%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO573+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 01:18:11 PM UTC 2026
% Result : Theorem 160.32s 33.34s
% Output : Proof 160.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 32
% Syntax : Number of formulae : 215 ( 65 unt; 0 def)
% Number of atoms : 455 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 403 ( 163 ~; 159 |; 48 &)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 735 ( 38 sgn 453 !; 9 ?)
% 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/sandbox/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(f94,conjecture,
! [A,B,C,O,D,E,K,H,NWPNT1] :
( ( coll(H,B,E)
& coll(H,C,D)
& coll(K,C,D)
& circle(O,C,K,NWPNT1)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,A,B)
& perp(D,C,A,B)
& circle(O,A,B,C) )
=> cong(A,K,A,H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL214035) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,O,D,E,K,H,NWPNT1] :
( ( coll(H,B,E)
& coll(H,C,D)
& coll(K,C,D)
& circle(O,C,K,NWPNT1)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,A,B)
& perp(D,C,A,B)
& circle(O,A,B,C) )
=> cong(A,K,A,H) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,O,D,E,K,H,NWPNT1] :
( ~ cong(A,K,A,H)
& coll(H,B,E)
& coll(H,C,D)
& coll(K,C,D)
& circle(O,C,K,NWPNT1)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,A,B)
& perp(D,C,A,B)
& circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ cong(sk20,sk26,sk20,sk27)
& coll(sk27,sk21,sk25)
& coll(sk27,sk22,sk24)
& coll(sk26,sk22,sk24)
& circle(sk23,sk22,sk26,sk28)
& coll(sk25,sk20,sk22)
& perp(sk25,sk21,sk20,sk22)
& coll(sk24,sk20,sk21)
& perp(sk24,sk22,sk20,sk21)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28])],[f94_nnf]) ).
cnf(c114,plain,
perp(sk24,sk22,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p185,plain,
( para(sk24,sk22,X0,X1)
| ~ perp(sk20,sk21,X0,X1) ),
inference(resolution,[status(thm)],[c8,c114]) ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox/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]) ).
cnf(p179,plain,
perp(sk20,sk21,sk24,sk22),
inference(resolution,[status(thm)],[c7,c114]) ).
cnf(p1011,plain,
para(sk24,sk22,sk24,sk22),
inference(resolution,[status(thm)],[p185,p179]) ).
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/sandbox/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(p1013,plain,
eqangle(sk24,sk22,X0,X1,sk24,sk22,X0,X1),
inference(resolution,[status(thm)],[p1011,c39]) ).
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/sandbox/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(p1150,plain,
eqangle(X0,X1,sk24,sk22,X0,X1,sk24,sk22),
inference(resolution,[status(thm)],[p1013,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/sandbox/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(p1256,plain,
para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[p1150,c38]) ).
cnf(p1263,plain,
eqangle(X0,X1,X2,X3,X0,X1,X2,X3),
inference(resolution,[status(thm)],[p1256,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/sandbox/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(p1400,plain,
( cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[p1263,c42]) ).
fof(f66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox/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(p1265,plain,
coll(X0,X1,X1),
inference(resolution,[status(thm)],[p1256,c66]) ).
fof(f2,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox/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(p137,plain,
( coll(X2,X2,X0)
| ~ coll(X0,X1,X2) ),
inference(factoring,[status(thm)],[c2]) ).
cnf(p1271,plain,
coll(X0,X0,X1),
inference(resolution,[status(thm)],[p1265,p137]) ).
cnf(p1273,plain,
( coll(X2,X1,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[p1271,c2]) ).
cnf(p1404,plain,
coll(X0,X1,X2),
inference(resolution,[status(thm)],[p1273,p1271]) ).
cnf(p2253,plain,
cyclic(X0,X1,X2,X2),
inference(resolution,[status(thm)],[p1400,p1404]) ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox/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(p2254,plain,
cyclic(X0,X1,X2,X1),
inference(resolution,[status(thm)],[p2253,c14]) ).
