%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO616+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Thu Sep 24 12:25:23 PM UTC 2026
% Result : Theorem 4.78s 1.05s
% Output : CNFRefutation 4.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 23
% Syntax : Number of formulae : 143 ( 41 unt; 0 def)
% Number of atoms : 353 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 343 ( 133 ~; 128 |; 58 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 479 ( 456 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,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') ).
fof(f11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,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') ).
fof(f25,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') ).
fof(f40,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') ).
fof(f41,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') ).
fof(f43,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') ).
fof(f44,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') ).
fof(f58,axiom,
! [A,B,P,Q] :
( ( cyclic(A,B,P,Q)
& cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(P,A,A,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,axiom,
! [A,B,C,D,M] :
( ( midp(M,C,D)
& midp(M,A,B) )
=> para(A,C,B,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f70,axiom,
! [A,B,C] :
( midp(A,B,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [A,B,C,D,M,N,Q] :
? [P] :
( ( coll(D,A,B)
& coll(C,A,B)
& midp(N,C,D)
& midp(M,A,B) )
=> midp(P,A,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [A,B,C,O,G,E,K,H,N,NWPNT1] :
( ( circle(N,K,G,H)
& coll(H,O,G)
& perp(H,A,O,G)
& coll(K,A,B)
& perp(K,E,A,B)
& circle(O,A,E,NWPNT1)
& coll(E,O,G)
& midp(G,C,B)
& circle(O,A,B,C) )
=> perp(E,K,K,N) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,O,G,E,K,H,N,NWPNT1] :
( ( circle(N,K,G,H)
& coll(H,O,G)
& perp(H,A,O,G)
& coll(K,A,B)
& perp(K,E,A,B)
& circle(O,A,E,NWPNT1)
& coll(E,O,G)
& midp(G,C,B)
& circle(O,A,B,C) )
=> perp(E,K,K,N) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f97,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f98,plain,
! [X0,X1,X2] :
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f99,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f100,plain,
! [X0,X1,X2] :
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f102,plain,
! [A,C,D] :
( coll(C,D,A)
| ! [B] :
( ~ coll(A,B,D)
| ~ coll(A,B,C) ) ),
inference(miniscoping,[status(thm)],[f101]) ).
fof(f103,plain,
! [X0,X1,X2,X3] :
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f105,plain,
! [X0,X1,X2,X3] :
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f113,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f114,plain,
! [X0,X1,X2,X3] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f116,plain,
! [A,B,E,F] :
( para(A,B,E,F)
| ! [C,D] :
( ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f121,plain,
! [A,B,M] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f122,plain,
! [X0,X1,X2] :
( midp(X0,X2,X1)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f128,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f131,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f134,plain,
! [A,B,C,D,E] :
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f135,plain,
! [B,C,D,E] :
( cyclic(B,C,D,E)
| ! [A] :
( ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f134]) ).
fof(f136,plain,
! [X0,X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f152,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f153,plain,
! [A,B,E,F] :
( cong(A,B,E,F)
| ! [C,D] :
( ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f152]) ).
fof(f154,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X0,X1,X4,X5)
| ~ cong(X2,X3,X4,X5)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f187,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f188,plain,
! [A,B,C,D] :
( ! [P,Q] : eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(miniscoping,[status(thm)],[f187]) ).
fof(f189,plain,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f190,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f191,plain,
! [X0,X1,X2,X3] :
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f194,plain,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f195,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X2,X0,X3)
| ~ coll(X0,X3,X2)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f196,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(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f197,plain,
! [A,B,P,Q] :
( cong(A,B,P,Q)
| ! [C,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) ) ),
inference(miniscoping,[status(thm)],[f196]) ).
fof(f198,plain,
! [X0,X1,X2,X3,X4,X5] :
( 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(thm)],[f197]) ).
