%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN201-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:38:28 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.47s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 33
% Syntax : Number of formulae : 72 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 278 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 360 ( 168 ~; 161 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 142 ( 126 !; 0 ?; 142 :)
% Comments :
%------------------------------------------------------------------------------
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(s1_type,type,
s1: $i > $o ).
tff(q2_type,type,
q2: ( $i * $i * $i ) > $o ).
tff(q1_type,type,
q1: ( $i * $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(s2_type,type,
s2: $i > $o ).
tff(1,plain,
^ [B: $i,A: $i,J: $i,C: $i] :
refl(( ( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) )
<=> ( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) )
<=> ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) )
<=> ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [B: $i,A: $i,J: $i,C: $i] :
trans(monotonicity(rewrite(( ( q1(J,A,J)
| ~ n0(B,A) )
<=> ( ~ n0(B,A)
| q1(J,A,J) ) )),
( ( q1(J,A,J)
| ~ n0(B,A)
| ~ p0(C,J) )
<=> ( ~ n0(B,A)
| q1(J,A,J)
| ~ p0(C,J) ) )),
rewrite(( ( ~ n0(B,A)
| q1(J,A,J)
| ~ p0(C,J) )
<=> ( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ) )),
( ( q1(J,A,J)
| ~ n0(B,A)
| ~ p0(C,J) )
<=> ( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [B: $i,A: $i,J: $i,C: $i] :
( q1(J,A,J)
| ~ n0(B,A)
| ~ p0(C,J) )
<=> ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [B: $i,A: $i,J: $i,C: $i] :
( q1(J,A,J)
| ~ n0(B,A)
| ~ p0(C,J) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_092) ).
tff(7,plain,
! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( n0(d,c)
<=> n0(d,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
n0(d,c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_26) ).
tff(13,plain,
n0(d,c),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( p0(c,b)
<=> p0(c,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
p0(c,b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_18) ).
tff(16,plain,
p0(c,b),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) )
| ~ p0(c,b)
| ~ n0(d,c)
| q1(b,c,b) )
<=> ( ~ ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) )
| ~ p0(c,b)
| ~ n0(d,c)
| q1(b,c,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) )
| ~ p0(c,b)
| ~ n0(d,c)
| q1(b,c,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) )
| ~ p0(c,b)
| ~ n0(d,c)
| q1(b,c,b) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
q1(b,c,b),
inference(unit_resolution,[status(thm)],[19,16,13,10]) ).
tff(21,plain,
^ [B: $i,C: $i] :
refl(( ( ~ q1(C,c,B)
| q2(B,B,B) )
<=> ( ~ q1(C,c,B)
| q2(B,B,B) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [B: $i,C: $i] :
( ~ q1(C,c,B)
| q2(B,B,B) )
<=> ! [B: $i,C: $i] :
( ~ q1(C,c,B)
| q2(B,B,B) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [B: $i,C: $i] :
( ~ q1(C,c,B)
| q2(B,B,B) )
<=> ! [B: $i,C: $i] :
( ~ q1(C,c,B)
| q2(B,B,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [B: $i,C: $i] :
rewrite(( ( q2(B,B,B)
| ~ q1(C,c,B) )
<=> ( ~ q1(C,c,B)
| q2(B,B,B) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [B: $i,C: $i] :
( q2(B,B,B)
| ~ q1(C,c,B) )
<=> ! [B: $i,C: $i] :
( ~ q1(C,c,B)
| q2(B,B,B) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [B: $i,C: $i] :
( q2(B,B,B)
| ~ q1(C,c,B) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_184) ).
tff(27,plain,
! [B: $i,C: $i] :
( ~ q1(C,c,B)
| q2(B,B,B) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [B: $i,C: $i] :
( ~ q1(C,c,B)
| q2(B,B,B) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [B: $i,C: $i] :
( ~ q1(C,c,B)
| q2(B,B,B) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [B: $i,C: $i] :
( ~ q1(C,c,B)
| q2(B,B,B) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [B: $i,C: $i] :
( ~ q1(C,c,B)
| q2(B,B,B) )
| ~ q1(b,c,b)
| q2(b,b,b) )
<=> ( ~ ! [B: $i,C: $i] :
( ~ q1(C,c,B)
| q2(B,B,B) )
| ~ q1(b,c,b)
| q2(b,b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [B: $i,C: $i] :
( ~ q1(C,c,B)
| q2(B,B,B) )
| ~ q1(b,c,b)
| q2(b,b,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [B: $i,C: $i] :
( ~ q1(C,c,B)
| q2(B,B,B) )
| ~ q1(b,c,b)
| q2(b,b,b) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
q2(b,b,b),
inference(unit_resolution,[status(thm)],[33,30,20]) ).
