%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO560+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 : n003.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 01:18:09 PM UTC 2026
% Result : Theorem 29.78s 9.72s
% Output : Proof 29.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 27
% Syntax : Number of formulae : 179 ( 52 unt; 0 def)
% Number of atoms : 386 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 348 ( 141 ~; 137 |; 42 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 967 ( 90 sgn 506 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f43,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD43) ).
fof(f43_nnf,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c43,plain,
( cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
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]) ).
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]) ).
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,D,E,H,G] :
( ( coll(G,A,B)
& perp(G,H,A,B)
& coll(H,B,E)
& coll(H,A,D)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) )
=> eqangle(E,G,G,H,H,G,G,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL012020) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,H,G] :
( ( coll(G,A,B)
& perp(G,H,A,B)
& coll(H,B,E)
& coll(H,A,D)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) )
=> eqangle(E,G,G,H,H,G,G,D) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,H,G] :
( ~ eqangle(E,G,G,H,H,G,G,D)
& coll(G,A,B)
& perp(G,H,A,B)
& coll(H,B,E)
& coll(H,A,D)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ eqangle(sk24,sk26,sk26,sk25,sk25,sk26,sk26,sk23)
& coll(sk26,sk20,sk21)
& perp(sk26,sk25,sk20,sk21)
& coll(sk25,sk21,sk24)
& coll(sk25,sk20,sk23)
& coll(sk24,sk20,sk22)
& perp(sk24,sk21,sk20,sk22)
& coll(sk23,sk21,sk22)
& perp(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26])],[f94_nnf]) ).
cnf(c113,plain,
perp(sk23,sk20,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p821,plain,
( para(sk23,sk20,X0,X1)
| ~ perp(sk21,sk22,X0,X1) ),
inference(resolution,[status(thm)],[c8,c113]) ).
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(p150,plain,
perp(sk21,sk22,sk23,sk20),
inference(resolution,[status(thm)],[c7,c113]) ).
cnf(p845,plain,
para(sk23,sk20,sk23,sk20),
inference(resolution,[status(thm)],[p821,p150]) ).
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(p847,plain,
eqangle(sk23,sk20,X0,X1,sk23,sk20,X0,X1),
inference(resolution,[status(thm)],[p845,c39]) ).
cnf(p920,plain,
eqangle(X0,X1,sk23,sk20,X0,X1,sk23,sk20),
inference(resolution,[status(thm)],[c18,p847]) ).
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(p944,plain,
para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[p920,c38]) ).
cnf(p948,plain,
eqangle(X0,X1,X2,X3,X0,X1,X2,X3),
inference(resolution,[status(thm)],[p944,c39]) ).
cnf(p988,plain,
( cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[c42,p948]) ).
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(p946,plain,
coll(X0,X1,X1),
inference(resolution,[status(thm)],[p944,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(p168,plain,
( coll(X2,X2,X0)
| ~ coll(X0,X1,X2) ),
inference(factoring,[status(thm)],[c2]) ).
cnf(p951,plain,
coll(X0,X0,X1),
inference(resolution,[status(thm)],[p946,p168]) ).
cnf(p952,plain,
( coll(X2,X1,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[p951,c2]) ).
cnf(p968,plain,
coll(X0,X1,X2),
inference(resolution,[status(thm)],[p952,p951]) ).
cnf(p990,plain,
cyclic(X0,X1,X2,X2),
inference(resolution,[status(thm)],[p988,p968]) ).
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(p991,plain,
cyclic(X0,X1,X2,X1),
inference(resolution,[status(thm)],[p990,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(p993,plain,
cyclic(X0,X1,X1,X2),
inference(resolution,[status(thm)],[p991,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(p997,plain,
cyclic(X0,X1,X0,X2),
inference(resolution,[status(thm)],[p993,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(p1004,plain,
( cyclic(X1,X0,X3,X2)
| ~ cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[p997,c16]) ).
cnf(p1034,plain,
cyclic(X0,X1,X2,X3),
inference(resolution,[status(thm)],[p1004,p997]) ).
cnf(p3757,plain,
( cong(X0,X1,X5,X3)
| ~ eqangle(X2,X0,X2,X1,X4,X5,X4,X3)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c43,p1034]) ).
cnf(p3759,plain,
( cong(X0,X1,X4,X5)
| ~ eqangle(X2,X0,X2,X1,X3,X4,X3,X5)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[p3757,p1034]) ).
