%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO085-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:05:33 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 24
% Syntax : Number of formulae : 53 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 239 ( 58 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 344 ( 169 ~; 150 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 107 ( 98 !; 0 ?; 107 :)
% Comments :
%------------------------------------------------------------------------------
tff(end_point_type,type,
end_point: ( $i * $i ) > $o ).
tff(sk14_type,type,
sk14: $i ).
tff(ax0_sk11_type,type,
ax0_sk11: ( $i * $i ) > $i ).
tff(ax0_sk7_type,type,
ax0_sk7: $i > $i ).
tff(open_type,type,
open: $i > $o ).
tff(1,plain,
( open(sk14)
<=> open(sk14) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
open(sk14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_2_7_1_67) ).
tff(3,plain,
open(sk14),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [A: $i] :
refl(( ( ~ open(A)
| end_point(ax0_sk7(A),A) )
<=> ( ~ open(A)
| end_point(ax0_sk7(A),A) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [A: $i] :
( ~ open(A)
| end_point(ax0_sk7(A),A) )
<=> ! [A: $i] :
( ~ open(A)
| end_point(ax0_sk7(A),A) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [A: $i] :
( ~ open(A)
| end_point(ax0_sk7(A),A) )
<=> ! [A: $i] :
( ~ open(A)
| end_point(ax0_sk7(A),A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [A: $i] :
( ~ open(A)
| end_point(ax0_sk7(A),A) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax',open_defn_33) ).
tff(8,plain,
! [A: $i] :
( ~ open(A)
| end_point(ax0_sk7(A),A) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [A: $i] :
( ~ open(A)
| end_point(ax0_sk7(A),A) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [A: $i] :
( ~ open(A)
| end_point(ax0_sk7(A),A) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [A: $i] :
( ~ open(A)
| end_point(ax0_sk7(A),A) )
| ~ open(sk14)
| end_point(ax0_sk7(sk14),sk14) )
<=> ( ~ ! [A: $i] :
( ~ open(A)
| end_point(ax0_sk7(A),A) )
| ~ open(sk14)
| end_point(ax0_sk7(sk14),sk14) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [A: $i] :
( ~ open(A)
| end_point(ax0_sk7(A),A) )
| ~ open(sk14)
| end_point(ax0_sk7(sk14),sk14) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [A: $i] :
( ~ open(A)
| end_point(ax0_sk7(A),A) )
| ~ open(sk14)
| end_point(ax0_sk7(sk14),sk14) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
end_point(ax0_sk7(sk14),sk14),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [B: $i,A: $i] :
refl(( ( ~ end_point(A,B)
| end_point(ax0_sk11(A,B),B) )
<=> ( ~ end_point(A,B)
| end_point(ax0_sk11(A,B),B) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [B: $i,A: $i] :
( ~ end_point(A,B)
| end_point(ax0_sk11(A,B),B) )
<=> ! [B: $i,A: $i] :
( ~ end_point(A,B)
| end_point(ax0_sk11(A,B),B) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [B: $i,A: $i] :
( ~ end_point(A,B)
| end_point(ax0_sk11(A,B),B) )
<=> ! [B: $i,A: $i] :
( ~ end_point(A,B)
| end_point(ax0_sk11(A,B),B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [B: $i,A: $i] :
( ~ end_point(A,B)
| end_point(ax0_sk11(A,B),B) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax',c6_41) ).
tff(19,plain,
! [B: $i,A: $i] :
( ~ end_point(A,B)
| end_point(ax0_sk11(A,B),B) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [B: $i,A: $i] :
( ~ end_point(A,B)
| end_point(ax0_sk11(A,B),B) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [B: $i,A: $i] :
( ~ end_point(A,B)
| end_point(ax0_sk11(A,B),B) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ end_point(A,B)
| end_point(ax0_sk11(A,B),B) )
| ~ end_point(ax0_sk7(sk14),sk14)
| end_point(ax0_sk11(ax0_sk7(sk14),sk14),sk14) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ end_point(A,B)
| end_point(ax0_sk11(A,B),B) )
| ~ end_point(ax0_sk7(sk14),sk14)
| end_point(ax0_sk11(ax0_sk7(sk14),sk14),sk14) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [B: $i,A: $i] :
( ~ end_point(A,B)
| end_point(ax0_sk11(A,B),B) )
| ~ end_point(ax0_sk7(sk14),sk14)
| end_point(ax0_sk11(ax0_sk7(sk14),sk14),sk14) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [B: $i,A: $i] :
( ~ end_point(A,B)
| end_point(ax0_sk11(A,B),B) )
| ~ end_point(ax0_sk7(sk14),sk14)
| end_point(ax0_sk11(ax0_sk7(sk14),sk14),sk14) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
end_point(ax0_sk11(ax0_sk7(sk14),sk14),sk14),
inference(unit_resolution,[status(thm)],[24,21,14]) ).
