%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO112-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:05:37 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 31
% Syntax : Number of formulae : 72 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 480 ( 59 equ)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 682 ( 304 ~; 337 |; 0 &)
% ( 41 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 30 ( 30 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 313 ( 287 !; 0 ?; 313 :)
% Comments :
%------------------------------------------------------------------------------
tff(between_c_type,type,
between_c: ( $i * $i * $i * $i ) > $o ).
tff(sk16_type,type,
sk16: $i ).
tff(sk17_type,type,
sk17: $i ).
tff(sk18_type,type,
sk18: $i ).
tff(sk15_type,type,
sk15: $i ).
tff(part_of_type,type,
part_of: ( $i * $i ) > $o ).
tff(ax1_sk1_type,type,
ax1_sk1: ( $i * $i * $i * $i ) > $i ).
tff(end_point_type,type,
end_point: ( $i * $i ) > $o ).
tff(inner_point_type,type,
inner_point: ( $i * $i ) > $o ).
tff(1,plain,
( between_c(sk15,sk16,sk17,sk18)
<=> between_c(sk15,sk16,sk17,sk18) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
between_c(sk15,sk16,sk17,sk18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_3_8_2_77) ).
tff(3,plain,
between_c(sk15,sk16,sk17,sk18),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(( ( ~ between_c(A,B,C,D)
| part_of(ax1_sk1(D,C,B,A),A) )
<=> ( ~ between_c(A,B,C,D)
| part_of(ax1_sk1(D,C,B,A),A) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| part_of(ax1_sk1(D,C,B,A),A) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| part_of(ax1_sk1(D,C,B,A),A) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| part_of(ax1_sk1(D,C,B,A),A) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| part_of(ax1_sk1(D,C,B,A),A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| part_of(ax1_sk1(D,C,B,A),A) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-1.ax',between_c_defn_2) ).
tff(8,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| part_of(ax1_sk1(D,C,B,A),A) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| part_of(ax1_sk1(D,C,B,A),A) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| part_of(ax1_sk1(D,C,B,A),A) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| part_of(ax1_sk1(D,C,B,A),A) )
| ~ between_c(sk15,sk16,sk17,sk18)
| part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| part_of(ax1_sk1(D,C,B,A),A) )
| ~ between_c(sk15,sk16,sk17,sk18)
| part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| part_of(ax1_sk1(D,C,B,A),A) )
| ~ between_c(sk15,sk16,sk17,sk18)
| part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| part_of(ax1_sk1(D,C,B,A),A) )
| ~ between_c(sk15,sk16,sk17,sk18)
| part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(( ( ~ between_c(A,B,C,D)
| end_point(B,ax1_sk1(D,C,B,A)) )
<=> ( ~ between_c(A,B,C,D)
| end_point(B,ax1_sk1(D,C,B,A)) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(B,ax1_sk1(D,C,B,A)) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(B,ax1_sk1(D,C,B,A)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(B,ax1_sk1(D,C,B,A)) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(B,ax1_sk1(D,C,B,A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(B,ax1_sk1(D,C,B,A)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-1.ax',between_c_defn_3) ).
tff(19,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(B,ax1_sk1(D,C,B,A)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(B,ax1_sk1(D,C,B,A)) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(B,ax1_sk1(D,C,B,A)) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(B,ax1_sk1(D,C,B,A)) )
| ~ between_c(sk15,sk16,sk17,sk18)
| end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15)) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(B,ax1_sk1(D,C,B,A)) )
| ~ between_c(sk15,sk16,sk17,sk18)
| end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(B,ax1_sk1(D,C,B,A)) )
| ~ between_c(sk15,sk16,sk17,sk18)
| end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(B,ax1_sk1(D,C,B,A)) )
| ~ between_c(sk15,sk16,sk17,sk18)
| end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(unit_resolution,[status(thm)],[24,21,3]) ).
tff(26,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(( ( ~ between_c(A,B,C,D)
| end_point(D,ax1_sk1(D,C,B,A)) )
<=> ( ~ between_c(A,B,C,D)
| end_point(D,ax1_sk1(D,C,B,A)) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(D,ax1_sk1(D,C,B,A)) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(D,ax1_sk1(D,C,B,A)) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(D,ax1_sk1(D,C,B,A)) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(D,ax1_sk1(D,C,B,A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(D,ax1_sk1(D,C,B,A)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-1.ax',between_c_defn_4) ).
