%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO613+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 : n004.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 01:18:17 PM UTC 2026
% Result : Theorem 152.36s 24.65s
% Output : Proof 152.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 71
% Number of leaves : 26
% Syntax : Number of formulae : 259 ( 159 unt; 0 def)
% Number of atoms : 451 ( 156 equ)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 312 ( 120 ~; 114 |; 52 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 18 ( 18 usr; 17 con; 0-4 aty)
% Number of variables : 979 ( 108 sgn 407 !; 16 ?)
% 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/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(t304,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(t184,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(t306,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)],[t184]) ).
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(t181,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(t312,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)],[t181]) ).
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(t151,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(t346,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(orient,[status(thm)],[t151]) ).
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(t191,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(t285,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)],[t191]) ).
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(t96,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t292,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t96]) ).
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(t178,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(t271,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)],[t178]) ).
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(t73,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t336,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t73]) ).
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(t333,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(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/sandbox/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(t305,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]) ).
fof(f10,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD11) ).
fof(f10_nnf,plain,
! [A,B,M] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [M,B,A] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( midp(X2,X0,X1)
| ~ midp(X2,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(midp(X0,X1,X2),true,midp(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
fof(f94,conjecture,
! [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8] :
( ( coll(H,C,G)
& coll(H,A,F)
& coll(G,B,F)
& circle(C,B,G,NWPNT8)
& circle(A,B,F,NWPNT7)
& midp(E,D,B)
& circle(C,B,D,NWPNT6)
& circle(A,B,D,NWPNT5)
& circle(C,B,NWPNT3,NWPNT4)
& circle(A,B,NWPNT1,NWPNT2) )
=> eqangle(F,D,D,G,A,H,H,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL618075y) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8] :
( ( coll(H,C,G)
& coll(H,A,F)
& coll(G,B,F)
& circle(C,B,G,NWPNT8)
& circle(A,B,F,NWPNT7)
& midp(E,D,B)
& circle(C,B,D,NWPNT6)
& circle(A,B,D,NWPNT5)
& circle(C,B,NWPNT3,NWPNT4)
& circle(A,B,NWPNT1,NWPNT2) )
=> eqangle(F,D,D,G,A,H,H,C) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8] :
( ~ eqangle(F,D,D,G,A,H,H,C)
& coll(H,C,G)
& coll(H,A,F)
& coll(G,B,F)
& circle(C,B,G,NWPNT8)
& circle(A,B,F,NWPNT7)
& midp(E,D,B)
& circle(C,B,D,NWPNT6)
& circle(A,B,D,NWPNT5)
& circle(C,B,NWPNT3,NWPNT4)
& circle(A,B,NWPNT1,NWPNT2) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ eqangle(sk25,sk23,sk23,sk26,sk20,sk27,sk27,sk22)
& coll(sk27,sk22,sk26)
& coll(sk27,sk20,sk25)
& coll(sk26,sk21,sk25)
& circle(sk22,sk21,sk26,sk35)
& circle(sk20,sk21,sk25,sk34)
& midp(sk24,sk23,sk21)
& circle(sk22,sk21,sk23,sk33)
& circle(sk20,sk21,sk23,sk32)
& circle(sk22,sk21,sk30,sk31)
& circle(sk20,sk21,sk28,sk29) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29,sk30,sk31,sk32,sk33,sk34,sk35])],[f94_nnf]) ).
cnf(c117,plain,
midp(sk24,sk23,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
midp(sk24,sk23,sk21) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h12,plain,
midp(sk24,sk21,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi117]) ).
fof(f63,axiom,
! [A,B,C,D,M] :
( ( midp(M,C,D)
& midp(M,A,B) )
=> para(A,C,B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD63) ).
fof(f63_nnf,plain,
! [A,B,C,D,M] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f63]) ).
fof(f63_sk,plain,
! [M,A,B,C,D] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f63_nnf]) ).
cnf(c63,plain,
( para(X0,X2,X1,X3)
| ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f63_sk]) ).
cnf(hi63,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(midp(X0,X3,X4),true,para(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c63]) ).
cnf(h46,plain,
para(sk21,sk21,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi63,h12,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(t44,plain,
eqangle(sk21,sk21,X1,X2,sk23,sk23,X1,X2) = true,
inference(hyper_resolution,[status(thm)],[hi39,h46]) ).