fof(f13,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox/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(p2264,plain,
cyclic(X0,X1,X1,X2),
inference(resolution,[status(thm)],[p2254,c13]) ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox/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(p2275,plain,
cyclic(X0,X1,X0,X2),
inference(resolution,[status(thm)],[p2264,c15]) ).
fof(f16,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,E)
& cyclic(A,B,C,D) )
=> cyclic(B,C,D,E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD17) ).
fof(f16_nnf,plain,
! [A,B,C,D,E] :
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A,B,C,D,E] :
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p2296,plain,
( cyclic(X1,X0,X3,X2)
| ~ cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[p2275,c16]) ).
cnf(p10867,plain,
cyclic(X0,X1,X2,X3),
inference(resolution,[status(thm)],[p2296,p2275]) ).
fof(f40,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('/export/starexec/sandbox/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(p10868,plain,
eqangle(X0,X1,X0,X2,X3,X1,X3,X2),
inference(resolution,[status(thm)],[p10867,c40]) ).
fof(f51,axiom,
! [A,B,C,O,M] :
( ( eqangle(A,B,A,C,O,B,O,M)
& coll(M,B,C)
& circle(O,A,B,C) )
=> midp(M,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD51) ).
fof(f51_nnf,plain,
! [A,B,C,O,M] :
( midp(M,B,C)
| ~ eqangle(A,B,A,C,O,B,O,M)
| ~ coll(M,B,C)
| ~ circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f51]) ).
fof(f51_sk,plain,
! [O,A,B,C,M] :
( midp(M,B,C)
| ~ eqangle(A,B,A,C,O,B,O,M)
| ~ coll(M,B,C)
| ~ circle(O,A,B,C) ),
inference(skolemisation,[status(esa)],[f51_nnf]) ).
cnf(c51,plain,
( midp(X4,X1,X2)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X4)
| ~ coll(X4,X1,X2)
| ~ circle(X3,X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f51_sk]) ).
cnf(c113,plain,
circle(sk23,sk20,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p506,plain,
( midp(X0,sk21,sk22)
| ~ eqangle(sk20,sk21,sk20,sk22,sk23,sk21,sk23,X0)
| ~ coll(X0,sk21,sk22) ),
inference(resolution,[status(thm)],[c51,c113]) ).
cnf(p1405,plain,
( midp(X0,sk21,sk22)
| ~ eqangle(sk20,sk21,sk20,sk22,sk23,sk21,sk23,X0) ),
inference(resolution,[status(thm)],[p1404,p506]) ).
cnf(p10892,plain,
midp(sk22,sk21,sk22),
inference(resolution,[status(thm)],[p10868,p1405]) ).
fof(f64,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD64) ).
fof(f64_nnf,plain,
! [A,B,C,D,M] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f64]) ).
fof(f64_sk,plain,
! [M,A,B,C,D] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f64_nnf]) ).
cnf(c64,plain,
( midp(X4,X2,X3)
| ~ para(X0,X3,X1,X2)
| ~ para(X0,X2,X1,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(p615,plain,
( midp(X0,X3,X3)
| ~ para(X1,X3,X2,X3)
| ~ midp(X0,X1,X2) ),
inference(factoring,[status(thm)],[c64]) ).
cnf(p10945,plain,
( midp(sk22,X0,X0)
| ~ para(sk21,X0,sk22,X0) ),
inference(resolution,[status(thm)],[p10892,p615]) ).
fof(f10,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD11) ).
fof(f10_nnf,plain,
! [A,B,M] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [M,B,A] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( midp(X2,X0,X1)
| ~ midp(X2,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p10932,plain,
midp(sk22,sk22,sk21),
inference(resolution,[status(thm)],[p10892,c10]) ).
fof(f68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD68) ).
fof(f68_nnf,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f68]) ).
fof(f68_sk,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(skolemisation,[status(esa)],[f68_nnf]) ).
cnf(c68,plain,
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f68_sk]) ).
cnf(p10977,plain,
cong(sk22,sk22,sk22,sk21),
inference(resolution,[status(thm)],[p10932,c68]) ).
fof(f46,axiom,
! [A,B,O] :
( cong(O,A,O,B)
=> eqangle(O,A,A,B,A,B,O,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD46) ).