tff(30,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(D,ax1_sk1(D,C,B,A)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(D,ax1_sk1(D,C,B,A)) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(D,ax1_sk1(D,C,B,A)) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(D,ax1_sk1(D,C,B,A)) )
| ~ between_c(sk15,sk16,sk17,sk18)
| end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15)) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(D,ax1_sk1(D,C,B,A)) )
| ~ between_c(sk15,sk16,sk17,sk18)
| end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(D,ax1_sk1(D,C,B,A)) )
| ~ between_c(sk15,sk16,sk17,sk18)
| end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| end_point(D,ax1_sk1(D,C,B,A)) )
| ~ between_c(sk15,sk16,sk17,sk18)
| end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(unit_resolution,[status(thm)],[35,32,3]) ).
tff(37,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(( ( ~ between_c(A,B,C,D)
| inner_point(C,ax1_sk1(D,C,B,A)) )
<=> ( ~ between_c(A,B,C,D)
| inner_point(C,ax1_sk1(D,C,B,A)) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| inner_point(C,ax1_sk1(D,C,B,A)) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| inner_point(C,ax1_sk1(D,C,B,A)) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| inner_point(C,ax1_sk1(D,C,B,A)) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| inner_point(C,ax1_sk1(D,C,B,A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| inner_point(C,ax1_sk1(D,C,B,A)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-1.ax',between_c_defn_5) ).
tff(41,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| inner_point(C,ax1_sk1(D,C,B,A)) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| inner_point(C,ax1_sk1(D,C,B,A)) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| inner_point(C,ax1_sk1(D,C,B,A)) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| inner_point(C,ax1_sk1(D,C,B,A)) )
| ~ between_c(sk15,sk16,sk17,sk18)
| inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| inner_point(C,ax1_sk1(D,C,B,A)) )
| ~ between_c(sk15,sk16,sk17,sk18)
| inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| inner_point(C,ax1_sk1(D,C,B,A)) )
| ~ between_c(sk15,sk16,sk17,sk18)
| inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ between_c(A,B,C,D)
| inner_point(C,ax1_sk1(D,C,B,A)) )
| ~ between_c(sk15,sk16,sk17,sk18)
| inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(unit_resolution,[status(thm)],[46,43,3]) ).
tff(48,plain,
( ~ between_c(sk15,sk18,sk17,sk16)
<=> ~ between_c(sk15,sk18,sk17,sk16) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
~ between_c(sk15,sk18,sk17,sk16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_3_8_2_78) ).
tff(50,plain,
~ between_c(sk15,sk18,sk17,sk16),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
^ [B: $i,D: $i,A: $i,E: $i,C: $i] :
refl(( ( ~ part_of(C,D)
| between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) )
<=> ( ~ part_of(C,D)
| between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ part_of(C,D)
| between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) )
<=> ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ part_of(C,D)
| between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ part_of(C,D)
| between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) )
<=> ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ part_of(C,D)
| between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
^ [B: $i,D: $i,A: $i,E: $i,C: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ( A = B )
| ~ part_of(C,D) )
<=> ( ~ part_of(C,D)
| ( A = B ) ) )),
( ( ( A = B )
| ~ part_of(C,D)
| ~ end_point(A,C) )
<=> ( ~ part_of(C,D)
| ( A = B )
| ~ end_point(A,C) ) )),
rewrite(( ( ~ part_of(C,D)
| ( A = B )
| ~ end_point(A,C) )
<=> ( ~ part_of(C,D)
| ~ end_point(A,C)
| ( A = B ) ) )),
( ( ( A = B )
| ~ part_of(C,D)
| ~ end_point(A,C) )
<=> ( ~ part_of(C,D)
| ~ end_point(A,C)
| ( A = B ) ) )),
( ( ( A = B )
| ~ part_of(C,D)
| ~ end_point(A,C)
| ~ end_point(B,C) )
<=> ( ~ part_of(C,D)
| ~ end_point(A,C)
| ( A = B )
| ~ end_point(B,C) ) )),
rewrite(( ( ~ part_of(C,D)
| ~ end_point(A,C)
| ( A = B )
| ~ end_point(B,C) )
<=> ( ~ part_of(C,D)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) ) )),
( ( ( A = B )
| ~ part_of(C,D)
| ~ end_point(A,C)
| ~ end_point(B,C) )
<=> ( ~ part_of(C,D)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) ) )),
( ( ( A = B )
| ~ part_of(C,D)
| ~ end_point(A,C)
| ~ end_point(B,C)
| ~ inner_point(E,C) )
<=> ( ~ part_of(C,D)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B )
| ~ inner_point(E,C) ) )),
rewrite(( ( ~ part_of(C,D)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B )
| ~ inner_point(E,C) )
<=> ( ~ part_of(C,D)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) ) )),
( ( ( A = B )
| ~ part_of(C,D)
| ~ end_point(A,C)
| ~ end_point(B,C)
| ~ inner_point(E,C) )
<=> ( ~ part_of(C,D)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) ) )),
( ( ( A = B )
| ~ part_of(C,D)
| ~ end_point(A,C)
| ~ end_point(B,C)
| ~ inner_point(E,C)
| between_c(D,A,E,B) )
