%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO652+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 : n005.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 12:25:28 PM UTC 2026
% Result : Theorem 7.22s 1.48s
% Output : CNFRefutation 7.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 22
% Syntax : Number of formulae : 112 ( 16 unt; 4 def)
% Number of atoms : 330 ( 0 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 338 ( 120 ~; 115 |; 80 &)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 5 prp; 0-8 aty)
% Number of functors : 23 ( 23 usr; 22 con; 0-2 aty)
% Number of variables : 433 ( 386 !; 47 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,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(f19,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') ).
fof(f21,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') ).
fof(f39,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') ).
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(f42,axiom,
! [A,B,P,Q] :
( ( ~ coll(P,Q,A)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
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(f46,axiom,
! [A,B,C,E,F] :
( ( coll(F,A,C)
& para(E,F,B,C)
& midp(E,A,B) )
=> midp(F,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,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') ).
fof(f65,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/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(f87,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [A,B,C,D,E,F,G,H,I,J,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9,NWPNT01,NWPNT11,NWPNT21] :
( ( circle(C,B,J,NWPNT21)
& coll(B,G,J)
& circle(C,D,I,NWPNT11)
& coll(D,H,I)
& circle(A,B,H,NWPNT01)
& coll(B,F,H)
& circle(A,D,G,NWPNT9)
& coll(D,E,G)
& circle(C,B,F,NWPNT8)
& circle(C,B,E,NWPNT7)
& circle(C,B,D,NWPNT6)
& circle(A,B,D,NWPNT5)
& circle(C,B,NWPNT3,NWPNT4)
& circle(A,B,NWPNT1,NWPNT2) )
=> para(E,F,I,J) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H,I,J,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9,NWPNT01,NWPNT11,NWPNT21] :
( ( circle(C,B,J,NWPNT21)
& coll(B,G,J)
& circle(C,D,I,NWPNT11)
& coll(D,H,I)
& circle(A,B,H,NWPNT01)
& coll(B,F,H)
& circle(A,D,G,NWPNT9)
& coll(D,E,G)
& circle(C,B,F,NWPNT8)
& circle(C,B,E,NWPNT7)
& circle(C,B,D,NWPNT6)
& circle(A,B,D,NWPNT5)
& circle(C,B,NWPNT3,NWPNT4)
& circle(A,B,NWPNT1,NWPNT2) )
=> para(E,F,I,J) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
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(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(f139,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(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f140,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f143,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(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f144,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f184,plain,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
| ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f185,plain,
! [A,B,C,D] :
( para(A,B,C,D)
| ! [P,Q] : ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(miniscoping,[status(thm)],[f184]) ).
fof(f186,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f185]) ).
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(f192,plain,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
| coll(P,Q,A)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f193,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X2,X0,X3)
| coll(X0,X3,X1)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
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(f202,plain,
! [A,B,C,E,F] :
( midp(F,A,C)
| ~ coll(F,A,C)
| ~ para(E,F,B,C)
| ~ midp(E,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f203,plain,
! [A,C,F] :
( midp(F,A,C)
| ~ coll(F,A,C)
| ! [B,E] :
( ~ para(E,F,B,C)
| ~ midp(E,A,B) ) ),
inference(miniscoping,[status(thm)],[f202]) ).
fof(f204,plain,
! [X0,X1,X2,X3,X4] :
( midp(X3,X1,X4)
| ~ coll(X3,X1,X4)
| ~ para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f231,plain,
! [A,B,P,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f232,plain,
! [X0,X1,X2,X3] :
( perp(X0,X2,X1,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f250,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(pre_NNF_transformation,[status(thm)],[f65]) ).
fof(f251,plain,
! [C,D,M] :
( midp(M,C,D)
| ! [A,B] :
( ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ) ),
inference(miniscoping,[status(thm)],[f250]) ).
fof(f252,plain,
! [X0,X1,X2,X3,X4] :
( midp(X0,X3,X4)
| ~ para(X1,X4,X2,X3)
| ~ para(X1,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f251]) ).