fof(f46_nnf,plain,
! [A,B,O] :
( eqangle(O,A,A,B,A,B,O,B)
| ~ cong(O,A,O,B) ),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
! [O,A,B] :
( eqangle(O,A,A,B,A,B,O,B)
| ~ cong(O,A,O,B) ),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c46,plain,
( eqangle(X2,X0,X0,X1,X0,X1,X2,X1)
| ~ cong(X2,X0,X2,X1) ),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(p11047,plain,
eqangle(sk22,sk22,sk22,sk21,sk22,sk21,sk22,sk21),
inference(resolution,[status(thm)],[p10977,c46]) ).
cnf(p11731,plain,
para(sk22,sk22,sk22,sk21),
inference(resolution,[status(thm)],[p11047,c38]) ).
fof(f3,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('/export/starexec/sandbox/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(p11735,plain,
para(sk22,sk22,sk21,sk22),
inference(resolution,[status(thm)],[p11731,c3]) ).
fof(f4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('/export/starexec/sandbox/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(p11743,plain,
para(sk21,sk22,sk22,sk22),
inference(resolution,[status(thm)],[p11735,c4]) ).
cnf(p21719,plain,
midp(sk22,sk22,sk22),
inference(resolution,[status(thm)],[p10945,p11743]) ).
cnf(p21725,plain,
cong(sk22,sk22,sk22,sk22),
inference(resolution,[status(thm)],[p21719,c68]) ).
fof(f56,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD56) ).
fof(f56_nnf,plain,
! [A,B,P,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [A,P,B,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c56,plain,
( perp(X0,X1,X2,X3)
| ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(p551,plain,
( perp(X0,X2,X1,X1)
| ~ cong(X0,X1,X2,X1) ),
inference(factoring,[status(thm)],[c56]) ).
cnf(p21744,plain,
perp(sk22,sk22,sk22,sk22),
inference(resolution,[status(thm)],[p21725,p551]) ).
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/sandbox/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(p1399,plain,
eqangle(X0,X1,X0,X1,X2,X3,X2,X3),
inference(resolution,[status(thm)],[p1263,c20]) ).
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/sandbox/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(p1608,plain,
( perp(X2,X3,X2,X3)
| ~ perp(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[p1399,c74]) ).
cnf(p21760,plain,
perp(X0,X1,X0,X1),
inference(resolution,[status(thm)],[p21744,p1608]) ).
fof(f53,axiom,
! [A,B,C,O] :
( ( coll(O,A,C)
& circle(O,A,B,C) )
=> perp(A,B,B,C) ),
file('/export/starexec/sandbox/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(p528,plain,
( perp(sk20,sk21,sk21,sk22)
| ~ coll(sk23,sk20,sk22) ),
inference(resolution,[status(thm)],[c53,c113]) ).
cnf(p1407,plain,
perp(sk20,sk21,sk21,sk22),
inference(resolution,[status(thm)],[p1404,p528]) ).
fof(f6,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('/export/starexec/sandbox/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(p1409,plain,
perp(sk20,sk21,sk22,sk21),
inference(resolution,[status(thm)],[p1407,c6]) ).
cnf(p1428,plain,
( para(sk20,sk21,X0,X1)
| ~ perp(sk22,sk21,X0,X1) ),
inference(resolution,[status(thm)],[p1409,c8]) ).
cnf(p21799,plain,
para(sk20,sk21,sk22,sk21),
inference(resolution,[status(thm)],[p21760,p1428]) ).
cnf(p22121,plain,
eqangle(sk20,sk21,X0,X1,sk22,sk21,X0,X1),
inference(resolution,[status(thm)],[p21799,c39]) ).
cnf(p23447,plain,
eqangle(X0,X1,sk20,sk21,X0,X1,sk22,sk21),
inference(resolution,[status(thm)],[p22121,c18]) ).
fof(f17,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(B,A,C,D,P,Q,U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD18) ).
