%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO013-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:05:19 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 34
% Syntax : Number of formulae : 74 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 422 ( 76 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 571 ( 239 ~; 295 |; 0 &)
% ( 37 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 226 ( 212 !; 0 ?; 226 :)
% Comments :
%------------------------------------------------------------------------------
tff(colinear_type,type,
colinear: ( $i * $i * $i ) > $o ).
tff(d1_type,type,
d1: $i ).
tff(d3_type,type,
d3: $i ).
tff(b_type,type,
b: $i ).
tff(d2_type,type,
d2: $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
( ~ colinear(d1,d2,d3)
<=> ~ colinear(d1,d2,d3) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ colinear(d1,d2,d3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d1d2d3_colinear) ).
tff(3,plain,
~ colinear(d1,d2,d3),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ colinear(U,V,W)
| colinear(V,U,W) )
<=> ( ~ colinear(U,V,W)
| colinear(V,U,W) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_5) ).
tff(8,plain,
! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) )
| ~ colinear(d2,d1,d3)
| colinear(d1,d2,d3) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) )
| ~ colinear(d2,d1,d3)
| colinear(d1,d2,d3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) )
| ~ colinear(d2,d1,d3)
| colinear(d1,d2,d3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) )
| ~ colinear(d2,d1,d3)
| colinear(d1,d2,d3) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ colinear(d2,d1,d3),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( colinear(a,b,d3)
<=> colinear(a,b,d3) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
colinear(a,b,d3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abd3_colinear) ).
tff(17,plain,
colinear(a,b,d3),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( colinear(a,b,d2)
<=> colinear(a,b,d2) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
colinear(a,b,d2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abd2_colinear) ).
tff(20,plain,
colinear(a,b,d2),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ( a != b )
<=> ( a != b ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_b) ).
tff(23,plain,
a != b,
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( ( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
<=> ( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ colinear(U,V,W)
| ~ colinear(U,V,X) )
<=> ( ~ colinear(U,V,X)
| ~ colinear(U,V,W) ) )),
( ( ~ colinear(U,V,W)
| ~ colinear(U,V,X)
| colinear(V,W,X) )
<=> ( ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ) )),
rewrite(( ( ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
<=> ( ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ) )),
( ( ~ colinear(U,V,W)
| ~ colinear(U,V,X)
| colinear(V,W,X) )
<=> ( ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ) )),
( ( ~ colinear(U,V,W)
| ~ colinear(U,V,X)
| colinear(V,W,X)
| ( U = V ) )
<=> ( ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X)
| ( U = V ) ) )),
rewrite(( ( ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X)
| ( U = V ) )
<=> ( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ) )),
( ( ~ colinear(U,V,W)
| ~ colinear(U,V,X)
| colinear(V,W,X)
| ( U = V ) )
<=> ( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ colinear(U,V,W)
| ~ colinear(U,V,X)
| colinear(V,W,X)
| ( U = V ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ colinear(U,V,W)
| ~ colinear(U,V,X)
| colinear(V,W,X)
| ( U = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_2) ).
tff(30,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( a = b )
| ~ colinear(a,b,d2)
| ~ colinear(a,b,d3)
| colinear(b,d2,d3) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( a = b )
| ~ colinear(a,b,d2)
| ~ colinear(a,b,d3)
| colinear(b,d2,d3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ( ( a = b )
| ~ colinear(a,b,d3)
| ~ colinear(a,b,d2)
| colinear(b,d2,d3) )
<=> ( ( a = b )
| ~ colinear(a,b,d2)
| ~ colinear(a,b,d3)
| colinear(b,d2,d3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( a = b )
| ~ colinear(a,b,d3)
| ~ colinear(a,b,d2)
| colinear(b,d2,d3) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( a = b )
| ~ colinear(a,b,d2)
| ~ colinear(a,b,d3)
| colinear(b,d2,d3) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( a = b )
| ~ colinear(a,b,d3)
| ~ colinear(a,b,d2)
| colinear(b,d2,d3) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( a = b )
| ~ colinear(a,b,d2)
| ~ colinear(a,b,d3)
| colinear(b,d2,d3) ) ),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( a = b )
| ~ colinear(a,b,d3)
| ~ colinear(a,b,d2)
| colinear(b,d2,d3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( a = b )
| ~ colinear(a,b,d2)
| ~ colinear(a,b,d3)
| colinear(b,d2,d3) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
colinear(b,d2,d3),
inference(unit_resolution,[status(thm)],[39,33,23,20,17]) ).
