%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN301-1 : 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 05:38:42 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 38
% Syntax : Number of formulae : 82 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 345 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 465 ( 216 ~; 212 |; 0 &)
% ( 37 <=>; 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 : 13 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 200 ( 181 !; 0 ?; 200 :)
% Comments :
%------------------------------------------------------------------------------
tff(p3_type,type,
p3: ( $i * $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(k1_type,type,
k1: $i > $o ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(n2_type,type,
n2: $i > $o ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(l0_type,type,
l0: $i > $o ).
tff(l1_type,type,
l1: ( $i * $i ) > $o ).
tff(s4_type,type,
s4: $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,
^ [H: $i] :
refl(( ( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
<=> ( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
<=> ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
<=> ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
^ [H: $i] :
trans(monotonicity(rewrite(( ( p3(H,H,H)
| ~ k1(H) )
<=> ( ~ k1(H)
| p3(H,H,H) ) )),
( ( p3(H,H,H)
| ~ k1(H)
| ~ n2(H) )
<=> ( ~ k1(H)
| p3(H,H,H)
| ~ n2(H) ) )),
rewrite(( ( ~ k1(H)
| p3(H,H,H)
| ~ n2(H) )
<=> ( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) )),
( ( p3(H,H,H)
| ~ k1(H)
| ~ n2(H) )
<=> ( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [H: $i] :
( p3(H,H,H)
| ~ k1(H)
| ~ n2(H) )
<=> ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [H: $i] :
( p3(H,H,H)
| ~ k1(H)
| ~ n2(H) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_249) ).
tff(21,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( n2(A)
| ~ p1(B,C,A) )
<=> ( n2(A)
| ~ p1(B,C,A) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
<=> ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
<=> ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_137) ).
tff(29,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( l0(a)
<=> l0(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
l0(a),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_20) ).
tff(34,plain,
l0(a),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( ( ~ l0(a)
| p1(a,a,a) )
<=> ( ~ l0(a)
| p1(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ( p1(a,a,a)
| ~ l0(a) )
<=> ( ~ l0(a)
| p1(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
( p1(a,a,a)
| ~ l0(a) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_088) ).
tff(38,plain,
( ~ l0(a)
| p1(a,a,a) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
( ~ l0(a)
| p1(a,a,a) ),
inference(modus_ponens,[status(thm)],[38,35]) ).
tff(40,plain,
p1(a,a,a),
inference(unit_resolution,[status(thm)],[39,34]) ).
tff(41,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(a)
| ~ p1(a,a,a) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(a)
| ~ p1(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(a)
| ~ p1(a,a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(a)
| ~ p1(a,a,a) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
n2(a),
inference(unit_resolution,[status(thm)],[43,40,31]) ).
tff(45,plain,
( ( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(a)
| ~ n2(a)
| p3(a,a,a) )
<=> ( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(a)
| ~ n2(a)
| p3(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(a)
| ~ n2(a)
| p3(a,a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(a)
| ~ n2(a)
| p3(a,a,a) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
p3(a,a,a),
inference(unit_resolution,[status(thm)],[47,44,24,14]) ).
tff(49,plain,
^ [H: $i,G: $i] :
refl(( ( ~ n0(H,G)
| l1(G,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
<=> ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
<=> ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
^ [H: $i,G: $i] :
rewrite(( ( l1(G,G)
| ~ n0(H,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [H: $i,G: $i] :
( l1(G,G)
| ~ n0(H,G) )
<=> ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,axiom,
! [H: $i,G: $i] :
( l1(G,G)
| ~ n0(H,G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_002) ).
tff(55,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[57,50]) ).
tff(59,plain,
( ( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(b,a)
| l1(a,a) )
<=> ( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(b,a)
| l1(a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(b,a)
| l1(a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(b,a)
| l1(a,a) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
l1(a,a),
inference(unit_resolution,[status(thm)],[61,10,58]) ).
tff(63,plain,
( ~ s4(a)
<=> ~ s4(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,axiom,
~ s4(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(65,plain,
~ s4(a),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(( ( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
<=> ( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
rewrite(( ( s4(A)
| ~ p3(B,C,D)
| ~ l1(A,C) )
<=> ( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( s4(A)
| ~ p3(B,C,D)
| ~ l1(A,C) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( s4(A)
| ~ p3(B,C,D)
| ~ l1(A,C) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_299) ).
tff(72,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(modus_ponens,[status(thm)],[74,67]) ).
tff(76,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| s4(a)
| ~ l1(a,a)
| ~ p3(a,a,a) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| s4(a)
| ~ l1(a,a)
| ~ p3(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( ( ~ l1(a,a)
| ~ p3(a,a,a)
| s4(a) )
<=> ( s4(a)
| ~ l1(a,a)
| ~ p3(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(a,a)
| ~ p3(a,a,a)
| s4(a) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| s4(a)
| ~ l1(a,a)
| ~ p3(a,a,a) ) ),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(a,a)
| ~ p3(a,a,a)
| s4(a) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| s4(a)
| ~ l1(a,a)
| ~ p3(a,a,a) ) ),
inference(transitivity,[status(thm)],[78,76]) ).
tff(80,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(a,a)
| ~ p3(a,a,a)
| s4(a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| s4(a)
| ~ l1(a,a)
| ~ p3(a,a,a) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
$false,
inference(unit_resolution,[status(thm)],[81,75,65,62,48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN301-1 : TPTP v9.0.0. Released v1.1.0.
% 0.07/0.12 % 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 12:32:01 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46 % SZS output start Proof
% See solution above
% 0.19/0.48 % E exiting
%------------------------------------------------------------------------------