%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO576+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 01:18:12 PM UTC 2026
% Result : Theorem 158.91s 20.60s
% Output : Proof 158.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 75
% Number of leaves : 25
% Syntax : Number of formulae : 279 ( 183 unt; 0 def)
% Number of atoms : 443 ( 177 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 272 ( 108 ~; 102 |; 37 &)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-4 aty)
% Number of variables : 933 ( 108 sgn 364 !; 8 ?)
% 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(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(t174,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)],[t174]) ).
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(t171,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)],[t171]) ).
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(t135,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(t330,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(orient,[status(thm)],[t135]) ).
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(t181,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)],[t181]) ).
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(t86,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)],[t86]) ).
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(t168,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(t311,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)],[t168]) ).
fof(f68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD68) ).
fof(f68_nnf,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f68]) ).
fof(f68_sk,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(skolemisation,[status(esa)],[f68_nnf]) ).
cnf(c68,plain,
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f68_sk]) ).
cnf(t69,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t363,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t69]) ).
fof(f64,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD64) ).
fof(f64_nnf,plain,
! [A,B,C,D,M] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f64]) ).
fof(f64_sk,plain,
! [M,A,B,C,D] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f64_nnf]) ).
cnf(c64,plain,
( midp(X4,X2,X3)
| ~ para(X0,X3,X1,X2)
| ~ para(X0,X2,X1,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(t227,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)],[t227]) ).
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(t134,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)],[t134]) ).
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(t173,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)],[t173]) ).
fof(f46,axiom,
! [A,B,O] :
( cong(O,A,O,B)
=> eqangle(O,A,A,B,A,B,O,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD46) ).
fof(f46_nnf,plain,
! [A,B,O] :
( eqangle(O,A,A,B,A,B,O,B)
| ~ cong(O,A,O,B) ),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
! [O,A,B] :
( eqangle(O,A,A,B,A,B,O,B)
| ~ cong(O,A,O,B) ),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c46,plain,
( eqangle(X2,X0,X0,X1,X0,X1,X2,X1)
| ~ cong(X2,X0,X2,X1) ),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(t129,plain,
ifeq(cong(X1,X2,X1,X3),true,eqangle(X1,X2,X2,X3,X2,X3,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t322,plain,
ifeq(cong(X1,X2,X1,X3),true,eqangle(X1,X2,X2,X3,X2,X3,X1,X3),true) = true,
inference(orient,[status(thm)],[t129]) ).
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,D,O,D1,P,NWPNT1] :
( ( coll(P,B,C)
& perp(A,C,D1,P)
& coll(D1,A,D)
& circle(O,A,D1,NWPNT1)
& circle(O,A,B,C)
& coll(D,B,C)
& perp(D,A,B,C) )
=> eqangle(O,A,A,D,C,A,A,P) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL214038) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,O,D1,P,NWPNT1] :
( ( coll(P,B,C)
& perp(A,C,D1,P)
& coll(D1,A,D)
& circle(O,A,D1,NWPNT1)
& circle(O,A,B,C)
& coll(D,B,C)
& perp(D,A,B,C) )
=> eqangle(O,A,A,D,C,A,A,P) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,O,D1,P,NWPNT1] :
( ~ eqangle(O,A,A,D,C,A,A,P)
& coll(P,B,C)
& perp(A,C,D1,P)
& coll(D1,A,D)
& circle(O,A,D1,NWPNT1)
& circle(O,A,B,C)
& coll(D,B,C)
& perp(D,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ eqangle(sk24,sk20,sk20,sk23,sk22,sk20,sk20,sk26)
& coll(sk26,sk21,sk22)
& perp(sk20,sk22,sk25,sk26)
& coll(sk25,sk20,sk23)
& circle(sk24,sk20,sk25,sk27)
& circle(sk24,sk20,sk21,sk22)
& coll(sk23,sk21,sk22)
& perp(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27])],[f94_nnf]) ).
cnf(c113,plain,
perp(sk23,sk20,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
perp(sk23,sk20,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h0,plain,
perp(sk21,sk22,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi113]) ).
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(h15,plain,
para(sk23,sk20,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi113,h0]) ).
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(h52,plain,
eqangle(sk23,sk20,V0,V1,sk23,sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h15]) ).
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(h133,plain,
eqangle(sk23,sk20,sk23,sk20,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h52]) ).