cnf(t1638,plain,
eqangle(sk21,sk21,X1,X2,sk23,sk23,X1,X2) = true,
inference(orient,[status(thm)],[t44]) ).
cnf(t1641,plain,
true = ifeq(true,true,eqangle(sk21,sk21,sk23,sk23,X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t312,t1638]) ).
cnf(t42,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t42]) ).
cnf(t19076,plain,
true = eqangle(sk21,sk21,sk23,sk23,X1,X2,X1,X2),
inference(step,[status(thm)],[t1641,t256]) ).
cnf(t4700,plain,
eqangle(sk21,sk21,sk23,sk23,X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t19076]) ).
cnf(t4703,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,sk21,sk21,sk23,sk23),true),
inference(cp,[status(thm)],[t306,t4700]) ).
cnf(t19285,plain,
true = eqangle(X1,X2,X1,X2,sk21,sk21,sk23,sk23),
inference(step,[status(thm)],[t4703,t256]) ).
cnf(t7676,plain,
eqangle(X1,X2,X1,X2,sk21,sk21,sk23,sk23) = true,
inference(orient,[status(thm)],[t19285]) ).
cnf(t7681,plain,
true = ifeq(true,true,ifeq(para(sk21,sk21,sk23,sk23),true,para(X1,X2,X1,X2),true),true),
inference(cp,[status(thm)],[t305,t7676]) ).
cnf(t19286,plain,
true = ifeq(para(sk21,sk21,sk23,sk23),true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t7681,t256]) ).
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(t150,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(t314,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(orient,[status(thm)],[t150]) ).
cnf(t1640,plain,
true = ifeq(true,true,para(sk21,sk21,sk23,sk23),true),
inference(cp,[status(thm)],[t314,t1638]) ).
cnf(t19051,plain,
true = para(sk21,sk21,sk23,sk23),
inference(step,[status(thm)],[t1640,t256]) ).
cnf(t4009,plain,
para(sk21,sk21,sk23,sk23) = true,
inference(orient,[status(thm)],[t19051]) ).
cnf(t19287,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t19286,t4009]) ).
cnf(t19288,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t19287,t256]) ).
cnf(t7686,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t19288]) ).
cnf(t7703,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)],[t333,t7686]) ).
cnf(t20488,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)],[t7703,t256]) ).
cnf(t20489,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t20488,t7686]) ).
cnf(t20490,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t20489,t256]) ).
cnf(t18169,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t20490]) ).
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(t169,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(t272,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)],[t169]) ).
fof(f22,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD23) ).
fof(f22_nnf,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( cong(X0,X1,X3,X2)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t88,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t268,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t88]) ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD24) ).
fof(f23_nnf,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( cong(X2,X3,X0,X1)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(t89,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t266,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t89]) ).
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(t357,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/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(t149,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(t359,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(orient,[status(thm)],[t149]) ).
cnf(hi68,axiom,
ifeq(midp(X0,X1,X2),true,cong(X0,X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(h9,plain,
cong(sk24,sk23,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi68,hi117]) ).
fof(f12,axiom,
! [A,B,C,D,O] :
( ( cong(O,A,O,D)
& cong(O,A,O,C)
& cong(O,A,O,B) )
=> cyclic(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD13) ).
fof(f12_nnf,plain,
! [A,B,C,D,O] :
( cyclic(A,B,C,D)
| ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [O,A,B,C,D] :
( cyclic(A,B,C,D)
| ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( cyclic(X0,X1,X2,X3)
| ~ cong(X4,X0,X4,X3)
| ~ cong(X4,X0,X4,X2)
| ~ cong(X4,X0,X4,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi12,axiom,
ifeq(cong(X0,X1,X0,X2),true,ifeq(cong(X0,X1,X0,X3),true,ifeq(cong(X0,X1,X0,X4),true,cyclic(X1,X2,X3,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h88,plain,
cyclic(sk23,sk21,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi12,h9,h9,h9]) ).