fof(f233,plain,
! [A,B,P,Q] :
( perp(P,A,A,Q)
| ~ cyclic(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f234,plain,
! [A,P,Q] :
( perp(P,A,A,Q)
| ! [B] :
( ~ cyclic(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ) ),
inference(miniscoping,[status(thm)],[f233]) ).
fof(f235,plain,
! [X0,X1,X2,X3] :
( perp(X1,X0,X0,X3)
| ~ cyclic(X0,X2,X1,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f247,plain,
! [A,B,C,D,M] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f64]) ).
fof(f248,plain,
! [A,B,C,D] :
( para(A,C,B,D)
| ! [M] :
( ~ midp(M,C,D)
| ~ midp(M,A,B) ) ),
inference(miniscoping,[status(thm)],[f247]) ).
fof(f249,plain,
! [X0,X1,X2,X3,X4] :
( para(X1,X3,X2,X4)
| ~ midp(X0,X3,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f248]) ).
fof(f255,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(pre_NNF_transformation,[status(thm)],[f67]) ).
fof(f256,plain,
! [X0,X1,X2] :
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f257,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(pre_NNF_transformation,[status(thm)],[f68]) ).
fof(f258,plain,
! [X0,X1,X2] :
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f257]) ).
fof(f259,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f69]) ).
fof(f260,plain,
! [X0,X1,X2] :
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f259]) ).
fof(f261,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f70]) ).
fof(f262,plain,
! [X0,X1,X2] :
( coll(X0,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f261]) ).
fof(f309,plain,
! [A,B,C,D,M,N,Q] :
? [P] :
( midp(P,A,Q)
| ~ coll(D,A,B)
| ~ coll(C,A,B)
| ~ midp(N,C,D)
| ~ midp(M,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f83]) ).
fof(f310,plain,
! [A] :
( ! [Q] :
? [P] : midp(P,A,Q)
| ! [B,D] :
( ~ coll(D,A,B)
| ! [C] :
( ~ coll(C,A,B)
| ! [N] : ~ midp(N,C,D)
| ! [M] : ~ midp(M,A,B) ) ) ),
inference(miniscoping,[status(thm)],[f309]) ).
fof(f311,plain,
! [A] :
( ! [Q] : midp(sK6_skl(Q,A),A,Q)
| ! [B,D] :
( ~ coll(D,A,B)
| ! [C] :
( ~ coll(C,A,B)
| ! [N] : ~ midp(N,C,D)
| ! [M] : ~ midp(M,A,B) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(P,sK6_skl(Q,A))],[f310]) ).
fof(f312,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( midp(sK6_skl(X6,X1),X1,X6)
| ~ coll(X5,X1,X2)
| ~ coll(X4,X1,X2)
| ~ midp(X3,X4,X5)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f311]) ).
fof(f369,plain,
? [A,B,C,O,G,E,K,H,N,NWPNT1] :
( ~ perp(E,K,K,N)
& circle(N,K,G,H)
& coll(H,O,G)
& perp(H,A,O,G)
& coll(K,A,B)
& perp(K,E,A,B)
& circle(O,A,E,NWPNT1)
& coll(E,O,G)
& midp(G,C,B)
& circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [E,K,N] :
( ~ perp(E,K,K,N)
& ? [G,H] :
( circle(N,K,G,H)
& ? [O] :
( coll(H,O,G)
& ? [A] :
( perp(H,A,O,G)
& ? [B] :
( coll(K,A,B)
& perp(K,E,A,B)
& ? [NWPNT1] : circle(O,A,E,NWPNT1)
& coll(E,O,G)
& ? [C] :
( midp(G,C,B)
& circle(O,A,B,C) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ perp(sK20_skl,sK21_skl,sK21_skl,sK22_skl)
& circle(sK22_skl,sK21_skl,sK23_skl,sK24_skl)
& coll(sK24_skl,sK25_skl,sK23_skl)
& perp(sK24_skl,sK26_skl,sK25_skl,sK23_skl)
& coll(sK21_skl,sK26_skl,sK27_skl)
& perp(sK21_skl,sK20_skl,sK26_skl,sK27_skl)
& circle(sK25_skl,sK26_skl,sK20_skl,sK29_skl)
& coll(sK20_skl,sK25_skl,sK23_skl)
& midp(sK23_skl,sK28_skl,sK27_skl)
& circle(sK25_skl,sK26_skl,sK27_skl,sK28_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl,sK27_skl,sK28_skl,sK29_skl]),skolemize(E,sK20_skl),skolemize(K,sK21_skl),skolemize(N,sK22_skl),skolemize(G,sK23_skl),skolemize(H,sK24_skl),skolemize(O,sK25_skl),skolemize(A,sK26_skl),skolemize(B,sK27_skl),skolemize(C,sK28_skl),skolemize(NWPNT1,sK29_skl)],[f370]) ).