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(h51,plain,
coll(sk23,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi66,h15]) ).
fof(f42,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD42b) ).
fof(f42_nnf,plain,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [P,A,B,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c42,plain,
( cyclic(X0,X1,X2,X3)
| ~ coll(X2,X3,X1)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi42,axiom,
ifeq(eqangle(X0,X1,X0,X2,X3,X1,X3,X2),true,ifeq(coll(X0,X3,X2),true,cyclic(X1,X2,X0,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c42]) ).
cnf(h468,plain,
cyclic(sk20,sk20,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h133,h51]) ).
fof(f43,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD43) ).
fof(f43_nnf,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c43,plain,
( cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(hi43,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,ifeq(cyclic(X0,X1,X2,X4),true,ifeq(cyclic(X0,X1,X2,X5),true,ifeq(eqangle(X2,X0,X2,X1,X5,X3,X5,X4),true,cong(X0,X1,X3,X4),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(t10,plain,
cong(sk20,sk20,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi43,h468,h468,h468,h133]) ).
cnf(t1872,plain,
cong(sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t1875,plain,
true = ifeq(true,true,eqangle(sk20,sk20,sk20,sk20,sk20,sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t322,t1872]) ).
cnf(t35,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t35]) ).
cnf(t21626,plain,
true = eqangle(sk20,sk20,sk20,sk20,sk20,sk20,sk20,sk20),
inference(step,[status(thm)],[t1875,t256]) ).
cnf(t4906,plain,
eqangle(sk20,sk20,sk20,sk20,sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t21626]) ).
cnf(t4908,plain,
true = ifeq(true,true,para(sk20,sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t296,t4906]) ).
cnf(t21627,plain,
true = para(sk20,sk20,sk20,sk20),
inference(step,[status(thm)],[t4908,t256]) ).
cnf(t4929,plain,
para(sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t21627]) ).
cnf(t4931,plain,
true = ifeq(true,true,eqangle(sk20,sk20,X1,X2,sk20,sk20,X1,X2),true),
inference(cp,[status(thm)],[t330,t4929]) ).
cnf(t21938,plain,
true = eqangle(sk20,sk20,X1,X2,sk20,sk20,X1,X2),
inference(step,[status(thm)],[t4931,t256]) ).
cnf(t9062,plain,
eqangle(sk20,sk20,X1,X2,sk20,sk20,X1,X2) = true,
inference(orient,[status(thm)],[t21938]) ).
cnf(t9066,plain,
true = ifeq(true,true,eqangle(X1,X2,sk20,sk20,X1,X2,sk20,sk20),true),
inference(cp,[status(thm)],[t290,t9062]) ).
cnf(t22316,plain,
true = eqangle(X1,X2,sk20,sk20,X1,X2,sk20,sk20),
inference(step,[status(thm)],[t9066,t256]) ).
cnf(t13099,plain,
eqangle(X1,X2,sk20,sk20,X1,X2,sk20,sk20) = true,
inference(orient,[status(thm)],[t22316]) ).
cnf(t13100,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t296,t13099]) ).
cnf(t22317,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t13100,t256]) ).
cnf(t13122,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t22317]) ).
cnf(t13138,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,t13122]) ).
cnf(t23130,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)],[t13138,t256]) ).
cnf(t23131,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t23130,t13122]) ).
cnf(t23132,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t23131,t256]) ).
cnf(t20016,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t23132]) ).
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(t150,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(t312,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)],[t150]) ).
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(t78,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t308,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t78]) ).
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(t79,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t306,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t79]) ).
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/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(t133,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)],[t133]) ).
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(c114,plain,
coll(sk23,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
coll(sk23,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h2,plain,
coll(sk22,sk22,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi114,hi114]) ).
cnf(h20,plain,
coll(sk23,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h2,h2]) ).
cnf(h130,plain,
cyclic(sk20,sk22,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi42,h52,h20]) ).
