%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO640+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 : n015.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 01:18:22 PM UTC 2026
% Result : Theorem 191.41s 24.78s
% Output : Proof 191.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 101
% Number of leaves : 26
% Syntax : Number of formulae : 301 ( 201 unt; 0 def)
% Number of atoms : 545 ( 196 equ)
% Maximal formula atoms : 26 ( 1 avg)
% Number of connectives : 358 ( 114 ~; 108 |; 110 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 57 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 33 ( 33 usr; 31 con; 0-4 aty)
% Number of variables : 1076 ( 157 sgn 423 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/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(t158,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,cyclic(X2,X3,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t342,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,cyclic(X2,X3,X4,X5),true),true) = true,
inference(orient,[status(thm)],[t158]) ).
fof(f13,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox/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(t109,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t348,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t109]) ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox/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(t110,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t346,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(orient,[status(thm)],[t110]) ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox/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(t111,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t344,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(orient,[status(thm)],[t111]) ).
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(t186,plain,
ifeq(eqangle(X1,X2,X1,X3,X4,X2,X4,X3),true,ifeq(coll(X1,X4,X3),true,cyclic(X2,X3,X1,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c42]) ).
cnf(t303,plain,
ifeq(eqangle(X1,X2,X1,X3,X4,X2,X4,X3),true,ifeq(coll(X1,X4,X3),true,cyclic(X2,X3,X1,X4),true),true) = true,
inference(orient,[status(thm)],[t186]) ).
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,
! [Q4,Q1,Q3,Q0,Q2,P0,P1,P2,P3,P4,O0,O4,O3,O2,O1,M0,M4,M3,M2,M1,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9,NWPNT01] :
( ( circle(O1,Q1,M1,NWPNT01)
& circle(O2,Q2,M1,NWPNT9)
& circle(O2,Q2,M2,NWPNT8)
& circle(O3,Q3,M2,NWPNT7)
& circle(O3,Q3,M3,NWPNT6)
& circle(O4,Q4,M3,NWPNT5)
& circle(O4,Q4,M4,NWPNT4)
& circle(O0,Q0,M4,NWPNT3)
& circle(O1,Q1,M0,NWPNT2)
& circle(O0,Q0,M0,NWPNT1)
& circle(O1,P1,Q1,P0)
& circle(O2,P1,P2,Q2)
& circle(O3,P3,P2,Q3)
& circle(O4,P4,P3,Q4)
& circle(O0,Q0,P0,P4)
& coll(P4,Q3,Q0)
& coll(P4,Q4,Q1)
& coll(P3,Q4,Q2)
& coll(P3,Q3,Q0)
& coll(P2,Q4,Q2)
& coll(P2,Q1,Q3)
& coll(P1,Q0,Q2)
& coll(P1,Q1,Q3)
& coll(P0,Q0,Q2)
& coll(P0,Q4,Q1) )
=> cyclic(M4,M3,M2,M1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL81109106) ).
