%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO571+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 01:18:11 PM UTC 2026
% Result : Theorem 275.57s 36.55s
% Output : Proof 275.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 72
% Number of leaves : 28
% Syntax : Number of formulae : 308 ( 199 unt; 0 def)
% Number of atoms : 507 ( 192 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 324 ( 125 ~; 119 |; 52 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-4 aty)
% Number of variables : 1046 ( 108 sgn 414 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/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/sandbox2/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(t186,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)],[t186]) ).
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/sandbox2/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(t183,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)],[t183]) ).
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/sandbox2/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(t165,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)],[t165]) ).
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/sandbox2/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(t193,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)],[t193]) ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox2/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(t144,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)],[t144]) ).
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/sandbox2/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(t180,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)],[t180]) ).
fof(f68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox2/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(t121,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)],[t121]) ).
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/sandbox2/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/sandbox2/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(t164,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)],[t164]) ).
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/sandbox2/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(t185,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)],[t185]) ).
fof(f3,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD4) ).
fof(f3_nnf,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t141,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t316,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t141]) ).
fof(f73,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( para(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> para(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD73) ).
fof(f73_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
fof(f73_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f73_nnf]) ).
cnf(c73,plain,
( para(X0,X1,X2,X3)
| ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f73_sk]) ).
cnf(t212,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(t287,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t212]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
fof(f94,conjecture,
! [A,B,C,O,D,I,E,F,NWPNT1] :
( ( perp(A,B,B,F)
& perp(C,D,C,F)
& perp(A,B,A,E)
& perp(C,D,D,E)
& coll(I,C,D)
& coll(I,A,B)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> eqangle(A,I,I,E,F,I,I,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL214033) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,O,D,I,E,F,NWPNT1] :
( ( perp(A,B,B,F)
& perp(C,D,C,F)
& perp(A,B,A,E)
& perp(C,D,D,E)
& coll(I,C,D)
& coll(I,A,B)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> eqangle(A,I,I,E,F,I,I,C) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,O,D,I,E,F,NWPNT1] :
( ~ eqangle(A,I,I,E,F,I,I,C)
& perp(A,B,B,F)
& perp(C,D,C,F)
& perp(A,B,A,E)
& perp(C,D,D,E)
& coll(I,C,D)
& coll(I,A,B)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ eqangle(sk20,sk25,sk25,sk26,sk27,sk25,sk25,sk22)
& perp(sk20,sk21,sk21,sk27)
& perp(sk22,sk24,sk22,sk27)
& perp(sk20,sk21,sk20,sk26)
& perp(sk22,sk24,sk24,sk26)
& coll(sk25,sk22,sk24)
& coll(sk25,sk20,sk21)
& circle(sk23,sk20,sk24,sk28)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28])],[f94_nnf]) ).
cnf(c117,plain,
perp(sk22,sk24,sk24,sk26),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
perp(sk22,sk24,sk24,sk26) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h8,plain,
perp(sk24,sk26,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi117]) ).
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(c119,plain,
perp(sk22,sk24,sk22,sk27),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi119,negated_conjecture,
perp(sk22,sk24,sk22,sk27) = true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(h41,plain,
para(sk24,sk26,sk22,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi8,h8,hi119]) ).
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(h126,plain,
eqangle(sk24,sk26,V0,V1,sk22,sk27,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h41]) ).
cnf(hi18,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X2,X3,X0,X1,X6,X7,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h478,plain,
eqangle(V0,V1,sk24,sk26,V0,V1,sk22,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi18,h126]) ).
fof(f86,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('/export/starexec/sandbox2/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]) ).