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(hi14,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,cyclic(X0,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t21,plain,
cyclic(sk20,sk23,sk22,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi14,h130]) ).
cnf(t2558,plain,
cyclic(sk20,sk23,sk22,sk23) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(t2563,plain,
true = ifeq(true,true,eqangle(sk22,sk20,sk22,sk23,sk23,sk20,sk23,sk23),true),
inference(cp,[status(thm)],[t343,t2558]) ).
cnf(t21681,plain,
true = eqangle(sk22,sk20,sk22,sk23,sk23,sk20,sk23,sk23),
inference(step,[status(thm)],[t2563,t256]) ).
cnf(t5729,plain,
eqangle(sk22,sk20,sk22,sk23,sk23,sk20,sk23,sk23) = true,
inference(orient,[status(thm)],[t21681]) ).
cnf(t5745,plain,
true = ifeq(cyclic(sk20,sk23,sk22,sk20),true,ifeq(cyclic(sk20,sk23,sk22,sk23),true,ifeq(cyclic(sk20,sk23,sk22,sk23),true,ifeq(true,true,cong(sk20,sk23,sk20,sk23),true),true),true),true),
inference(cp,[status(thm)],[t341,t5729]) ).
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(t80,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)],[t80]) ).
cnf(t81,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)],[t81]) ).
cnf(c118,plain,
perp(sk20,sk22,sk25,sk26),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi118,negated_conjecture,
perp(sk20,sk22,sk25,sk26) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(h10,plain,
perp(sk25,sk26,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi118]) ).
cnf(h36,plain,
para(sk20,sk22,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi118,h10]) ).
cnf(h99,plain,
coll(sk20,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi66,h36]) ).
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(c117,plain,
coll(sk25,sk20,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
coll(sk25,sk20,sk23) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h8,plain,
coll(sk20,sk25,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi117]) ).
cnf(h32,plain,
coll(sk23,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h8,h8]) ).
cnf(h93,plain,
coll(sk20,sk22,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h32,h20]) ).
cnf(h339,plain,
coll(sk23,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h93,h99]) ).
cnf(t19,plain,
cyclic(sk20,sk20,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi42,h133,h339]) ).
cnf(t2522,plain,
cyclic(sk20,sk20,sk23,sk22) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t2523,plain,
true = ifeq(true,true,cyclic(sk20,sk23,sk20,sk22),true),
inference(cp,[status(thm)],[t346,t2522]) ).
cnf(t21557,plain,
true = cyclic(sk20,sk23,sk20,sk22),
inference(step,[status(thm)],[t2523,t256]) ).
cnf(t3657,plain,
cyclic(sk20,sk23,sk20,sk22) = true,
inference(orient,[status(thm)],[t21557]) ).
cnf(t3658,plain,
true = ifeq(true,true,cyclic(sk20,sk23,sk22,sk20),true),
inference(cp,[status(thm)],[t348,t3657]) ).
cnf(t21574,plain,
true = cyclic(sk20,sk23,sk22,sk20),
inference(step,[status(thm)],[t3658,t256]) ).
cnf(t3955,plain,
cyclic(sk20,sk23,sk22,sk20) = true,
inference(orient,[status(thm)],[t21574]) ).
cnf(t21682,plain,
true = ifeq(true,true,ifeq(cyclic(sk20,sk23,sk22,sk23),true,ifeq(cyclic(sk20,sk23,sk22,sk23),true,ifeq(true,true,cong(sk20,sk23,sk20,sk23),true),true),true),true),
inference(step,[status(thm)],[t5745,t3955]) ).
cnf(t21683,plain,
true = ifeq(cyclic(sk20,sk23,sk22,sk23),true,ifeq(cyclic(sk20,sk23,sk22,sk23),true,ifeq(true,true,cong(sk20,sk23,sk20,sk23),true),true),true),
inference(step,[status(thm)],[t21682,t256]) ).
cnf(t21684,plain,
true = ifeq(true,true,ifeq(cyclic(sk20,sk23,sk22,sk23),true,ifeq(true,true,cong(sk20,sk23,sk20,sk23),true),true),true),
inference(step,[status(thm)],[t21683,t2558]) ).
cnf(t21685,plain,
true = ifeq(cyclic(sk20,sk23,sk22,sk23),true,ifeq(true,true,cong(sk20,sk23,sk20,sk23),true),true),
inference(step,[status(thm)],[t21684,t256]) ).
cnf(t21686,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk20,sk23,sk20,sk23),true),true),
inference(step,[status(thm)],[t21685,t2558]) ).
cnf(t21687,plain,
true = ifeq(true,true,cong(sk20,sk23,sk20,sk23),true),
inference(step,[status(thm)],[t21686,t256]) ).