fof(f373,plain,
midp(sK23_skl,sK28_skl,sK27_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f378,plain,
perp(sK24_skl,sK26_skl,sK25_skl,sK23_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f381,plain,
~ perp(sK20_skl,sK21_skl,sK21_skl,sK22_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f412,plain,
midp(sK23_skl,sK27_skl,sK28_skl),
inference(resolution,[status(thm)],[f122,f373]) ).
fof(f428,plain,
! [X0,X1] :
( para(X0,X1,sK25_skl,sK23_skl)
| ~ perp(X0,X1,sK24_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f378,f117]) ).
fof(f429,plain,
perp(sK25_skl,sK23_skl,sK24_skl,sK26_skl),
inference(resolution,[status(thm)],[f378,f114]) ).
fof(f457,plain,
cong(sK23_skl,sK27_skl,sK23_skl,sK28_skl),
inference(resolution,[status(thm)],[f260,f412]) ).
fof(f458,plain,
cong(sK23_skl,sK28_skl,sK23_skl,sK27_skl),
inference(resolution,[status(thm)],[f260,f373]) ).
fof(f460,plain,
coll(sK23_skl,sK28_skl,sK27_skl),
inference(resolution,[status(thm)],[f262,f373]) ).
fof(f467,plain,
! [X0] :
( coll(X0,sK27_skl,sK23_skl)
| ~ coll(sK23_skl,sK28_skl,X0) ),
inference(resolution,[status(thm)],[f460,f103]) ).
fof(f502,plain,
para(sK25_skl,sK23_skl,sK25_skl,sK23_skl),
inference(resolution,[status(thm)],[f429,f428]) ).
fof(f536,plain,
! [X0,X1] :
( cong(X0,X1,sK23_skl,sK27_skl)
| ~ cong(X0,X1,sK23_skl,sK28_skl) ),
inference(resolution,[status(thm)],[f458,f154]) ).
fof(f566,plain,
! [X0,X1] : eqangle(sK25_skl,sK23_skl,X0,X1,sK25_skl,sK23_skl,X0,X1),
inference(resolution,[status(thm)],[f502,f189]) ).
fof(f600,plain,
coll(sK27_skl,sK27_skl,sK23_skl),
inference(resolution,[status(thm)],[f467,f460]) ).
fof(f612,plain,
! [X0,X1] :
( para(X0,sK27_skl,X1,sK28_skl)
| ~ midp(sK23_skl,X0,X1) ),
inference(resolution,[status(thm)],[f249,f412]) ).
fof(f613,plain,
! [X0,X1] :
( para(X0,sK28_skl,X1,sK27_skl)
| ~ midp(sK23_skl,X0,X1) ),
inference(resolution,[status(thm)],[f249,f373]) ).
fof(f625,plain,
para(sK27_skl,sK28_skl,sK28_skl,sK27_skl),
inference(resolution,[status(thm)],[f613,f412]) ).
fof(f647,plain,
coll(sK27_skl,sK23_skl,sK27_skl),
inference(resolution,[status(thm)],[f600,f98]) ).
