%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO147-1 : 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 05:05:41 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.40s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 26
% Syntax : Number of formulae : 55 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 182 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 231 ( 108 ~; 104 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 4 ( 4 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; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 125 ( 116 !; 0 ?; 125 :)
% Comments :
%------------------------------------------------------------------------------
tff(incident_o_type,type,
incident_o: ( $i * $i ) > $o ).
tff(trajectory_of_type,type,
trajectory_of: $i > $i ).
tff(sk29_type,type,
sk29: $i ).
tff(sk27_type,type,
sk27: $i ).
tff(once_type,type,
once: $i > $o ).
tff(at_type,type,
at: ( $i * $i ) > $i ).
tff(at_the_same_time_type,type,
at_the_same_time: ( $i * $i ) > $i ).
tff(sk28_type,type,
sk28: $i ).
tff(connect_type,type,
connect: ( $i * $i * $i ) > $o ).
tff(1,plain,
( connect(sk28,sk29,sk27)
<=> connect(sk28,sk29,sk27) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
connect(sk28,sk29,sk27),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_156) ).
tff(3,plain,
connect(sk28,sk29,sk27),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ connect(A,B,C)
| once(at_the_same_time(at(A,C),at(B,C))) )
<=> ( ~ connect(A,B,C)
| once(at_the_same_time(at(A,C),at(B,C))) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ connect(A,B,C)
| once(at_the_same_time(at(A,C),at(B,C))) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ connect(A,B,C)
| once(at_the_same_time(at(A,C),at(B,C))) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ connect(A,B,C)
| once(at_the_same_time(at(A,C),at(B,C))) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ connect(A,B,C)
| once(at_the_same_time(at(A,C),at(B,C))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [B: $i,A: $i,C: $i] :
( ~ connect(A,B,C)
| once(at_the_same_time(at(A,C),at(B,C))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-3.ax',connect_defn_1) ).
tff(8,plain,
! [B: $i,A: $i,C: $i] :
( ~ connect(A,B,C)
| once(at_the_same_time(at(A,C),at(B,C))) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [B: $i,A: $i,C: $i] :
( ~ connect(A,B,C)
| once(at_the_same_time(at(A,C),at(B,C))) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [B: $i,A: $i,C: $i] :
( ~ connect(A,B,C)
| once(at_the_same_time(at(A,C),at(B,C))) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ connect(A,B,C)
| once(at_the_same_time(at(A,C),at(B,C))) )
| ~ connect(sk28,sk29,sk27)
| once(at_the_same_time(at(sk28,sk27),at(sk29,sk27))) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ connect(A,B,C)
| once(at_the_same_time(at(A,C),at(B,C))) )
| ~ connect(sk28,sk29,sk27)
| once(at_the_same_time(at(sk28,sk27),at(sk29,sk27))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ connect(A,B,C)
| once(at_the_same_time(at(A,C),at(B,C))) )
| ~ connect(sk28,sk29,sk27)
| once(at_the_same_time(at(sk28,sk27),at(sk29,sk27))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ connect(A,B,C)
| once(at_the_same_time(at(A,C),at(B,C))) )
| ~ connect(sk28,sk29,sk27)
| once(at_the_same_time(at(sk28,sk27),at(sk29,sk27))) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
once(at_the_same_time(at(sk28,sk27),at(sk29,sk27))),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [B: $i,A: $i] :
refl(( ( ~ once(at_the_same_time(A,B))
| once(B) )
<=> ( ~ once(at_the_same_time(A,B))
| once(B) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(B) )
<=> ! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(B) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(B) )
<=> ! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(B) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-3.ax',conjunction_at_the_same_time_9) ).
tff(19,plain,
! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(B) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(B) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(B) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(B) )
| ~ once(at_the_same_time(at(sk28,sk27),at(sk29,sk27)))
| once(at(sk29,sk27)) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(B) )
| ~ once(at_the_same_time(at(sk28,sk27),at(sk29,sk27)))
| once(at(sk29,sk27)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(B) )
| ~ once(at_the_same_time(at(sk28,sk27),at(sk29,sk27)))
| once(at(sk29,sk27)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(B) )
| ~ once(at_the_same_time(at(sk28,sk27),at(sk29,sk27)))
| once(at(sk29,sk27)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
once(at(sk29,sk27)),
inference(unit_resolution,[status(thm)],[24,21,14]) ).
