%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO641+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:18:22 PM UTC 2026
% Result : Theorem 20.74s 3.72s
% Output : Proof 20.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 21
% Syntax : Number of formulae : 136 ( 40 unt; 0 def)
% Number of atoms : 288 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 249 ( 97 ~; 93 |; 37 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 512 ( 16 sgn 325 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD9) ).
fof(f8_nnf,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD8) ).
fof(f7_nnf,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f94,conjecture,
! [A,B,C,O,D,U,V,NWPNT1] :
( ( perp(C,D,A,V)
& perp(A,D,C,V)
& perp(A,C,D,V)
& perp(B,D,A,U)
& perp(A,D,B,U)
& perp(A,B,D,U)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> para(U,V,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL81109107) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,O,D,U,V,NWPNT1] :
( ( perp(C,D,A,V)
& perp(A,D,C,V)
& perp(A,C,D,V)
& perp(B,D,A,U)
& perp(A,D,B,U)
& perp(A,B,D,U)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> para(U,V,B,C) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,O,D,U,V,NWPNT1] :
( ~ para(U,V,B,C)
& perp(C,D,A,V)
& perp(A,D,C,V)
& perp(A,C,D,V)
& perp(B,D,A,U)
& perp(A,D,B,U)
& perp(A,B,D,U)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ para(sk25,sk26,sk21,sk22)
& perp(sk22,sk24,sk20,sk26)
& perp(sk20,sk24,sk22,sk26)
& perp(sk20,sk22,sk24,sk26)
& perp(sk21,sk24,sk20,sk25)
& perp(sk20,sk24,sk21,sk25)
& perp(sk20,sk21,sk24,sk25)
& circle(sk23,sk20,sk24,sk27)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27])],[f94_nnf]) ).
cnf(c115,plain,
perp(sk20,sk21,sk24,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p129,plain,
perp(sk24,sk25,sk20,sk21),
inference(resolution,[status(thm)],[c7,c115]) ).
cnf(p155,plain,
( para(sk24,sk25,X0,X1)
| ~ perp(sk20,sk21,X0,X1) ),
inference(resolution,[status(thm)],[c8,p129]) ).
fof(f53,axiom,
! [A,B,C,O] :
( ( coll(O,A,C)
& circle(O,A,B,C) )
=> perp(A,B,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD53) ).
fof(f53_nnf,plain,
! [A,B,C,O] :
( perp(A,B,B,C)
| ~ coll(O,A,C)
| ~ circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f53]) ).
fof(f53_sk,plain,
! [O,A,B,C] :
( perp(A,B,B,C)
| ~ coll(O,A,C)
| ~ circle(O,A,B,C) ),
inference(skolemisation,[status(esa)],[f53_nnf]) ).
cnf(c53,plain,
( perp(X0,X1,X1,X2)
| ~ coll(X3,X0,X2)
| ~ circle(X3,X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f53_sk]) ).
cnf(c113,plain,
circle(sk23,sk20,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p436,plain,
( perp(sk20,sk21,sk21,sk22)
| ~ coll(sk23,sk20,sk22) ),
inference(resolution,[status(thm)],[c53,c113]) ).
fof(f39,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD40) ).
fof(f39_nnf,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(p143,plain,
( para(sk20,sk21,X0,X1)
| ~ perp(sk24,sk25,X0,X1) ),
inference(resolution,[status(thm)],[c8,c115]) ).
cnf(p219,plain,
para(sk20,sk21,sk20,sk21),
inference(resolution,[status(thm)],[p143,p129]) ).
cnf(p310,plain,
eqangle(sk20,sk21,X0,X1,sk20,sk21,X0,X1),
inference(resolution,[status(thm)],[c39,p219]) ).
fof(f18,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(C,D,A,B,U,V,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD19) ).
fof(f18_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p397,plain,
eqangle(X0,X1,sk20,sk21,X0,X1,sk20,sk21),
inference(resolution,[status(thm)],[p310,c18]) ).
