%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWX233-1 : TPTP v9.3.0. Released v9.3.0.
% 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 : Tue May 5 07:08:19 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 38 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 51 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 3 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 27 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
tff(btrue_type,type,
btrue: $i ).
tff(eq_type,type,
eq: ( $i * $i ) > $i ).
tff(bfalse_type,type,
bfalse: $i ).
tff(prop1_type,type,
prop1: $i > $i ).
tff(nil_type,type,
nil: $i ).
tff(f_type,type,
f: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( eq(X,X) = btrue )
<=> ( eq(X,X) = btrue ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( eq(X,X) = btrue )
<=> ! [X: $i] : ( eq(X,X) = btrue ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( eq(X,X) = btrue )
<=> ! [X: $i] : ( eq(X,X) = btrue ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( eq(X,X) = btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
tff(5,plain,
! [X: $i] : ( eq(X,X) = btrue ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( eq(X,X) = btrue ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( eq(X,X) = btrue ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( eq(X,X) = btrue )
| ( eq(bfalse,bfalse) = btrue ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
eq(bfalse,bfalse) = btrue,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( eq(btrue,bfalse) = bfalse )
<=> ( eq(btrue,bfalse) = bfalse ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
eq(btrue,bfalse) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
tff(12,plain,
eq(btrue,bfalse) = bfalse,
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( ( f(nil) = btrue )
<=> ( f(nil) = btrue ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
f(nil) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
tff(15,plain,
f(nil) = btrue,
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
eq(f(nil),bfalse) = eq(btrue,bfalse),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
^ [X: $i] :
refl(( ( prop1(X) = eq(f(X),bfalse) )
<=> ( prop1(X) = eq(f(X),bfalse) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [X: $i] : ( prop1(X) = eq(f(X),bfalse) )
<=> ! [X: $i] : ( prop1(X) = eq(f(X),bfalse) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [X: $i] : ( prop1(X) = eq(f(X),bfalse) )
<=> ! [X: $i] : ( prop1(X) = eq(f(X),bfalse) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
! [X: $i] : ( prop1(X) = eq(f(X),bfalse) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
tff(21,plain,
! [X: $i] : ( prop1(X) = eq(f(X),bfalse) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [X: $i] : ( prop1(X) = eq(f(X),bfalse) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [X: $i] : ( prop1(X) = eq(f(X),bfalse) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
( ~ ! [X: $i] : ( prop1(X) = eq(f(X),bfalse) )
| ( prop1(nil) = eq(f(nil),bfalse) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
prop1(nil) = eq(f(nil),bfalse),
inference(unit_resolution,[status(thm)],[24,23]) ).
tff(26,plain,
prop1(nil) = bfalse,
inference(transitivity,[status(thm)],[25,16,12]) ).
tff(27,plain,
eq(prop1(nil),bfalse) = eq(bfalse,bfalse),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
eq(prop1(nil),bfalse) = btrue,
inference(transitivity,[status(thm)],[27,9]) ).
tff(29,plain,
^ [X: $i] :
refl(( ( eq(prop1(X),bfalse) != btrue )
<=> ( eq(prop1(X),bfalse) != btrue ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [X: $i] : ( eq(prop1(X),bfalse) != btrue )
<=> ! [X: $i] : ( eq(prop1(X),bfalse) != btrue ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [X: $i] : ( eq(prop1(X),bfalse) != btrue )
<=> ! [X: $i] : ( eq(prop1(X),bfalse) != btrue ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
! [X: $i] : ( eq(prop1(X),bfalse) != btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(33,plain,
! [X: $i] : ( eq(prop1(X),bfalse) != btrue ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [X: $i] : ( eq(prop1(X),bfalse) != btrue ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [X: $i] : ( eq(prop1(X),bfalse) != btrue ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [X: $i] : ( eq(prop1(X),bfalse) != btrue )
| ( eq(prop1(nil),bfalse) != btrue ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
eq(prop1(nil),bfalse) != btrue,
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
$false,
inference(unit_resolution,[status(thm)],[37,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX233-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.16/0.33 % Computer : n016.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 13:07:38 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.19/0.37 % SZS status Unsatisfiable
% 0.19/0.37 % SZS output start Proof
% See solution above
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------