%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO570+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 : 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 01:18:11 PM UTC 2026
% Result : Theorem 21.94s 28.80s
% Output : Proof 21.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 75
% Number of leaves : 24
% Syntax : Number of formulae : 252 ( 160 unt; 0 def)
% Number of atoms : 416 ( 155 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 269 ( 105 ~; 99 |; 41 &)
% ( 0 <=>; 24 =>; 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 : 11 ( 11 usr; 10 con; 0-4 aty)
% Number of variables : 909 ( 108 sgn 357 !; 9 ?)
% 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(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/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(t180,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)],[t180]) ).
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(t177,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)],[t177]) ).
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(t150,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)],[t150]) ).
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(t187,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)],[t187]) ).
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(t130,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)],[t130]) ).
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(t174,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(t289,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)],[t174]) ).
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(t118,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)],[t118]) ).
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(t149,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)],[t149]) ).
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(t179,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(t308,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)],[t179]) ).
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,
! [B,C,R,O,S,A,M,N,NWPNT1] :
( ( coll(N,B,C)
& perp(N,A,B,C)
& coll(M,R,S)
& perp(M,A,R,S)
& coll(A,C,S)
& coll(A,B,R)
& circle(O,B,S,NWPNT1)
& circle(O,B,C,R) )
=> eqangle(B,A,A,M,N,A,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL214032) ).
fof(f94_neg,negated_conjecture,
~ ! [B,C,R,O,S,A,M,N,NWPNT1] :
( ( coll(N,B,C)
& perp(N,A,B,C)
& coll(M,R,S)
& perp(M,A,R,S)
& coll(A,C,S)
& coll(A,B,R)
& circle(O,B,S,NWPNT1)
& circle(O,B,C,R) )
=> eqangle(B,A,A,M,N,A,A,C) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [B,C,R,O,S,A,M,N,NWPNT1] :
( ~ eqangle(B,A,A,M,N,A,A,C)
& coll(N,B,C)
& perp(N,A,B,C)
& coll(M,R,S)
& perp(M,A,R,S)
& coll(A,C,S)
& coll(A,B,R)
& circle(O,B,S,NWPNT1)
& circle(O,B,C,R) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ eqangle(sk20,sk25,sk25,sk26,sk27,sk25,sk25,sk21)
& coll(sk27,sk20,sk21)
& perp(sk27,sk25,sk20,sk21)
& coll(sk26,sk22,sk24)
& perp(sk26,sk25,sk22,sk24)
& coll(sk25,sk21,sk24)
& coll(sk25,sk20,sk22)
& 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(c119,plain,
perp(sk27,sk25,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi119,negated_conjecture,
perp(sk27,sk25,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(h13,plain,
perp(sk20,sk21,sk27,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi119]) ).
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(t34,plain,
para(sk20,sk21,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi8,h13,hi119]) ).
cnf(t2023,plain,
para(sk20,sk21,sk20,sk21) = true,
inference(orient,[status(thm)],[t34]) ).
cnf(t2027,plain,
true = ifeq(true,true,eqangle(sk20,sk21,X1,X2,sk20,sk21,X1,X2),true),
inference(cp,[status(thm)],[t330,t2023]) ).
cnf(t33,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t33]) ).
cnf(t22137,plain,
true = eqangle(sk20,sk21,X1,X2,sk20,sk21,X1,X2),
inference(step,[status(thm)],[t2027,t256]) ).
cnf(t6433,plain,
eqangle(sk20,sk21,X1,X2,sk20,sk21,X1,X2) = true,
inference(orient,[status(thm)],[t22137]) ).
cnf(t6440,plain,
true = ifeq(true,true,eqangle(X1,X2,sk20,sk21,X1,X2,sk20,sk21),true),
inference(cp,[status(thm)],[t308,t6433]) ).
cnf(t22440,plain,
true = eqangle(X1,X2,sk20,sk21,X1,X2,sk20,sk21),
inference(step,[status(thm)],[t6440,t256]) ).
cnf(t10270,plain,
eqangle(X1,X2,sk20,sk21,X1,X2,sk20,sk21) = true,
inference(orient,[status(thm)],[t22440]) ).
cnf(t10272,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t314,t10270]) ).
cnf(t22441,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t10272,t256]) ).
cnf(t10293,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t22441]) ).
cnf(t10309,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,t10293]) ).
cnf(t23657,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)],[t10309,t256]) ).
cnf(t23658,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t23657,t10293]) ).
cnf(t23659,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t23658,t256]) ).
cnf(t20394,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t23659]) ).