fof(f94_neg,negated_conjecture,
~ ! [Q4,Q1,Q3,Q0,Q2,P0,P1,P2,P3,P4,O0,O4,O3,O2,O1,M0,M4,M3,M2,M1,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9,NWPNT01] :
( ( circle(O1,Q1,M1,NWPNT01)
& circle(O2,Q2,M1,NWPNT9)
& circle(O2,Q2,M2,NWPNT8)
& circle(O3,Q3,M2,NWPNT7)
& circle(O3,Q3,M3,NWPNT6)
& circle(O4,Q4,M3,NWPNT5)
& circle(O4,Q4,M4,NWPNT4)
& circle(O0,Q0,M4,NWPNT3)
& circle(O1,Q1,M0,NWPNT2)
& circle(O0,Q0,M0,NWPNT1)
& circle(O1,P1,Q1,P0)
& circle(O2,P1,P2,Q2)
& circle(O3,P3,P2,Q3)
& circle(O4,P4,P3,Q4)
& circle(O0,Q0,P0,P4)
& coll(P4,Q3,Q0)
& coll(P4,Q4,Q1)
& coll(P3,Q4,Q2)
& coll(P3,Q3,Q0)
& coll(P2,Q4,Q2)
& coll(P2,Q1,Q3)
& coll(P1,Q0,Q2)
& coll(P1,Q1,Q3)
& coll(P0,Q0,Q2)
& coll(P0,Q4,Q1) )
=> cyclic(M4,M3,M2,M1) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [Q4,Q1,Q3,Q0,Q2,P0,P1,P2,P3,P4,O0,O4,O3,O2,O1,M0,M4,M3,M2,M1,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9,NWPNT01] :
( ~ cyclic(M4,M3,M2,M1)
& circle(O1,Q1,M1,NWPNT01)
& circle(O2,Q2,M1,NWPNT9)
& circle(O2,Q2,M2,NWPNT8)
& circle(O3,Q3,M2,NWPNT7)
& circle(O3,Q3,M3,NWPNT6)
& circle(O4,Q4,M3,NWPNT5)
& circle(O4,Q4,M4,NWPNT4)
& circle(O0,Q0,M4,NWPNT3)
& circle(O1,Q1,M0,NWPNT2)
& circle(O0,Q0,M0,NWPNT1)
& circle(O1,P1,Q1,P0)
& circle(O2,P1,P2,Q2)
& circle(O3,P3,P2,Q3)
& circle(O4,P4,P3,Q4)
& circle(O0,Q0,P0,P4)
& coll(P4,Q3,Q0)
& coll(P4,Q4,Q1)
& coll(P3,Q4,Q2)
& coll(P3,Q3,Q0)
& coll(P2,Q4,Q2)
& coll(P2,Q1,Q3)
& coll(P1,Q0,Q2)
& coll(P1,Q1,Q3)
& coll(P0,Q0,Q2)
& coll(P0,Q4,Q1) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ cyclic(sk36,sk37,sk38,sk39)
& circle(sk34,sk21,sk39,sk49)
& circle(sk33,sk24,sk39,sk48)
& circle(sk33,sk24,sk38,sk47)
& circle(sk32,sk22,sk38,sk46)
& circle(sk32,sk22,sk37,sk45)
& circle(sk31,sk20,sk37,sk44)
& circle(sk31,sk20,sk36,sk43)
& circle(sk30,sk23,sk36,sk42)
& circle(sk34,sk21,sk35,sk41)
& circle(sk30,sk23,sk35,sk40)
& circle(sk34,sk26,sk21,sk25)
& circle(sk33,sk26,sk27,sk24)
& circle(sk32,sk28,sk27,sk22)
& circle(sk31,sk29,sk28,sk20)
& circle(sk30,sk23,sk25,sk29)
& coll(sk29,sk22,sk23)
& coll(sk29,sk20,sk21)
& coll(sk28,sk20,sk24)
& coll(sk28,sk22,sk23)
& coll(sk27,sk20,sk24)
& coll(sk27,sk21,sk22)
& coll(sk26,sk23,sk24)
& coll(sk26,sk21,sk22)
& coll(sk25,sk23,sk24)
& coll(sk25,sk20,sk21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29,sk30,sk31,sk32,sk33,sk34,sk35,sk36,sk37,sk38,sk39,sk40,sk41,sk42,sk43,sk44,sk45,sk46,sk47,sk48,sk49])],[f94_nnf]) ).
cnf(c131,plain,
circle(sk31,sk20,sk36,sk43),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi131,negated_conjecture,
circle(sk31,sk20,sk36,sk43) = true,
inference(equality_encoding,[status(esa)],[c131]) ).
cnf(h42,plain,
perp(sk11(sk20,sk36,sk43,sk31),sk20,sk20,sk31) = true,
inference(hyper_resolution,[status(thm)],[hi99,hi131]) ).
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(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h141,plain,
perp(sk20,sk31,sk11(sk20,sk36,sk43,sk31),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi7,h42]) ).
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(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(h369,plain,
para(sk11(sk20,sk36,sk43,sk31),sk20,sk11(sk20,sk36,sk43,sk31),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,h42,h141]) ).