tff(26,plain,
^ [B: $i,A: $i] :
refl(( ( ~ end_point(A,B)
| ( A != ax0_sk11(A,B) ) )
<=> ( ~ end_point(A,B)
| ( A != ax0_sk11(A,B) ) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [B: $i,A: $i] :
( ~ end_point(A,B)
| ( A != ax0_sk11(A,B) ) )
<=> ! [B: $i,A: $i] :
( ~ end_point(A,B)
| ( A != ax0_sk11(A,B) ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [B: $i,A: $i] :
( ~ end_point(A,B)
| ( A != ax0_sk11(A,B) ) )
<=> ! [B: $i,A: $i] :
( ~ end_point(A,B)
| ( A != ax0_sk11(A,B) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
! [B: $i,A: $i] :
( ~ end_point(A,B)
| ( A != ax0_sk11(A,B) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax',c6_42) ).
tff(30,plain,
! [B: $i,A: $i] :
( ~ end_point(A,B)
| ( A != ax0_sk11(A,B) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [B: $i,A: $i] :
( ~ end_point(A,B)
| ( A != ax0_sk11(A,B) ) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [B: $i,A: $i] :
( ~ end_point(A,B)
| ( A != ax0_sk11(A,B) ) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ end_point(A,B)
| ( A != ax0_sk11(A,B) ) )
| ~ end_point(ax0_sk7(sk14),sk14)
| ( ax0_sk7(sk14) != ax0_sk11(ax0_sk7(sk14),sk14) ) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ end_point(A,B)
| ( A != ax0_sk11(A,B) ) )
| ~ end_point(ax0_sk7(sk14),sk14)
| ( ax0_sk7(sk14) != ax0_sk11(ax0_sk7(sk14),sk14) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [B: $i,A: $i] :
( ~ end_point(A,B)
| ( A != ax0_sk11(A,B) ) )
| ~ end_point(ax0_sk7(sk14),sk14)
| ( ax0_sk7(sk14) != ax0_sk11(ax0_sk7(sk14),sk14) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [B: $i,A: $i] :
( ~ end_point(A,B)
| ( A != ax0_sk11(A,B) ) )
| ~ end_point(ax0_sk7(sk14),sk14)
| ( ax0_sk7(sk14) != ax0_sk11(ax0_sk7(sk14),sk14) ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
ax0_sk7(sk14) != ax0_sk11(ax0_sk7(sk14),sk14),
inference(unit_resolution,[status(thm)],[35,32,14]) ).
tff(37,plain,
^ [B: $i,A: $i] :
refl(( ( ( A = B )
| ~ end_point(B,sk14)
| ~ end_point(A,sk14) )
<=> ( ( A = B )
| ~ end_point(B,sk14)
| ~ end_point(A,sk14) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [B: $i,A: $i] :
( ( A = B )
| ~ end_point(B,sk14)
| ~ end_point(A,sk14) )
<=> ! [B: $i,A: $i] :
( ( A = B )
| ~ end_point(B,sk14)
| ~ end_point(A,sk14) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [B: $i,A: $i] :
( ( A = B )
| ~ end_point(B,sk14)
| ~ end_point(A,sk14) )
<=> ! [B: $i,A: $i] :
( ( A = B )
| ~ end_point(B,sk14)
| ~ end_point(A,sk14) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
^ [B: $i,A: $i] :
trans(monotonicity(rewrite(( ( ( A = B )
| ~ end_point(A,sk14) )
<=> ( ( A = B )
| ~ end_point(A,sk14) ) )),
( ( ( A = B )
| ~ end_point(A,sk14)
| ~ end_point(B,sk14) )
<=> ( ( A = B )
| ~ end_point(A,sk14)
| ~ end_point(B,sk14) ) )),
rewrite(( ( ( A = B )
| ~ end_point(A,sk14)
| ~ end_point(B,sk14) )
<=> ( ( A = B )
| ~ end_point(B,sk14)
| ~ end_point(A,sk14) ) )),
( ( ( A = B )
| ~ end_point(A,sk14)
| ~ end_point(B,sk14) )
<=> ( ( A = B )
| ~ end_point(B,sk14)
| ~ end_point(A,sk14) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [B: $i,A: $i] :
( ( A = B )
| ~ end_point(A,sk14)
| ~ end_point(B,sk14) )
<=> ! [B: $i,A: $i] :
( ( A = B )
| ~ end_point(B,sk14)
| ~ end_point(A,sk14) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ end_point(A,sk14)
| ~ end_point(B,sk14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_2_7_1_68) ).