fof(f17_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(B,A,C,D,P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(B,A,C,D,P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( eqangle(X1,X0,X2,X3,X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p24698,plain,
eqangle(X0,X1,sk20,sk21,X1,X0,sk22,sk21),
inference(resolution,[status(thm)],[p23447,c17]) ).
fof(f49,axiom,
! [A,B,C,O,X] :
( ( eqangle(A,X,A,B,C,A,C,B)
& circle(O,A,B,C) )
=> perp(O,A,A,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD49) ).
fof(f49_nnf,plain,
! [A,B,C,O,X] :
( perp(O,A,A,X)
| ~ eqangle(A,X,A,B,C,A,C,B)
| ~ circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f49]) ).
fof(f49_sk,plain,
! [O,A,B,C,X] :
( perp(O,A,A,X)
| ~ eqangle(A,X,A,B,C,A,C,B)
| ~ circle(O,A,B,C) ),
inference(skolemisation,[status(esa)],[f49_nnf]) ).
cnf(c49,plain,
( perp(X3,X0,X0,X4)
| ~ eqangle(X0,X4,X0,X1,X2,X0,X2,X1)
| ~ circle(X3,X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f49_sk]) ).
cnf(p484,plain,
( perp(sk23,sk20,sk20,X0)
| ~ eqangle(sk20,X0,sk20,sk21,sk22,sk20,sk22,sk21) ),
inference(resolution,[status(thm)],[c49,c113]) ).
cnf(p28299,plain,
perp(sk23,sk20,sk20,sk22),
inference(resolution,[status(thm)],[p24698,p484]) ).
fof(f52,axiom,
! [A,B,C,M] :
( ( midp(M,A,C)
& perp(A,B,B,C) )
=> cong(A,M,B,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD52) ).
fof(f52_nnf,plain,
! [A,B,C,M] :
( cong(A,M,B,M)
| ~ midp(M,A,C)
| ~ perp(A,B,B,C) ),
inference(nnf_transformation,[status(thm)],[f52]) ).
fof(f52_sk,plain,
! [A,B,C,M] :
( cong(A,M,B,M)
| ~ midp(M,A,C)
| ~ perp(A,B,B,C) ),
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c52,plain,
( cong(X0,X3,X1,X3)
| ~ midp(X3,X0,X2)
| ~ perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(p28304,plain,
( cong(sk23,X0,sk20,X0)
| ~ midp(X0,sk23,sk22) ),
inference(resolution,[status(thm)],[p28299,c52]) ).
cnf(p21761,plain,
perp(X0,X1,X1,X0),
inference(resolution,[status(thm)],[p21760,c6]) ).
cnf(p22021,plain,
( cong(X1,X0,X2,X0)
| ~ midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[p21761,c52]) ).
cnf(p21731,plain,
( midp(sk22,X0,X0)
| ~ para(sk22,X0,sk22,X0) ),
inference(resolution,[status(thm)],[p21719,p615]) ).
cnf(p37865,plain,
midp(sk22,X0,X0),
inference(resolution,[status(thm)],[p21731,p1256]) ).
cnf(p37880,plain,
cong(sk22,X0,sk22,X0),
inference(resolution,[status(thm)],[p37865,c68]) ).
fof(f22,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD23) ).
fof(f22_nnf,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( cong(X0,X1,X3,X2)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p37897,plain,
cong(sk22,X0,X0,sk22),
inference(resolution,[status(thm)],[p37880,c22]) ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD24) ).
fof(f23_nnf,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( cong(X2,X3,X0,X1)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p37988,plain,
cong(X0,sk22,sk22,X0),
inference(resolution,[status(thm)],[p37897,c23]) ).
cnf(p38164,plain,
cong(X0,sk22,X0,sk22),
inference(resolution,[status(thm)],[p37988,c22]) ).
fof(f67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD67) ).
fof(f67_nnf,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f67]) ).
fof(f67_sk,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f67_nnf]) ).
cnf(c67,plain,
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f67_sk]) ).
cnf(p38206,plain,
( midp(X0,sk22,sk22)
| ~ coll(X0,sk22,sk22) ),
inference(resolution,[status(thm)],[p38164,c67]) ).