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(t49,plain,
coll(sk11(sk20,sk36,sk43,sk31),sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi66,h369]) ).
cnf(t406,plain,
coll(sk11(sk20,sk36,sk43,sk31),sk20,sk20) = true,
inference(orient,[status(thm)],[t49]) ).
cnf(t417,plain,
true = ifeq(eqangle(sk11(sk20,sk36,sk43,sk31),X1,sk11(sk20,sk36,sk43,sk31),sk20,sk20,X1,sk20,sk20),true,ifeq(true,true,cyclic(X1,sk20,sk11(sk20,sk36,sk43,sk31),sk20),true),true),
inference(cp,[status(thm)],[t303,t406]) ).
cnf(t47,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t47]) ).
cnf(t38286,plain,
true = ifeq(eqangle(sk11(sk20,sk36,sk43,sk31),X1,sk11(sk20,sk36,sk43,sk31),sk20,sk20,X1,sk20,sk20),true,cyclic(X1,sk20,sk11(sk20,sk36,sk43,sk31),sk20),true),
inference(step,[status(thm)],[t417,t256]) ).
cnf(t18857,plain,
ifeq(eqangle(sk11(sk20,sk36,sk43,sk31),X1,sk11(sk20,sk36,sk43,sk31),sk20,sk20,X1,sk20,sk20),true,cyclic(X1,sk20,sk11(sk20,sk36,sk43,sk31),sk20),true) = true,
inference(orient,[status(thm)],[t38286]) ).
fof(f21,axiom,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( ( eqangle(P,Q,U,V,E,F,G,H)
& eqangle(A,B,C,D,P,Q,U,V) )
=> eqangle(A,B,C,D,E,F,G,H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD22) ).
fof(f21_nnf,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(t242,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(eqangle(X5,X6,X7,X8,X9,X10,X11,X12),true,eqangle(X1,X2,X3,X4,X9,X10,X11,X12),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t286,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(eqangle(X5,X6,X7,X8,X9,X10,X11,X12),true,eqangle(X1,X2,X3,X4,X9,X10,X11,X12),true),true) = true,
inference(orient,[status(thm)],[t242]) ).
fof(f19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(P,Q,U,V,A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD20) ).
fof(f19_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t162,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X5,X6,X7,X8,X1,X2,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t288,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X5,X6,X7,X8,X1,X2,X3,X4),true) = true,
inference(orient,[status(thm)],[t162]) ).
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(t159,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t294,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(orient,[status(thm)],[t159]) ).
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(t142,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(t312,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(orient,[status(thm)],[t142]) ).
cnf(t169,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)],[t169]) ).
cnf(t115,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)],[t115]) ).
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(t156,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)],[t156]) ).
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(t99,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)],[t99]) ).
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(t228,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)],[t228]) ).
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(t141,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(t296,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(orient,[status(thm)],[t141]) ).
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(t161,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(t290,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)],[t161]) ).
fof(f40,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD41) ).
fof(f40_nnf,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(t140,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t343,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(orient,[status(thm)],[t140]) ).
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox/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(hi1,axiom,
ifeq(coll(X0,X1,X2),true,coll(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(c121,plain,
coll(sk29,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi121,negated_conjecture,
coll(sk29,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c121]) ).
cnf(h25,plain,
coll(sk20,sk29,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi121]) ).
fof(f0,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox/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(hi0,axiom,
ifeq(coll(X0,X1,X2),true,coll(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h108,plain,
coll(sk20,sk21,sk29) = true,
inference(hyper_resolution,[status(thm)],[hi0,h25]) ).
fof(f2,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox/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(hi2,axiom,
ifeq(coll(X0,X1,X2),true,ifeq(coll(X0,X1,X3),true,coll(X2,X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h283,plain,
coll(sk29,sk29,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h108,h108]) ).
cnf(c124,plain,
circle(sk31,sk29,sk28,sk20),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi124,negated_conjecture,
circle(sk31,sk29,sk28,sk20) = true,
inference(equality_encoding,[status(esa)],[c124]) ).
cnf(h31,plain,
perp(sk11(sk29,sk28,sk20,sk31),sk29,sk29,sk31) = true,
inference(hyper_resolution,[status(thm)],[hi99,hi124]) ).
cnf(h120,plain,
perp(sk29,sk31,sk11(sk29,sk28,sk20,sk31),sk29) = true,
inference(hyper_resolution,[status(thm)],[hi7,h31]) ).
cnf(h317,plain,
para(sk29,sk31,sk29,sk31) = true,
inference(hyper_resolution,[status(thm)],[hi8,h120,h31]) ).