<=> ( ~ part_of(C,D)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B )
| between_c(D,A,E,B) ) )),
rewrite(( ( ~ part_of(C,D)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B )
| between_c(D,A,E,B) )
<=> ( ~ part_of(C,D)
| between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) ) )),
( ( ( A = B )
| ~ part_of(C,D)
| ~ end_point(A,C)
| ~ end_point(B,C)
| ~ inner_point(E,C)
| between_c(D,A,E,B) )
<=> ( ~ part_of(C,D)
| between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ( A = B )
| ~ part_of(C,D)
| ~ end_point(A,C)
| ~ end_point(B,C)
| ~ inner_point(E,C)
| between_c(D,A,E,B) )
<=> ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ part_of(C,D)
| between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,axiom,
! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ( A = B )
| ~ part_of(C,D)
| ~ end_point(A,C)
| ~ end_point(B,C)
| ~ inner_point(E,C)
| between_c(D,A,E,B) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-1.ax',between_c_defn_6) ).
tff(57,plain,
! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ part_of(C,D)
| between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ part_of(C,D)
| between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ part_of(C,D)
| between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ part_of(C,D)
| between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
( ( ~ ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ part_of(C,D)
| between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) )
| between_c(sk15,sk18,sk17,sk16)
| ~ inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15)
| ( sk18 = sk16 ) )
<=> ( ~ ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ part_of(C,D)
| between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) )
| between_c(sk15,sk18,sk17,sk16)
| ~ inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15)
| ( sk18 = sk16 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
( ( ~ part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15)
| between_c(sk15,sk18,sk17,sk16)
| ~ inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15))
| ( sk18 = sk16 ) )
<=> ( between_c(sk15,sk18,sk17,sk16)
| ~ inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15)
| ( sk18 = sk16 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ( ~ ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ part_of(C,D)
| between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) )
| ~ part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15)
| between_c(sk15,sk18,sk17,sk16)
| ~ inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15))
| ( sk18 = sk16 ) )
<=> ( ~ ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ part_of(C,D)
| between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) )
| between_c(sk15,sk18,sk17,sk16)
| ~ inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15)
| ( sk18 = sk16 ) ) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( ( ~ ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ part_of(C,D)
| between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) )
| ~ part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15)
| between_c(sk15,sk18,sk17,sk16)
| ~ inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15))
| ( sk18 = sk16 ) )
<=> ( ~ ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ part_of(C,D)
| between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) )
| between_c(sk15,sk18,sk17,sk16)
| ~ inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15)
| ( sk18 = sk16 ) ) ),
inference(transitivity,[status(thm)],[63,61]) ).
tff(65,plain,
( ~ ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ part_of(C,D)
| between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) )
| ~ part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15)
| between_c(sk15,sk18,sk17,sk16)
| ~ inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15))
| ( sk18 = sk16 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ part_of(C,D)
| between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ( A = B ) )
| between_c(sk15,sk18,sk17,sk16)
| ~ inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15)
| ( sk18 = sk16 ) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
sk18 = sk16,
inference(unit_resolution,[status(thm)],[66,60,50,47,36,25,14]) ).
tff(68,plain,
sk16 = sk18,
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
( between_c(sk15,sk18,sk17,sk16)
<=> between_c(sk15,sk16,sk17,sk18) ),
inference(monotonicity,[status(thm)],[67,68]) ).
tff(70,plain,
( between_c(sk15,sk16,sk17,sk18)
<=> between_c(sk15,sk18,sk17,sk16) ),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
between_c(sk15,sk18,sk17,sk16),
inference(modus_ponens,[status(thm)],[3,70]) ).
tff(72,plain,
$false,
inference(unit_resolution,[status(thm)],[50,71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO112-1 : TPTP v9.0.0. Released v2.4.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 14:27:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38 % SZS output start Proof
% See solution above
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------