%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO559+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 : n012.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 87.12s 11.32s
% Output : Proof 87.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 17
% Syntax : Number of formulae : 158 ( 94 unt; 0 def)
% Number of atoms : 278 ( 91 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 198 ( 78 ~; 72 |; 31 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-4 aty)
% Number of variables : 552 ( 32 sgn 239 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
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]) ).
cnf(t154,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t265,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(orient,[status(thm)],[t154]) ).
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(t81,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t274,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t81]) ).
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/sandbox/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(t141,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(t326,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(orient,[status(thm)],[t141]) ).
fof(f68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD68) ).
fof(f68_nnf,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f68]) ).
fof(f68_sk,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(skolemisation,[status(esa)],[f68_nnf]) ).
cnf(c68,plain,
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f68_sk]) ).
cnf(t69,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t363,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t69]) ).
fof(f64,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/sandbox/benchmark/theBenchmark.p',ruleD64) ).
fof(f64_nnf,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(nnf_transformation,[status(thm)],[f64]) ).
fof(f64_sk,plain,
! [M,A,B,C,D] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f64_nnf]) ).
cnf(c64,plain,
( midp(X4,X2,X3)
| ~ para(X0,X3,X1,X2)
| ~ para(X0,X2,X1,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(t211,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X4,X3,X5),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(t353,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X4,X3,X5),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(orient,[status(thm)],[t211]) ).
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(t104,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(t311,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(orient,[status(thm)],[t104]) ).
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]) ).
cnf(t146,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X3,X4,X1,X2,X7,X8,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t305,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X3,X4,X1,X2,X7,X8,X5,X6),true) = true,
inference(orient,[status(thm)],[t146]) ).
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(t105,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t294,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(orient,[status(thm)],[t105]) ).
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(t99,plain,
ifeq(cong(X1,X2,X1,X3),true,eqangle(X1,X2,X2,X3,X2,X3,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t337,plain,
ifeq(cong(X1,X2,X1,X3),true,eqangle(X1,X2,X2,X3,X2,X3,X1,X3),true) = true,
inference(orient,[status(thm)],[t99]) ).
fof(f86,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleX11) ).
fof(f86_nnf,plain,
! [A,B,C,O] :
? [P] :
( perp(P,A,A,O)
| ~ circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f86]) ).
fof(f86_sk,plain,
! [O,A,B,C] :
( perp(sk11(A,B,C,O),A,A,O)
| ~ circle(O,A,B,C) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f86_nnf]) ).
cnf(c99,plain,
( perp(sk11(X0,X1,X2,X3),X0,X0,X3)
| ~ circle(X3,X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f86_sk]) ).
cnf(hi99,axiom,
ifeq(circle(X0,X1,X2,X3),true,perp(sk11(X1,X2,X3,X0),X1,X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c99]) ).
fof(f94,conjecture,
! [A,B,C,O,F,P,E,D,NWPNT1,NWPNT2] :
( ( coll(D,B,F)
& circle(O,B,D,NWPNT2)
& coll(E,A,C)
& circle(P,A,E,NWPNT1)
& circle(P,A,B,F)
& circle(O,A,B,C) )
=> para(C,D,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL012019) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,O,F,P,E,D,NWPNT1,NWPNT2] :
( ( coll(D,B,F)
& circle(O,B,D,NWPNT2)
& coll(E,A,C)
& circle(P,A,E,NWPNT1)
& circle(P,A,B,F)
& circle(O,A,B,C) )
=> para(C,D,E,F) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,O,F,P,E,D,NWPNT1,NWPNT2] :
( ~ para(C,D,E,F)
& coll(D,B,F)
& circle(O,B,D,NWPNT2)
& coll(E,A,C)
& circle(P,A,E,NWPNT1)
& circle(P,A,B,F)
& circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ para(sk22,sk27,sk26,sk24)
& coll(sk27,sk21,sk24)
& circle(sk23,sk21,sk27,sk29)
& coll(sk26,sk20,sk22)
& circle(sk25,sk20,sk26,sk28)
& circle(sk25,sk20,sk21,sk24)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29])],[f94_nnf]) ).
cnf(c113,plain,
circle(sk23,sk20,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
circle(sk23,sk20,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h0,plain,
perp(sk11(sk20,sk21,sk22,sk23),sk20,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi99,hi113]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h12,plain,
perp(sk20,sk23,sk11(sk20,sk21,sk22,sk23),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi7,h0]) ).