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(h708,plain,
eqangle(sk29,sk31,V0,V1,sk29,sk31,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h317]) ).
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(t37,plain,
cyclic(sk31,sk20,sk29,sk29) = true,
inference(hyper_resolution,[status(thm)],[hi42,h708,h283]) ).
cnf(t2479,plain,
cyclic(sk31,sk20,sk29,sk29) = true,
inference(orient,[status(thm)],[t37]) ).
cnf(t2484,plain,
true = ifeq(true,true,eqangle(sk29,sk31,sk29,sk20,sk29,sk31,sk29,sk20),true),
inference(cp,[status(thm)],[t343,t2479]) ).
cnf(t37490,plain,
true = eqangle(sk29,sk31,sk29,sk20,sk29,sk31,sk29,sk20),
inference(step,[status(thm)],[t2484,t256]) ).
cnf(t8235,plain,
eqangle(sk29,sk31,sk29,sk20,sk29,sk31,sk29,sk20) = true,
inference(orient,[status(thm)],[t37490]) ).
cnf(t8236,plain,
true = ifeq(true,true,para(sk29,sk31,sk29,sk31),true),
inference(cp,[status(thm)],[t296,t8235]) ).
cnf(t37491,plain,
true = para(sk29,sk31,sk29,sk31),
inference(step,[status(thm)],[t8236,t256]) ).
cnf(t8250,plain,
para(sk29,sk31,sk29,sk31) = true,
inference(orient,[status(thm)],[t37491]) ).
cnf(t8254,plain,
true = ifeq(true,true,eqangle(sk29,sk31,X1,X2,sk29,sk31,X1,X2),true),
inference(cp,[status(thm)],[t312,t8250]) ).
cnf(t38112,plain,
true = eqangle(sk29,sk31,X1,X2,sk29,sk31,X1,X2),
inference(step,[status(thm)],[t8254,t256]) ).
cnf(t16699,plain,
eqangle(sk29,sk31,X1,X2,sk29,sk31,X1,X2) = true,
inference(orient,[status(thm)],[t38112]) ).
cnf(t16704,plain,
true = ifeq(true,true,eqangle(X1,X2,sk29,sk31,X1,X2,sk29,sk31),true),
inference(cp,[status(thm)],[t290,t16699]) ).
cnf(t38720,plain,
true = eqangle(X1,X2,sk29,sk31,X1,X2,sk29,sk31),
inference(step,[status(thm)],[t16704,t256]) ).
cnf(t22779,plain,
eqangle(X1,X2,sk29,sk31,X1,X2,sk29,sk31) = true,
inference(orient,[status(thm)],[t38720]) ).
cnf(t22781,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t296,t22779]) ).
cnf(t38721,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t22781,t256]) ).
cnf(t22803,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t38721]) ).
cnf(t22821,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,t22803]) ).
cnf(t40142,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)],[t22821,t256]) ).
cnf(t40143,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t40142,t22803]) ).
cnf(t40144,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t40143,t256]) ).
cnf(t36133,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t40144]) ).
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(t147,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)],[t147]) ).
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(t253,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(t341,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(orient,[status(thm)],[t253]) ).
cnf(h24,plain,
coll(sk21,sk21,sk29) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi121,hi121]) ).
cnf(h104,plain,
coll(sk29,sk29,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h24,h24]) ).
cnf(h279,plain,
coll(sk29,sk21,sk29) = true,
inference(hyper_resolution,[status(thm)],[hi0,h104]) ).
cnf(h626,plain,
coll(sk29,sk29,sk29) = true,
inference(hyper_resolution,[status(thm)],[hi2,h279,h279]) ).
cnf(t43,plain,
cyclic(sk31,sk29,sk29,sk29) = true,
inference(hyper_resolution,[status(thm)],[hi42,h708,h626]) ).
cnf(t2536,plain,
cyclic(sk31,sk29,sk29,sk29) = true,
inference(orient,[status(thm)],[t43]) ).