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]) ).
fof(f6,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD7) ).
fof(f6_nnf,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X0,X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h25,plain,
perp(sk11(sk20,sk21,sk22,sk23),sk20,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi6,h0]) ).
cnf(h24,plain,
perp(sk20,sk23,sk11(sk20,sk21,sk22,sk23),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi7,h0]) ).
cnf(h107,plain,
para(sk20,sk23,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,h24,h25]) ).
cnf(h417,plain,
eqangle(sk20,sk23,V0,V1,sk23,sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h107]) ).
cnf(hi21,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,ifeq(eqangle(X4,X5,X6,X7,X8,X9,X10,X11),true,eqangle(X0,X1,X2,X3,X8,X9,X10,X11),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t62,plain,
eqangle(sk20,sk23,sk24,sk26,sk23,sk20,sk22,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi21,h417,h478]) ).
cnf(t1768,plain,
eqangle(sk20,sk23,sk24,sk26,sk23,sk20,sk22,sk27) = true,
inference(orient,[status(thm)],[t62]) ).
cnf(t1769,plain,
true = ifeq(true,true,eqangle(sk20,sk23,sk23,sk20,sk24,sk26,sk22,sk27),true),
inference(cp,[status(thm)],[t294,t1768]) ).
cnf(t15,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t15]) ).
cnf(t54477,plain,
true = eqangle(sk20,sk23,sk23,sk20,sk24,sk26,sk22,sk27),
inference(step,[status(thm)],[t1769,t256]) ).
cnf(t12842,plain,
eqangle(sk20,sk23,sk23,sk20,sk24,sk26,sk22,sk27) = true,
inference(orient,[status(thm)],[t54477]) ).
cnf(t12849,plain,
true = ifeq(true,true,ifeq(para(sk24,sk26,sk22,sk27),true,para(sk20,sk23,sk23,sk20),true),true),
inference(cp,[status(thm)],[t287,t12842]) ).
cnf(t54478,plain,
true = ifeq(para(sk24,sk26,sk22,sk27),true,para(sk20,sk23,sk23,sk20),true),
inference(step,[status(thm)],[t12849,t256]) ).
cnf(t22,plain,
para(sk24,sk26,sk22,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi8,h8,hi119]) ).
cnf(t2252,plain,
para(sk24,sk26,sk22,sk27) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t54479,plain,
true = ifeq(true,true,para(sk20,sk23,sk23,sk20),true),
inference(step,[status(thm)],[t54478,t2252]) ).
cnf(t54480,plain,
true = para(sk20,sk23,sk23,sk20),
inference(step,[status(thm)],[t54479,t256]) ).
cnf(t12854,plain,
para(sk20,sk23,sk23,sk20) = true,
inference(orient,[status(thm)],[t54480]) ).
cnf(t12855,plain,
true = ifeq(true,true,para(sk20,sk23,sk20,sk23),true),
inference(cp,[status(thm)],[t316,t12854]) ).
cnf(t54481,plain,
true = para(sk20,sk23,sk20,sk23),
inference(step,[status(thm)],[t12855,t256]) ).
cnf(t12879,plain,
para(sk20,sk23,sk20,sk23) = true,
inference(orient,[status(thm)],[t54481]) ).
cnf(t12881,plain,
true = ifeq(true,true,eqangle(sk20,sk23,X1,X2,sk20,sk23,X1,X2),true),
inference(cp,[status(thm)],[t312,t12879]) ).
cnf(t54953,plain,
true = eqangle(sk20,sk23,X1,X2,sk20,sk23,X1,X2),
inference(step,[status(thm)],[t12881,t256]) ).
cnf(t19871,plain,
eqangle(sk20,sk23,X1,X2,sk20,sk23,X1,X2) = true,
inference(orient,[status(thm)],[t54953]) ).
cnf(t19876,plain,
true = ifeq(true,true,eqangle(X1,X2,sk20,sk23,X1,X2,sk20,sk23),true),
inference(cp,[status(thm)],[t290,t19871]) ).
cnf(t55483,plain,
true = eqangle(X1,X2,sk20,sk23,X1,X2,sk20,sk23),
inference(step,[status(thm)],[t19876,t256]) ).
cnf(t26899,plain,
eqangle(X1,X2,sk20,sk23,X1,X2,sk20,sk23) = true,
inference(orient,[status(thm)],[t55483]) ).
cnf(t26901,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t296,t26899]) ).
cnf(t55484,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t26901,t256]) ).
cnf(t26923,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t55484]) ).
cnf(t26939,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,t26923]) ).
cnf(t57654,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)],[t26939,t256]) ).
cnf(t57655,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t57654,t26923]) ).
cnf(t57656,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t57655,t256]) ).
cnf(t52536,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t57656]) ).
fof(f67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox2/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(t171,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)],[t171]) ).
