%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO081-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:05:32 AM UTC 2025
% Result : Unsatisfiable 0.77s 0.98s
% Output : Proof 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 27
% Syntax : Number of formulae : 58 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 275 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 368 ( 162 ~; 177 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 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 : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 147 ( 135 !; 0 ?; 147 :)
% Comments :
%------------------------------------------------------------------------------
tff(incident_c_type,type,
incident_c: ( $i * $i ) > $o ).
tff(sk15_type,type,
sk15: $i ).
tff(ax0_sk1_type,type,
ax0_sk1: ( $i * $i ) > $i ).
tff(sk16_type,type,
sk16: $i ).
tff(sk14_type,type,
sk14: $i ).
tff(part_of_type,type,
part_of: ( $i * $i ) > $o ).
tff(1,plain,
( ~ part_of(sk14,sk16)
<=> ~ part_of(sk14,sk16) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ part_of(sk14,sk16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_transitivity_69) ).
tff(3,plain,
~ part_of(sk14,sk16),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [B: $i,A: $i] :
refl(( ( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) )
<=> ( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) )
<=> ! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) )
<=> ! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax',part_of_defn_3) ).
tff(8,plain,
! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) )
| ~ incident_c(ax0_sk1(sk14,sk16),sk16)
| part_of(sk14,sk16) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) )
| ~ incident_c(ax0_sk1(sk14,sk16),sk16)
| part_of(sk14,sk16) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) )
| ~ incident_c(ax0_sk1(sk14,sk16),sk16)
| part_of(sk14,sk16) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) )
| ~ incident_c(ax0_sk1(sk14,sk16),sk16)
| part_of(sk14,sk16) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ incident_c(ax0_sk1(sk14,sk16),sk16),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( part_of(sk15,sk16)
<=> part_of(sk15,sk16) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
part_of(sk15,sk16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_transitivity_68) ).
tff(17,plain,
part_of(sk15,sk16),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
<=> ( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
<=> ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
<=> ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [B: $i,A: $i,C: $i] :
trans(monotonicity(rewrite(( ( ~ part_of(A,B)
| ~ incident_c(C,A) )
<=> ( ~ incident_c(C,A)
| ~ part_of(A,B) ) )),
( ( ~ part_of(A,B)
| ~ incident_c(C,A)
| incident_c(C,B) )
<=> ( ~ incident_c(C,A)
| ~ part_of(A,B)
| incident_c(C,B) ) )),
rewrite(( ( ~ incident_c(C,A)
| ~ part_of(A,B)
| incident_c(C,B) )
<=> ( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ) )),
( ( ~ part_of(A,B)
| ~ incident_c(C,A)
| incident_c(C,B) )
<=> ( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ part_of(A,B)
| ~ incident_c(C,A)
| incident_c(C,B) )
<=> ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [B: $i,A: $i,C: $i] :
( ~ part_of(A,B)
| ~ incident_c(C,A)
| incident_c(C,B) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax',part_of_defn_1) ).
tff(24,plain,
! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| ~ part_of(sk15,sk16)
| incident_c(ax0_sk1(sk14,sk16),sk16)
| ~ incident_c(ax0_sk1(sk14,sk16),sk15) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| ~ part_of(sk15,sk16)
| incident_c(ax0_sk1(sk14,sk16),sk16)
| ~ incident_c(ax0_sk1(sk14,sk16),sk15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ( incident_c(ax0_sk1(sk14,sk16),sk16)
| ~ incident_c(ax0_sk1(sk14,sk16),sk15)
| ~ part_of(sk15,sk16) )
<=> ( ~ part_of(sk15,sk16)
| incident_c(ax0_sk1(sk14,sk16),sk16)
| ~ incident_c(ax0_sk1(sk14,sk16),sk15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| incident_c(ax0_sk1(sk14,sk16),sk16)
| ~ incident_c(ax0_sk1(sk14,sk16),sk15)
| ~ part_of(sk15,sk16) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| ~ part_of(sk15,sk16)
| incident_c(ax0_sk1(sk14,sk16),sk16)
| ~ incident_c(ax0_sk1(sk14,sk16),sk15) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| incident_c(ax0_sk1(sk14,sk16),sk16)
| ~ incident_c(ax0_sk1(sk14,sk16),sk15)
| ~ part_of(sk15,sk16) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| ~ part_of(sk15,sk16)
| incident_c(ax0_sk1(sk14,sk16),sk16)
| ~ incident_c(ax0_sk1(sk14,sk16),sk15) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| incident_c(ax0_sk1(sk14,sk16),sk16)
| ~ incident_c(ax0_sk1(sk14,sk16),sk15)
| ~ part_of(sk15,sk16) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| ~ part_of(sk15,sk16)
| incident_c(ax0_sk1(sk14,sk16),sk16)
| ~ incident_c(ax0_sk1(sk14,sk16),sk15) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
~ incident_c(ax0_sk1(sk14,sk16),sk15),
inference(unit_resolution,[status(thm)],[33,27,17,14]) ).