tff(26,plain,
^ [B: $i,A: $i] :
refl(( ( ~ once(at(A,B))
| incident_o(B,trajectory_of(A)) )
<=> ( ~ once(at(A,B))
| incident_o(B,trajectory_of(A)) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [B: $i,A: $i] :
( ~ once(at(A,B))
| incident_o(B,trajectory_of(A)) )
<=> ! [B: $i,A: $i] :
( ~ once(at(A,B))
| incident_o(B,trajectory_of(A)) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [B: $i,A: $i] :
( ~ once(at(A,B))
| incident_o(B,trajectory_of(A)) )
<=> ! [B: $i,A: $i] :
( ~ once(at(A,B))
| incident_o(B,trajectory_of(A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
! [B: $i,A: $i] :
( ~ once(at(A,B))
| incident_o(B,trajectory_of(A)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-3.ax',at_on_trajectory_10) ).
tff(30,plain,
! [B: $i,A: $i] :
( ~ once(at(A,B))
| incident_o(B,trajectory_of(A)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [B: $i,A: $i] :
( ~ once(at(A,B))
| incident_o(B,trajectory_of(A)) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [B: $i,A: $i] :
( ~ once(at(A,B))
| incident_o(B,trajectory_of(A)) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ once(at(A,B))
| incident_o(B,trajectory_of(A)) )
| ~ once(at(sk29,sk27))
| incident_o(sk27,trajectory_of(sk29)) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ once(at(A,B))
| incident_o(B,trajectory_of(A)) )
| ~ once(at(sk29,sk27))
| incident_o(sk27,trajectory_of(sk29)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [B: $i,A: $i] :
( ~ once(at(A,B))
| incident_o(B,trajectory_of(A)) )
| ~ once(at(sk29,sk27))
| incident_o(sk27,trajectory_of(sk29)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [B: $i,A: $i] :
( ~ once(at(A,B))
| incident_o(B,trajectory_of(A)) )
| ~ once(at(sk29,sk27))
| incident_o(sk27,trajectory_of(sk29)) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
incident_o(sk27,trajectory_of(sk29)),
inference(unit_resolution,[status(thm)],[35,32,25]) ).
tff(37,plain,
^ [B: $i,A: $i] :
refl(( ( ~ once(at_the_same_time(A,B))
| once(A) )
<=> ( ~ once(at_the_same_time(A,B))
| once(A) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(A) )
<=> ! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(A) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(A) )
<=> ! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(A) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-3.ax',conjunction_at_the_same_time_8) ).
tff(41,plain,
! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(A) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(A) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(A) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(A) )
| ~ once(at_the_same_time(at(sk28,sk27),at(sk29,sk27)))
| once(at(sk28,sk27)) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(A) )
| ~ once(at_the_same_time(at(sk28,sk27),at(sk29,sk27)))
| once(at(sk28,sk27)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(A) )
| ~ once(at_the_same_time(at(sk28,sk27),at(sk29,sk27)))
| once(at(sk28,sk27)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [B: $i,A: $i] :
( ~ once(at_the_same_time(A,B))
| once(A) )
| ~ once(at_the_same_time(at(sk28,sk27),at(sk29,sk27)))
| once(at(sk28,sk27)) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
once(at(sk28,sk27)),
inference(unit_resolution,[status(thm)],[46,43,14]) ).
tff(48,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ once(at(A,B))
| incident_o(B,trajectory_of(A)) )
| ~ once(at(sk28,sk27))
| incident_o(sk27,trajectory_of(sk28)) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ once(at(A,B))
| incident_o(B,trajectory_of(A)) )
| ~ once(at(sk28,sk27))
| incident_o(sk27,trajectory_of(sk28)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [B: $i,A: $i] :
( ~ once(at(A,B))
| incident_o(B,trajectory_of(A)) )
| ~ once(at(sk28,sk27))
| incident_o(sk27,trajectory_of(sk28)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [B: $i,A: $i] :
( ~ once(at(A,B))
| incident_o(B,trajectory_of(A)) )
| ~ once(at(sk28,sk27))
| incident_o(sk27,trajectory_of(sk28)) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
incident_o(sk27,trajectory_of(sk28)),
inference(unit_resolution,[status(thm)],[50,32,47]) ).
tff(52,plain,
( ( ~ incident_o(sk27,trajectory_of(sk28))
| ~ incident_o(sk27,trajectory_of(sk29)) )
<=> ( ~ incident_o(sk27,trajectory_of(sk28))
| ~ incident_o(sk27,trajectory_of(sk29)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
( ~ incident_o(sk27,trajectory_of(sk28))
| ~ incident_o(sk27,trajectory_of(sk29)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_157) ).
tff(54,plain,
( ~ incident_o(sk27,trajectory_of(sk28))
| ~ incident_o(sk27,trajectory_of(sk29)) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
$false,
inference(unit_resolution,[status(thm)],[54,51,36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO147-1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % 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 14:33:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.40 % SZS status Unsatisfiable
% 0.12/0.40 % SZS output start Proof
% See solution above
% 0.12/0.41 % E exiting
%------------------------------------------------------------------------------