tff(41,plain,
( colinear(a,b,d1)
<=> colinear(a,b,d1) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
colinear(a,b,d1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and1_colinear) ).
tff(43,plain,
colinear(a,b,d1),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( a = b )
| ~ colinear(a,b,d1)
| ~ colinear(a,b,d2)
| colinear(b,d2,d1) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( a = b )
| ~ colinear(a,b,d1)
| ~ colinear(a,b,d2)
| colinear(b,d2,d1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( a = b )
| ~ colinear(a,b,d1)
| ~ colinear(a,b,d2)
| colinear(b,d2,d1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( a = b )
| ~ colinear(a,b,d1)
| ~ colinear(a,b,d2)
| colinear(b,d2,d1) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
colinear(b,d2,d1),
inference(unit_resolution,[status(thm)],[46,33,23,43,20]) ).
tff(48,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| colinear(d2,d1,d3)
| ( b = d2 )
| ~ colinear(b,d2,d1)
| ~ colinear(b,d2,d3) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| colinear(d2,d1,d3)
| ( b = d2 )
| ~ colinear(b,d2,d1)
| ~ colinear(b,d2,d3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ( ( b = d2 )
| ~ colinear(b,d2,d3)
| ~ colinear(b,d2,d1)
| colinear(d2,d1,d3) )
<=> ( colinear(d2,d1,d3)
| ( b = d2 )
| ~ colinear(b,d2,d1)
| ~ colinear(b,d2,d3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( b = d2 )
| ~ colinear(b,d2,d3)
| ~ colinear(b,d2,d1)
| colinear(d2,d1,d3) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| colinear(d2,d1,d3)
| ( b = d2 )
| ~ colinear(b,d2,d1)
| ~ colinear(b,d2,d3) ) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( b = d2 )
| ~ colinear(b,d2,d3)
| ~ colinear(b,d2,d1)
| colinear(d2,d1,d3) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| colinear(d2,d1,d3)
| ( b = d2 )
| ~ colinear(b,d2,d1)
| ~ colinear(b,d2,d3) ) ),
inference(transitivity,[status(thm)],[50,48]) ).
tff(52,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( b = d2 )
| ~ colinear(b,d2,d3)
| ~ colinear(b,d2,d1)
| colinear(d2,d1,d3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| colinear(d2,d1,d3)
| ( b = d2 )
| ~ colinear(b,d2,d1)
| ~ colinear(b,d2,d3) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
b = d2,
inference(unit_resolution,[status(thm)],[53,33,47,40,14]) ).
tff(55,plain,
( colinear(b,d3,d1)
<=> colinear(d2,d3,d1) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( colinear(d2,d3,d1)
<=> colinear(b,d3,d1) ),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
( ~ colinear(d2,d3,d1)
<=> ~ colinear(b,d3,d1) ),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ colinear(U,V,W)
| colinear(W,U,V) )
<=> ( ~ colinear(U,V,W)
| colinear(W,U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_4) ).
tff(62,plain,
! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) )
| ~ colinear(d2,d3,d1)
| colinear(d1,d2,d3) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) )
| ~ colinear(d2,d3,d1)
| colinear(d1,d2,d3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) )
| ~ colinear(d2,d3,d1)
| colinear(d1,d2,d3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) )
| ~ colinear(d2,d3,d1)
| colinear(d1,d2,d3) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
~ colinear(d2,d3,d1),
inference(unit_resolution,[status(thm)],[67,64,3]) ).
tff(69,plain,
~ colinear(b,d3,d1),
inference(modus_ponens,[status(thm)],[68,57]) ).
tff(70,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( a = b )
| ~ colinear(a,b,d1)
| ~ colinear(a,b,d3)
| colinear(b,d3,d1) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( a = b )
| ~ colinear(a,b,d1)
| ~ colinear(a,b,d3)
| colinear(b,d3,d1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( a = b )
| ~ colinear(a,b,d1)
| ~ colinear(a,b,d3)
| colinear(b,d3,d1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( a = b )
| ~ colinear(a,b,d1)
| ~ colinear(a,b,d3)
| colinear(b,d3,d1) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
colinear(b,d3,d1),
inference(unit_resolution,[status(thm)],[72,33,23,43,17]) ).
tff(74,plain,
$false,
inference(unit_resolution,[status(thm)],[73,69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO013-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n002.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 14:05:46 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40 % SZS output start Proof
% See solution above
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------