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/sandbox2/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]) ).
fof(f40,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',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(t163,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)],[t163]) ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox2/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(t139,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)],[t139]) ).
fof(f85,axiom,
! [A,B,C,H] :
? [P,Q] :
( ( perp(B,H,A,C)
& perp(A,H,B,C) )
=> ( perp(B,Q,C,A)
& coll(Q,C,A)
& perp(A,P,C,B)
& coll(P,C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX10) ).
fof(f85_nnf,plain,
! [A,B,C,H] :
? [P,Q] :
( ( perp(B,Q,C,A)
& coll(Q,C,A)
& perp(A,P,C,B)
& coll(P,C,B) )
| ~ perp(B,H,A,C)
| ~ perp(A,H,B,C) ),
inference(nnf_transformation,[status(thm)],[f85]) ).
fof(f85_sk,plain,
! [A,H,B,C] :
( ( perp(B,sk10(A,B,C,H),C,A)
& coll(sk10(A,B,C,H),C,A)
& perp(A,sk9(A,B,C,H),C,B)
& coll(sk9(A,B,C,H),C,B) )
| ~ perp(B,H,A,C)
| ~ perp(A,H,B,C) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9,sk10])],[f85_nnf]) ).
cnf(c97,plain,
( coll(sk10(X0,X1,X2,X3),X2,X0)
| ~ perp(X1,X3,X0,X2)
| ~ perp(X0,X3,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f85_sk]) ).
cnf(hi97,axiom,
ifeq(perp(X0,X1,X2,X3),true,ifeq(perp(X2,X1,X0,X3),true,coll(sk10(X0,X2,X3,X1),X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c97]) ).
cnf(c118,plain,
perp(sk20,sk21,sk20,sk26),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi118,negated_conjecture,
perp(sk20,sk21,sk20,sk26) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(h11,plain,
coll(sk10(sk20,sk20,sk26,sk21),sk26,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi97,hi118,hi118]) ).
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox2/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(h50,plain,
coll(sk26,sk10(sk20,sk20,sk26,sk21),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi1,h11]) ).
fof(f2,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox2/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(h172,plain,
coll(sk20,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h50,h50]) ).
fof(f0,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox2/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(c115,plain,
coll(sk25,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi115,negated_conjecture,
coll(sk25,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(h4,plain,
coll(sk25,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi115]) ).
cnf(h32,plain,
coll(sk20,sk20,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h4,h4]) ).
cnf(h511,plain,
coll(sk25,sk26,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h32,h172]) ).
cnf(h1325,plain,
coll(sk25,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi0,h511]) ).
cnf(h2839,plain,
coll(sk26,sk26,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h1325,h1325]) ).
cnf(c98,plain,
( perp(X1,sk10(X0,X1,X2,X3),X2,X0)
| ~ perp(X1,X3,X0,X2)
| ~ perp(X0,X3,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f85_sk]) ).
cnf(hi98,axiom,
ifeq(perp(X0,X1,X2,X3),true,ifeq(perp(X2,X1,X0,X3),true,perp(X2,sk10(X0,X2,X3,X1),X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c98]) ).
cnf(h10,plain,
perp(sk20,sk10(sk20,sk20,sk26,sk21),sk26,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi98,hi118,hi118]) ).
cnf(h47,plain,
perp(sk26,sk20,sk20,sk10(sk20,sk20,sk26,sk21)) = true,
inference(hyper_resolution,[status(thm)],[hi7,h10]) ).
cnf(h157,plain,
para(sk26,sk20,sk26,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,h47,h10]) ).
cnf(h687,plain,
eqangle(sk26,sk20,V0,V1,sk26,sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h157]) ).
