,X10)
| ~ p_10(X10,X1) )
<=> ! [X9: $i,X6: $i,X4: $i,X3: $i,X10: $i,X2: $i,X7: $i,X5: $i,X8: $i,X1: $i] :
( ~ p_10(X10,X1)
| ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,axiom,
! [X9: $i,X6: $i,X4: $i,X3: $i,X10: $i,X2: $i,X7: $i,X5: $i,X8: $i,X1: $i] :
( ~ p_1(X1,X2)
| ~ p_2(X2,X3)
| ~ p_3(X3,X4)
| ~ p_4(X4,X5)
| ~ p_5(X5,X6)
| ~ p_6(X6,X7)
| ~ p_7(X7,X8)
| ~ p_8(X8,X9)
| ~ p_9(X9,X10)
| ~ p_10(X10,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjunction) ).
tff(37,plain,
! [X9: $i,X6: $i,X4: $i,X3: $i,X10: $i,X2: $i,X7: $i,X5: $i,X8: $i,X1: $i] :
( ~ p_10(X10,X1)
| ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [X9: $i,X6: $i,X4: $i,X3: $i,X10: $i,X2: $i,X7: $i,X5: $i,X8: $i,X1: $i] :
( ~ p_10(X10,X1)
| ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [X9: $i,X6: $i,X4: $i,X3: $i,X10: $i,X2: $i,X7: $i,X5: $i,X8: $i,X1: $i] :
( ~ p_10(X10,X1)
| ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [X9: $i,X6: $i,X4: $i,X3: $i,X10: $i,X2: $i,X7: $i,X5: $i,X8: $i,X1: $i] :
( ~ p_10(X10,X1)
| ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
( ( ~ ! [X9: $i,X6: $i,X4: $i,X3: $i,X10: $i,X2: $i,X7: $i,X5: $i,X8: $i,X1: $i] :
( ~ p_10(X10,X1)
| ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) )
| ~ p_10(a,a)
| ~ p_9(a,a)
| ~ p_8(a,a)
| ~ p_7(a,a)
| ~ p_6(a,a)
| ~ p_5(a,a)
| ~ p_4(a,a)
| ~ p_3(a,a)
| ~ p_2(a,a)
| ~ p_1(a,a) )
<=> ( ~ ! [X9: $i,X6: $i,X4: $i,X3: $i,X10: $i,X2: $i,X7: $i,X5: $i,X8: $i,X1: $i] :
( ~ p_10(X10,X1)
| ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) )
| ~ p_10(a,a)
| ~ p_9(a,a)
| ~ p_8(a,a)
| ~ p_7(a,a)
| ~ p_6(a,a)
| ~ p_5(a,a)
| ~ p_4(a,a)
| ~ p_3(a,a)
| ~ p_2(a,a)
| ~ p_1(a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [X9: $i,X6: $i,X4: $i,X3: $i,X10: $i,X2: $i,X7: $i,X5: $i,X8: $i,X1: $i] :
( ~ p_10(X10,X1)
| ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) )
| ~ p_10(a,a)
| ~ p_9(a,a)
| ~ p_8(a,a)
| ~ p_7(a,a)
| ~ p_6(a,a)
| ~ p_5(a,a)
| ~ p_4(a,a)
| ~ p_3(a,a)
| ~ p_2(a,a)
| ~ p_1(a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [X9: $i,X6: $i,X4: $i,X3: $i,X10: $i,X2: $i,X7: $i,X5: $i,X8: $i,X1: $i] :
( ~ p_10(X10,X1)
| ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) )
| ~ p_10(a,a)
| ~ p_9(a,a)
| ~ p_8(a,a)
| ~ p_7(a,a)
| ~ p_6(a,a)
| ~ p_5(a,a)
| ~ p_4(a,a)
| ~ p_3(a,a)
| ~ p_2(a,a)
| ~ p_1(a,a) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
$false,
inference(unit_resolution,[status(thm)],[43,40,30,27,24,21,18,15,12,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN005-1.010 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 12:25:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Unsatisfiable
% 0.19/0.37 % SZS output start Proof
% See solution above
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------