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(t165,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(t290,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)],[t165]) ).
fof(f22,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox2/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(t122,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t286,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t122]) ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox2/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(t123,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t284,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t123]) ).
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(t148,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)],[t148]) ).
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(c120,plain,
coll(sk27,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi120,negated_conjecture,
coll(sk27,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(h15,plain,
coll(sk21,sk21,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi120,hi120]) ).
cnf(h50,plain,
coll(sk27,sk27,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h15,h15]) ).
cnf(h47,plain,
para(sk27,sk25,sk27,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi119,h13]) ).
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(h123,plain,
eqangle(sk27,sk25,V0,V1,sk27,sk25,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h47]) ).
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(h369,plain,
cyclic(sk25,sk21,sk27,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi42,h123,h50]) ).
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(hi14,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,cyclic(X0,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t31,plain,
cyclic(sk25,sk27,sk21,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi14,h369]) ).
cnf(t2655,plain,
cyclic(sk25,sk27,sk21,sk27) = true,
inference(orient,[status(thm)],[t31]) ).
cnf(t2660,plain,
true = ifeq(true,true,eqangle(sk21,sk25,sk21,sk27,sk27,sk25,sk27,sk27),true),
inference(cp,[status(thm)],[t343,t2655]) ).
cnf(t22181,plain,
true = eqangle(sk21,sk25,sk21,sk27,sk27,sk25,sk27,sk27),
inference(step,[status(thm)],[t2660,t256]) ).
cnf(t7306,plain,
eqangle(sk21,sk25,sk21,sk27,sk27,sk25,sk27,sk27) = true,
inference(orient,[status(thm)],[t22181]) ).
cnf(t7322,plain,
true = ifeq(cyclic(sk25,sk27,sk21,sk25),true,ifeq(cyclic(sk25,sk27,sk21,sk27),true,ifeq(cyclic(sk25,sk27,sk21,sk27),true,ifeq(true,true,cong(sk25,sk27,sk25,sk27),true),true),true),true),
inference(cp,[status(thm)],[t341,t7306]) ).
fof(f13,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox2/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(t124,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)],[t124]) ).
cnf(t125,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)],[t125]) ).
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(c116,plain,
coll(sk25,sk21,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
coll(sk25,sk21,sk24) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h7,plain,
coll(sk25,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi116]) ).
cnf(h32,plain,
coll(sk21,sk21,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h7,h7]) ).
cnf(h88,plain,
coll(sk27,sk25,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h15,h32]) ).
cnf(h221,plain,
coll(sk27,sk21,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi0,h88]) ).
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(h371,plain,
eqangle(sk27,sk25,sk27,sk25,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h123]) ).
cnf(t30,plain,
cyclic(sk25,sk25,sk27,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi42,h371,h221]) ).
cnf(t2617,plain,
cyclic(sk25,sk25,sk27,sk21) = true,
inference(orient,[status(thm)],[t30]) ).
cnf(t2620,plain,
true = ifeq(true,true,cyclic(sk25,sk27,sk25,sk21),true),
inference(cp,[status(thm)],[t346,t2617]) ).
cnf(t22011,plain,
true = cyclic(sk25,sk27,sk25,sk21),
inference(step,[status(thm)],[t2620,t256]) ).
cnf(t4546,plain,
cyclic(sk25,sk27,sk25,sk21) = true,
inference(orient,[status(thm)],[t22011]) ).
cnf(t4547,plain,
true = ifeq(true,true,cyclic(sk25,sk27,sk21,sk25),true),
inference(cp,[status(thm)],[t348,t4546]) ).
cnf(t22034,plain,
true = cyclic(sk25,sk27,sk21,sk25),
inference(step,[status(thm)],[t4547,t256]) ).
cnf(t4971,plain,
cyclic(sk25,sk27,sk21,sk25) = true,
inference(orient,[status(thm)],[t22034]) ).
cnf(t22182,plain,
true = ifeq(true,true,ifeq(cyclic(sk25,sk27,sk21,sk27),true,ifeq(cyclic(sk25,sk27,sk21,sk27),true,ifeq(true,true,cong(sk25,sk27,sk25,sk27),true),true),true),true),
inference(step,[status(thm)],[t7322,t4971]) ).
cnf(t22183,plain,
true = ifeq(cyclic(sk25,sk27,sk21,sk27),true,ifeq(cyclic(sk25,sk27,sk21,sk27),true,ifeq(true,true,cong(sk25,sk27,sk25,sk27),true),true),true),
inference(step,[status(thm)],[t22182,t256]) ).
