%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN232-1 : 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 05:38:33 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 31
% Syntax : Number of formulae : 67 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 269 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 356 ( 166 ~; 160 |; 0 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 12 ( 12 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 120 ( 109 !; 0 ?; 120 :)
% Comments :
%------------------------------------------------------------------------------
tff(n2_type,type,
n2: $i > $o ).
tff(d_type,type,
d: $i ).
tff(m2_type,type,
m2: $i > $o ).
tff(b_type,type,
b: $i ).
tff(k1_type,type,
k1: $i > $o ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(l3_type,type,
l3: ( $i * $i ) > $o ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(p0_type,type,
p0: ( $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/sandbox2/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(d,b)
<=> n0(d,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
n0(d,b),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_7) ).
tff(10,plain,
n0(d,b),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(b)
| ~ n0(d,b) )
<=> ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(b)
| ~ n0(d,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(b)
| ~ n0(d,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(b)
| ~ n0(d,b) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
k1(b),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
( ( m2(b)
| ~ k1(b) )
<=> ( m2(b)
| ~ k1(b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
( m2(b)
| ~ k1(b) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_136) ).
tff(17,plain,
( m2(b)
| ~ k1(b) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
m2(b),
inference(unit_resolution,[status(thm)],[17,14]) ).
tff(19,plain,
( ~ l3(d,d)
<=> ~ l3(d,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
~ l3(d,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(21,plain,
~ l3(d,d),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
^ [C: $i] :
refl(( ( ~ n2(C)
| ~ m2(b)
| l3(C,C) )
<=> ( ~ n2(C)
| ~ m2(b)
| l3(C,C) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [C: $i] :
( ~ n2(C)
| ~ m2(b)
| l3(C,C) )
<=> ! [C: $i] :
( ~ n2(C)
| ~ m2(b)
| l3(C,C) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [C: $i] :
( ~ n2(C)
| ~ m2(b)
| l3(C,C) )
<=> ! [C: $i] :
( ~ n2(C)
| ~ m2(b)
| l3(C,C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
^ [C: $i] :
trans(monotonicity(rewrite(( ( l3(C,C)
| ~ n2(C) )
<=> ( ~ n2(C)
| l3(C,C) ) )),
( ( l3(C,C)
| ~ n2(C)
| ~ m2(b) )
<=> ( ~ n2(C)
| l3(C,C)
| ~ m2(b) ) )),
rewrite(( ( ~ n2(C)
| l3(C,C)
| ~ m2(b) )
<=> ( ~ n2(C)
| ~ m2(b)
| l3(C,C) ) )),
( ( l3(C,C)
| ~ n2(C)
| ~ m2(b) )
<=> ( ~ n2(C)
| ~ m2(b)
| l3(C,C) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [C: $i] :
( l3(C,C)
| ~ n2(C)
| ~ m2(b) )
<=> ! [C: $i] :
( ~ n2(C)
| ~ m2(b)
| l3(C,C) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,axiom,
! [C: $i] :
( l3(C,C)
| ~ n2(C)
| ~ m2(b) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_217) ).
tff(28,plain,
! [C: $i] :
( ~ n2(C)
| ~ m2(b)
| l3(C,C) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [C: $i] :
( ~ n2(C)
| ~ m2(b)
| l3(C,C) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
! [C: $i] :
( ~ n2(C)
| ~ m2(b)
| l3(C,C) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [C: $i] :
( ~ n2(C)
| ~ m2(b)
| l3(C,C) ),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,plain,
( ( ~ ! [C: $i] :
( ~ n2(C)
| ~ m2(b)
| l3(C,C) )
| l3(d,d)
| ~ m2(b)
| ~ n2(d) )
<=> ( ~ ! [C: $i] :
( ~ n2(C)
| ~ m2(b)
| l3(C,C) )
| l3(d,d)
| ~ m2(b)
| ~ n2(d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ( ~ n2(d)
| ~ m2(b)
| l3(d,d) )
<=> ( l3(d,d)
| ~ m2(b)
| ~ n2(d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ( ~ ! [C: $i] :
( ~ n2(C)
| ~ m2(b)
| l3(C,C) )
| ~ n2(d)
| ~ m2(b)
| l3(d,d) )
<=> ( ~ ! [C: $i] :
( ~ n2(C)
| ~ m2(b)
| l3(C,C) )
| l3(d,d)
| ~ m2(b)
| ~ n2(d) ) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ( ~ ! [C: $i] :
( ~ n2(C)
| ~ m2(b)
| l3(C,C) )
| ~ n2(d)
| ~ m2(b)
| l3(d,d) )
<=> ( ~ ! [C: $i] :
( ~ n2(C)
| ~ m2(b)
| l3(C,C) )
| l3(d,d)
| ~ m2(b)
| ~ n2(d) ) ),
inference(transitivity,[status(thm)],[34,32]) ).
tff(36,plain,
( ~ ! [C: $i] :
( ~ n2(C)
| ~ m2(b)
| l3(C,C) )
| ~ n2(d)
| ~ m2(b)
| l3(d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [C: $i] :
( ~ n2(C)
| ~ m2(b)
| l3(C,C) )
| l3(d,d)
| ~ m2(b)
| ~ n2(d) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( ~ m2(b)
| ~ n2(d) ),
inference(unit_resolution,[status(thm)],[37,31,21]) ).
tff(39,plain,
~ n2(d),
inference(unit_resolution,[status(thm)],[38,18]) ).
tff(40,plain,
^ [B: $i,C: $i] :
refl(( ( ~ p0(C,B)
| p1(B,B,B) )
<=> ( ~ p0(C,B)
| p1(B,B,B) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
<=> ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
<=> ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
^ [B: $i,C: $i] :
rewrite(( ( p1(B,B,B)
| ~ p0(C,B) )
<=> ( ~ p0(C,B)
| p1(B,B,B) ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [B: $i,C: $i] :
( p1(B,B,B)
| ~ p0(C,B) )
<=> ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,axiom,
! [B: $i,C: $i] :
( p1(B,B,B)
| ~ p0(C,B) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_085) ).
tff(46,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
( p0(b,d)
<=> p0(b,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,axiom,
p0(b,d),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_10) ).
tff(52,plain,
p0(b,d),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
( ( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(b,d)
| p1(d,d,d) )
<=> ( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(b,d)
| p1(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(b,d)
| p1(d,d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(b,d)
| p1(d,d,d) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
p1(d,d,d),
inference(unit_resolution,[status(thm)],[55,52,49]) ).
tff(57,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(58,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)],[57]) ).
tff(59,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(60,axiom,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_137) ).
tff(61,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(d)
| ~ p1(d,d,d) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(d)
| ~ p1(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(d)
| ~ p1(d,d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(d)
| ~ p1(d,d,d) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
$false,
inference(unit_resolution,[status(thm)],[66,63,56,39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN232-1 : TPTP v9.0.0. Released v1.1.0.
% 0.03/0.12 % 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 12:30:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.46 % SZS status Unsatisfiable
% 0.20/0.46 % SZS output start Proof
% See solution above
% 0.20/0.48 % E exiting
%------------------------------------------------------------------------------