cnf(t21688,plain,
true = cong(sk20,sk23,sk20,sk23),
inference(step,[status(thm)],[t21687,t256]) ).
cnf(t5746,plain,
cong(sk20,sk23,sk20,sk23) = true,
inference(orient,[status(thm)],[t21688]) ).
cnf(t5749,plain,
true = ifeq(true,true,cong(sk20,sk23,sk23,sk20),true),
inference(cp,[status(thm)],[t308,t5746]) ).
cnf(t21692,plain,
true = cong(sk20,sk23,sk23,sk20),
inference(step,[status(thm)],[t5749,t256]) ).
cnf(t5814,plain,
cong(sk20,sk23,sk23,sk20) = true,
inference(orient,[status(thm)],[t21692]) ).
cnf(t5816,plain,
true = ifeq(true,true,cong(sk23,sk20,sk20,sk23),true),
inference(cp,[status(thm)],[t306,t5814]) ).
cnf(t21693,plain,
true = cong(sk23,sk20,sk20,sk23),
inference(step,[status(thm)],[t5816,t256]) ).
cnf(t5824,plain,
cong(sk23,sk20,sk20,sk23) = true,
inference(orient,[status(thm)],[t21693]) ).
cnf(t5826,plain,
true = ifeq(true,true,cong(sk23,sk20,sk23,sk20),true),
inference(cp,[status(thm)],[t308,t5824]) ).
cnf(t21694,plain,
true = cong(sk23,sk20,sk23,sk20),
inference(step,[status(thm)],[t5826,t256]) ).
cnf(t5833,plain,
cong(sk23,sk20,sk23,sk20) = true,
inference(orient,[status(thm)],[t21694]) ).
cnf(t5842,plain,
true = ifeq(true,true,ifeq(coll(sk23,sk20,sk20),true,midp(sk23,sk20,sk20),true),true),
inference(cp,[status(thm)],[t312,t5833]) ).
cnf(t21695,plain,
true = ifeq(coll(sk23,sk20,sk20),true,midp(sk23,sk20,sk20),true),
inference(step,[status(thm)],[t5842,t256]) ).
cnf(t70,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t337,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t70]) ).
cnf(t20,plain,
cyclic(sk20,sk22,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi42,h52,h20]) ).
cnf(t2539,plain,
cyclic(sk20,sk22,sk23,sk23) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(t2544,plain,
true = ifeq(true,true,eqangle(sk23,sk20,sk23,sk22,sk23,sk20,sk23,sk22),true),
inference(cp,[status(thm)],[t343,t2539]) ).
cnf(t21658,plain,
true = eqangle(sk23,sk20,sk23,sk22,sk23,sk20,sk23,sk22),
inference(step,[status(thm)],[t2544,t256]) ).
cnf(t5316,plain,
eqangle(sk23,sk20,sk23,sk22,sk23,sk20,sk23,sk22) = true,
inference(orient,[status(thm)],[t21658]) ).
cnf(t5317,plain,
true = ifeq(true,true,para(sk23,sk20,sk23,sk20),true),
inference(cp,[status(thm)],[t296,t5316]) ).
cnf(t21659,plain,
true = para(sk23,sk20,sk23,sk20),
inference(step,[status(thm)],[t5317,t256]) ).
cnf(t5333,plain,
para(sk23,sk20,sk23,sk20) = true,
inference(orient,[status(thm)],[t21659]) ).
cnf(t5334,plain,
true = ifeq(true,true,coll(sk23,sk20,sk20),true),
inference(cp,[status(thm)],[t337,t5333]) ).
cnf(t21660,plain,
true = coll(sk23,sk20,sk20),
inference(step,[status(thm)],[t5334,t256]) ).
cnf(t5360,plain,
coll(sk23,sk20,sk20) = true,
inference(orient,[status(thm)],[t21660]) ).
cnf(t21696,plain,
true = ifeq(true,true,midp(sk23,sk20,sk20),true),
inference(step,[status(thm)],[t21695,t5360]) ).
cnf(t21697,plain,
true = midp(sk23,sk20,sk20),
inference(step,[status(thm)],[t21696,t256]) ).
cnf(t5872,plain,
midp(sk23,sk20,sk20) = true,
inference(orient,[status(thm)],[t21697]) ).
cnf(t20017,plain,
true = ifeq(true,true,midp(sk23,X1,X1),true),
inference(cp,[status(thm)],[t20016,t5872]) ).