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/sandbox2/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(t10,plain,
cyclic(sk20,sk25,sk26,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi42,h687,h2839]) ).
cnf(t2515,plain,
cyclic(sk20,sk25,sk26,sk26) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t2516,plain,
true = ifeq(true,true,cyclic(sk20,sk26,sk25,sk26),true),
inference(cp,[status(thm)],[t346,t2515]) ).
cnf(t54083,plain,
true = cyclic(sk20,sk26,sk25,sk26),
inference(step,[status(thm)],[t2516,t256]) ).
cnf(t3812,plain,
cyclic(sk20,sk26,sk25,sk26) = true,
inference(orient,[status(thm)],[t54083]) ).
cnf(t3817,plain,
true = ifeq(true,true,eqangle(sk25,sk20,sk25,sk26,sk26,sk20,sk26,sk26),true),
inference(cp,[status(thm)],[t343,t3812]) ).
cnf(t54687,plain,
true = eqangle(sk25,sk20,sk25,sk26,sk26,sk20,sk26,sk26),
inference(step,[status(thm)],[t3817,t256]) ).
cnf(t15932,plain,
eqangle(sk25,sk20,sk25,sk26,sk26,sk20,sk26,sk26) = true,
inference(orient,[status(thm)],[t54687]) ).
cnf(t15948,plain,
true = ifeq(cyclic(sk20,sk26,sk25,sk20),true,ifeq(cyclic(sk20,sk26,sk25,sk26),true,ifeq(cyclic(sk20,sk26,sk25,sk26),true,ifeq(true,true,cong(sk20,sk26,sk20,sk26),true),true),true),true),
inference(cp,[status(thm)],[t341,t15932]) ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox2/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(t140,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)],[t140]) ).
cnf(h14,plain,
perp(sk20,sk26,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi118]) ).
cnf(h65,plain,
para(sk20,sk26,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi8,h14,hi118]) ).
cnf(h224,plain,
eqangle(sk20,sk26,V0,V1,sk20,sk26,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h65]) ).
cnf(t12,plain,
cyclic(sk26,sk25,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h224,h32]) ).
cnf(t2591,plain,
cyclic(sk26,sk25,sk20,sk20) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t2592,plain,
true = ifeq(true,true,cyclic(sk26,sk20,sk25,sk20),true),
inference(cp,[status(thm)],[t346,t2591]) ).
cnf(t54087,plain,
true = cyclic(sk26,sk20,sk25,sk20),
inference(step,[status(thm)],[t2592,t256]) ).
cnf(t3882,plain,
cyclic(sk26,sk20,sk25,sk20) = true,
inference(orient,[status(thm)],[t54087]) ).
cnf(t3885,plain,
true = ifeq(true,true,cyclic(sk20,sk26,sk25,sk20),true),
inference(cp,[status(thm)],[t344,t3882]) ).
cnf(t54108,plain,
true = cyclic(sk20,sk26,sk25,sk20),
inference(step,[status(thm)],[t3885,t256]) ).
cnf(t4346,plain,
cyclic(sk20,sk26,sk25,sk20) = true,
inference(orient,[status(thm)],[t54108]) ).
cnf(t54688,plain,
true = ifeq(true,true,ifeq(cyclic(sk20,sk26,sk25,sk26),true,ifeq(cyclic(sk20,sk26,sk25,sk26),true,ifeq(true,true,cong(sk20,sk26,sk20,sk26),true),true),true),true),
inference(step,[status(thm)],[t15948,t4346]) ).
cnf(t54689,plain,
true = ifeq(cyclic(sk20,sk26,sk25,sk26),true,ifeq(cyclic(sk20,sk26,sk25,sk26),true,ifeq(true,true,cong(sk20,sk26,sk20,sk26),true),true),true),
inference(step,[status(thm)],[t54688,t256]) ).
cnf(t54690,plain,
true = ifeq(true,true,ifeq(cyclic(sk20,sk26,sk25,sk26),true,ifeq(true,true,cong(sk20,sk26,sk20,sk26),true),true),true),
inference(step,[status(thm)],[t54689,t3812]) ).
cnf(t54691,plain,
true = ifeq(cyclic(sk20,sk26,sk25,sk26),true,ifeq(true,true,cong(sk20,sk26,sk20,sk26),true),true),
inference(step,[status(thm)],[t54690,t256]) ).
cnf(t54692,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk20,sk26,sk20,sk26),true),true),
inference(step,[status(thm)],[t54691,t3812]) ).