cnf(t22184,plain,
true = ifeq(true,true,ifeq(cyclic(sk25,sk27,sk21,sk27),true,ifeq(true,true,cong(sk25,sk27,sk25,sk27),true),true),true),
inference(step,[status(thm)],[t22183,t2655]) ).
cnf(t22185,plain,
true = ifeq(cyclic(sk25,sk27,sk21,sk27),true,ifeq(true,true,cong(sk25,sk27,sk25,sk27),true),true),
inference(step,[status(thm)],[t22184,t256]) ).
cnf(t22186,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk25,sk27,sk25,sk27),true),true),
inference(step,[status(thm)],[t22185,t2655]) ).
cnf(t22187,plain,
true = ifeq(true,true,cong(sk25,sk27,sk25,sk27),true),
inference(step,[status(thm)],[t22186,t256]) ).
cnf(t22188,plain,
true = cong(sk25,sk27,sk25,sk27),
inference(step,[status(thm)],[t22187,t256]) ).
cnf(t7323,plain,
cong(sk25,sk27,sk25,sk27) = true,
inference(orient,[status(thm)],[t22188]) ).
cnf(t7326,plain,
true = ifeq(true,true,cong(sk25,sk27,sk27,sk25),true),
inference(cp,[status(thm)],[t286,t7323]) ).
cnf(t22192,plain,
true = cong(sk25,sk27,sk27,sk25),
inference(step,[status(thm)],[t7326,t256]) ).
cnf(t7391,plain,
cong(sk25,sk27,sk27,sk25) = true,
inference(orient,[status(thm)],[t22192]) ).
cnf(t7393,plain,
true = ifeq(true,true,cong(sk27,sk25,sk25,sk27),true),
inference(cp,[status(thm)],[t284,t7391]) ).
cnf(t22193,plain,
true = cong(sk27,sk25,sk25,sk27),
inference(step,[status(thm)],[t7393,t256]) ).
cnf(t7401,plain,
cong(sk27,sk25,sk25,sk27) = true,
inference(orient,[status(thm)],[t22193]) ).
cnf(t7403,plain,
true = ifeq(true,true,cong(sk27,sk25,sk27,sk25),true),
inference(cp,[status(thm)],[t286,t7401]) ).
cnf(t22194,plain,
true = cong(sk27,sk25,sk27,sk25),
inference(step,[status(thm)],[t7403,t256]) ).
cnf(t7410,plain,
cong(sk27,sk25,sk27,sk25) = true,
inference(orient,[status(thm)],[t22194]) ).
cnf(t7419,plain,
true = ifeq(true,true,ifeq(coll(sk27,sk25,sk25),true,midp(sk27,sk25,sk25),true),true),
inference(cp,[status(thm)],[t290,t7410]) ).
cnf(t22195,plain,
true = ifeq(coll(sk27,sk25,sk25),true,midp(sk27,sk25,sk25),true),
inference(step,[status(thm)],[t7419,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(t119,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)],[t119]) ).
cnf(t45,plain,
para(sk27,sk25,sk27,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi119,h13]) ).
cnf(t2331,plain,
para(sk27,sk25,sk27,sk25) = true,
inference(orient,[status(thm)],[t45]) ).
cnf(t2332,plain,
true = ifeq(true,true,coll(sk27,sk25,sk25),true),
inference(cp,[status(thm)],[t337,t2331]) ).
cnf(t21967,plain,
true = coll(sk27,sk25,sk25),
inference(step,[status(thm)],[t2332,t256]) ).
cnf(t3453,plain,
coll(sk27,sk25,sk25) = true,
inference(orient,[status(thm)],[t21967]) ).
cnf(t22196,plain,
true = ifeq(true,true,midp(sk27,sk25,sk25),true),
inference(step,[status(thm)],[t22195,t3453]) ).
cnf(t22197,plain,
true = midp(sk27,sk25,sk25),
inference(step,[status(thm)],[t22196,t256]) ).
cnf(t7449,plain,
midp(sk27,sk25,sk25) = true,
inference(orient,[status(thm)],[t22197]) ).
cnf(t20395,plain,
true = ifeq(true,true,midp(sk27,X1,X1),true),
inference(cp,[status(thm)],[t20394,t7449]) ).
cnf(t23660,plain,
true = midp(sk27,X1,X1),
inference(step,[status(thm)],[t20395,t256]) ).
cnf(t20399,plain,
midp(sk27,X1,X1) = true,
inference(orient,[status(thm)],[t23660]) ).