cnf(p3760,plain,
( cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(resolution,[status(thm)],[p3759,p1034]) ).
cnf(p3761,plain,
cong(X0,X1,X0,X1),
inference(resolution,[status(thm)],[p3760,p948]) ).
fof(f29,axiom,
! [A,B,C,D,E,F,G,H,P,Q,U,V] :
( ( eqratio(P,Q,U,V,E,F,G,H)
& eqratio(A,B,C,D,P,Q,U,V) )
=> eqratio(A,B,C,D,E,F,G,H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD30) ).
fof(f29_nnf,plain,
! [A,B,C,D,E,F,G,H,P,Q,U,V] :
( eqratio(A,B,C,D,E,F,G,H)
| ~ eqratio(P,Q,U,V,E,F,G,H)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqratio(A,B,C,D,E,F,G,H)
| ~ eqratio(P,Q,U,V,E,F,G,H)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
( eqratio(X0,X1,X2,X3,X4,X5,X6,X7)
| ~ eqratio(X8,X9,X10,X11,X4,X5,X6,X7)
| ~ eqratio(X0,X1,X2,X3,X8,X9,X10,X11) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
fof(f65,axiom,
! [A,B,C,D,O] :
( ( coll(O,B,D)
& coll(O,A,C)
& para(A,B,C,D) )
=> eqratio(O,A,A,C,O,B,B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD65) ).
fof(f65_nnf,plain,
! [A,B,C,D,O] :
( eqratio(O,A,A,C,O,B,B,D)
| ~ coll(O,B,D)
| ~ coll(O,A,C)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f65]) ).
fof(f65_sk,plain,
! [A,B,C,D,O] :
( eqratio(O,A,A,C,O,B,B,D)
| ~ coll(O,B,D)
| ~ coll(O,A,C)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f65_nnf]) ).
cnf(c65,plain,
( eqratio(X4,X0,X0,X2,X4,X1,X1,X3)
| ~ coll(X4,X1,X3)
| ~ coll(X4,X0,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
cnf(p1146,plain,
( eqratio(X0,X1,X1,X1,X0,X2,X2,X2)
| ~ coll(X0,X2,X2)
| ~ coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[c65,p944]) ).
cnf(p1149,plain,
( eqratio(X0,X2,X2,X2,X0,X1,X1,X1)
| ~ coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[p1146,p968]) ).
cnf(p1150,plain,
eqratio(X0,X1,X1,X1,X0,X2,X2,X2),
inference(resolution,[status(thm)],[p1149,p968]) ).
fof(f28,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,C,D,P,Q,U,V)
=> eqratio(A,B,P,Q,C,D,U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD29) ).
fof(f28_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,P,Q,C,D,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,P,Q,C,D,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
( eqratio(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p1153,plain,
eqratio(X0,X1,X0,X2,X1,X1,X2,X2),
inference(resolution,[status(thm)],[p1150,c28]) ).
cnf(p1340,plain,
( eqratio(X6,X0,X6,X1,X2,X3,X4,X5)
| ~ eqratio(X0,X0,X1,X1,X2,X3,X4,X5) ),
inference(resolution,[status(thm)],[c29,p1153]) ).
fof(f26,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,C,D,P,Q,U,V)
=> eqratio(C,D,A,B,U,V,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD27) ).
fof(f26_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(C,D,A,B,U,V,P,Q)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(C,D,A,B,U,V,P,Q)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c26,plain,
( eqratio(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p1152,plain,
eqratio(X0,X0,X1,X0,X2,X2,X1,X2),
inference(resolution,[status(thm)],[p1150,c26]) ).
cnf(p1159,plain,
eqratio(X0,X0,X1,X1,X2,X0,X2,X1),
inference(resolution,[status(thm)],[p1152,c28]) ).
cnf(p1729,plain,
eqratio(X0,X1,X0,X2,X3,X1,X3,X2),
inference(resolution,[status(thm)],[p1340,p1159]) ).
cnf(p1750,plain,
( eqratio(X7,X1,X7,X2,X3,X4,X5,X6)
| ~ eqratio(X0,X1,X0,X2,X3,X4,X5,X6) ),
inference(resolution,[status(thm)],[p1729,c29]) ).