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(f331,plain,
! [A,B,C,O] :
? [P] :
( perp(P,A,A,O)
| ~ circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f87]) ).
fof(f332,plain,
! [A,O] :
( ? [P] : perp(P,A,A,O)
| ! [B,C] : ~ circle(O,A,B,C) ),
inference(miniscoping,[status(thm)],[f331]) ).
fof(f333,plain,
! [A,O] :
( perp(sK11_skl(O,A),A,A,O)
| ! [B,C] : ~ circle(O,A,B,C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(P,sK11_skl(O,A))],[f332]) ).
fof(f334,plain,
! [X0,X1,X2,X3] :
( perp(sK11_skl(X0,X1),X1,X1,X0)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f333]) ).
fof(f369,plain,
? [A,B,C,D,E,F,G,H,I,J,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9,NWPNT01,NWPNT11,NWPNT21] :
( ~ para(E,F,I,J)
& circle(C,B,J,NWPNT21)
& coll(B,G,J)
& circle(C,D,I,NWPNT11)
& coll(D,H,I)
& circle(A,B,H,NWPNT01)
& coll(B,F,H)
& circle(A,D,G,NWPNT9)
& coll(D,E,G)
& circle(C,B,F,NWPNT8)
& circle(C,B,E,NWPNT7)
& circle(C,B,D,NWPNT6)
& circle(A,B,D,NWPNT5)
& circle(C,B,NWPNT3,NWPNT4)
& circle(A,B,NWPNT1,NWPNT2) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [E,F,I,J] :
( ~ para(E,F,I,J)
& ? [B,C] :
( ? [NWPNT21] : circle(C,B,J,NWPNT21)
& ? [G] :
( coll(B,G,J)
& ? [D] :
( ? [NWPNT11] : circle(C,D,I,NWPNT11)
& ? [H] :
( coll(D,H,I)
& ? [A] :
( ? [NWPNT01] : circle(A,B,H,NWPNT01)
& coll(B,F,H)
& ? [NWPNT9] : circle(A,D,G,NWPNT9)
& coll(D,E,G)
& ? [NWPNT8] : circle(C,B,F,NWPNT8)
& ? [NWPNT7] : circle(C,B,E,NWPNT7)
& ? [NWPNT6] : circle(C,B,D,NWPNT6)
& ? [NWPNT5] : circle(A,B,D,NWPNT5)
& ? [NWPNT3,NWPNT4] : circle(C,B,NWPNT3,NWPNT4)
& ? [NWPNT1,NWPNT2] : circle(A,B,NWPNT1,NWPNT2) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ para(sK20_skl,sK21_skl,sK22_skl,sK23_skl)
& circle(sK25_skl,sK24_skl,sK23_skl,sK41_skl)
& coll(sK24_skl,sK26_skl,sK23_skl)
& circle(sK25_skl,sK27_skl,sK22_skl,sK40_skl)
& coll(sK27_skl,sK28_skl,sK22_skl)
& circle(sK29_skl,sK24_skl,sK28_skl,sK39_skl)
& coll(sK24_skl,sK21_skl,sK28_skl)
& circle(sK29_skl,sK27_skl,sK26_skl,sK38_skl)
& coll(sK27_skl,sK20_skl,sK26_skl)
& circle(sK25_skl,sK24_skl,sK21_skl,sK37_skl)
& circle(sK25_skl,sK24_skl,sK20_skl,sK36_skl)
& circle(sK25_skl,sK24_skl,sK27_skl,sK35_skl)
& circle(sK29_skl,sK24_skl,sK27_skl,sK34_skl)
& circle(sK25_skl,sK24_skl,sK32_skl,sK33_skl)
& circle(sK29_skl,sK24_skl,sK30_skl,sK31_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,sK30_skl,sK31_skl,sK32_skl,sK33_skl,sK34_skl,sK35_skl,sK36_skl,sK37_skl,sK38_skl,sK39_skl,sK40_skl,sK41_skl]),skolemize(E,sK20_skl),skolemize(F,sK21_skl),skolemize(I,sK22_skl),skolemize(J,sK23_skl),skolemize(B,sK24_skl),skolemize(C,sK25_skl),skolemize(G,sK26_skl),skolemize(D,sK27_skl),skolemize(H,sK28_skl),skolemize(A,sK29_skl),skolemize(NWPNT1,sK30_skl),skolemize(NWPNT2,sK31_skl),skolemize(NWPNT3,sK32_skl),skolemize(NWPNT4,sK33_skl),skolemize(NWPNT5,sK34_skl),skolemize(NWPNT6,sK35_skl),skolemize(NWPNT7,sK36_skl),skolemize(NWPNT8,sK37_skl),skolemize(NWPNT9,sK38_skl),skolemize(NWPNT01,sK39_skl),skolemize(NWPNT11,sK40_skl),skolemize(NWPNT21,sK41_skl)],[f370]) ).
fof(f377,plain,
circle(sK25_skl,sK24_skl,sK21_skl,sK37_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f386,plain,
~ para(sK20_skl,sK21_skl,sK22_skl,sK23_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f451,plain,
perp(sK11_skl(sK25_skl,sK24_skl),sK24_skl,sK24_skl,sK25_skl),
inference(resolution,[status(thm)],[f334,f377]) ).