cnf(hi8,axiom,
ifeq(perp(X0,X1,X2,X3),true,ifeq(perp(X2,X3,X4,X5),true,para(X0,X1,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h35,plain,
para(sk11(sk20,sk21,sk22,sk23),sk20,sk11(sk20,sk21,sk22,sk23),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,h0,h12]) ).
cnf(hi39,axiom,
ifeq(para(X0,X1,X2,X3),true,eqangle(X0,X1,X4,X5,X2,X3,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(h74,plain,
eqangle(sk11(sk20,sk21,sk22,sk23),sk20,V0,V1,sk11(sk20,sk21,sk22,sk23),sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h35]) ).
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(hi20,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X0,X1,X4,X5,X2,X3,X6,X7),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(h179,plain,
eqangle(sk11(sk20,sk21,sk22,sk23),sk20,sk11(sk20,sk21,sk22,sk23),sk20,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h74]) ).
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(hi66,axiom,
ifeq(para(X0,X1,X0,X2),true,coll(X0,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(h73,plain,
coll(sk11(sk20,sk21,sk22,sk23),sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi66,h35]) ).
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]) ).
cnf(hi42,axiom,
ifeq(eqangle(X0,X1,X0,X2,X3,X1,X3,X2),true,ifeq(coll(X0,X3,X2),true,cyclic(X1,X2,X0,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c42]) ).
cnf(h730,plain,
cyclic(sk20,sk20,sk11(sk20,sk21,sk22,sk23),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h179,h73]) ).
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]) ).
cnf(hi43,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,ifeq(cyclic(X0,X1,X2,X4),true,ifeq(cyclic(X0,X1,X2,X5),true,ifeq(eqangle(X2,X0,X2,X1,X5,X3,X5,X4),true,cong(X0,X1,X3,X4),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(t29,plain,
cong(sk20,sk20,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi43,h730,h730,h730,h179]) ).
cnf(t2265,plain,
cong(sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t29]) ).
cnf(t2268,plain,
true = ifeq(true,true,eqangle(sk20,sk20,sk20,sk20,sk20,sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t337,t2265]) ).
cnf(t40,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t40]) ).
cnf(t19815,plain,
true = eqangle(sk20,sk20,sk20,sk20,sk20,sk20,sk20,sk20),
inference(step,[status(thm)],[t2268,t256]) ).
cnf(t4840,plain,
eqangle(sk20,sk20,sk20,sk20,sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t19815]) ).
cnf(t4842,plain,
true = ifeq(true,true,para(sk20,sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t311,t4840]) ).
cnf(t19816,plain,
true = para(sk20,sk20,sk20,sk20),
inference(step,[status(thm)],[t4842,t256]) ).
cnf(t4863,plain,
para(sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t19816]) ).
cnf(t4866,plain,
true = ifeq(true,true,eqangle(sk20,sk20,X1,X2,sk20,sk20,X1,X2),true),
inference(cp,[status(thm)],[t294,t4863]) ).
cnf(t20136,plain,
true = eqangle(sk20,sk20,X1,X2,sk20,sk20,X1,X2),
inference(step,[status(thm)],[t4866,t256]) ).
cnf(t9291,plain,
eqangle(sk20,sk20,X1,X2,sk20,sk20,X1,X2) = true,
inference(orient,[status(thm)],[t20136]) ).
cnf(t9295,plain,
true = ifeq(true,true,eqangle(X1,X2,sk20,sk20,X1,X2,sk20,sk20),true),
inference(cp,[status(thm)],[t305,t9291]) ).
cnf(t20448,plain,
true = eqangle(X1,X2,sk20,sk20,X1,X2,sk20,sk20),
inference(step,[status(thm)],[t9295,t256]) ).
cnf(t12395,plain,
eqangle(X1,X2,sk20,sk20,X1,X2,sk20,sk20) = true,
inference(orient,[status(thm)],[t20448]) ).
cnf(t12396,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t311,t12395]) ).
cnf(t20449,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t12396,t256]) ).
cnf(t12418,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t20449]) ).
cnf(t12434,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,ifeq(para(X2,X3,X2,X3),true,midp(X1,X3,X3),true),true),true),
inference(cp,[status(thm)],[t353,t12418]) ).
cnf(t21253,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(para(X2,X3,X2,X3),true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t12434,t256]) ).
