%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO546+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 : n019.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 01:18:07 PM UTC 2026
% Result : Theorem 43.30s 5.96s
% Output : Proof 43.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 24
% Syntax : Number of formulae : 142 ( 32 unt; 0 def)
% Number of atoms : 324 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 309 ( 127 ~; 123 |; 34 &)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 646 ( 38 sgn 387 !; 6 ?)
% 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/sandbox2/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]) ).
cnf(p446,plain,
( cong(X0,X1,X3,X3)
| ~ eqangle(X2,X0,X2,X1,X4,X3,X4,X3)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(factoring,[status(thm)],[c43]) ).
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(f94,conjecture,
! [A,B,C,E,F,H] :
( ( coll(H,A,F)
& coll(H,C,E)
& coll(F,B,C)
& perp(F,A,B,C)
& coll(E,A,B)
& perp(E,C,A,B) )
=> perp(B,H,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL012006) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,E,F,H] :
( ( coll(H,A,F)
& coll(H,C,E)
& coll(F,B,C)
& perp(F,A,B,C)
& coll(E,A,B)
& perp(E,C,A,B) )
=> perp(B,H,A,C) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,E,F,H] :
( ~ perp(B,H,A,C)
& coll(H,A,F)
& coll(H,C,E)
& coll(F,B,C)
& perp(F,A,B,C)
& coll(E,A,B)
& perp(E,C,A,B) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ perp(sk21,sk25,sk20,sk22)
& coll(sk25,sk20,sk24)
& coll(sk25,sk22,sk23)
& coll(sk24,sk21,sk22)
& perp(sk24,sk20,sk21,sk22)
& coll(sk23,sk20,sk21)
& perp(sk23,sk22,sk20,sk21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25])],[f94_nnf]) ).
cnf(c113,plain,
perp(sk23,sk22,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p181,plain,
( para(sk23,sk22,X0,X1)
| ~ perp(sk20,sk21,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/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]) ).
cnf(p173,plain,
perp(sk20,sk21,sk23,sk22),
inference(resolution,[status(thm)],[c7,c113]) ).
cnf(p730,plain,
para(sk23,sk22,sk23,sk22),
inference(resolution,[status(thm)],[p181,p173]) ).
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(p732,plain,
eqangle(sk23,sk22,X0,X1,sk23,sk22,X0,X1),
inference(resolution,[status(thm)],[p730,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/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(p753,plain,
eqangle(X0,X1,sk23,sk22,X0,X1,sk23,sk22),
inference(resolution,[status(thm)],[p732,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(p778,plain,
para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[p753,c38]) ).
cnf(p785,plain,
eqangle(X0,X1,X2,X3,X0,X1,X2,X3),
inference(resolution,[status(thm)],[p778,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(p825,plain,
( cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[p785,c42]) ).
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(p787,plain,
coll(X0,X1,X1),
inference(resolution,[status(thm)],[p778,c66]) ).
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD2) ).
fof(f1_nnf,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p790,plain,
coll(X0,X1,X0),
inference(resolution,[status(thm)],[p787,c1]) ).
fof(f0,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD1) ).
fof(f0_nnf,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p792,plain,
coll(X0,X0,X1),
inference(resolution,[status(thm)],[p790,c0]) ).
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(p793,plain,
( coll(X2,X1,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[p792,c2]) ).
cnf(p829,plain,
coll(X0,X1,X2),
inference(resolution,[status(thm)],[p793,p792]) ).
cnf(p868,plain,
cyclic(X0,X1,X2,X2),
inference(resolution,[status(thm)],[p825,p829]) ).
cnf(p1023,plain,
( cong(X0,X1,X2,X2)
| ~ eqangle(X2,X0,X2,X1,X3,X2,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[p446,p868]) ).
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(p869,plain,
cyclic(X0,X1,X2,X1),
inference(resolution,[status(thm)],[p868,c14]) ).
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(p874,plain,
cyclic(X0,X1,X1,X2),
inference(resolution,[status(thm)],[p869,c13]) ).
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(p880,plain,
cyclic(X0,X1,X0,X2),
inference(resolution,[status(thm)],[p874,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/sandbox2/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(p892,plain,
( cyclic(X1,X0,X3,X2)
| ~ cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[p880,c16]) ).
cnf(p1044,plain,
cyclic(X0,X1,X2,X3),
inference(resolution,[status(thm)],[p892,p880]) ).
cnf(p1202,plain,
( cong(X1,X2,X0,X0)
| ~ eqangle(X0,X1,X0,X2,X3,X0,X3,X0) ),
inference(resolution,[status(thm)],[p1023,p1044]) ).
