%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO629+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 12:25:24 PM UTC 2026
% Result : Theorem 0.11s 0.59s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 25
% Syntax : Number of formulae : 135 ( 10 unt; 2 def)
% Number of atoms : 379 ( 0 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 396 ( 152 ~; 144 |; 74 &)
% ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-8 aty)
% Number of functors : 14 ( 14 usr; 14 con; 0-0 aty)
% Number of variables : 532 ( 504 !; 28 ?)
% 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(f5,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(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(f10,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& para(A,B,C,D) )
=> perp(A,B,E,F) ),
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(f16,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,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(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(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(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(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(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(f67,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [A,B,C,O,P1,F1,G1,P,F,G,K,NWPNT1,NWPNT2,NWPNT3] :
( ( circle(O,A,K,NWPNT3)
& para(F1,G1,K,P)
& coll(G,A,B)
& perp(G,P,A,B)
& coll(F,A,C)
& perp(F,P,A,C)
& circle(O,A,P,NWPNT2)
& coll(G1,A,B)
& perp(G1,P1,A,B)
& coll(F1,A,C)
& perp(F1,P1,A,C)
& circle(O,A,P1,NWPNT1)
& circle(O,A,B,C) )
=> para(K,P1,G,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,O,P1,F1,G1,P,F,G,K,NWPNT1,NWPNT2,NWPNT3] :
( ( circle(O,A,K,NWPNT3)
& para(F1,G1,K,P)
& coll(G,A,B)
& perp(G,P,A,B)
& coll(F,A,C)
& perp(F,P,A,C)
& circle(O,A,P,NWPNT2)
& coll(G1,A,B)
& perp(G1,P1,A,B)
& coll(F1,A,C)
& perp(F1,P1,A,C)
& circle(O,A,P1,NWPNT1)
& circle(O,A,B,C) )
=> para(K,P1,G,F) ),
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(f106,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f111,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
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(f118,plain,
! [A,B,C,D,E,F] :
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f119,plain,
! [A,B,E,F] :
( perp(A,B,E,F)
| ! [C,D] :
( ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f120,plain,
! [X0,X1,X2,X3,X4,X5] :
( perp(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
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(f132,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f133,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
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(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(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(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(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(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(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(f369,plain,
? [A,B,C,O,P1,F1,G1,P,F,G,K,NWPNT1,NWPNT2,NWPNT3] :
( ~ para(K,P1,G,F)
& circle(O,A,K,NWPNT3)
& para(F1,G1,K,P)
& coll(G,A,B)
& perp(G,P,A,B)
& coll(F,A,C)
& perp(F,P,A,C)
& circle(O,A,P,NWPNT2)
& coll(G1,A,B)
& perp(G1,P1,A,B)
& coll(F1,A,C)
& perp(F1,P1,A,C)
& circle(O,A,P1,NWPNT1)
& circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [P1,F,G,K] :
( ~ para(K,P1,G,F)
& ? [A,O] :
( ? [NWPNT3] : circle(O,A,K,NWPNT3)
& ? [F1,G1,P] :
( para(F1,G1,K,P)
& ? [B] :
( coll(G,A,B)
& perp(G,P,A,B)
& ? [C] :
( coll(F,A,C)
