%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO080-1 : 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 05:05:32 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 28 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 90 ( 30 ~; 49 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 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 : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 60 ( 54 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
tff(incident_c_type,type,
incident_c: ( $i * $i ) > $o ).
tff(sk14_type,type,
sk14: $i ).
tff(ax0_sk1_type,type,
ax0_sk1: ( $i * $i ) > $i ).
tff(part_of_type,type,
part_of: ( $i * $i ) > $o ).
tff(1,plain,
( ~ part_of(sk14,sk14)
<=> ~ part_of(sk14,sk14) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ part_of(sk14,sk14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_reflexivity) ).
tff(3,plain,
~ part_of(sk14,sk14),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,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(5,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)],[4]) ).
tff(6,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(7,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(8,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)],[7]) ).
tff(9,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(10,plain,
! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) )
| part_of(sk14,sk14)
| incident_c(ax0_sk1(sk14,sk14),sk14) )
<=> ( ~ ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) )
| part_of(sk14,sk14)
| incident_c(ax0_sk1(sk14,sk14),sk14) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) )
| part_of(sk14,sk14)
| incident_c(ax0_sk1(sk14,sk14),sk14) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [B: $i,A: $i] :
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) )
| part_of(sk14,sk14)
| incident_c(ax0_sk1(sk14,sk14),sk14) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
incident_c(ax0_sk1(sk14,sk14),sk14),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,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(19,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)],[18]) ).
tff(20,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(21,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(22,plain,
! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) )
| ~ incident_c(ax0_sk1(sk14,sk14),sk14)
| part_of(sk14,sk14) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) )
| ~ incident_c(ax0_sk1(sk14,sk14),sk14)
| part_of(sk14,sk14) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) )
| ~ incident_c(ax0_sk1(sk14,sk14),sk14)
| part_of(sk14,sk14) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [B: $i,A: $i] :
( ~ incident_c(ax0_sk1(A,B),B)
| part_of(A,B) )
| ~ incident_c(ax0_sk1(sk14,sk14),sk14)
| part_of(sk14,sk14) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
$false,
inference(unit_resolution,[status(thm)],[27,24,3,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO080-1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % 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 14:16:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% See solution above
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------