%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO148-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 19
% Syntax : Number of formulae : 37 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 193 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 297 ( 156 ~; 121 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 141 ( 126 !; 0 ?; 141 :)
% Comments :
%------------------------------------------------------------------------------
tff(once_type,type,
once: $i > $o ).
tff(at_the_same_time_type,type,
at_the_same_time: ( $i * $i ) > $i ).
tff(at_type,type,
at: ( $i * $i ) > $i ).
tff(sk27_type,type,
sk27: $i ).
tff(sk29_type,type,
sk29: $i ).
tff(sk28_type,type,
sk28: $i ).
tff(connect_type,type,
connect: ( $i * $i * $i ) > $o ).
tff(sk31_type,type,
sk31: $i ).
tff(sk30_type,type,
sk30: $i ).
tff(ordered_by_type,type,
ordered_by: ( $i * $i * $i ) > $o ).
tff(trajectory_of_type,type,
trajectory_of: $i > $i ).
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/sandbox/benchmark/theBenchmark.p',t14_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/sandbox/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,
( once(at_the_same_time(at(sk28,sk30),at(sk29,sk31)))
<=> once(at_the_same_time(at(sk28,sk30),at(sk29,sk31))) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
once(at_the_same_time(at(sk28,sk30),at(sk29,sk31))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_159) ).
tff(17,plain,
once(at_the_same_time(at(sk28,sk30),at(sk29,sk31))),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( ordered_by(trajectory_of(sk28),sk27,sk30)
<=> ordered_by(trajectory_of(sk28),sk27,sk30) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
ordered_by(trajectory_of(sk28),sk27,sk30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_158) ).
tff(20,plain,
ordered_by(trajectory_of(sk28),sk27,sk30),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ordered_by(trajectory_of(sk29),sk31,sk27)
<=> ordered_by(trajectory_of(sk29),sk31,sk27) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
ordered_by(trajectory_of(sk29),sk31,sk27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_157) ).
tff(23,plain,
ordered_by(trajectory_of(sk29),sk31,sk27),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
refl(( ( ~ ordered_by(trajectory_of(C),F,D)
| ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) )
<=> ( ~ ordered_by(trajectory_of(C),F,D)
| ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ordered_by(trajectory_of(C),F,D)
| ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) )
<=> ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ordered_by(trajectory_of(C),F,D)
| ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ordered_by(trajectory_of(C),F,D)
| ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) )
<=> ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ordered_by(trajectory_of(C),F,D)
| ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
^ [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ once(at_the_same_time(at(A,B),at(C,D)))
| ~ once(at_the_same_time(at(A,E),at(C,F))) )
<=> ( ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) ) )),
( ( ~ once(at_the_same_time(at(A,B),at(C,D)))
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ ordered_by(trajectory_of(A),B,E) )
<=> ( ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D)))
| ~ ordered_by(trajectory_of(A),B,E) ) )),
rewrite(( ( ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D)))
| ~ ordered_by(trajectory_of(A),B,E) )
<=> ( ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) ) )),
( ( ~ once(at_the_same_time(at(A,B),at(C,D)))
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ ordered_by(trajectory_of(A),B,E) )
<=> ( ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) ) )),
( ( ~ once(at_the_same_time(at(A,B),at(C,D)))
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ ordered_by(trajectory_of(A),B,E)
| ~ ordered_by(trajectory_of(C),F,D) )
<=> ( ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D)))
| ~ ordered_by(trajectory_of(C),F,D) ) )),
rewrite(( ( ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D)))
| ~ ordered_by(trajectory_of(C),F,D) )
<=> ( ~ ordered_by(trajectory_of(C),F,D)
| ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) ) )),
( ( ~ once(at_the_same_time(at(A,B),at(C,D)))
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ ordered_by(trajectory_of(A),B,E)
| ~ ordered_by(trajectory_of(C),F,D) )
<=> ( ~ ordered_by(trajectory_of(C),F,D)
| ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ once(at_the_same_time(at(A,B),at(C,D)))
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ ordered_by(trajectory_of(A),B,E)
| ~ ordered_by(trajectory_of(C),F,D) )
<=> ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ordered_by(trajectory_of(C),F,D)
| ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ once(at_the_same_time(at(A,B),at(C,D)))
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ ordered_by(trajectory_of(A),B,E)
| ~ ordered_by(trajectory_of(C),F,D) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-3.ax',homogeneous_behaviour_13) ).
tff(30,plain,
! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ordered_by(trajectory_of(C),F,D)
| ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ordered_by(trajectory_of(C),F,D)
| ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ordered_by(trajectory_of(C),F,D)
| ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ordered_by(trajectory_of(C),F,D)
| ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ordered_by(trajectory_of(C),F,D)
| ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) )
| ~ ordered_by(trajectory_of(sk29),sk31,sk27)
| ~ ordered_by(trajectory_of(sk28),sk27,sk30)
| ~ once(at_the_same_time(at(sk28,sk30),at(sk29,sk31)))
| ~ once(at_the_same_time(at(sk28,sk27),at(sk29,sk27))) )
<=> ( ~ ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ordered_by(trajectory_of(C),F,D)
| ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) )
| ~ ordered_by(trajectory_of(sk29),sk31,sk27)
| ~ ordered_by(trajectory_of(sk28),sk27,sk30)
| ~ once(at_the_same_time(at(sk28,sk30),at(sk29,sk31)))
| ~ once(at_the_same_time(at(sk28,sk27),at(sk29,sk27))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ordered_by(trajectory_of(C),F,D)
| ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) )
| ~ ordered_by(trajectory_of(sk29),sk31,sk27)
| ~ ordered_by(trajectory_of(sk28),sk27,sk30)
| ~ once(at_the_same_time(at(sk28,sk30),at(sk29,sk31)))
| ~ once(at_the_same_time(at(sk28,sk27),at(sk29,sk27))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ordered_by(trajectory_of(C),F,D)
| ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) )
| ~ ordered_by(trajectory_of(sk29),sk31,sk27)
| ~ ordered_by(trajectory_of(sk28),sk27,sk30)
| ~ once(at_the_same_time(at(sk28,sk30),at(sk29,sk31)))
| ~ once(at_the_same_time(at(sk28,sk27),at(sk29,sk27))) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
$false,
inference(unit_resolution,[status(thm)],[36,33,23,20,17,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO148-1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.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 14:33:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40 % SZS output start Proof
% See solution above
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------