& perp(F,P,A,C)
& ? [NWPNT2] : circle(O,A,P,NWPNT2)
& coll(G1,A,B)
& perp(G1,P1,A,B)
& coll(F1,A,C)
& perp(F1,P1,A,C)
& ? [NWPNT1] : circle(O,A,P1,NWPNT1)
& circle(O,A,B,C) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ para(sK23_skl,sK20_skl,sK22_skl,sK21_skl)
& circle(sK25_skl,sK24_skl,sK23_skl,sK33_skl)
& para(sK26_skl,sK27_skl,sK23_skl,sK28_skl)
& coll(sK22_skl,sK24_skl,sK29_skl)
& perp(sK22_skl,sK28_skl,sK24_skl,sK29_skl)
& coll(sK21_skl,sK24_skl,sK30_skl)
& perp(sK21_skl,sK28_skl,sK24_skl,sK30_skl)
& circle(sK25_skl,sK24_skl,sK28_skl,sK32_skl)
& coll(sK27_skl,sK24_skl,sK29_skl)
& perp(sK27_skl,sK20_skl,sK24_skl,sK29_skl)
& coll(sK26_skl,sK24_skl,sK30_skl)
& perp(sK26_skl,sK20_skl,sK24_skl,sK30_skl)
& circle(sK25_skl,sK24_skl,sK20_skl,sK31_skl)
& circle(sK25_skl,sK24_skl,sK29_skl,sK30_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]),skolemize(P1,sK20_skl),skolemize(F,sK21_skl),skolemize(G,sK22_skl),skolemize(K,sK23_skl),skolemize(A,sK24_skl),skolemize(O,sK25_skl),skolemize(F1,sK26_skl),skolemize(G1,sK27_skl),skolemize(P,sK28_skl),skolemize(B,sK29_skl),skolemize(C,sK30_skl),skolemize(NWPNT1,sK31_skl),skolemize(NWPNT2,sK32_skl),skolemize(NWPNT3,sK33_skl)],[f370]) ).
fof(f374,plain,
perp(sK26_skl,sK20_skl,sK24_skl,sK30_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f379,plain,
perp(sK21_skl,sK28_skl,sK24_skl,sK30_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f385,plain,
~ para(sK23_skl,sK20_skl,sK22_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f460,plain,
perp(sK21_skl,sK28_skl,sK30_skl,sK24_skl),
inference(resolution,[status(thm)],[f379,f112]) ).
fof(f499,plain,
perp(sK30_skl,sK24_skl,sK21_skl,sK28_skl),
inference(resolution,[status(thm)],[f114,f460]) ).
fof(f508,plain,
! [X0,X1] :
( para(X0,X1,sK24_skl,sK30_skl)
| ~ perp(X0,X1,sK21_skl,sK28_skl) ),
inference(resolution,[status(thm)],[f117,f379]) ).
fof(f512,plain,
! [X0,X1] :
( para(X0,X1,sK24_skl,sK30_skl)
| ~ perp(X0,X1,sK26_skl,sK20_skl) ),
inference(resolution,[status(thm)],[f117,f374]) ).
fof(f685,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ para(X2,X3,X4,X5)
| eqangle(X0,X1,X2,X3,X0,X1,X4,X5) ),
inference(resolution,[status(thm)],[f140,f189]) ).
fof(f1093,plain,
para(sK30_skl,sK24_skl,sK24_skl,sK30_skl),
inference(resolution,[status(thm)],[f508,f499]) ).
fof(f1117,plain,
para(sK30_skl,sK24_skl,sK30_skl,sK24_skl),
inference(resolution,[status(thm)],[f1093,f105]) ).
fof(f1543,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f685,f186]) ).
fof(f1544,definition,
! [X0,X1] :
( sQ8_spl
<=> ~ para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f1545,plain,
! [X0,X1] :
( ~ sQ8_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f1544]) ).
fof(f1547,definition,
! [X2,X3] :
( sQ9_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f1548,plain,
! [X0,X1] :
( ~ sQ9_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f1547]) ).
fof(f1550,plain,
( sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f1543,f1544,f1547]) ).
fof(f1561,plain,
( ~ sQ8_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1117,f1545]) ).
fof(f1567,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f1561]) ).
fof(f1571,plain,
! [X0,X1] :
( ~ sQ9_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f1548,f256]) ).
fof(f1606,plain,
! [X0,X1] :
( ~ sQ9_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f1571,f100]) ).
fof(f1639,plain,
! [X0,X1] :
( ~ sQ9_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f1606,f98]) ).
fof(f1643,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f1639,f103]) ).