cnf(t23133,plain,
true = midp(sk23,X1,X1),
inference(step,[status(thm)],[t20017,t256]) ).
cnf(t20025,plain,
midp(sk23,X1,X1) = true,
inference(orient,[status(thm)],[t23133]) ).
cnf(t20026,plain,
true = ifeq(true,true,cong(sk23,X1,sk23,X1),true),
inference(cp,[status(thm)],[t363,t20025]) ).
cnf(t23136,plain,
true = cong(sk23,X1,sk23,X1),
inference(step,[status(thm)],[t20026,t256]) ).
cnf(t20085,plain,
cong(sk23,X1,sk23,X1) = true,
inference(orient,[status(thm)],[t23136]) ).
cnf(t20096,plain,
true = ifeq(true,true,ifeq(cong(sk23,X1,sk23,X1),true,perp(sk23,sk23,X2,X1),true),true),
inference(cp,[status(thm)],[t311,t20085]) ).
cnf(t23141,plain,
true = ifeq(cong(sk23,X1,sk23,X1),true,perp(sk23,sk23,X2,X1),true),
inference(step,[status(thm)],[t20096,t256]) ).
cnf(t23142,plain,
true = ifeq(true,true,perp(sk23,sk23,X2,X1),true),
inference(step,[status(thm)],[t23141,t20085]) ).
cnf(t23143,plain,
true = perp(sk23,sk23,X2,X1),
inference(step,[status(thm)],[t23142,t256]) ).
cnf(t20234,plain,
perp(sk23,sk23,X1,X2) = true,
inference(orient,[status(thm)],[t23143]) ).
cnf(t20238,plain,
true = ifeq(true,true,perp(X1,X2,sk23,sk23),true),
inference(cp,[status(thm)],[t274,t20234]) ).
cnf(t23154,plain,
true = perp(X1,X2,sk23,sk23),
inference(step,[status(thm)],[t20238,t256]) ).
cnf(t20410,plain,
perp(X1,X2,sk23,sk23) = true,
inference(orient,[status(thm)],[t23154]) ).
cnf(t20422,plain,
true = ifeq(true,true,ifeq(perp(sk23,sk23,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t20410]) ).
cnf(t23165,plain,
true = ifeq(perp(sk23,sk23,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t20422,t256]) ).
cnf(t23166,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t23165,t20234]) ).
cnf(t23167,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t23166,t256]) ).
cnf(t20640,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t23167]) ).
cnf(t23174,plain,
ifeq(true,true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(step,[status(thm)],[t330,t20640]) ).
cnf(t23175,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(step,[status(thm)],[t23174,t256]) ).
cnf(t20645,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(rw,[status(thm)],[t23175]) ).
cnf(t21084,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4) = true,
inference(orient,[status(thm)],[t20645]) ).
cnf(t21087,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true),
inference(cp,[status(thm)],[t294,t21084]) ).
cnf(t23246,plain,
true = eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(step,[status(thm)],[t21087,t256]) ).
cnf(t21174,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6) = true,
inference(orient,[status(thm)],[t23246]) ).
cnf(t21176,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,X3,X4,X5,X6),true),
inference(cp,[status(thm)],[t288,t21174]) ).
cnf(t23264,plain,
true = eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(step,[status(thm)],[t21176,t256]) ).
cnf(t21387,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6) = true,
inference(orient,[status(thm)],[t23264]) ).
cnf(t21396,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,t21387]) ).
cnf(t23310,plain,
true = ifeq(true,true,ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),true),
inference(step,[status(thm)],[t21396,t21174]) ).
cnf(t23311,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),
inference(step,[status(thm)],[t23310,t256]) ).
cnf(t23312,plain,
true = eqangle(X1,X2,X3,X4,X7,X8,X9,X10),
inference(step,[status(thm)],[t23311,t256]) ).
cnf(t21532,plain,
eqangle(X1,X2,X3,X4,X5,X6,X7,X8) = true,
inference(orient,[status(thm)],[t23312]) ).
cnf(c120,plain,
~ eqangle(sk24,sk20,sk20,sk23,sk22,sk20,sk20,sk26),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
eqangle(sk24,sk20,sk20,sk23,sk22,sk20,sk20,sk26) != true,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t21532]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO576+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 12:30:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 158.91/20.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 158.91/20.60 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------