%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN248-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:38:35 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 21
% Syntax : Number of formulae : 41 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 210 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 291 ( 137 ~; 133 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 15 ( 15 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 68 ( 62 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
tff(k1_type,type,
k1: $i > $o ).
tff(a_type,type,
a: $i ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(d_type,type,
d: $i ).
tff(q0_type,type,
q0: ( $i * $i ) > $o ).
tff(1,plain,
^ [I: $i,J: $i] :
refl(( ( k1(I)
| ~ n0(J,I) )
<=> ( k1(I)
| ~ n0(J,I) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_001) ).
tff(5,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( n0(b,a)
<=> n0(b,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
n0(b,a),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_37) ).
tff(10,plain,
n0(b,a),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(a)
| ~ n0(b,a) )
<=> ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(a)
| ~ n0(b,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(a)
| ~ n0(b,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(a)
| ~ n0(b,a) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
k1(a),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
( ~ m1(d,c,c)
<=> ~ m1(d,c,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
~ m1(d,c,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(17,plain,
~ m1(d,c,c),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( n0(d,c)
<=> n0(d,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
n0(d,c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_26) ).
tff(20,plain,
n0(d,c),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) )
<=> ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
k1(c),
inference(unit_resolution,[status(thm)],[23,20,7]) ).
tff(25,plain,
^ [B: $i,A: $i] :
refl(( ( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) )
<=> ( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) )
<=> ! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) )
<=> ! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
^ [B: $i,A: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( m1(A,B,B)
| ~ k1(a) )
<=> ( ~ k1(a)
| m1(A,B,B) ) )),
( ( m1(A,B,B)
| ~ k1(a)
| ~ k1(B) )
<=> ( ~ k1(a)
| m1(A,B,B)
| ~ k1(B) ) )),
rewrite(( ( ~ k1(a)
| m1(A,B,B)
| ~ k1(B) )
<=> ( ~ k1(a)
| ~ k1(B)
| m1(A,B,B) ) )),
( ( m1(A,B,B)
| ~ k1(a)
| ~ k1(B) )
<=> ( ~ k1(a)
| ~ k1(B)
| m1(A,B,B) ) )),
( ( m1(A,B,B)
| ~ k1(a)
| ~ k1(B)
| ~ q0(A,A) )
<=> ( ~ k1(a)
| ~ k1(B)
| m1(A,B,B)
| ~ q0(A,A) ) )),
rewrite(( ( ~ k1(a)
| ~ k1(B)
| m1(A,B,B)
| ~ q0(A,A) )
<=> ( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) ) )),
( ( m1(A,B,B)
| ~ k1(a)
| ~ k1(B)
| ~ q0(A,A) )
<=> ( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [B: $i,A: $i] :
( m1(A,B,B)
| ~ k1(a)
| ~ k1(B)
| ~ q0(A,A) )
<=> ! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,axiom,
! [B: $i,A: $i] :
( m1(A,B,B)
| ~ k1(a)
| ~ k1(B)
| ~ q0(A,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_034) ).
tff(31,plain,
! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) ),
inference(modus_ponens,[status(thm)],[33,26]) ).
tff(35,plain,
( q0(d,d)
<=> q0(d,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
q0(d,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_25) ).
tff(37,plain,
q0(d,d),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) )
| ~ k1(a)
| ~ q0(d,d)
| ~ k1(c)
| m1(d,c,c) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) )
| ~ k1(a)
| ~ q0(d,d)
| ~ k1(c)
| m1(d,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) )
| ~ k1(a)
| ~ q0(d,d)
| ~ k1(c)
| m1(d,c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) )
| ~ k1(a)
| ~ q0(d,d)
| ~ k1(c)
| m1(d,c,c) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
$false,
inference(unit_resolution,[status(thm)],[40,37,34,24,17,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN248-1 : TPTP v9.0.0. Released v1.1.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n002.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:31:32 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.45 % SZS status Unsatisfiable
% 0.19/0.45 % SZS output start Proof
% See solution above
% 0.19/0.47 % E exiting
%------------------------------------------------------------------------------