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(p824,plain,
eqangle(X0,X1,X0,X1,X2,X3,X2,X3),
inference(resolution,[status(thm)],[p785,c20]) ).
cnf(p1729,plain,
cong(X0,X0,X1,X1),
inference(resolution,[status(thm)],[p1202,p824]) ).
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/sandbox2/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(p786,plain,
( eqratio(X0,X1,X1,X1,X0,X2,X2,X2)
| ~ coll(X0,X2,X2)
| ~ coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[p778,c65]) ).
cnf(p1151,plain,
( eqratio(X0,X2,X2,X2,X0,X1,X1,X1)
| ~ coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[p786,p829]) ).
cnf(p1152,plain,
eqratio(X0,X1,X1,X1,X0,X2,X2,X2),
inference(resolution,[status(thm)],[p1151,p829]) ).
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/sandbox2/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(p1153,plain,
eqratio(X0,X1,X0,X0,X1,X2,X2,X2),
inference(resolution,[status(thm)],[p1152,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/sandbox2/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(p1159,plain,
eqratio(X0,X1,X1,X1,X2,X0,X2,X2),
inference(resolution,[status(thm)],[p1153,c27]) ).
cnf(p1173,plain,
eqratio(X0,X1,X0,X0,X2,X1,X2,X2),
inference(resolution,[status(thm)],[p1159,c25]) ).
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/sandbox2/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(p1187,plain,
eqratio(X0,X1,X2,X1,X0,X0,X2,X2),
inference(resolution,[status(thm)],[p1173,c28]) ).
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/sandbox2/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(p1198,plain,
( cong(X0,X2,X1,X2)
| ~ cong(X0,X0,X1,X1) ),
inference(resolution,[status(thm)],[p1187,c75]) ).
cnf(p1745,plain,
cong(X0,X1,X2,X1),
inference(resolution,[status(thm)],[p1729,p1198]) ).
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/sandbox2/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(p1792,plain,
( perp(X0,X2,X3,X1)
| ~ cong(X0,X1,X2,X1) ),
inference(resolution,[status(thm)],[p1745,c56]) ).
cnf(p1155,plain,
eqratio(X0,X1,X0,X2,X1,X1,X2,X2),
inference(resolution,[status(thm)],[p1152,c28]) ).
cnf(p1167,plain,
( cong(X2,X0,X2,X1)
| ~ cong(X0,X0,X1,X1) ),
inference(resolution,[status(thm)],[p1155,c75]) ).
cnf(p1742,plain,
cong(X0,X1,X0,X2),
inference(resolution,[status(thm)],[p1729,p1167]) ).
fof(f24,axiom,
! [A,B,C,D,E,F] :
( ( cong(C,D,E,F)
& cong(A,B,C,D) )
=> cong(A,B,E,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD25) ).
fof(f24_nnf,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( cong(X0,X1,X4,X5)
| ~ cong(X2,X3,X4,X5)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p1757,plain,
( cong(X0,X4,X2,X3)
| ~ cong(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[p1742,c24]) ).
cnf(p1160,plain,
eqratio(X0,X1,X1,X2,X0,X0,X2,X2),
inference(resolution,[status(thm)],[p1153,c28]) ).
cnf(p1178,plain,
( cong(X0,X2,X2,X1)
| ~ cong(X0,X0,X1,X1) ),
inference(resolution,[status(thm)],[p1160,c75]) ).
cnf(p1743,plain,
cong(X0,X1,X1,X2),
inference(resolution,[status(thm)],[p1729,p1178]) ).
cnf(p4917,plain,
cong(X0,X1,X2,X3),
inference(resolution,[status(thm)],[p1757,p1743]) ).
cnf(p4941,plain,
perp(X0,X1,X2,X3),
inference(resolution,[status(thm)],[p1792,p4917]) ).
cnf(c119,plain,
~ perp(sk21,sk25,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p4942,plain,
$false,
inference(resolution,[status(thm)],[p4941,c119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO546+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 12:21:49 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 43.30/5.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 43.30/5.96 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------