fof(f38,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD39) ).
fof(f38_nnf,plain,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
| ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [A,B,P,Q,C,D] :
( para(A,B,C,D)
| ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c38,plain,
( para(X0,X1,X2,X3)
| ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(p458,plain,
para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[p397,c38]) ).
fof(f66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD66) ).
fof(f66_nnf,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f66]) ).
fof(f66_sk,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f66_nnf]) ).
cnf(c66,plain,
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f66_sk]) ).
cnf(p462,plain,
coll(X0,X1,X1),
inference(resolution,[status(thm)],[p458,c66]) ).
fof(f2,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD3) ).
fof(f2_nnf,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p122,plain,
( coll(X2,X2,X0)
| ~ coll(X0,X1,X2) ),
inference(factoring,[status(thm)],[c2]) ).
cnf(p467,plain,
coll(X0,X0,X1),
inference(resolution,[status(thm)],[p462,p122]) ).
cnf(p468,plain,
( coll(X2,X1,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[p467,c2]) ).
cnf(p548,plain,
coll(X0,X1,X2),
inference(resolution,[status(thm)],[p468,p467]) ).
cnf(p652,plain,
perp(sk20,sk21,sk21,sk22),
inference(resolution,[status(thm)],[p436,p548]) ).
cnf(p1056,plain,
para(sk24,sk25,sk21,sk22),
inference(resolution,[status(thm)],[p155,p652]) ).
fof(f4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD5) ).
fof(f4_nnf,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p1058,plain,
para(sk21,sk22,sk24,sk25),
inference(resolution,[status(thm)],[p1056,c4]) ).
fof(f5,axiom,
! [A,B,C,D,E,F] :
( ( para(C,D,E,F)
& para(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD6) ).
fof(f5_nnf,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ para(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ para(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( para(X0,X1,X4,X5)
| ~ para(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p1069,plain,
( para(sk21,sk22,X0,X1)
| ~ para(sk24,sk25,X0,X1) ),
inference(resolution,[status(thm)],[p1058,c5]) ).
cnf(p464,plain,
eqangle(X0,X1,X2,X3,X0,X1,X2,X3),
inference(resolution,[status(thm)],[p458,c39]) ).
fof(f42,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD42b) ).
fof(f42_nnf,plain,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [P,A,B,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c42,plain,
( cyclic(X0,X1,X2,X3)
| ~ coll(X2,X3,X1)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(p546,plain,
( cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[p464,c42]) ).
cnf(p882,plain,
cyclic(X0,X1,X2,X2),
inference(resolution,[status(thm)],[p546,p548]) ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD15) ).
fof(f14_nnf,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p883,plain,
cyclic(X0,X1,X2,X1),
inference(resolution,[status(thm)],[p882,c14]) ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD16) ).
fof(f15_nnf,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p889,plain,
cyclic(X0,X1,X2,X0),
inference(resolution,[status(thm)],[p883,c15]) ).
fof(f40,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD41) ).
fof(f40_nnf,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(p909,plain,
eqangle(X0,X1,X0,X2,X1,X1,X1,X2),
inference(resolution,[status(thm)],[p889,c40]) ).
fof(f20,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(A,B,P,Q,C,D,U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD21) ).
fof(f20_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,P,Q,C,D,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,P,Q,C,D,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p943,plain,
eqangle(X0,X1,X1,X1,X0,X2,X1,X2),
inference(resolution,[status(thm)],[p909,c20]) ).
fof(f73,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( para(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> para(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD73) ).
fof(f73_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
fof(f73_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f73_nnf]) ).
cnf(c73,plain,
( para(X0,X1,X2,X3)
| ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f73_sk]) ).
cnf(p976,plain,
( para(X0,X2,X2,X2)
| ~ para(X0,X1,X2,X1) ),
inference(resolution,[status(thm)],[p943,c73]) ).
fof(f13,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD14) ).
fof(f13_nnf,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p888,plain,
cyclic(X0,X1,X1,X2),
inference(resolution,[status(thm)],[p883,c13]) ).