cnf(t20400,plain,
true = ifeq(true,true,cong(sk27,X1,sk27,X1),true),
inference(cp,[status(thm)],[t363,t20399]) ).
cnf(t23663,plain,
true = cong(sk27,X1,sk27,X1),
inference(step,[status(thm)],[t20400,t256]) ).
cnf(t20459,plain,
cong(sk27,X1,sk27,X1) = true,
inference(orient,[status(thm)],[t23663]) ).
cnf(t20470,plain,
true = ifeq(true,true,ifeq(cong(sk27,X1,sk27,X1),true,perp(sk27,sk27,X2,X1),true),true),
inference(cp,[status(thm)],[t289,t20459]) ).
cnf(t23667,plain,
true = ifeq(cong(sk27,X1,sk27,X1),true,perp(sk27,sk27,X2,X1),true),
inference(step,[status(thm)],[t20470,t256]) ).
cnf(t23668,plain,
true = ifeq(true,true,perp(sk27,sk27,X2,X1),true),
inference(step,[status(thm)],[t23667,t20459]) ).
cnf(t23669,plain,
true = perp(sk27,sk27,X2,X1),
inference(step,[status(thm)],[t23668,t256]) ).
cnf(t20577,plain,
perp(sk27,sk27,X1,X2) = true,
inference(orient,[status(thm)],[t23669]) ).
cnf(t20582,plain,
true = ifeq(true,true,perp(X1,X2,sk27,sk27),true),
inference(cp,[status(thm)],[t274,t20577]) ).
cnf(t23681,plain,
true = perp(X1,X2,sk27,sk27),
inference(step,[status(thm)],[t20582,t256]) ).
cnf(t20773,plain,
perp(X1,X2,sk27,sk27) = true,
inference(orient,[status(thm)],[t23681]) ).
cnf(t20787,plain,
true = ifeq(true,true,ifeq(perp(sk27,sk27,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t20773]) ).
cnf(t23694,plain,
true = ifeq(perp(sk27,sk27,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t20787,t256]) ).
cnf(t23695,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t23694,t20577]) ).
cnf(t23696,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t23695,t256]) ).
cnf(t21036,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t23696]) ).
cnf(t23705,plain,
ifeq(true,true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(step,[status(thm)],[t330,t21036]) ).
cnf(t23706,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(step,[status(thm)],[t23705,t256]) ).
cnf(t21043,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(rw,[status(thm)],[t23706]) ).
cnf(t21492,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4) = true,
inference(orient,[status(thm)],[t21043]) ).
cnf(t21494,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true),
inference(cp,[status(thm)],[t312,t21492]) ).
cnf(t23778,plain,
true = eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(step,[status(thm)],[t21494,t256]) ).
cnf(t21584,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6) = true,
inference(orient,[status(thm)],[t23778]) ).
cnf(t21586,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,X3,X4,X5,X6),true),
inference(cp,[status(thm)],[t306,t21584]) ).
cnf(t23796,plain,
true = eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(step,[status(thm)],[t21586,t256]) ).
cnf(t21802,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6) = true,
inference(orient,[status(thm)],[t23796]) ).
cnf(t21811,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,t21802]) ).
cnf(t23845,plain,
true = ifeq(true,true,ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),true),
inference(step,[status(thm)],[t21811,t21584]) ).
cnf(t23846,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),
inference(step,[status(thm)],[t23845,t256]) ).
cnf(t23847,plain,
true = eqangle(X1,X2,X3,X4,X7,X8,X9,X10),
inference(step,[status(thm)],[t23846,t256]) ).
cnf(t21950,plain,
eqangle(X1,X2,X3,X4,X5,X6,X7,X8) = true,
inference(orient,[status(thm)],[t23847]) ).
cnf(c121,plain,
~ eqangle(sk20,sk25,sk25,sk26,sk27,sk25,sk25,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
eqangle(sk20,sk25,sk25,sk26,sk27,sk25,sk25,sk21) != true,
inference(equality_encoding,[status(esa)],[c121]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t21950]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO570+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/10.60 % Computer : n004.cluster.edu
% 0.10/10.60 % Model : x86_64 x86_64
% 0.10/10.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.60 % Memory : 8046.5625MB
% 0.10/10.60 % OS : Linux 6.8.0-71-generic
% 0.10/10.60 % CPULimit : 300
% 0.10/10.60 % WCLimit : 300
% 0.10/10.60 % DateTime : Wed Sep 23 12:26:02 UTC 2026
% 0.10/10.61 % CPUTime :
% 0.10/10.61 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 21.94/28.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.94/28.80 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------