cnf(t21254,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t21253,t12418]) ).
cnf(t21255,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t21254,t256]) ).
cnf(t19313,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t21255]) ).
fof(f67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD67) ).
fof(f67_nnf,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f67]) ).
fof(f67_sk,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f67_nnf]) ).
cnf(c67,plain,
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f67_sk]) ).
cnf(t130,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(t327,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(orient,[status(thm)],[t130]) ).
cnf(t70,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t295,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t70]) ).
cnf(t4865,plain,
true = ifeq(true,true,coll(sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t295,t4863]) ).
cnf(t19817,plain,
true = coll(sk20,sk20,sk20),
inference(step,[status(thm)],[t4865,t256]) ).
cnf(t4884,plain,
coll(sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t19817]) ).
cnf(t4888,plain,
true = ifeq(cong(sk20,sk20,sk20,sk20),true,ifeq(true,true,midp(sk20,sk20,sk20),true),true),
inference(cp,[status(thm)],[t327,t4884]) ).
cnf(t19818,plain,
true = ifeq(true,true,ifeq(true,true,midp(sk20,sk20,sk20),true),true),
inference(step,[status(thm)],[t4888,t2265]) ).
cnf(t19819,plain,
true = ifeq(true,true,midp(sk20,sk20,sk20),true),
inference(step,[status(thm)],[t19818,t256]) ).
cnf(t19820,plain,
true = midp(sk20,sk20,sk20),
inference(step,[status(thm)],[t19819,t256]) ).
cnf(t4911,plain,
midp(sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t19820]) ).
cnf(t19314,plain,
true = ifeq(true,true,midp(sk20,X1,X1),true),
inference(cp,[status(thm)],[t19313,t4911]) ).
cnf(t21256,plain,
true = midp(sk20,X1,X1),
inference(step,[status(thm)],[t19314,t256]) ).
cnf(t19316,plain,
midp(sk20,X1,X1) = true,
inference(orient,[status(thm)],[t21256]) ).
cnf(t19317,plain,
true = ifeq(true,true,cong(sk20,X1,sk20,X1),true),
inference(cp,[status(thm)],[t363,t19316]) ).
cnf(t21258,plain,
true = cong(sk20,X1,sk20,X1),
inference(step,[status(thm)],[t19317,t256]) ).
cnf(t19360,plain,
cong(sk20,X1,sk20,X1) = true,
inference(orient,[status(thm)],[t21258]) ).
cnf(t19371,plain,
true = ifeq(true,true,ifeq(cong(sk20,X1,sk20,X1),true,perp(sk20,sk20,X2,X1),true),true),
inference(cp,[status(thm)],[t326,t19360]) ).
cnf(t21261,plain,
true = ifeq(cong(sk20,X1,sk20,X1),true,perp(sk20,sk20,X2,X1),true),
inference(step,[status(thm)],[t19371,t256]) ).
cnf(t21262,plain,
true = ifeq(true,true,perp(sk20,sk20,X2,X1),true),
inference(step,[status(thm)],[t21261,t19360]) ).
cnf(t21263,plain,
true = perp(sk20,sk20,X2,X1),
inference(step,[status(thm)],[t21262,t256]) ).
cnf(t19448,plain,
perp(sk20,sk20,X1,X2) = true,
inference(orient,[status(thm)],[t21263]) ).
cnf(t19449,plain,
true = ifeq(true,true,perp(X1,X2,sk20,sk20),true),
inference(cp,[status(thm)],[t274,t19448]) ).
cnf(t21270,plain,
true = perp(X1,X2,sk20,sk20),
inference(step,[status(thm)],[t19449,t256]) ).
cnf(t19606,plain,
perp(X1,X2,sk20,sk20) = true,
inference(orient,[status(thm)],[t21270]) ).
cnf(t19614,plain,
true = ifeq(true,true,ifeq(perp(sk20,sk20,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t19606]) ).
cnf(t21274,plain,
true = ifeq(perp(sk20,sk20,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t19614,t256]) ).
cnf(t21275,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t21274,t19448]) ).
cnf(t21276,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t21275,t256]) ).
cnf(t19713,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t21276]) ).
cnf(c119,plain,
~ para(sk22,sk27,sk26,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
para(sk22,sk27,sk26,sk24) != true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t19713]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO559+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Wed Sep 23 12:23:21 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 87.12/11.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 87.12/11.32 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------