%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN150-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:38:21 AM UTC 2025
% Result : Unsatisfiable 0.17s 0.43s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 31 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 114 ( 53 ~; 49 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 73 ( 66 !; 0 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
tff(n2_type,type,
n2: $i > $o ).
tff(b_type,type,
b: $i ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(1,plain,
( ~ n2(b)
<=> ~ n2(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ n2(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(3,plain,
~ n2(b),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,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(5,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)],[4]) ).
tff(6,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(7,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(8,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
^ [B: $i,C: $i] :
refl(( ( ~ p0(C,B)
| p1(B,B,C) )
<=> ( ~ p0(C,B)
| p1(B,B,C) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,C) )
<=> ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,C) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,C) )
<=> ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,plain,
^ [B: $i,C: $i] :
rewrite(( ( p1(B,B,C)
| ~ p0(C,B) )
<=> ( ~ p0(C,B)
| p1(B,B,C) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [B: $i,C: $i] :
( p1(B,B,C)
| ~ p0(C,B) )
<=> ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,C) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,axiom,
! [B: $i,C: $i] :
( p1(B,B,C)
| ~ p0(C,B) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_069) ).
tff(17,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,C) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,C) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,C) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,C) ),
inference(modus_ponens,[status(thm)],[19,12]) ).
tff(21,plain,
( p0(b,d)
<=> p0(b,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
p0(b,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_10) ).
tff(23,plain,
p0(b,d),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
( ( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,C) )
| ~ p0(b,d)
| p1(d,d,b) )
<=> ( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,C) )
| ~ p0(b,d)
| p1(d,d,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,C) )
| ~ p0(b,d)
| p1(d,d,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,C) )
| ~ p0(b,d)
| p1(d,d,b) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
p1(d,d,b),
inference(unit_resolution,[status(thm)],[26,23,20]) ).
tff(28,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(b)
| ~ p1(d,d,b) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(b)
| ~ p1(d,d,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(b)
| ~ p1(d,d,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(b)
| ~ p1(d,d,b) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
$false,
inference(unit_resolution,[status(thm)],[30,27,10,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN150-1 : TPTP v9.0.0. Released v1.1.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n011.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 12:29:12 EDT 2025
% 0.11/0.31 % CPUTime :
% 0.17/0.43 % SZS status Unsatisfiable
% 0.17/0.43 % SZS output start Proof
% See solution above
% 0.17/0.44 % E exiting
%------------------------------------------------------------------------------