tff(35,plain,
( ~ s2(b)
<=> ~ s2(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
~ s2(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(37,plain,
~ s2(b),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
^ [H: $i] :
refl(( ( ~ s1(b)
| s2(H)
| ~ q2(b,H,b) )
<=> ( ~ s1(b)
| s2(H)
| ~ q2(b,H,b) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [H: $i] :
( ~ s1(b)
| s2(H)
| ~ q2(b,H,b) )
<=> ! [H: $i] :
( ~ s1(b)
| s2(H)
| ~ q2(b,H,b) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [H: $i] :
( ~ s1(b)
| s2(H)
| ~ q2(b,H,b) )
<=> ! [H: $i] :
( ~ s1(b)
| s2(H)
| ~ q2(b,H,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
^ [H: $i] :
rewrite(( ( s2(H)
| ~ q2(b,H,b)
| ~ s1(b) )
<=> ( ~ s1(b)
| s2(H)
| ~ q2(b,H,b) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [H: $i] :
( s2(H)
| ~ q2(b,H,b)
| ~ s1(b) )
<=> ! [H: $i] :
( ~ s1(b)
| s2(H)
| ~ q2(b,H,b) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,axiom,
! [H: $i] :
( s2(H)
| ~ q2(b,H,b)
| ~ s1(b) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_189) ).
tff(44,plain,
! [H: $i] :
( ~ s1(b)
| s2(H)
| ~ q2(b,H,b) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [H: $i] :
( ~ s1(b)
| s2(H)
| ~ q2(b,H,b) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [H: $i] :
( ~ s1(b)
| s2(H)
| ~ q2(b,H,b) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [H: $i] :
( ~ s1(b)
| s2(H)
| ~ q2(b,H,b) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( ( ~ ! [H: $i] :
( ~ s1(b)
| s2(H)
| ~ q2(b,H,b) )
| ~ s1(b)
| s2(b)
| ~ q2(b,b,b) )
<=> ( ~ ! [H: $i] :
( ~ s1(b)
| s2(H)
| ~ q2(b,H,b) )
| ~ s1(b)
| s2(b)
| ~ q2(b,b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [H: $i] :
( ~ s1(b)
| s2(H)
| ~ q2(b,H,b) )
| ~ s1(b)
| s2(b)
| ~ q2(b,b,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [H: $i] :
( ~ s1(b)
| s2(H)
| ~ q2(b,H,b) )
| ~ s1(b)
| s2(b)
| ~ q2(b,b,b) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( ~ s1(b)
| ~ q2(b,b,b) ),
inference(unit_resolution,[status(thm)],[50,47,37]) ).
tff(52,plain,
~ s1(b),
inference(unit_resolution,[status(thm)],[51,34]) ).
tff(53,plain,
^ [I: $i] :
refl(( ( s1(I)
| ~ p0(I,I) )
<=> ( s1(I)
| ~ p0(I,I) ) )),
inference(bind,[status(th)],[]) ).
tff(54,plain,
( ! [I: $i] :
( s1(I)
| ~ p0(I,I) )
<=> ! [I: $i] :
( s1(I)
| ~ p0(I,I) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [I: $i] :
( s1(I)
| ~ p0(I,I) )
<=> ! [I: $i] :
( s1(I)
| ~ p0(I,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
! [I: $i] :
( s1(I)
| ~ p0(I,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_125) ).
tff(57,plain,
! [I: $i] :
( s1(I)
| ~ p0(I,I) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [I: $i] :
( s1(I)
| ~ p0(I,I) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [I: $i] :
( s1(I)
| ~ p0(I,I) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
( ( ~ ! [I: $i] :
( s1(I)
| ~ p0(I,I) )
| s1(b)
| ~ p0(b,b) )
<=> ( ~ ! [I: $i] :
( s1(I)
| ~ p0(I,I) )
| s1(b)
| ~ p0(b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [I: $i] :
( s1(I)
| ~ p0(I,I) )
| s1(b)
| ~ p0(b,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [I: $i] :
( s1(I)
| ~ p0(I,I) )
| s1(b)
| ~ p0(b,b) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
~ p0(b,b),
inference(unit_resolution,[status(thm)],[62,59,52]) ).
tff(64,plain,
^ [X: $i] :
refl(( p0(b,X)
<=> p0(b,X) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [X: $i] : p0(b,X)
<=> ! [X: $i] : p0(b,X) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [X: $i] : p0(b,X)
<=> ! [X: $i] : p0(b,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
! [X: $i] : p0(b,X),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_14) ).
tff(68,plain,
! [X: $i] : p0(b,X),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [X: $i] : p0(b,X),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [X: $i] : p0(b,X),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ~ ! [X: $i] : p0(b,X)
| p0(b,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
$false,
inference(unit_resolution,[status(thm)],[71,70,63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYN201-1 : TPTP v9.0.0. Released v1.1.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:29:47 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.47 % SZS status Unsatisfiable
% 0.21/0.47 % SZS output start Proof
% See solution above
% 0.21/0.49 % E exiting
%------------------------------------------------------------------------------