%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN224-1 : TPTP v9.0.0. Released v1.1.0.
% 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 05:38:32 AM UTC 2025
% Result : Unsatisfiable 0.17s 0.44s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 39
% Syntax : Number of formulae : 83 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 415 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 594 ( 282 ~; 270 |; 0 &)
% ( 42 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 154 ( 138 !; 0 ?; 154 :)
% Comments :
%------------------------------------------------------------------------------
tff(l3_type,type,
l3: ( $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(r2_type,type,
r2: $i > $o ).
tff(r1_type,type,
r1: $i > $o ).
tff(q1_type,type,
q1: ( $i * $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(b_type,type,
b: $i ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(s0_type,type,
s0: $i > $o ).
tff(q0_type,type,
q0: ( $i * $i ) > $o ).
tff(l0_type,type,
l0: $i > $o ).
tff(1,plain,
^ [B: $i] :
refl(( ( l3(B,B)
| ~ r2(B) )
<=> ( l3(B,B)
| ~ r2(B) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i] :
( l3(B,B)
| ~ r2(B) )
<=> ! [B: $i] :
( l3(B,B)
| ~ r2(B) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i] :
( l3(B,B)
| ~ r2(B) )
<=> ! [B: $i] :
( l3(B,B)
| ~ r2(B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i] :
( l3(B,B)
| ~ r2(B) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_218) ).
tff(5,plain,
! [B: $i] :
( l3(B,B)
| ~ r2(B) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i] :
( l3(B,B)
| ~ r2(B) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i] :
( l3(B,B)
| ~ r2(B) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,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(9,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)],[8]) ).
tff(10,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(11,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(12,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)],[11]) ).
tff(13,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(14,plain,
! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
inference(modus_ponens,[status(thm)],[16,9]) ).
tff(18,plain,
( p0(b,d)
<=> p0(b,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
p0(b,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_10) ).
tff(20,plain,
p0(b,d),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( n0(d,b)
<=> n0(d,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
n0(d,b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_7) ).
tff(23,plain,
n0(d,b),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
( ( ~ ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) )
| ~ p0(b,d)
| ~ n0(d,b)
| q1(d,b,d) )
<=> ( ~ ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) )
| ~ p0(b,d)
| ~ n0(d,b)
| q1(d,b,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) )
| ~ p0(b,d)
| ~ n0(d,b)
| q1(d,b,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [B: $i,A: $i,J: $i,C: $i] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) )
| ~ p0(b,d)
| ~ n0(d,b)
| q1(d,b,d) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
q1(d,b,d),
inference(unit_resolution,[status(thm)],[26,23,20,17]) ).
tff(28,plain,
^ [D: $i,E: $i] :
refl(( ( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
<=> ( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
<=> ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
<=> ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
^ [D: $i,E: $i] :
trans(monotonicity(rewrite(( ( r1(D)
| ~ q0(D,E)
| ~ s0(d) )
<=> ( ~ q0(D,E)
| ~ s0(d)
| r1(D) ) )),
( ( r1(D)
| ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d) )
<=> ( ~ q0(D,E)
| ~ s0(d)
| r1(D)
| ~ q1(d,E,d) ) )),
rewrite(( ( ~ q0(D,E)
| ~ s0(d)
| r1(D)
| ~ q1(d,E,d) )
<=> ( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ) )),
( ( r1(D)
| ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d) )
<=> ( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [D: $i,E: $i] :
( r1(D)
| ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d) )
<=> ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,axiom,
! [D: $i,E: $i] :
( r1(D)
| ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_124) ).
tff(34,plain,
! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ),
inference(modus_ponens,[status(thm)],[36,29]) ).
tff(38,plain,
( q0(a,b)
<=> q0(a,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
q0(a,b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_36) ).
tff(40,plain,
q0(a,b),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( s0(d)
<=> s0(d) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
s0(d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_1) ).