cnf(p1337,plain,
( eqratio(X0,X6,X6,X6,X2,X3,X4,X5)
| ~ eqratio(X0,X1,X1,X1,X2,X3,X4,X5) ),
inference(resolution,[status(thm)],[c29,p1150]) ).
fof(f25,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,C,D,P,Q,U,V)
=> eqratio(B,A,C,D,P,Q,U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD26) ).
fof(f25_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(B,A,C,D,P,Q,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(B,A,C,D,P,Q,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
( eqratio(X1,X0,X2,X3,X4,X5,X6,X7)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p1151,plain,
eqratio(X0,X1,X0,X0,X1,X2,X2,X2),
inference(resolution,[status(thm)],[p1150,c25]) ).
cnf(p1157,plain,
eqratio(X0,X1,X1,X2,X0,X0,X2,X2),
inference(resolution,[status(thm)],[p1151,c28]) ).
cnf(p1418,plain,
eqratio(X0,X1,X1,X1,X0,X0,X2,X2),
inference(resolution,[status(thm)],[p1337,p1157]) ).
cnf(p1429,plain,
eqratio(X0,X1,X0,X0,X1,X1,X2,X2),
inference(resolution,[status(thm)],[p1418,c25]) ).
fof(f27,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,C,D,P,Q,U,V)
=> eqratio(P,Q,U,V,A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD28) ).
fof(f27_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(P,Q,U,V,A,B,C,D)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(P,Q,U,V,A,B,C,D)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
( eqratio(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p1473,plain,
eqratio(X0,X0,X1,X1,X2,X0,X2,X2),
inference(resolution,[status(thm)],[p1429,c27]) ).
cnf(p1736,plain,
eqratio(X0,X1,X0,X2,X3,X1,X3,X3),
inference(resolution,[status(thm)],[p1340,p1473]) ).
cnf(p1769,plain,
eqratio(X0,X1,X0,X0,X2,X1,X2,X3),
inference(resolution,[status(thm)],[p1736,c27]) ).
cnf(p2957,plain,
eqratio(X0,X1,X0,X2,X3,X1,X3,X4),
inference(resolution,[status(thm)],[p1750,p1769]) ).
cnf(p3010,plain,
( eqratio(X7,X1,X7,X8,X3,X4,X5,X6)
| ~ eqratio(X0,X1,X0,X2,X3,X4,X5,X6) ),
inference(resolution,[status(thm)],[p2957,c29]) ).
cnf(p1770,plain,
eqratio(X0,X1,X2,X1,X0,X3,X2,X2),
inference(resolution,[status(thm)],[p1736,c28]) ).
cnf(p1339,plain,
( eqratio(X6,X6,X1,X6,X2,X3,X4,X5)
| ~ eqratio(X0,X0,X1,X0,X2,X3,X4,X5) ),
inference(resolution,[status(thm)],[c29,p1152]) ).
cnf(p1867,plain,
eqratio(X0,X0,X1,X0,X2,X3,X1,X1),
inference(resolution,[status(thm)],[p1770,p1339]) ).
cnf(p2025,plain,
eqratio(X0,X1,X1,X1,X0,X0,X2,X3),
inference(resolution,[status(thm)],[p1867,c26]) ).
cnf(p2236,plain,
eqratio(X0,X1,X0,X0,X1,X1,X2,X3),
inference(resolution,[status(thm)],[p2025,c25]) ).
cnf(p2989,plain,
eqratio(X0,X1,X0,X2,X1,X1,X3,X4),
inference(resolution,[status(thm)],[p1750,p2236]) ).
cnf(p3079,plain,
eqratio(X0,X1,X1,X2,X0,X0,X3,X4),
inference(resolution,[status(thm)],[p2989,c25]) ).
cnf(p3266,plain,
eqratio(X0,X0,X1,X2,X0,X3,X3,X4),
inference(resolution,[status(thm)],[p3079,c27]) ).
cnf(p3477,plain,
eqratio(X0,X0,X0,X1,X2,X3,X1,X4),
inference(resolution,[status(thm)],[p3266,c28]) ).
cnf(p3695,plain,
eqratio(X0,X1,X0,X2,X3,X4,X5,X6),
inference(resolution,[status(thm)],[p3010,p3477]) ).
cnf(p3696,plain,
eqratio(X0,X1,X2,X3,X4,X5,X4,X6),
inference(resolution,[status(thm)],[p3695,c27]) ).