fof(f678,plain,
cong(sK23_skl,sK27_skl,sK23_skl,sK27_skl),
inference(resolution,[status(thm)],[f536,f457]) ).
fof(f703,plain,
coll(sK23_skl,sK27_skl,sK27_skl),
inference(resolution,[status(thm)],[f647,f100]) ).
fof(f780,plain,
! [X0,X1,X2,X3] :
( midp(sK6_skl(X3,X1),X1,X3)
| ~ coll(sK27_skl,X1,X2)
| ~ coll(sK28_skl,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f312,f373]) ).
fof(f808,plain,
! [X0] :
( midp(sK6_skl(X0,sK27_skl),sK27_skl,X0)
| ~ coll(sK27_skl,sK27_skl,sK28_skl)
| ~ coll(sK28_skl,sK27_skl,sK28_skl) ),
inference(resolution,[status(thm)],[f780,f412]) ).
fof(f836,plain,
para(sK27_skl,sK28_skl,sK27_skl,sK28_skl),
inference(resolution,[status(thm)],[f625,f105]) ).
fof(f1025,plain,
( midp(sK23_skl,sK27_skl,sK27_skl)
| ~ coll(sK23_skl,sK27_skl,sK27_skl) ),
inference(resolution,[status(thm)],[f678,f258]) ).
fof(f1033,plain,
midp(sK23_skl,sK27_skl,sK27_skl),
inference(forward_subsumption_resolution,[status(thm)],[f1025,f703]) ).
fof(f1034,plain,
para(sK27_skl,sK27_skl,sK27_skl,sK28_skl),
inference(resolution,[status(thm)],[f1033,f612]) ).
fof(f1322,plain,
coll(sK27_skl,sK28_skl,sK28_skl),
inference(resolution,[status(thm)],[f836,f256]) ).
fof(f1333,plain,
coll(sK28_skl,sK27_skl,sK28_skl),
inference(resolution,[status(thm)],[f1322,f100]) ).
fof(f1359,plain,
! [X0] :
( midp(sK6_skl(X0,sK27_skl),sK27_skl,X0)
| ~ coll(sK27_skl,sK27_skl,sK28_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f808,f1333]) ).
fof(f1413,plain,
coll(sK27_skl,sK27_skl,sK28_skl),
inference(resolution,[status(thm)],[f1034,f256]) ).
fof(f1569,plain,
! [X0] : midp(sK6_skl(X0,sK27_skl),sK27_skl,X0),
inference(forward_subsumption_resolution,[status(thm)],[f1359,f1413]) ).
fof(f1586,plain,
! [X0,X1,X2] :
( para(X1,sK27_skl,X2,X0)
| ~ midp(sK6_skl(X0,sK27_skl),X1,X2) ),
inference(resolution,[status(thm)],[f1569,f249]) ).
fof(f1590,plain,
! [X0] : midp(sK6_skl(X0,sK27_skl),X0,sK27_skl),
inference(resolution,[status(thm)],[f1569,f122]) ).
fof(f3623,plain,
! [X0] : para(X0,sK27_skl,sK27_skl,X0),
inference(resolution,[status(thm)],[f1586,f1590]) ).
fof(f3723,plain,
! [X0] : para(X0,sK27_skl,X0,sK27_skl),
inference(resolution,[status(thm)],[f3623,f105]) ).
fof(f3959,plain,
! [X0] : coll(X0,sK27_skl,sK27_skl),
inference(resolution,[status(thm)],[f3723,f256]) ).
fof(f4006,plain,
! [X0] : coll(sK27_skl,X0,sK27_skl),
inference(resolution,[status(thm)],[f3959,f100]) ).
fof(f4025,plain,
! [X0] : coll(sK27_skl,sK27_skl,X0),
inference(resolution,[status(thm)],[f4006,f98]) ).