cnf(t54693,plain,
true = ifeq(true,true,cong(sk20,sk26,sk20,sk26),true),
inference(step,[status(thm)],[t54692,t256]) ).
cnf(t54694,plain,
true = cong(sk20,sk26,sk20,sk26),
inference(step,[status(thm)],[t54693,t256]) ).
cnf(t15949,plain,
cong(sk20,sk26,sk20,sk26) = true,
inference(orient,[status(thm)],[t54694]) ).
cnf(t15960,plain,
true = ifeq(true,true,ifeq(coll(sk20,sk26,sk26),true,midp(sk20,sk26,sk26),true),true),
inference(cp,[status(thm)],[t327,t15949]) ).
cnf(t54695,plain,
true = ifeq(coll(sk20,sk26,sk26),true,midp(sk20,sk26,sk26),true),
inference(step,[status(thm)],[t15960,t256]) ).
fof(f66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox2/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(t122,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)],[t122]) ).
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(h477,plain,
eqangle(sk24,sk26,sk22,sk27,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h126]) ).
cnf(t74,plain,
eqangle(sk24,sk26,sk22,sk27,sk20,sk26,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi21,h477,h224]) ).
cnf(t1836,plain,
eqangle(sk24,sk26,sk22,sk27,sk20,sk26,sk20,sk26) = true,
inference(orient,[status(thm)],[t74]) ).
cnf(t1843,plain,
true = ifeq(true,true,eqangle(sk20,sk26,sk20,sk26,sk24,sk26,sk22,sk27),true),
inference(cp,[status(thm)],[t288,t1836]) ).
cnf(t54520,plain,
true = eqangle(sk20,sk26,sk20,sk26,sk24,sk26,sk22,sk27),
inference(step,[status(thm)],[t1843,t256]) ).
cnf(t13601,plain,
eqangle(sk20,sk26,sk20,sk26,sk24,sk26,sk22,sk27) = true,
inference(orient,[status(thm)],[t54520]) ).
cnf(t13608,plain,
true = ifeq(true,true,ifeq(para(sk24,sk26,sk22,sk27),true,para(sk20,sk26,sk20,sk26),true),true),
inference(cp,[status(thm)],[t287,t13601]) ).
cnf(t54521,plain,
true = ifeq(para(sk24,sk26,sk22,sk27),true,para(sk20,sk26,sk20,sk26),true),
inference(step,[status(thm)],[t13608,t256]) ).
cnf(t54522,plain,
true = ifeq(true,true,para(sk20,sk26,sk20,sk26),true),
inference(step,[status(thm)],[t54521,t2252]) ).
cnf(t54523,plain,
true = para(sk20,sk26,sk20,sk26),
inference(step,[status(thm)],[t54522,t256]) ).
cnf(t13613,plain,
para(sk20,sk26,sk20,sk26) = true,
inference(orient,[status(thm)],[t54523]) ).
cnf(t13614,plain,
true = ifeq(true,true,coll(sk20,sk26,sk26),true),
inference(cp,[status(thm)],[t319,t13613]) ).
cnf(t54524,plain,
true = coll(sk20,sk26,sk26),
inference(step,[status(thm)],[t13614,t256]) ).
cnf(t13639,plain,
coll(sk20,sk26,sk26) = true,
inference(orient,[status(thm)],[t54524]) ).
cnf(t54696,plain,
true = ifeq(true,true,midp(sk20,sk26,sk26),true),
inference(step,[status(thm)],[t54695,t13639]) ).
cnf(t54697,plain,
true = midp(sk20,sk26,sk26),
inference(step,[status(thm)],[t54696,t256]) ).
cnf(t15990,plain,
midp(sk20,sk26,sk26) = true,
inference(orient,[status(thm)],[t54697]) ).
cnf(t52537,plain,
true = ifeq(true,true,midp(sk20,X1,X1),true),
inference(cp,[status(thm)],[t52536,t15990]) ).
cnf(t57657,plain,
true = midp(sk20,X1,X1),
inference(step,[status(thm)],[t52537,t256]) ).
cnf(t52539,plain,
midp(sk20,X1,X1) = true,
inference(orient,[status(thm)],[t57657]) ).