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(hi15,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,cyclic(X1,X0,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t31,plain,
cyclic(sk21,sk23,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi15,h88]) ).
cnf(t2683,plain,
cyclic(sk21,sk23,sk21,sk21) = true,
inference(orient,[status(thm)],[t31]) ).
cnf(t2686,plain,
true = ifeq(true,true,eqangle(sk21,sk21,sk21,sk23,sk21,sk21,sk21,sk23),true),
inference(cp,[status(thm)],[t359,t2683]) ).
cnf(t19092,plain,
true = eqangle(sk21,sk21,sk21,sk23,sk21,sk21,sk21,sk23),
inference(step,[status(thm)],[t2686,t256]) ).
cnf(t4858,plain,
eqangle(sk21,sk21,sk21,sk23,sk21,sk21,sk21,sk23) = true,
inference(orient,[status(thm)],[t19092]) ).
cnf(t4871,plain,
true = ifeq(cyclic(sk21,sk23,sk21,sk21),true,ifeq(cyclic(sk21,sk23,sk21,sk23),true,ifeq(cyclic(sk21,sk23,sk21,sk21),true,ifeq(true,true,cong(sk21,sk23,sk21,sk23),true),true),true),true),
inference(cp,[status(thm)],[t357,t4858]) ).
cnf(t19098,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk23,sk21,sk23),true,ifeq(cyclic(sk21,sk23,sk21,sk21),true,ifeq(true,true,cong(sk21,sk23,sk21,sk23),true),true),true),true),
inference(step,[status(thm)],[t4871,t2683]) ).
cnf(t19099,plain,
true = ifeq(cyclic(sk21,sk23,sk21,sk23),true,ifeq(cyclic(sk21,sk23,sk21,sk21),true,ifeq(true,true,cong(sk21,sk23,sk21,sk23),true),true),true),
inference(step,[status(thm)],[t19098,t256]) ).
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(t90,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t364,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t90]) ).
cnf(h45,plain,
cong(sk24,sk21,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi68,h12]) ).
fof(f24,axiom,
! [A,B,C,D,E,F] :
( ( cong(C,D,E,F)
& cong(A,B,C,D) )
=> cong(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD25) ).
fof(f24_nnf,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( cong(X0,X1,X4,X5)
| ~ cong(X2,X3,X4,X5)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi24,axiom,
ifeq(cong(X0,X1,X2,X3),true,ifeq(cong(X2,X3,X4,X5),true,cong(X0,X1,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(h316,plain,
cong(sk24,sk21,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi24,h45,h9]) ).
cnf(t32,plain,
cyclic(sk21,sk23,sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi12,h45,h45,h316]) ).
cnf(t2699,plain,
cyclic(sk21,sk23,sk23,sk21) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(t2700,plain,
true = ifeq(true,true,cyclic(sk21,sk23,sk21,sk23),true),
inference(cp,[status(thm)],[t364,t2699]) ).
cnf(t19055,plain,
true = cyclic(sk21,sk23,sk21,sk23),
inference(step,[status(thm)],[t2700,t256]) ).
cnf(t4099,plain,
cyclic(sk21,sk23,sk21,sk23) = true,
inference(orient,[status(thm)],[t19055]) ).
cnf(t19100,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk23,sk21,sk21),true,ifeq(true,true,cong(sk21,sk23,sk21,sk23),true),true),true),
inference(step,[status(thm)],[t19099,t4099]) ).
cnf(t19101,plain,
true = ifeq(cyclic(sk21,sk23,sk21,sk21),true,ifeq(true,true,cong(sk21,sk23,sk21,sk23),true),true),
inference(step,[status(thm)],[t19100,t256]) ).
cnf(t19102,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk21,sk23,sk21,sk23),true),true),
inference(step,[status(thm)],[t19101,t2683]) ).
cnf(t19103,plain,
true = ifeq(true,true,cong(sk21,sk23,sk21,sk23),true),
inference(step,[status(thm)],[t19102,t256]) ).
cnf(t19104,plain,
true = cong(sk21,sk23,sk21,sk23),
inference(step,[status(thm)],[t19103,t256]) ).
cnf(t4950,plain,
cong(sk21,sk23,sk21,sk23) = true,
inference(orient,[status(thm)],[t19104]) ).
cnf(t4953,plain,
true = ifeq(true,true,cong(sk21,sk23,sk23,sk21),true),
inference(cp,[status(thm)],[t268,t4950]) ).
cnf(t19108,plain,
true = cong(sk21,sk23,sk23,sk21),
inference(step,[status(thm)],[t4953,t256]) ).