cnf(t2537,plain,
true = ifeq(true,true,cyclic(sk29,sk31,sk29,sk29),true),
inference(cp,[status(thm)],[t344,t2536]) ).
cnf(t37312,plain,
true = cyclic(sk29,sk31,sk29,sk29),
inference(step,[status(thm)],[t2537,t256]) ).
cnf(t4904,plain,
cyclic(sk29,sk31,sk29,sk29) = true,
inference(orient,[status(thm)],[t37312]) ).
cnf(t4905,plain,
true = ifeq(true,true,cyclic(sk29,sk29,sk31,sk29),true),
inference(cp,[status(thm)],[t346,t4904]) ).
cnf(t37345,plain,
true = cyclic(sk29,sk29,sk31,sk29),
inference(step,[status(thm)],[t4905,t256]) ).
cnf(t5483,plain,
cyclic(sk29,sk29,sk31,sk29) = true,
inference(orient,[status(thm)],[t37345]) ).
cnf(t5486,plain,
true = ifeq(true,true,eqangle(sk31,sk29,sk31,sk29,sk29,sk29,sk29,sk29),true),
inference(cp,[status(thm)],[t343,t5483]) ).
cnf(t37789,plain,
true = eqangle(sk31,sk29,sk31,sk29,sk29,sk29,sk29,sk29),
inference(step,[status(thm)],[t5486,t256]) ).
cnf(t14260,plain,
eqangle(sk31,sk29,sk31,sk29,sk29,sk29,sk29,sk29) = true,
inference(orient,[status(thm)],[t37789]) ).
cnf(t14273,plain,
true = ifeq(cyclic(sk29,sk29,sk31,sk29),true,ifeq(cyclic(sk29,sk29,sk31,sk29),true,ifeq(cyclic(sk29,sk29,sk31,sk29),true,ifeq(true,true,cong(sk29,sk29,sk29,sk29),true),true),true),true),
inference(cp,[status(thm)],[t341,t14260]) ).
cnf(t37790,plain,
true = ifeq(true,true,ifeq(cyclic(sk29,sk29,sk31,sk29),true,ifeq(cyclic(sk29,sk29,sk31,sk29),true,ifeq(true,true,cong(sk29,sk29,sk29,sk29),true),true),true),true),
inference(step,[status(thm)],[t14273,t5483]) ).
cnf(t37791,plain,
true = ifeq(cyclic(sk29,sk29,sk31,sk29),true,ifeq(cyclic(sk29,sk29,sk31,sk29),true,ifeq(true,true,cong(sk29,sk29,sk29,sk29),true),true),true),
inference(step,[status(thm)],[t37790,t256]) ).
cnf(t37792,plain,
true = ifeq(true,true,ifeq(cyclic(sk29,sk29,sk31,sk29),true,ifeq(true,true,cong(sk29,sk29,sk29,sk29),true),true),true),
inference(step,[status(thm)],[t37791,t5483]) ).
cnf(t37793,plain,
true = ifeq(cyclic(sk29,sk29,sk31,sk29),true,ifeq(true,true,cong(sk29,sk29,sk29,sk29),true),true),
inference(step,[status(thm)],[t37792,t256]) ).
cnf(t37794,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk29,sk29,sk29,sk29),true),true),
inference(step,[status(thm)],[t37793,t5483]) ).
cnf(t37795,plain,
true = ifeq(true,true,cong(sk29,sk29,sk29,sk29),true),
inference(step,[status(thm)],[t37794,t256]) ).
cnf(t37796,plain,
true = cong(sk29,sk29,sk29,sk29),
inference(step,[status(thm)],[t37795,t256]) ).
cnf(t14274,plain,
cong(sk29,sk29,sk29,sk29) = true,
inference(orient,[status(thm)],[t37796]) ).
cnf(t14283,plain,
true = ifeq(true,true,ifeq(coll(sk29,sk29,sk29),true,midp(sk29,sk29,sk29),true),true),
inference(cp,[status(thm)],[t327,t14274]) ).
cnf(t37797,plain,
true = ifeq(coll(sk29,sk29,sk29),true,midp(sk29,sk29,sk29),true),
inference(step,[status(thm)],[t14283,t256]) ).