tff(43,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ end_point(B,sk14)
| ~ end_point(A,sk14) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ end_point(B,sk14)
| ~ end_point(A,sk14) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ end_point(B,sk14)
| ~ end_point(A,sk14) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ end_point(B,sk14)
| ~ end_point(A,sk14) ),
inference(modus_ponens,[status(thm)],[45,38]) ).
tff(47,plain,
( ( ~ ! [B: $i,A: $i] :
( ( A = B )
| ~ end_point(B,sk14)
| ~ end_point(A,sk14) )
| ~ end_point(ax0_sk7(sk14),sk14)
| ( ax0_sk7(sk14) = ax0_sk11(ax0_sk7(sk14),sk14) )
| ~ end_point(ax0_sk11(ax0_sk7(sk14),sk14),sk14) )
<=> ( ~ ! [B: $i,A: $i] :
( ( A = B )
| ~ end_point(B,sk14)
| ~ end_point(A,sk14) )
| ~ end_point(ax0_sk7(sk14),sk14)
| ( ax0_sk7(sk14) = ax0_sk11(ax0_sk7(sk14),sk14) )
| ~ end_point(ax0_sk11(ax0_sk7(sk14),sk14),sk14) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ( ( ax0_sk7(sk14) = ax0_sk11(ax0_sk7(sk14),sk14) )
| ~ end_point(ax0_sk11(ax0_sk7(sk14),sk14),sk14)
| ~ end_point(ax0_sk7(sk14),sk14) )
<=> ( ~ end_point(ax0_sk7(sk14),sk14)
| ( ax0_sk7(sk14) = ax0_sk11(ax0_sk7(sk14),sk14) )
| ~ end_point(ax0_sk11(ax0_sk7(sk14),sk14),sk14) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ( ~ ! [B: $i,A: $i] :
( ( A = B )
| ~ end_point(B,sk14)
| ~ end_point(A,sk14) )
| ( ax0_sk7(sk14) = ax0_sk11(ax0_sk7(sk14),sk14) )
| ~ end_point(ax0_sk11(ax0_sk7(sk14),sk14),sk14)
| ~ end_point(ax0_sk7(sk14),sk14) )
<=> ( ~ ! [B: $i,A: $i] :
( ( A = B )
| ~ end_point(B,sk14)
| ~ end_point(A,sk14) )
| ~ end_point(ax0_sk7(sk14),sk14)
| ( ax0_sk7(sk14) = ax0_sk11(ax0_sk7(sk14),sk14) )
| ~ end_point(ax0_sk11(ax0_sk7(sk14),sk14),sk14) ) ),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
( ( ~ ! [B: $i,A: $i] :
( ( A = B )
| ~ end_point(B,sk14)
| ~ end_point(A,sk14) )
| ( ax0_sk7(sk14) = ax0_sk11(ax0_sk7(sk14),sk14) )
| ~ end_point(ax0_sk11(ax0_sk7(sk14),sk14),sk14)
| ~ end_point(ax0_sk7(sk14),sk14) )
<=> ( ~ ! [B: $i,A: $i] :
( ( A = B )
| ~ end_point(B,sk14)
| ~ end_point(A,sk14) )
| ~ end_point(ax0_sk7(sk14),sk14)
| ( ax0_sk7(sk14) = ax0_sk11(ax0_sk7(sk14),sk14) )
| ~ end_point(ax0_sk11(ax0_sk7(sk14),sk14),sk14) ) ),
inference(transitivity,[status(thm)],[49,47]) ).
tff(51,plain,
( ~ ! [B: $i,A: $i] :
( ( A = B )
| ~ end_point(B,sk14)
| ~ end_point(A,sk14) )
| ( ax0_sk7(sk14) = ax0_sk11(ax0_sk7(sk14),sk14) )
| ~ end_point(ax0_sk11(ax0_sk7(sk14),sk14),sk14)
| ~ end_point(ax0_sk7(sk14),sk14) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [B: $i,A: $i] :
( ( A = B )
| ~ end_point(B,sk14)
| ~ end_point(A,sk14) )
| ~ end_point(ax0_sk7(sk14),sk14)
| ( ax0_sk7(sk14) = ax0_sk11(ax0_sk7(sk14),sk14) )
| ~ end_point(ax0_sk11(ax0_sk7(sk14),sk14),sk14) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
$false,
inference(unit_resolution,[status(thm)],[52,46,14,36,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO085-1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 14:16:33 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% See solution above
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------