%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN088-1.010 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:38:13 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 29
% Syntax : Number of formulae : 50 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 797 ( 0 equ)
% Maximal formula atoms : 44 ( 15 avg)
% Number of connectives : 1339 ( 648 ~; 644 |; 0 &)
% ( 47 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 56 ( 56 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-10 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 210 ( 190 !; 0 ?; 210 :)
% Comments :
%------------------------------------------------------------------------------
tff(q_10_type,type,
q_10: $i > $o ).
tff(a_type,type,
a: $i ).
tff(q_9_type,type,
q_9: $i > $o ).
tff(q_8_type,type,
q_8: $i > $o ).
tff(q_7_type,type,
q_7: $i > $o ).
tff(q_6_type,type,
q_6: $i > $o ).
tff(q_5_type,type,
q_5: $i > $o ).
tff(q_4_type,type,
q_4: $i > $o ).
tff(q_3_type,type,
q_3: $i > $o ).
tff(q_2_type,type,
q_2: $i > $o ).
tff(q_1_type,type,
q_1: $i > $o ).
tff(p_type,type,
p: ( $i * $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).
tff(1,plain,
( q_10(a)
<=> q_10(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
q_10(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_20) ).
tff(3,plain,
q_10(a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( q_9(a)
<=> q_9(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
q_9(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_18) ).
tff(6,plain,
q_9(a),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( q_8(a)
<=> q_8(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
q_8(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_16) ).
tff(9,plain,
q_8(a),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
( q_7(a)
<=> q_7(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
q_7(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_14) ).
tff(12,plain,
q_7(a),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( q_6(a)
<=> q_6(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
q_6(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_12) ).
tff(15,plain,
q_6(a),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
( q_5(a)
<=> q_5(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
q_5(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_10) ).
tff(18,plain,
q_5(a),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( q_4(a)
<=> q_4(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
q_4(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_8) ).
tff(21,plain,
q_4(a),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
( q_3(a)
<=> q_3(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
q_3(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_6) ).
tff(24,plain,
q_3(a),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
( q_2(a)
<=> q_2(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
q_2(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_4) ).
tff(27,plain,
q_2(a),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( q_1(a)
<=> q_1(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
q_1(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_2) ).
tff(30,plain,
q_1(a),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
^ [X_5: $i,X_2: $i,X_9: $i,X_7: $i,X_8: $i,X_10: $i,X_3: $i,X_6: $i,X_4: $i,X_1: $i] :
refl(( ( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) )
<=> ( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [X_5: $i,X_2: $i,X_9: $i,X_7: $i,X_8: $i,X_10: $i,X_3: $i,X_6: $i,X_4: $i,X_1: $i] :
( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) )
<=> ! [X_5: $i,X_2: $i,X_9: $i,X_7: $i,X_8: $i,X_10: $i,X_3: $i,X_6: $i,X_4: $i,X_1: $i] :
( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [X_5: $i,X_2: $i,X_9: $i,X_7: $i,X_8: $i,X_10: $i,X_3: $i,X_6: $i,X_4: $i,X_1: $i] :
( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) )
<=> ! [X_5: $i,X_2: $i,X_9: $i,X_7: $i,X_8: $i,X_10: $i,X_3: $i,X_6: $i,X_4: $i,X_1: $i] :
( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
^ [X_5: $i,X_2: $i,X_9: $i,X_7: $i,X_8: $i,X_10: $i,X_3: $i,X_6: $i,X_4: $i,X_1: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_1(X_1) )
<=> ( ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) )),
( ( p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_1(X_1)
| ~ q_2(X_2) )
<=> ( ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_2(X_2) ) )),
rewrite(( ( ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_2(X_2) )
<=> ( ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) )),
( ( p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_1(X_1)
| ~ q_2(X_2) )
<=> ( ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) )),
( ( p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_1(X_1)
| ~ q_2(X_2)
| ~ q_3(X_3) )
<=> ( ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_3(X_3) ) )),
rewrite(( ( ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_3(X_3) )
<=> ( ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) )),
( ( p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_1(X_1)
| ~ q_2(X_2)
| ~ q_3(X_3) )
<=> ( ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) )),
( ( p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_1(X_1)
| ~ q_2(X_2)
| ~ q_3(X_3)
| ~ q_4(X_4) )
<=> ( ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_4(X_4) ) )),
rewrite(( ( ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_4(X_4) )
<=> ( ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) )),
( ( p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_1(X_1)
| ~ q_2(X_2)
| ~ q_3(X_3)
| ~ q_4(X_4) )
<=> ( ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) )),
( ( p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_1(X_1)
| ~ q_2(X_2)
| ~ q_3(X_3)
| ~ q_4(X_4)
| ~ q_5(X_5) )
<=> ( ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_5(X_5) ) )),
rewrite(( ( ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_5(X_5) )
<=> ( ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) )),
( ( p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_1(X_1)
| ~ q_2(X_2)
| ~ q_3(X_3)
| ~ q_4(X_4)
| ~ q_5(X_5) )
<=> ( ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) )),
( ( p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_1(X_1)
| ~ q_2(X_2)
| ~ q_3(X_3)
| ~ q_4(X_4)
| ~ q_5(X_5)
| ~ q_6(X_6) )
<=> ( ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_6(X_6) ) )),
rewrite(( ( ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_6(X_6) )
<=> ( ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) )),
( ( p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_1(X_1)
| ~ q_2(X_2)
| ~ q_3(X_3)
| ~ q_4(X_4)
| ~ q_5(X_5)
| ~ q_6(X_6) )
<=> ( ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) )),
( ( p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_1(X_1)
| ~ q_2(X_2)
| ~ q_3(X_3)
| ~ q_4(X_4)
| ~ q_5(X_5)
| ~ q_6(X_6)
| ~ q_7(X_7) )
<=> ( ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_7(X_7) ) )),
rewrite(( ( ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_7(X_7) )
<=> ( ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) )),
( ( p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_1(X_1)