tff(35,plain,
^ [B: $i,A: $i] :
refl(( ( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) )
<=> ( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) )
<=> ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) )
<=> ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
^ [B: $i,A: $i] :
rewrite(( ( incident_c(ax0_sk1(A,B),A)
| part_of(A,B) )
<=> ( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [B: $i,A: $i] :
( incident_c(ax0_sk1(A,B),A)
| part_of(A,B) )
<=> ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,axiom,
! [B: $i,A: $i] :
( incident_c(ax0_sk1(A,B),A)
| part_of(A,B) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax',part_of_defn_2) ).
tff(41,plain,
! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
( ( ~ ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) )
| part_of(sk14,sk16)
| incident_c(ax0_sk1(sk14,sk16),sk14) )
<=> ( ~ ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) )
| part_of(sk14,sk16)
| incident_c(ax0_sk1(sk14,sk16),sk14) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) )
| part_of(sk14,sk16)
| incident_c(ax0_sk1(sk14,sk16),sk14) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) )
| part_of(sk14,sk16)
| incident_c(ax0_sk1(sk14,sk16),sk14) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
incident_c(ax0_sk1(sk14,sk16),sk14),
inference(unit_resolution,[status(thm)],[47,44,3]) ).
tff(49,plain,
( part_of(sk14,sk15)
<=> part_of(sk14,sk15) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
part_of(sk14,sk15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_transitivity_67) ).
tff(51,plain,
part_of(sk14,sk15),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| ~ part_of(sk14,sk15)
| ~ incident_c(ax0_sk1(sk14,sk16),sk14)
| incident_c(ax0_sk1(sk14,sk16),sk15) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| ~ part_of(sk14,sk15)
| ~ incident_c(ax0_sk1(sk14,sk16),sk14)
| incident_c(ax0_sk1(sk14,sk16),sk15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ( incident_c(ax0_sk1(sk14,sk16),sk15)
| ~ incident_c(ax0_sk1(sk14,sk16),sk14)
| ~ part_of(sk14,sk15) )
<=> ( ~ part_of(sk14,sk15)
| ~ incident_c(ax0_sk1(sk14,sk16),sk14)
| incident_c(ax0_sk1(sk14,sk16),sk15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| incident_c(ax0_sk1(sk14,sk16),sk15)
| ~ incident_c(ax0_sk1(sk14,sk16),sk14)
| ~ part_of(sk14,sk15) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| ~ part_of(sk14,sk15)
| ~ incident_c(ax0_sk1(sk14,sk16),sk14)
| incident_c(ax0_sk1(sk14,sk16),sk15) ) ),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| incident_c(ax0_sk1(sk14,sk16),sk15)
| ~ incident_c(ax0_sk1(sk14,sk16),sk14)
| ~ part_of(sk14,sk15) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| ~ part_of(sk14,sk15)
| ~ incident_c(ax0_sk1(sk14,sk16),sk14)
| incident_c(ax0_sk1(sk14,sk16),sk15) ) ),
inference(transitivity,[status(thm)],[54,52]) ).
tff(56,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| incident_c(ax0_sk1(sk14,sk16),sk15)
| ~ incident_c(ax0_sk1(sk14,sk16),sk14)
| ~ part_of(sk14,sk15) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) )
| ~ part_of(sk14,sk15)
| ~ incident_c(ax0_sk1(sk14,sk16),sk14)
| incident_c(ax0_sk1(sk14,sk16),sk15) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
$false,
inference(unit_resolution,[status(thm)],[57,27,51,48,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO081-1 : TPTP v9.0.0. Released v2.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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 14:16:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.77/0.98 % SZS status Unsatisfiable
% 0.77/0.98 % SZS output start Proof
% See solution above
% 0.77/0.98 % E exiting
%------------------------------------------------------------------------------