tff(43,plain,
s0(d),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ s0(d)
| r1(a)
| ~ q1(d,b,d)
| ~ q0(a,b) )
<=> ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ s0(d)
| r1(a)
| ~ q1(d,b,d)
| ~ q0(a,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ( ~ q0(a,b)
| ~ s0(d)
| ~ q1(d,b,d)
| r1(a) )
<=> ( ~ s0(d)
| r1(a)
| ~ q1(d,b,d)
| ~ q0(a,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ q0(a,b)
| ~ s0(d)
| ~ q1(d,b,d)
| r1(a) )
<=> ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ s0(d)
| r1(a)
| ~ q1(d,b,d)
| ~ q0(a,b) ) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ q0(a,b)
| ~ s0(d)
| ~ q1(d,b,d)
| r1(a) )
<=> ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ s0(d)
| r1(a)
| ~ q1(d,b,d)
| ~ q0(a,b) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,plain,
( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ q0(a,b)
| ~ s0(d)
| ~ q1(d,b,d)
| r1(a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ s0(d)
| r1(a)
| ~ q1(d,b,d)
| ~ q0(a,b) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
r1(a),
inference(unit_resolution,[status(thm)],[49,43,40,37,27]) ).
tff(51,plain,
^ [G: $i] :
refl(( ( ~ l0(G)
| ~ r1(G)
| r2(G) )
<=> ( ~ l0(G)
| ~ r1(G)
| r2(G) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) )
<=> ! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) )
<=> ! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
^ [G: $i] :
rewrite(( ( r2(G)
| ~ r1(G)
| ~ l0(G) )
<=> ( ~ l0(G)
| ~ r1(G)
| r2(G) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [G: $i] :
( r2(G)
| ~ r1(G)
| ~ l0(G) )
<=> ! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,axiom,
! [G: $i] :
( r2(G)
| ~ r1(G)
| ~ l0(G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_188) ).
tff(57,plain,
! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
( l0(a)
<=> l0(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,axiom,
l0(a),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_20) ).
tff(63,plain,
l0(a),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
( ( ~ ! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) )
| ~ l0(a)
| ~ r1(a)
| r2(a) )
<=> ( ~ ! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) )
| ~ l0(a)
| ~ r1(a)
| r2(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) )
| ~ l0(a)
| ~ r1(a)
| r2(a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [G: $i] :
( ~ l0(G)
| ~ r1(G)
| r2(G) )
| ~ l0(a)
| ~ r1(a)
| r2(a) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
r2(a),
inference(unit_resolution,[status(thm)],[66,63,60,50]) ).
tff(68,plain,
( ( ~ ! [B: $i] :
( l3(B,B)
| ~ r2(B) )
| ~ r2(a)
| l3(a,a) )
<=> ( ~ ! [B: $i] :
( l3(B,B)
| ~ r2(B) )
| ~ r2(a)
| l3(a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ( l3(a,a)
| ~ r2(a) )
<=> ( ~ r2(a)
| l3(a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
( ( ~ ! [B: $i] :
( l3(B,B)
| ~ r2(B) )
| l3(a,a)
| ~ r2(a) )
<=> ( ~ ! [B: $i] :
( l3(B,B)
| ~ r2(B) )
| ~ r2(a)
| l3(a,a) ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( ~ ! [B: $i] :
( l3(B,B)
| ~ r2(B) )
| l3(a,a)
| ~ r2(a) )
<=> ( ~ ! [B: $i] :
( l3(B,B)
| ~ r2(B) )
| ~ r2(a)
| l3(a,a) ) ),
inference(transitivity,[status(thm)],[70,68]) ).
tff(72,plain,
( ~ ! [B: $i] :
( l3(B,B)
| ~ r2(B) )
| l3(a,a)
| ~ r2(a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
( ~ ! [B: $i] :
( l3(B,B)
| ~ r2(B) )
| ~ r2(a)
| l3(a,a) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
l3(a,a),
inference(unit_resolution,[status(thm)],[73,67,7]) ).
tff(75,plain,
^ [X: $i] :
refl(( ~ l3(a,X)
<=> ~ l3(a,X) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [X: $i] : ~ l3(a,X)
<=> ! [X: $i] : ~ l3(a,X) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [X: $i] : ~ l3(a,X)
<=> ! [X: $i] : ~ l3(a,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
! [X: $i] : ~ l3(a,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(79,plain,
! [X: $i] : ~ l3(a,X),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [X: $i] : ~ l3(a,X),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [X: $i] : ~ l3(a,X),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
( ~ ! [X: $i] : ~ l3(a,X)
| ~ l3(a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
$false,
inference(unit_resolution,[status(thm)],[82,81,74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SYN224-1 : TPTP v9.0.0. Released v1.1.0.
% 0.03/0.10 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n007.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Jun 20 12:31:05 EDT 2025
% 0.11/0.31 % CPUTime :
% 0.17/0.44 % SZS status Unsatisfiable
% 0.17/0.44 % SZS output start Proof
% See solution above
% 0.17/0.46 % E exiting
%------------------------------------------------------------------------------