fof(f528,plain,
! [X0,X1] :
( para(X0,X1,sK24_skl,sK25_skl)
| ~ perp(X0,X1,sK11_skl(sK25_skl,sK24_skl),sK24_skl) ),
inference(resolution,[status(thm)],[f451,f117]) ).
fof(f529,plain,
perp(sK24_skl,sK25_skl,sK11_skl(sK25_skl,sK24_skl),sK24_skl),
inference(resolution,[status(thm)],[f451,f114]) ).
fof(f1475,plain,
para(sK24_skl,sK25_skl,sK24_skl,sK25_skl),
inference(resolution,[status(thm)],[f529,f528]) ).
fof(f2264,plain,
! [X0,X1] : eqangle(sK24_skl,sK25_skl,X0,X1,sK24_skl,sK25_skl,X0,X1),
inference(resolution,[status(thm)],[f1475,f189]) ).
fof(f2302,plain,
! [X0,X1] : eqangle(sK24_skl,sK25_skl,sK24_skl,sK25_skl,X0,X1,X0,X1),
inference(resolution,[status(thm)],[f2264,f144]) ).
fof(f2306,plain,
! [X0,X1] : eqangle(X0,X1,sK24_skl,sK25_skl,X0,X1,sK24_skl,sK25_skl),
inference(resolution,[status(thm)],[f2264,f140]) ).
fof(f2439,plain,
! [X0,X1] :
( cong(sK25_skl,sK25_skl,X0,X0)
| ~ cyclic(sK25_skl,sK25_skl,sK24_skl,X1)
| ~ cyclic(sK25_skl,sK25_skl,sK24_skl,X0)
| ~ cyclic(sK25_skl,sK25_skl,sK24_skl,X0) ),
inference(resolution,[status(thm)],[f2302,f198]) ).
fof(f2440,plain,
! [X0] :
( cyclic(sK25_skl,sK25_skl,sK24_skl,X0)
| coll(sK24_skl,X0,sK25_skl) ),
inference(resolution,[status(thm)],[f2302,f193]) ).
fof(f2441,plain,
! [X0] :
( cyclic(sK25_skl,sK25_skl,sK24_skl,X0)
| ~ coll(sK24_skl,X0,sK25_skl) ),
inference(resolution,[status(thm)],[f2302,f195]) ).
fof(f2469,definition,
! [X0] :
( sQ333_spl
<=> ( cong(sK25_skl,sK25_skl,X0,X0)
| ~ cyclic(sK25_skl,sK25_skl,sK24_skl,X0)
| ~ cyclic(sK25_skl,sK25_skl,sK24_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f2470,plain,
! [X0] :
( ~ sQ333_spl
| cong(sK25_skl,sK25_skl,X0,X0)
| ~ cyclic(sK25_skl,sK25_skl,sK24_skl,X0)
| ~ cyclic(sK25_skl,sK25_skl,sK24_skl,X0) ),
inference(component_clause,[status(thm)],[f2469]) ).
fof(f2472,definition,
! [X1] :
( sQ334_spl
<=> ~ cyclic(sK25_skl,sK25_skl,sK24_skl,X1) ),
introduced(definition,[new_symbols(definition,[sQ334_spl])],[split_symbol_definition]) ).
fof(f2473,plain,
! [X0] :
( ~ sQ334_spl
| ~ cyclic(sK25_skl,sK25_skl,sK24_skl,X0) ),
inference(component_clause,[status(thm)],[f2472]) ).
fof(f2475,plain,
( sQ334_spl
| sQ333_spl ),
inference(split_clause,[status(thm)],[f2439,f2469,f2472]) ).
fof(f2476,plain,
! [X0] : cyclic(sK25_skl,sK25_skl,sK24_skl,X0),
inference(forward_subsumption_resolution,[status(thm)],[f2441,f2440]) ).
fof(f2485,definition,
( sQ337_spl
<=> coll(sK25_skl,sK25_skl,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ337_spl])],[split_symbol_definition]) ).
fof(f2487,plain,
( sQ337_spl
| ~ coll(sK25_skl,sK25_skl,sK25_skl) ),
inference(component_clause,[status(thm)],[f2485]) ).
fof(f2488,definition,
( sQ338_spl
<=> midp(sK25_skl,sK25_skl,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ338_spl])],[split_symbol_definition]) ).
fof(f2489,plain,
( ~ sQ338_spl
| midp(sK25_skl,sK25_skl,sK25_skl) ),
inference(component_clause,[status(thm)],[f2488]) ).