cnf(t5018,plain,
cong(sk21,sk23,sk23,sk21) = true,
inference(orient,[status(thm)],[t19108]) ).
cnf(t5020,plain,
true = ifeq(true,true,cong(sk23,sk21,sk21,sk23),true),
inference(cp,[status(thm)],[t266,t5018]) ).
cnf(t19109,plain,
true = cong(sk23,sk21,sk21,sk23),
inference(step,[status(thm)],[t5020,t256]) ).
cnf(t5028,plain,
cong(sk23,sk21,sk21,sk23) = true,
inference(orient,[status(thm)],[t19109]) ).
cnf(t5030,plain,
true = ifeq(true,true,cong(sk23,sk21,sk23,sk21),true),
inference(cp,[status(thm)],[t268,t5028]) ).
cnf(t19110,plain,
true = cong(sk23,sk21,sk23,sk21),
inference(step,[status(thm)],[t5030,t256]) ).
cnf(t5037,plain,
cong(sk23,sk21,sk23,sk21) = true,
inference(orient,[status(thm)],[t19110]) ).
cnf(t5047,plain,
true = ifeq(true,true,ifeq(coll(sk23,sk21,sk21),true,midp(sk23,sk21,sk21),true),true),
inference(cp,[status(thm)],[t272,t5037]) ).
cnf(t19111,plain,
true = ifeq(coll(sk23,sk21,sk21),true,midp(sk23,sk21,sk21),true),
inference(step,[status(thm)],[t5047,t256]) ).
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(t74,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t353,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t74]) ).
fof(f3,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('/export/starexec/sandbox/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(t93,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t350,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t93]) ).
cnf(h47,plain,
para(sk23,sk21,sk21,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi63,hi117,h12]) ).
cnf(t45,plain,
eqangle(sk23,sk21,X1,X2,sk21,sk23,X1,X2) = true,
inference(hyper_resolution,[status(thm)],[hi39,h47]) ).
cnf(t1652,plain,
eqangle(sk23,sk21,X1,X2,sk21,sk23,X1,X2) = true,
inference(orient,[status(thm)],[t45]) ).
cnf(t1654,plain,
true = ifeq(true,true,para(sk23,sk21,sk21,sk23),true),
inference(cp,[status(thm)],[t314,t1652]) ).
cnf(t19052,plain,
true = para(sk23,sk21,sk21,sk23),
inference(step,[status(thm)],[t1654,t256]) ).
cnf(t4035,plain,
para(sk23,sk21,sk21,sk23) = true,
inference(orient,[status(thm)],[t19052]) ).
cnf(t4036,plain,
true = ifeq(true,true,para(sk23,sk21,sk23,sk21),true),
inference(cp,[status(thm)],[t350,t4035]) ).
cnf(t19057,plain,
true = para(sk23,sk21,sk23,sk21),
inference(step,[status(thm)],[t4036,t256]) ).
cnf(t4156,plain,
para(sk23,sk21,sk23,sk21) = true,
inference(orient,[status(thm)],[t19057]) ).
cnf(t4157,plain,
true = ifeq(true,true,coll(sk23,sk21,sk21),true),
inference(cp,[status(thm)],[t353,t4156]) ).
cnf(t19058,plain,
true = coll(sk23,sk21,sk21),
inference(step,[status(thm)],[t4157,t256]) ).
cnf(t4183,plain,
coll(sk23,sk21,sk21) = true,
inference(orient,[status(thm)],[t19058]) ).
cnf(t19112,plain,
true = ifeq(true,true,midp(sk23,sk21,sk21),true),
inference(step,[status(thm)],[t19111,t4183]) ).
cnf(t19113,plain,
true = midp(sk23,sk21,sk21),
inference(step,[status(thm)],[t19112,t256]) ).
cnf(t5076,plain,
midp(sk23,sk21,sk21) = true,
inference(orient,[status(thm)],[t19113]) ).
cnf(t18170,plain,
true = ifeq(true,true,midp(sk23,X1,X1),true),
inference(cp,[status(thm)],[t18169,t5076]) ).
cnf(t20491,plain,
true = midp(sk23,X1,X1),
inference(step,[status(thm)],[t18170,t256]) ).