fof(f1646,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1643,f1639]) ).
fof(f1664,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f1646]) ).
fof(f1666,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ para(X2,X1,X2,X1)
| cyclic(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f1664,f685]) ).
fof(f1672,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| cyclic(X0,X1,X2,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1666,f1548]) ).
fof(f1688,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| cyclic(X0,X1,X2,X1) ),
inference(resolution,[status(thm)],[f1672,f131]) ).
fof(f1691,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| cyclic(X0,X1,X2,X0) ),
inference(resolution,[status(thm)],[f1688,f133]) ).
fof(f1697,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f1691,f129]) ).
fof(f1703,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f1697,f136]) ).
fof(f1707,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f1703,f1697]) ).
fof(f1713,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ9_spl
| 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,f1707]) ).
fof(f1714,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f1707]) ).
fof(f1715,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ9_spl
| 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)],[f1713,f1707]) ).
fof(f1783,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ9_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f1715,f1707]) ).
fof(f1784,plain,
! [X0,X1] :
( ~ sQ9_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f1783,f1714]) ).
fof(f2567,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| perp(X0,X0,X1,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f232,f1784]) ).
fof(f2578,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| perp(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2567,f1784]) ).
fof(f2581,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| perp(X1,X0,X0,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f235,f1707]) ).
fof(f2584,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| perp(X1,X0,X0,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f2581,f1784]) ).
fof(f2595,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| perp(X0,X1,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2584,f1784]) ).
fof(f2607,plain,
! [X0] :
( ~ sQ9_spl
| para(X0,X0,sK24_skl,sK30_skl) ),
inference(resolution,[status(thm)],[f2578,f512]) ).
fof(f2628,plain,
! [X0] :
( ~ sQ9_spl
| para(X0,sK26_skl,sK24_skl,sK30_skl) ),
inference(resolution,[status(thm)],[f2595,f512]) ).
fof(f2792,plain,
! [X0] :
( ~ sQ9_spl
| para(sK24_skl,sK30_skl,X0,X0) ),
inference(resolution,[status(thm)],[f2607,f107]) ).
fof(f2802,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| perp(sK24_skl,sK30_skl,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f2792,f120]) ).
fof(f2806,plain,
! [X0,X1] :
( ~ sQ9_spl
| perp(sK24_skl,sK30_skl,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2802,f2578]) ).
fof(f2948,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| perp(X2,sK26_skl,X0,X1)
| ~ perp(sK24_skl,sK30_skl,X0,X1) ),
inference(resolution,[status(thm)],[f2628,f120]) ).
fof(f2952,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| perp(X0,sK26_skl,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2948,f2806]) ).
fof(f2959,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| perp(X0,X1,X2,sK26_skl) ),
inference(resolution,[status(thm)],[f2952,f114]) ).
fof(f2965,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| perp(X0,X1,sK26_skl,X2) ),
inference(resolution,[status(thm)],[f2959,f112]) ).
fof(f2970,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| perp(sK26_skl,X0,X1,X2) ),
inference(resolution,[status(thm)],[f2965,f114]) ).
fof(f2976,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ9_spl
| para(X0,X1,X3,X4)
| ~ perp(X0,X1,sK26_skl,X2) ),
inference(resolution,[status(thm)],[f2970,f117]) ).
fof(f2979,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| para(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f2976,f2965]) ).
fof(f2986,plain,
( ~ sQ9_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f385,f2979]) ).
fof(f2990,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f2986]) ).
fof(f2991,plain,
$false,
inference(sat_refutation,[status(thm)],[f1550,f1567,f2990]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO629+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 18:03:35 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.59 % Refutation found
% 0.11/0.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.13/0.61 % Elapsed time: 0.228980 seconds
% 1.13/0.61 % CPU time: 1.455494 seconds
% 1.13/0.61 % Total memory used: 103.856 MB
% 1.13/0.61 % Net memory used: 101.651 MB
%------------------------------------------------------------------------------