fof(f2497,plain,
! [X0] :
( ~ sQ333_spl
| cong(sK25_skl,sK25_skl,X0,X0)
| ~ cyclic(sK25_skl,sK25_skl,sK24_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2470]) ).
fof(f2498,plain,
! [X0] :
( ~ sQ333_spl
| cong(sK25_skl,sK25_skl,X0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2497,f2476]) ).
fof(f2519,plain,
( ~ sQ333_spl
| midp(sK25_skl,sK25_skl,sK25_skl)
| ~ coll(sK25_skl,sK25_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f2498,f258]) ).
fof(f2541,plain,
( ~ sQ333_spl
| sQ338_spl
| ~ sQ337_spl ),
inference(split_clause,[status(thm)],[f2519,f2485,f2488,f2469]) ).
fof(f2736,plain,
! [X0,X1] : para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f2306,f186]) ).
fof(f2780,plain,
! [X0,X1,X2] :
( midp(X0,X2,X2)
| ~ para(X1,X2,X1,X2)
| ~ midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[f2736,f252]) ).
fof(f2781,plain,
! [X0,X1,X2] :
( midp(X2,X1,X2)
| ~ coll(X2,X1,X2)
| ~ midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f2736,f204]) ).
fof(f2784,plain,
! [X0,X1] : coll(X0,X1,X1),
inference(resolution,[status(thm)],[f2736,f256]) ).
fof(f2788,plain,
! [X0,X1,X2] :
( midp(X0,X2,X2)
| ~ midp(X0,X1,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2780,f2736]) ).
fof(f2790,plain,
( sQ337_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f2487,f2784]) ).
fof(f2794,plain,
sQ337_spl,
inference(contradiction_clause,[status(thm)],[f2790]) ).
fof(f2833,plain,
! [X0,X1] : coll(X0,X1,X0),
inference(resolution,[status(thm)],[f2784,f100]) ).
fof(f2847,plain,
! [X0,X1,X2] :
( midp(X2,X1,X2)
| ~ midp(X0,X1,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f2781,f2833]) ).
fof(f3017,plain,
( ~ sQ334_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2473,f2476]) ).
fof(f3018,plain,
~ sQ334_spl,
inference(contradiction_clause,[status(thm)],[f3017]) ).
fof(f3328,plain,
! [X0] :
( ~ sQ338_spl
| midp(X0,sK25_skl,X0) ),
inference(resolution,[status(thm)],[f2847,f2489]) ).
fof(f3879,plain,
! [X0] :
( ~ sQ338_spl
| midp(sK25_skl,X0,X0) ),
inference(resolution,[status(thm)],[f2788,f3328]) ).
fof(f3910,plain,
! [X0] :
( ~ sQ338_spl
| cong(sK25_skl,X0,sK25_skl,X0) ),
inference(resolution,[status(thm)],[f3879,f260]) ).
fof(f3931,plain,
! [X0,X1] :
( ~ sQ338_spl
| perp(sK25_skl,sK25_skl,X0,X1)
| ~ cong(sK25_skl,X0,sK25_skl,X0) ),
inference(resolution,[status(thm)],[f3910,f232]) ).
fof(f3942,plain,
! [X0,X1] :
( ~ sQ338_spl
| perp(sK25_skl,sK25_skl,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f3931,f3910]) ).
fof(f4022,plain,
! [X0,X1,X2,X3] :
( ~ sQ338_spl
| para(X0,X1,X2,X3)
| ~ perp(X0,X1,sK25_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f3942,f117]) ).
fof(f4023,plain,
! [X0,X1] :
( ~ sQ338_spl
| perp(X0,X1,sK25_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f3942,f114]) ).
fof(f4040,plain,
! [X0,X1,X2,X3] :
( ~ sQ338_spl
| para(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f4022,f4023]) ).
fof(f4044,plain,
( ~ sQ338_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f386,f4040]) ).
fof(f4063,plain,
~ sQ338_spl,
inference(contradiction_clause,[status(thm)],[f4044]) ).
fof(f4064,plain,
$false,
inference(sat_refutation,[status(thm)],[f2475,f2541,f2794,f3018,f4063]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO652+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n005.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 20 18:12:18 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 7.22/1.48 % Refutation found
% 7.22/1.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.22/1.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.22/1.50 % Elapsed time: 1.130615 seconds
% 7.22/1.50 % CPU time: 8.650425 seconds
% 7.22/1.50 % Total memory used: 154.557 MB
% 7.22/1.50 % Net memory used: 145.748 MB
%------------------------------------------------------------------------------