cnf(t100,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t319,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t100]) ).
cnf(t4907,plain,
true = ifeq(true,true,eqangle(sk29,sk29,sk29,sk31,sk29,sk29,sk29,sk31),true),
inference(cp,[status(thm)],[t343,t4904]) ).
cnf(t37656,plain,
true = eqangle(sk29,sk29,sk29,sk31,sk29,sk29,sk29,sk31),
inference(step,[status(thm)],[t4907,t256]) ).
cnf(t11107,plain,
eqangle(sk29,sk29,sk29,sk31,sk29,sk29,sk29,sk31) = true,
inference(orient,[status(thm)],[t37656]) ).
cnf(t11108,plain,
true = ifeq(true,true,para(sk29,sk29,sk29,sk29),true),
inference(cp,[status(thm)],[t296,t11107]) ).
cnf(t37657,plain,
true = para(sk29,sk29,sk29,sk29),
inference(step,[status(thm)],[t11108,t256]) ).
cnf(t11120,plain,
para(sk29,sk29,sk29,sk29) = true,
inference(orient,[status(thm)],[t37657]) ).
cnf(t11121,plain,
true = ifeq(true,true,coll(sk29,sk29,sk29),true),
inference(cp,[status(thm)],[t319,t11120]) ).
cnf(t37658,plain,
true = coll(sk29,sk29,sk29),
inference(step,[status(thm)],[t11121,t256]) ).
cnf(t11140,plain,
coll(sk29,sk29,sk29) = true,
inference(orient,[status(thm)],[t37658]) ).
cnf(t37798,plain,
true = ifeq(true,true,midp(sk29,sk29,sk29),true),
inference(step,[status(thm)],[t37797,t11140]) ).
cnf(t37799,plain,
true = midp(sk29,sk29,sk29),
inference(step,[status(thm)],[t37798,t256]) ).
cnf(t14312,plain,
midp(sk29,sk29,sk29) = true,
inference(orient,[status(thm)],[t37799]) ).
cnf(t36134,plain,
true = ifeq(true,true,midp(sk29,X1,X1),true),
inference(cp,[status(thm)],[t36133,t14312]) ).
cnf(t40145,plain,
true = midp(sk29,X1,X1),
inference(step,[status(thm)],[t36134,t256]) ).
cnf(t36136,plain,
midp(sk29,X1,X1) = true,
inference(orient,[status(thm)],[t40145]) ).
cnf(t36137,plain,
true = ifeq(true,true,cong(sk29,X1,sk29,X1),true),
inference(cp,[status(thm)],[t363,t36136]) ).
cnf(t40147,plain,
true = cong(sk29,X1,sk29,X1),
inference(step,[status(thm)],[t36137,t256]) ).
cnf(t36178,plain,
cong(sk29,X1,sk29,X1) = true,
inference(orient,[status(thm)],[t40147]) ).
cnf(t36189,plain,
true = ifeq(true,true,ifeq(cong(sk29,X1,sk29,X1),true,perp(sk29,sk29,X2,X1),true),true),
inference(cp,[status(thm)],[t326,t36178]) ).
cnf(t40150,plain,
true = ifeq(cong(sk29,X1,sk29,X1),true,perp(sk29,sk29,X2,X1),true),
inference(step,[status(thm)],[t36189,t256]) ).
cnf(t40151,plain,
true = ifeq(true,true,perp(sk29,sk29,X2,X1),true),
inference(step,[status(thm)],[t40150,t36178]) ).
cnf(t40152,plain,
true = perp(sk29,sk29,X2,X1),
inference(step,[status(thm)],[t40151,t256]) ).
cnf(t36266,plain,
perp(sk29,sk29,X1,X2) = true,
inference(orient,[status(thm)],[t40152]) ).
cnf(t36267,plain,
true = ifeq(true,true,perp(X1,X2,sk29,sk29),true),
inference(cp,[status(thm)],[t274,t36266]) ).
cnf(t40158,plain,
true = perp(X1,X2,sk29,sk29),
inference(step,[status(thm)],[t36267,t256]) ).