| ~ q_2(X_2)
| ~ q_3(X_3)
| ~ q_4(X_4)
| ~ q_5(X_5)
| ~ q_6(X_6)
| ~ q_7(X_7) )
<=> ( ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) )),
( ( p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_1(X_1)
| ~ q_2(X_2)
| ~ q_3(X_3)
| ~ q_4(X_4)
| ~ q_5(X_5)
| ~ q_6(X_6)
| ~ q_7(X_7)
| ~ q_8(X_8) )
<=> ( ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_8(X_8) ) )),
rewrite(( ( ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_8(X_8) )
<=> ( ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) )),
( ( p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_1(X_1)
| ~ q_2(X_2)
| ~ q_3(X_3)
| ~ q_4(X_4)
| ~ q_5(X_5)
| ~ q_6(X_6)
| ~ q_7(X_7)
| ~ q_8(X_8) )
<=> ( ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) )),
( ( p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_1(X_1)
| ~ q_2(X_2)
| ~ q_3(X_3)
| ~ q_4(X_4)
| ~ q_5(X_5)
| ~ q_6(X_6)
| ~ q_7(X_7)
| ~ q_8(X_8)
| ~ q_9(X_9) )
<=> ( ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_9(X_9) ) )),
rewrite(( ( ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_9(X_9) )
<=> ( ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) )),
( ( p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_1(X_1)
| ~ q_2(X_2)
| ~ q_3(X_3)
| ~ q_4(X_4)
| ~ q_5(X_5)
| ~ q_6(X_6)
| ~ q_7(X_7)
| ~ q_8(X_8)
| ~ q_9(X_9) )
<=> ( ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) )),
( ( p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_1(X_1)
| ~ q_2(X_2)
| ~ q_3(X_3)
| ~ q_4(X_4)
| ~ q_5(X_5)
| ~ q_6(X_6)
| ~ q_7(X_7)
| ~ q_8(X_8)
| ~ q_9(X_9)
| ~ q_10(X_10) )
<=> ( ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_10(X_10) ) )),
rewrite(( ( ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_10(X_10) )
<=> ( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) )),
( ( p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_1(X_1)
| ~ q_2(X_2)
| ~ q_3(X_3)
| ~ q_4(X_4)
| ~ q_5(X_5)
| ~ q_6(X_6)
| ~ q_7(X_7)
| ~ q_8(X_8)
| ~ q_9(X_9)
| ~ q_10(X_10) )
<=> ( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [X_5: $i,X_2: $i,X_9: $i,X_7: $i,X_8: $i,X_10: $i,X_3: $i,X_6: $i,X_4: $i,X_1: $i] :
( p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_1(X_1)
| ~ q_2(X_2)
| ~ q_3(X_3)
| ~ q_4(X_4)
| ~ q_5(X_5)
| ~ q_6(X_6)
| ~ q_7(X_7)
| ~ q_8(X_8)
| ~ q_9(X_9)
| ~ q_10(X_10) )
<=> ! [X_5: $i,X_2: $i,X_9: $i,X_7: $i,X_8: $i,X_10: $i,X_3: $i,X_6: $i,X_4: $i,X_1: $i] :
( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,axiom,
! [X_5: $i,X_2: $i,X_9: $i,X_7: $i,X_8: $i,X_10: $i,X_3: $i,X_6: $i,X_4: $i,X_1: $i] :
( p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10)
| ~ q_1(X_1)
| ~ q_2(X_2)
| ~ q_3(X_3)
| ~ q_4(X_4)
| ~ q_5(X_5)
| ~ q_6(X_6)
| ~ q_7(X_7)
| ~ q_8(X_8)
| ~ q_9(X_9)
| ~ q_10(X_10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_1) ).
tff(37,plain,
! [X_5: $i,X_2: $i,X_9: $i,X_7: $i,X_8: $i,X_10: $i,X_3: $i,X_6: $i,X_4: $i,X_1: $i] :
( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [X_5: $i,X_2: $i,X_9: $i,X_7: $i,X_8: $i,X_10: $i,X_3: $i,X_6: $i,X_4: $i,X_1: $i] :
( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [X_5: $i,X_2: $i,X_9: $i,X_7: $i,X_8: $i,X_10: $i,X_3: $i,X_6: $i,X_4: $i,X_1: $i] :
( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [X_5: $i,X_2: $i,X_9: $i,X_7: $i,X_8: $i,X_10: $i,X_3: $i,X_6: $i,X_4: $i,X_1: $i] :
( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
( ~ p(a,a,a,a,a,a,a,a,a,a)
<=> ~ p(a,a,a,a,a,a,a,a,a,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
~ p(a,a,a,a,a,a,a,a,a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_goal_1) ).