cnf(t52540,plain,
true = ifeq(true,true,cong(sk20,X1,sk20,X1),true),
inference(cp,[status(thm)],[t363,t52539]) ).
cnf(t57659,plain,
true = cong(sk20,X1,sk20,X1),
inference(step,[status(thm)],[t52540,t256]) ).
cnf(t52583,plain,
cong(sk20,X1,sk20,X1) = true,
inference(orient,[status(thm)],[t57659]) ).
cnf(t52594,plain,
true = ifeq(true,true,ifeq(cong(sk20,X1,sk20,X1),true,perp(sk20,sk20,X2,X1),true),true),
inference(cp,[status(thm)],[t326,t52583]) ).
cnf(t57662,plain,
true = ifeq(cong(sk20,X1,sk20,X1),true,perp(sk20,sk20,X2,X1),true),
inference(step,[status(thm)],[t52594,t256]) ).
cnf(t57663,plain,
true = ifeq(true,true,perp(sk20,sk20,X2,X1),true),
inference(step,[status(thm)],[t57662,t52583]) ).
cnf(t57664,plain,
true = perp(sk20,sk20,X2,X1),
inference(step,[status(thm)],[t57663,t256]) ).
cnf(t52671,plain,
perp(sk20,sk20,X1,X2) = true,
inference(orient,[status(thm)],[t57664]) ).
cnf(t52676,plain,
true = ifeq(true,true,perp(X1,X2,sk20,sk20),true),
inference(cp,[status(thm)],[t274,t52671]) ).
cnf(t57672,plain,
true = perp(X1,X2,sk20,sk20),
inference(step,[status(thm)],[t52676,t256]) ).
cnf(t52817,plain,
perp(X1,X2,sk20,sk20) = true,
inference(orient,[status(thm)],[t57672]) ).
cnf(t52834,plain,
true = ifeq(true,true,ifeq(perp(sk20,sk20,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t52817]) ).
cnf(t57684,plain,
true = ifeq(perp(sk20,sk20,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t52834,t256]) ).
cnf(t57685,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t57684,t52671]) ).
cnf(t57686,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t57685,t256]) ).
cnf(t53050,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t57686]) ).
cnf(t57695,plain,
ifeq(true,true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(step,[status(thm)],[t312,t53050]) ).
cnf(t57696,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(step,[status(thm)],[t57695,t256]) ).
cnf(t53057,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(rw,[status(thm)],[t57696]) ).
cnf(t53522,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4) = true,
inference(orient,[status(thm)],[t53057]) ).
cnf(t53525,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true),
inference(cp,[status(thm)],[t294,t53522]) ).
cnf(t57770,plain,
true = eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(step,[status(thm)],[t53525,t256]) ).
cnf(t53609,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6) = true,
inference(orient,[status(thm)],[t57770]) ).
cnf(t53611,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,X3,X4,X5,X6),true),
inference(cp,[status(thm)],[t288,t53609]) ).
cnf(t57790,plain,
true = eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(step,[status(thm)],[t53611,t256]) ).
cnf(t53921,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6) = true,
inference(orient,[status(thm)],[t57790]) ).
cnf(t53933,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,t53921]) ).
cnf(t57839,plain,
true = ifeq(true,true,ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),true),
inference(step,[status(thm)],[t53933,t53609]) ).
cnf(t57840,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),
inference(step,[status(thm)],[t57839,t256]) ).
cnf(t57841,plain,
true = eqangle(X1,X2,X3,X4,X7,X8,X9,X10),
inference(step,[status(thm)],[t57840,t256]) ).
cnf(t54055,plain,
eqangle(X1,X2,X3,X4,X5,X6,X7,X8) = true,
inference(orient,[status(thm)],[t57841]) ).
cnf(c121,plain,
~ eqangle(sk20,sk25,sk25,sk26,sk27,sk25,sk25,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
eqangle(sk20,sk25,sk25,sk26,sk27,sk25,sk25,sk22) != true,
inference(equality_encoding,[status(esa)],[c121]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t54055]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO571+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.44 % Computer : n003.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Wed Sep 23 12:27:36 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 275.57/36.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 275.57/36.55 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
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