cnf(t36376,plain,
perp(X1,X2,sk29,sk29) = true,
inference(orient,[status(thm)],[t40158]) ).
cnf(t36390,plain,
true = ifeq(true,true,ifeq(perp(sk29,sk29,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t36376]) ).
cnf(t40165,plain,
true = ifeq(perp(sk29,sk29,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t36390,t256]) ).
cnf(t40166,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t40165,t36266]) ).
cnf(t40167,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t40166,t256]) ).
cnf(t36523,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t40167]) ).
cnf(t40168,plain,
ifeq(true,true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(step,[status(thm)],[t312,t36523]) ).
cnf(t40169,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(step,[status(thm)],[t40168,t256]) ).
cnf(t36524,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(rw,[status(thm)],[t40169]) ).
cnf(t36865,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4) = true,
inference(orient,[status(thm)],[t36524]) ).
cnf(t36868,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true),
inference(cp,[status(thm)],[t294,t36865]) ).
cnf(t40237,plain,
true = eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(step,[status(thm)],[t36868,t256]) ).
cnf(t36934,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6) = true,
inference(orient,[status(thm)],[t40237]) ).
cnf(t36936,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,X3,X4,X5,X6),true),
inference(cp,[status(thm)],[t288,t36934]) ).
cnf(t40247,plain,
true = eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(step,[status(thm)],[t36936,t256]) ).
cnf(t37027,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6) = true,
inference(orient,[status(thm)],[t40247]) ).
cnf(t37038,plain,
true = ifeq(eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true,ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),true),
inference(cp,[status(thm)],[t286,t37027]) ).
cnf(t40295,plain,
true = ifeq(true,true,ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),true),
inference(step,[status(thm)],[t37038,t36934]) ).
cnf(t40296,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),
inference(step,[status(thm)],[t40295,t256]) ).
cnf(t40297,plain,
true = eqangle(X1,X2,X3,X4,X7,X8,X9,X10),
inference(step,[status(thm)],[t40296,t256]) ).
cnf(t37168,plain,
eqangle(X1,X2,X3,X4,X5,X6,X7,X8) = true,
inference(orient,[status(thm)],[t40297]) ).
cnf(t40300,plain,
ifeq(true,true,cyclic(X1,sk20,sk11(sk20,sk36,sk43,sk31),sk20),true) = true,
inference(step,[status(thm)],[t18857,t37168]) ).
cnf(t40301,plain,
cyclic(X1,sk20,sk11(sk20,sk36,sk43,sk31),sk20) = true,
inference(step,[status(thm)],[t40300,t256]) ).
cnf(t37171,plain,
cyclic(X1,sk20,sk11(sk20,sk36,sk43,sk31),sk20) = true,
inference(rw,[status(thm)],[t40301]) ).
cnf(t37177,plain,
cyclic(X1,sk20,sk11(sk20,sk36,sk43,sk31),sk20) = true,
inference(orient,[status(thm)],[t37171]) ).
cnf(t37179,plain,
true = ifeq(true,true,cyclic(X1,sk11(sk20,sk36,sk43,sk31),sk20,sk20),true),
inference(cp,[status(thm)],[t346,t37177]) ).
cnf(t40306,plain,
true = cyclic(X1,sk11(sk20,sk36,sk43,sk31),sk20,sk20),
inference(step,[status(thm)],[t37179,t256]) ).
cnf(t37187,plain,
cyclic(X1,sk11(sk20,sk36,sk43,sk31),sk20,sk20) = true,
inference(orient,[status(thm)],[t40306]) ).
cnf(t37188,plain,
true = ifeq(true,true,cyclic(sk11(sk20,sk36,sk43,sk31),X1,sk20,sk20),true),
inference(cp,[status(thm)],[t344,t37187]) ).
cnf(t40309,plain,
true = cyclic(sk11(sk20,sk36,sk43,sk31),X1,sk20,sk20),
inference(step,[status(thm)],[t37188,t256]) ).
cnf(t37200,plain,
cyclic(sk11(sk20,sk36,sk43,sk31),X1,sk20,sk20) = true,
inference(orient,[status(thm)],[t40309]) ).