cnf(p896,plain,
eqangle(X0,X1,X0,X0,X2,X1,X2,X0),
inference(resolution,[status(thm)],[p888,c40]) ).
fof(f74,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( perp(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> perp(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD74) ).
fof(f74_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( perp(A,B,C,D)
| ~ perp(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f74]) ).
fof(f74_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( perp(A,B,C,D)
| ~ perp(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f74_nnf]) ).
cnf(c74,plain,
( perp(X0,X1,X2,X3)
| ~ perp(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f74_sk]) ).
cnf(p941,plain,
( perp(X2,X1,X2,X2)
| ~ perp(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[p896,c74]) ).
cnf(p654,plain,
perp(sk21,sk22,sk20,sk21),
inference(resolution,[status(thm)],[p652,c7]) ).
fof(f6,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD7) ).
fof(f6_nnf,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p659,plain,
perp(sk21,sk22,sk21,sk20),
inference(resolution,[status(thm)],[p654,c6]) ).
cnf(p7071,plain,
perp(sk20,sk22,sk20,sk20),
inference(resolution,[status(thm)],[p941,p659]) ).
cnf(p891,plain,
eqangle(X0,X1,X0,X2,X2,X1,X2,X2),
inference(resolution,[status(thm)],[p883,c40]) ).
cnf(p927,plain,
( perp(X2,X1,X2,X0)
| ~ perp(X0,X1,X0,X0) ),
inference(resolution,[status(thm)],[p891,c74]) ).
cnf(p7467,plain,
perp(X0,sk22,X0,sk20),
inference(resolution,[status(thm)],[p7071,p927]) ).
cnf(c119,plain,
perp(sk20,sk24,sk22,sk26),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p127,plain,
perp(sk20,sk24,sk26,sk22),
inference(resolution,[status(thm)],[c6,c119]) ).
cnf(p139,plain,
perp(sk26,sk22,sk20,sk24),
inference(resolution,[status(thm)],[p127,c7]) ).
cnf(p175,plain,
perp(sk26,sk22,sk24,sk20),
inference(resolution,[status(thm)],[p139,c6]) ).
cnf(p202,plain,
perp(sk24,sk20,sk26,sk22),
inference(resolution,[status(thm)],[p175,c7]) ).
cnf(p217,plain,
( para(sk24,sk20,X0,X1)
| ~ perp(sk26,sk22,X0,X1) ),
inference(resolution,[status(thm)],[p202,c8]) ).
cnf(p7582,plain,
para(sk24,sk20,sk26,sk20),
inference(resolution,[status(thm)],[p7467,p217]) ).
cnf(p8239,plain,
para(sk24,sk26,sk26,sk26),
inference(resolution,[status(thm)],[p976,p7582]) ).
cnf(p924,plain,
eqangle(X0,X1,X2,X1,X0,X2,X2,X2),
inference(resolution,[status(thm)],[p891,c20]) ).
cnf(p958,plain,
( para(X0,X2,X1,X2)
| ~ para(X0,X1,X1,X1) ),
inference(resolution,[status(thm)],[p924,c73]) ).
cnf(p8724,plain,
para(sk24,X0,sk26,X0),
inference(resolution,[status(thm)],[p8239,p958]) ).
fof(f3,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD4) ).
fof(f3_nnf,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p8870,plain,
para(sk24,X0,X0,sk26),
inference(resolution,[status(thm)],[p8724,c3]) ).
cnf(p9925,plain,
para(sk21,sk22,sk25,sk26),
inference(resolution,[status(thm)],[p1069,p8870]) ).
cnf(p9933,plain,
para(sk25,sk26,sk21,sk22),
inference(resolution,[status(thm)],[p9925,c4]) ).
cnf(c121,plain,
~ para(sk25,sk26,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p9962,plain,
$false,
inference(resolution,[status(thm)],[p9933,c121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO641+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 12:36:07 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 20.74/3.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.74/3.72 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------