cnf(t18186,plain,
midp(sk23,X1,X1) = true,
inference(orient,[status(thm)],[t20491]) ).
cnf(t18187,plain,
true = ifeq(true,true,cong(sk23,X1,sk23,X1),true),
inference(cp,[status(thm)],[t336,t18186]) ).
cnf(t20493,plain,
true = cong(sk23,X1,sk23,X1),
inference(step,[status(thm)],[t18187,t256]) ).
cnf(t18226,plain,
cong(sk23,X1,sk23,X1) = true,
inference(orient,[status(thm)],[t20493]) ).
cnf(t18241,plain,
true = ifeq(true,true,ifeq(cong(sk23,X1,sk23,X1),true,perp(sk23,sk23,X2,X1),true),true),
inference(cp,[status(thm)],[t271,t18226]) ).
cnf(t20496,plain,
true = ifeq(cong(sk23,X1,sk23,X1),true,perp(sk23,sk23,X2,X1),true),
inference(step,[status(thm)],[t18241,t256]) ).
cnf(t20497,plain,
true = ifeq(true,true,perp(sk23,sk23,X2,X1),true),
inference(step,[status(thm)],[t20496,t18226]) ).
cnf(t20498,plain,
true = perp(sk23,sk23,X2,X1),
inference(step,[status(thm)],[t20497,t256]) ).
cnf(t18326,plain,
perp(sk23,sk23,X1,X2) = true,
inference(orient,[status(thm)],[t20498]) ).
cnf(t18327,plain,
true = ifeq(true,true,perp(X1,X2,sk23,sk23),true),
inference(cp,[status(thm)],[t292,t18326]) ).
cnf(t20504,plain,
true = perp(X1,X2,sk23,sk23),
inference(step,[status(thm)],[t18327,t256]) ).
cnf(t18432,plain,
perp(X1,X2,sk23,sk23) = true,
inference(orient,[status(thm)],[t20504]) ).
cnf(t18439,plain,
true = ifeq(true,true,ifeq(perp(sk23,sk23,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t285,t18432]) ).
cnf(t20508,plain,
true = ifeq(perp(sk23,sk23,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t18439,t256]) ).
cnf(t20509,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t20508,t18326]) ).
cnf(t20510,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t20509,t256]) ).
cnf(t18539,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t20510]) ).
cnf(t20511,plain,
ifeq(true,true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(step,[status(thm)],[t346,t18539]) ).
cnf(t20512,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(step,[status(thm)],[t20511,t256]) ).
cnf(t18540,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(rw,[status(thm)],[t20512]) ).
cnf(t18793,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4) = true,
inference(orient,[status(thm)],[t18540]) ).
cnf(t18795,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true),
inference(cp,[status(thm)],[t312,t18793]) ).
cnf(t20557,plain,
true = eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(step,[status(thm)],[t18795,t256]) ).
cnf(t18856,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6) = true,
inference(orient,[status(thm)],[t20557]) ).
cnf(t18858,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,X3,X4,X5,X6),true),
inference(cp,[status(thm)],[t306,t18856]) ).
cnf(t20567,plain,
true = eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(step,[status(thm)],[t18858,t256]) ).
cnf(t18945,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6) = true,
inference(orient,[status(thm)],[t20567]) ).
cnf(t18952,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)],[t304,t18945]) ).
cnf(t20576,plain,
true = ifeq(true,true,ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),true),
inference(step,[status(thm)],[t18952,t18856]) ).
cnf(t20577,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),
inference(step,[status(thm)],[t20576,t256]) ).
cnf(t20578,plain,
true = eqangle(X1,X2,X3,X4,X7,X8,X9,X10),
inference(step,[status(thm)],[t20577,t256]) ).
cnf(t19018,plain,
eqangle(X1,X2,X3,X4,X5,X6,X7,X8) = true,
inference(orient,[status(thm)],[t20578]) ).
cnf(c123,plain,
~ eqangle(sk25,sk23,sk23,sk26,sk20,sk27,sk27,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
eqangle(sk25,sk23,sk23,sk26,sk20,sk27,sk27,sk22) != true,
inference(equality_encoding,[status(esa)],[c123]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t19018]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO613+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/5.38 % Computer : n004.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Wed Sep 23 12:33:25 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 152.36/24.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 152.36/24.65 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------