cnf(t37201,plain,
true = ifeq(true,true,cyclic(sk11(sk20,sk36,sk43,sk31),sk20,X1,sk20),true),
inference(cp,[status(thm)],[t346,t37200]) ).
cnf(t40312,plain,
true = cyclic(sk11(sk20,sk36,sk43,sk31),sk20,X1,sk20),
inference(step,[status(thm)],[t37201,t256]) ).
cnf(t37214,plain,
cyclic(sk11(sk20,sk36,sk43,sk31),sk20,X1,sk20) = true,
inference(orient,[status(thm)],[t40312]) ).
cnf(t37215,plain,
true = ifeq(true,true,cyclic(sk11(sk20,sk36,sk43,sk31),sk20,sk20,X1),true),
inference(cp,[status(thm)],[t348,t37214]) ).
cnf(t40315,plain,
true = cyclic(sk11(sk20,sk36,sk43,sk31),sk20,sk20,X1),
inference(step,[status(thm)],[t37215,t256]) ).
cnf(t37226,plain,
cyclic(sk11(sk20,sk36,sk43,sk31),sk20,sk20,X1) = true,
inference(orient,[status(thm)],[t40315]) ).
cnf(t37227,plain,
true = ifeq(true,true,ifeq(cyclic(sk11(sk20,sk36,sk43,sk31),sk20,sk20,X1),true,cyclic(sk20,sk20,X2,X1),true),true),
inference(cp,[status(thm)],[t342,t37226]) ).
cnf(t40316,plain,
true = ifeq(cyclic(sk11(sk20,sk36,sk43,sk31),sk20,sk20,X1),true,cyclic(sk20,sk20,X2,X1),true),
inference(step,[status(thm)],[t37227,t256]) ).
cnf(t40317,plain,
true = ifeq(true,true,cyclic(sk20,sk20,X2,X1),true),
inference(step,[status(thm)],[t40316,t37226]) ).
cnf(t40318,plain,
true = cyclic(sk20,sk20,X2,X1),
inference(step,[status(thm)],[t40317,t256]) ).
cnf(t37229,plain,
cyclic(sk20,sk20,X1,X2) = true,
inference(orient,[status(thm)],[t40318]) ).
cnf(t37231,plain,
true = ifeq(true,true,ifeq(cyclic(sk20,sk20,X1,X2),true,cyclic(sk20,X1,X3,X2),true),true),
inference(cp,[status(thm)],[t342,t37229]) ).
cnf(t40320,plain,
true = ifeq(cyclic(sk20,sk20,X1,X2),true,cyclic(sk20,X1,X3,X2),true),
inference(step,[status(thm)],[t37231,t256]) ).
cnf(t40321,plain,
true = ifeq(true,true,cyclic(sk20,X1,X3,X2),true),
inference(step,[status(thm)],[t40320,t37229]) ).
cnf(t40322,plain,
true = cyclic(sk20,X1,X3,X2),
inference(step,[status(thm)],[t40321,t256]) ).
cnf(t37238,plain,
cyclic(sk20,X1,X2,X3) = true,
inference(orient,[status(thm)],[t40322]) ).
cnf(t37240,plain,
true = ifeq(true,true,ifeq(cyclic(sk20,X1,X2,X3),true,cyclic(X1,X2,X4,X3),true),true),
inference(cp,[status(thm)],[t342,t37238]) ).
cnf(t40324,plain,
true = ifeq(cyclic(sk20,X1,X2,X3),true,cyclic(X1,X2,X4,X3),true),
inference(step,[status(thm)],[t37240,t256]) ).
cnf(t40325,plain,
true = ifeq(true,true,cyclic(X1,X2,X4,X3),true),
inference(step,[status(thm)],[t40324,t37238]) ).
cnf(t40326,plain,
true = cyclic(X1,X2,X4,X3),
inference(step,[status(thm)],[t40325,t256]) ).
cnf(t37244,plain,
cyclic(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t40326]) ).
cnf(c138,plain,
~ cyclic(sk36,sk37,sk38,sk39),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
cyclic(sk36,sk37,sk38,sk39) != true,
inference(equality_encoding,[status(esa)],[c138]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t37244]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO640+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 12:41:09 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 191.41/24.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 191.41/24.78 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------