fof(f4074,plain,
! [X0,X1] :
( coll(X0,X1,sK27_skl)
| ~ coll(sK27_skl,sK27_skl,X0) ),
inference(resolution,[status(thm)],[f4025,f103]) ).
fof(f4077,plain,
! [X0,X1] : coll(X0,X1,sK27_skl),
inference(forward_subsumption_resolution,[status(thm)],[f4074,f4025]) ).
fof(f4123,plain,
! [X0,X1] : coll(X0,sK27_skl,X1),
inference(resolution,[status(thm)],[f4077,f98]) ).
fof(f4133,plain,
! [X0,X1,X2] :
( coll(X1,X2,X0)
| ~ coll(X0,sK27_skl,X1) ),
inference(resolution,[status(thm)],[f4123,f103]) ).
fof(f4136,plain,
! [X0,X1,X2] : coll(X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f4133,f4123]) ).
fof(f4183,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f4136]) ).
fof(f4339,plain,
! [X0] : cyclic(sK23_skl,X0,sK25_skl,sK25_skl),
inference(resolution,[status(thm)],[f4183,f566]) ).
fof(f4816,plain,
! [X0] : cyclic(sK23_skl,sK25_skl,X0,sK25_skl),
inference(resolution,[status(thm)],[f4339,f131]) ).
fof(f4861,plain,
! [X0] : cyclic(sK23_skl,sK25_skl,sK25_skl,X0),
inference(resolution,[status(thm)],[f4816,f129]) ).
fof(f4918,plain,
! [X0,X1] :
( cyclic(sK25_skl,sK25_skl,X0,X1)
| ~ cyclic(sK23_skl,sK25_skl,sK25_skl,X0) ),
inference(resolution,[status(thm)],[f4861,f136]) ).
fof(f4922,plain,
! [X0,X1] : cyclic(sK25_skl,sK25_skl,X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f4918,f4861]) ).
fof(f4934,plain,
! [X0,X1,X2] :
( cyclic(sK25_skl,X0,X1,X2)
| ~ cyclic(sK25_skl,sK25_skl,X0,X1) ),
inference(resolution,[status(thm)],[f4922,f136]) ).
fof(f4938,plain,
! [X0,X1,X2] : cyclic(sK25_skl,X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f4934,f4922]) ).
fof(f4944,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
| ~ cyclic(sK25_skl,X0,X1,X2) ),
inference(resolution,[status(thm)],[f4938,f136]) ).
fof(f4948,plain,
! [X0,X1,X2,X3] : cyclic(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f4944,f4938]) ).
fof(f4950,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f198,f4948]) ).
fof(f4953,plain,
! [X0,X1,X2,X3] :
( perp(X1,X0,X0,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f235,f4948]) ).
fof(f4955,plain,
! [X0,X1,X2,X3] : eqangle(X0,X1,X0,X2,X3,X1,X3,X2),
inference(backward_subsumption_resolution,[status(thm)],[f191,f4948]) ).
fof(f4957,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X0,X1,X5,X3)
| ~ eqangle(X2,X0,X2,X1,X4,X5,X4,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f4950,f4948]) ).
fof(f4958,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f4957,f4948]) ).
fof(f5108,plain,
! [X0,X1] : cong(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f4955,f4958]) ).
fof(f5131,plain,
! [X0,X1,X2] :
( perp(X1,X0,X0,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f5108,f4953]) ).
fof(f5143,plain,
! [X0,X1,X2] : perp(X0,X1,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f5131,f5108]) ).
fof(f5268,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f381,f5143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO616+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 17:51:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 4.78/1.05 % Refutation found
% 4.78/1.05 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.78/1.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.78/1.06 % Elapsed time: 0.700129 seconds
% 4.78/1.06 % CPU time: 5.260170 seconds
% 4.78/1.06 % Total memory used: 141.586 MB
% 4.78/1.06 % Net memory used: 135.540 MB
%------------------------------------------------------------------------------