cnf(p39338,plain,
midp(X0,sk22,sk22),
inference(resolution,[status(thm)],[p38206,p1404]) ).
cnf(p57262,plain,
cong(sk22,X0,X1,X0),
inference(resolution,[status(thm)],[p22021,p39338]) ).
cnf(p57276,plain,
cong(sk22,X0,X0,X1),
inference(resolution,[status(thm)],[p57262,c22]) ).
cnf(p57379,plain,
cong(X0,X1,sk22,X0),
inference(resolution,[status(thm)],[p57276,c23]) ).
cnf(p57579,plain,
cong(X0,X1,X0,sk22),
inference(resolution,[status(thm)],[p57379,c22]) ).
cnf(p57745,plain,
( midp(X0,X1,sk22)
| ~ coll(X0,X1,sk22) ),
inference(resolution,[status(thm)],[p57579,c67]) ).
cnf(p59711,plain,
midp(X0,X1,sk22),
inference(resolution,[status(thm)],[p57745,p1404]) ).
cnf(p85784,plain,
cong(sk23,X0,sk20,X0),
inference(resolution,[status(thm)],[p28304,p59711]) ).
cnf(p85785,plain,
cong(sk23,X0,X0,sk20),
inference(resolution,[status(thm)],[p85784,c22]) ).
cnf(p85793,plain,
cong(X0,sk20,sk23,X0),
inference(resolution,[status(thm)],[p85785,c23]) ).
cnf(p85820,plain,
cong(X0,sk20,X0,sk23),
inference(resolution,[status(thm)],[p85793,c22]) ).
cnf(p85983,plain,
( midp(X0,sk20,sk23)
| ~ coll(X0,sk20,sk23) ),
inference(resolution,[status(thm)],[p85820,c67]) ).
cnf(p86079,plain,
midp(X0,sk20,sk23),
inference(resolution,[status(thm)],[p85983,p1404]) ).
cnf(p2297,plain,
eqangle(X0,X0,X0,X1,X2,X0,X2,X1),
inference(resolution,[status(thm)],[p2275,c40]) ).
cnf(p2332,plain,
perp(sk23,sk20,sk20,sk20),
inference(resolution,[status(thm)],[p2297,p484]) ).
cnf(p2334,plain,
perp(sk20,sk20,sk23,sk20),
inference(resolution,[status(thm)],[p2332,c7]) ).
cnf(p2348,plain,
perp(sk20,sk20,sk20,sk23),
inference(resolution,[status(thm)],[p2334,c6]) ).
cnf(p2358,plain,
( cong(sk20,X0,sk20,X0)
| ~ midp(X0,sk20,sk23) ),
inference(resolution,[status(thm)],[p2348,c52]) ).
cnf(p86094,plain,
cong(sk20,X0,sk20,X0),
inference(resolution,[status(thm)],[p86079,p2358]) ).
cnf(p86113,plain,
( midp(sk20,X0,X0)
| ~ coll(sk20,X0,X0) ),
inference(resolution,[status(thm)],[p86094,c67]) ).
cnf(p86454,plain,
midp(sk20,X0,X0),
inference(resolution,[status(thm)],[p86113,p1404]) ).
cnf(p86469,plain,
cong(X0,sk20,X1,sk20),
inference(resolution,[status(thm)],[p86454,p22021]) ).
cnf(p86470,plain,
cong(X0,sk20,sk20,X1),
inference(resolution,[status(thm)],[p86469,c22]) ).
cnf(p86485,plain,
cong(sk20,X0,X1,sk20),
inference(resolution,[status(thm)],[p86470,c23]) ).
cnf(p86513,plain,
cong(sk20,X0,sk20,X1),
inference(resolution,[status(thm)],[p86485,c22]) ).
cnf(c122,plain,
~ cong(sk20,sk26,sk20,sk27),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p86555,plain,
$false,
inference(resolution,[status(thm)],[p86513,c122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO573+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/10.39 % Computer : n007.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Wed Sep 23 12:24:33 UTC 2026
% 0.11/10.40 % CPUTime :
% 0.14/10.40 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 160.32/33.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 160.32/33.34 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------