tff(43,plain,
~ p(a,a,a,a,a,a,a,a,a,a),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ( ~ ! [X_5: $i,X_2: $i,X_9: $i,X_7: $i,X_8: $i,X_10: $i,X_3: $i,X_6: $i,X_4: $i,X_1: $i] :
( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) )
| p(a,a,a,a,a,a,a,a,a,a)
| ~ q_10(a)
| ~ q_9(a)
| ~ q_8(a)
| ~ q_7(a)
| ~ q_6(a)
| ~ q_5(a)
| ~ q_4(a)
| ~ q_3(a)
| ~ q_2(a)
| ~ q_1(a) )
<=> ( ~ ! [X_5: $i,X_2: $i,X_9: $i,X_7: $i,X_8: $i,X_10: $i,X_3: $i,X_6: $i,X_4: $i,X_1: $i] :
( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) )
| p(a,a,a,a,a,a,a,a,a,a)
| ~ q_10(a)
| ~ q_9(a)
| ~ q_8(a)
| ~ q_7(a)
| ~ q_6(a)
| ~ q_5(a)
| ~ q_4(a)
| ~ q_3(a)
| ~ q_2(a)
| ~ q_1(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ( ~ q_10(a)
| ~ q_9(a)
| ~ q_8(a)
| ~ q_7(a)
| ~ q_6(a)
| ~ q_5(a)
| ~ q_4(a)
| ~ q_3(a)
| ~ q_2(a)
| ~ q_1(a)
| p(a,a,a,a,a,a,a,a,a,a) )
<=> ( p(a,a,a,a,a,a,a,a,a,a)
| ~ q_10(a)
| ~ q_9(a)
| ~ q_8(a)
| ~ q_7(a)
| ~ q_6(a)
| ~ q_5(a)
| ~ q_4(a)
| ~ q_3(a)
| ~ q_2(a)
| ~ q_1(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ( ~ ! [X_5: $i,X_2: $i,X_9: $i,X_7: $i,X_8: $i,X_10: $i,X_3: $i,X_6: $i,X_4: $i,X_1: $i] :
( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) )
| ~ q_10(a)
| ~ q_9(a)
| ~ q_8(a)
| ~ q_7(a)
| ~ q_6(a)
| ~ q_5(a)
| ~ q_4(a)
| ~ q_3(a)
| ~ q_2(a)
| ~ q_1(a)
| p(a,a,a,a,a,a,a,a,a,a) )
<=> ( ~ ! [X_5: $i,X_2: $i,X_9: $i,X_7: $i,X_8: $i,X_10: $i,X_3: $i,X_6: $i,X_4: $i,X_1: $i] :
( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) )
| p(a,a,a,a,a,a,a,a,a,a)
| ~ q_10(a)
| ~ q_9(a)
| ~ q_8(a)
| ~ q_7(a)
| ~ q_6(a)
| ~ q_5(a)
| ~ q_4(a)
| ~ q_3(a)
| ~ q_2(a)
| ~ q_1(a) ) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( ( ~ ! [X_5: $i,X_2: $i,X_9: $i,X_7: $i,X_8: $i,X_10: $i,X_3: $i,X_6: $i,X_4: $i,X_1: $i] :
( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) )
| ~ q_10(a)
| ~ q_9(a)
| ~ q_8(a)
| ~ q_7(a)
| ~ q_6(a)
| ~ q_5(a)
| ~ q_4(a)
| ~ q_3(a)
| ~ q_2(a)
| ~ q_1(a)
| p(a,a,a,a,a,a,a,a,a,a) )
<=> ( ~ ! [X_5: $i,X_2: $i,X_9: $i,X_7: $i,X_8: $i,X_10: $i,X_3: $i,X_6: $i,X_4: $i,X_1: $i] :
( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) )
| p(a,a,a,a,a,a,a,a,a,a)
| ~ q_10(a)
| ~ q_9(a)
| ~ q_8(a)
| ~ q_7(a)
| ~ q_6(a)
| ~ q_5(a)
| ~ q_4(a)
| ~ q_3(a)
| ~ q_2(a)
| ~ q_1(a) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,plain,
( ~ ! [X_5: $i,X_2: $i,X_9: $i,X_7: $i,X_8: $i,X_10: $i,X_3: $i,X_6: $i,X_4: $i,X_1: $i] :
( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) )
| ~ q_10(a)
| ~ q_9(a)
| ~ q_8(a)
| ~ q_7(a)
| ~ q_6(a)
| ~ q_5(a)
| ~ q_4(a)
| ~ q_3(a)
| ~ q_2(a)
| ~ q_1(a)
| p(a,a,a,a,a,a,a,a,a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [X_5: $i,X_2: $i,X_9: $i,X_7: $i,X_8: $i,X_10: $i,X_3: $i,X_6: $i,X_4: $i,X_1: $i] :
( ~ q_10(X_10)
| ~ q_9(X_9)
| ~ q_8(X_8)
| ~ q_7(X_7)
| ~ q_6(X_6)
| ~ q_5(X_5)
| ~ q_4(X_4)
| ~ q_3(X_3)
| ~ q_2(X_2)
| ~ q_1(X_1)
| p(X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10) )
| p(a,a,a,a,a,a,a,a,a,a)
| ~ q_10(a)
| ~ q_9(a)
| ~ q_8(a)
| ~ q_7(a)
| ~ q_6(a)
| ~ q_5(a)
| ~ q_4(a)
| ~ q_3(a)
| ~ q_2(a)
| ~ q_1(a) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
$false,
inference(unit_resolution,[status(thm)],[49,43,40,30,27,24,21,18,15,12,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN088-1.010 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.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 12:29:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Unsatisfiable
% 0.11/0.36 % SZS output start Proof
% See solution above
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------