cnf(p3701,plain,
( eqratio(X7,X8,X9,X10,X3,X4,X5,X6)
| ~ eqratio(X0,X1,X0,X2,X3,X4,X5,X6) ),
inference(resolution,[status(thm)],[p3696,c29]) ).
cnf(p3749,plain,
eqratio(X0,X1,X2,X3,X4,X5,X6,X7),
inference(resolution,[status(thm)],[p3701,p3695]) ).
fof(f75,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( cong(P,Q,U,V)
& eqratio(A,B,C,D,P,Q,U,V) )
=> cong(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD75) ).
fof(f75_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( cong(A,B,C,D)
| ~ cong(P,Q,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f75]) ).
fof(f75_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( cong(A,B,C,D)
| ~ cong(P,Q,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f75_nnf]) ).
cnf(c75,plain,
( cong(X0,X1,X2,X3)
| ~ cong(X4,X5,X6,X7)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f75_sk]) ).
cnf(p3750,plain,
( cong(X4,X5,X6,X7)
| ~ cong(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[p3749,c75]) ).
cnf(p3772,plain,
cong(X0,X1,X2,X3),
inference(resolution,[status(thm)],[p3761,p3750]) ).
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(p3786,plain,
eqangle(X0,X1,X1,X2,X1,X2,X0,X2),
inference(resolution,[status(thm)],[p3772,c46]) ).
fof(f21,axiom,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( ( eqangle(P,Q,U,V,E,F,G,H)
& eqangle(A,B,C,D,P,Q,U,V) )
=> eqangle(A,B,C,D,E,F,G,H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD22) ).
fof(f21_nnf,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
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(p1035,plain,
eqangle(X0,X1,X0,X2,X3,X1,X3,X2),
inference(resolution,[status(thm)],[p1034,c40]) ).
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(p1036,plain,
eqangle(X0,X1,X1,X2,X3,X0,X3,X2),
inference(resolution,[status(thm)],[p1035,c17]) ).
fof(f19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(P,Q,U,V,A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD20) ).
fof(f19_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p1039,plain,
eqangle(X0,X1,X0,X2,X1,X3,X3,X2),
inference(resolution,[status(thm)],[p1036,c19]) ).
cnf(p1325,plain,
( eqangle(X7,X0,X7,X2,X3,X4,X5,X6)
| ~ eqangle(X0,X1,X1,X2,X3,X4,X5,X6) ),
inference(resolution,[status(thm)],[c21,p1039]) ).
cnf(p3970,plain,
eqangle(X0,X1,X0,X2,X3,X2,X1,X2),
inference(resolution,[status(thm)],[p3786,p1325]) ).
cnf(p4460,plain,
eqangle(X0,X1,X2,X1,X3,X2,X3,X1),
inference(resolution,[status(thm)],[p3970,c19]) ).
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(p1037,plain,
eqangle(X0,X1,X2,X1,X0,X3,X2,X3),
inference(resolution,[status(thm)],[p1035,c20]) ).
cnf(p1323,plain,
( eqangle(X0,X7,X2,X7,X3,X4,X5,X6)
| ~ eqangle(X0,X1,X2,X1,X3,X4,X5,X6) ),
inference(resolution,[status(thm)],[c21,p1037]) ).
cnf(p6161,plain,
eqangle(X0,X1,X2,X1,X3,X2,X3,X4),
inference(resolution,[status(thm)],[p4460,p1323]) ).
cnf(p8973,plain,
eqangle(X0,X1,X2,X3,X3,X1,X2,X4),
inference(resolution,[status(thm)],[p6161,c20]) ).
cnf(c121,plain,
~ eqangle(sk24,sk26,sk26,sk25,sk25,sk26,sk26,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p10267,plain,
$false,
inference(resolution,[status(thm)],[p8973,c121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO560+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/5.38 % Computer : n003.cluster.edu
% 0.08/5.38 % Model : x86_64 x86_64
% 0.08/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.38 % Memory : 8046.5625MB
% 0.08/5.38 % OS : Linux 6.8.0-71-generic
% 0.08/5.38 % CPULimit : 300
% 0.08/5.38 % WCLimit : 300
% 0.08/5.38 % DateTime : Wed Sep 23 12:25:39 UTC 2026
% 0.08/5.38 % CPUTime :
% 0.08/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 29.78/9.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.78/9.72 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------