%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO584+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 : n019.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 01:18:13 PM UTC 2026
% Result : Theorem 158.87s 26.22s
% Output : Proof 158.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 76
% Number of leaves : 25
% Syntax : Number of formulae : 272 ( 176 unt; 0 def)
% Number of atoms : 452 ( 169 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 288 ( 108 ~; 102 |; 53 &)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 14 ( 14 usr; 13 con; 0-4 aty)
% Number of variables : 937 ( 108 sgn 375 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( ( eqangle(P,Q,U,V,E,F,G,H)
& eqangle(A,B,C,D,P,Q,U,V) )
=> eqangle(A,B,C,D,E,F,G,H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD22) ).
fof(f21_nnf,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(t242,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(eqangle(X5,X6,X7,X8,X9,X10,X11,X12),true,eqangle(X1,X2,X3,X4,X9,X10,X11,X12),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t286,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(eqangle(X5,X6,X7,X8,X9,X10,X11,X12),true,eqangle(X1,X2,X3,X4,X9,X10,X11,X12),true),true) = true,
inference(orient,[status(thm)],[t242]) ).
fof(f19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(P,Q,U,V,A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD20) ).
fof(f19_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t181,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)],[t181]) ).
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(t178,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)],[t178]) ).
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(t161,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)],[t161]) ).
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(t188,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)],[t188]) ).
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(t151,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)],[t151]) ).
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(t175,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)],[t175]) ).
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(t129,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)],[t129]) ).
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(t160,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)],[t160]) ).
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(t180,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)],[t180]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
fof(f94,conjecture,
! [A,B,C,O,D,E,Q,P,S,R,NWPNT1,NWPNT2] :
( ( coll(R,C,D)
& perp(R,E,C,D)
& coll(S,A,D)
& perp(S,E,A,D)
& coll(P,A,B)
& perp(P,E,A,B)
& coll(Q,B,C)
& perp(Q,E,B,C)
& circle(O,A,E,NWPNT2)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> eqangle(E,P,P,S,E,Q,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL416046) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,O,D,E,Q,P,S,R,NWPNT1,NWPNT2] :
( ( coll(R,C,D)
& perp(R,E,C,D)
& coll(S,A,D)
& perp(S,E,A,D)
& coll(P,A,B)
& perp(P,E,A,B)
& coll(Q,B,C)
& perp(Q,E,B,C)
& circle(O,A,E,NWPNT2)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> eqangle(E,P,P,S,E,Q,Q,R) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,O,D,E,Q,P,S,R,NWPNT1,NWPNT2] :
( ~ eqangle(E,P,P,S,E,Q,Q,R)
& coll(R,C,D)
& perp(R,E,C,D)
& coll(S,A,D)
& perp(S,E,A,D)
& coll(P,A,B)
& perp(P,E,A,B)
& coll(Q,B,C)
& perp(Q,E,B,C)
& circle(O,A,E,NWPNT2)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ eqangle(sk25,sk27,sk27,sk28,sk25,sk26,sk26,sk29)
& coll(sk29,sk22,sk24)
& perp(sk29,sk25,sk22,sk24)
& coll(sk28,sk20,sk24)
& perp(sk28,sk25,sk20,sk24)
& coll(sk27,sk20,sk21)
& perp(sk27,sk25,sk20,sk21)
& coll(sk26,sk21,sk22)
& perp(sk26,sk25,sk21,sk22)
& circle(sk23,sk20,sk25,sk31)
& circle(sk23,sk20,sk24,sk30)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29,sk30,sk31])],[f94_nnf]) ).
cnf(c118,plain,
perp(sk27,sk25,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi118,negated_conjecture,
perp(sk27,sk25,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(h8,plain,
perp(sk20,sk21,sk27,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi118]) ).
fof(f6,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD7) ).
fof(f6_nnf,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X0,X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h42,plain,
perp(sk20,sk21,sk25,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi6,h8]) ).
cnf(h120,plain,
perp(sk25,sk27,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi7,h42]) ).
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(t36,plain,
para(sk25,sk27,sk25,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi8,h120,h42]) ).
cnf(t2001,plain,
para(sk25,sk27,sk25,sk27) = true,
inference(orient,[status(thm)],[t36]) ).
cnf(t2005,plain,
true = ifeq(true,true,eqangle(sk25,sk27,X1,X2,sk25,sk27,X1,X2),true),
inference(cp,[status(thm)],[t330,t2001]) ).
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(t28999,plain,
true = eqangle(sk25,sk27,X1,X2,sk25,sk27,X1,X2),
inference(step,[status(thm)],[t2005,t256]) ).
cnf(t7322,plain,
eqangle(sk25,sk27,X1,X2,sk25,sk27,X1,X2) = true,
inference(orient,[status(thm)],[t28999]) ).
cnf(t7328,plain,
true = ifeq(true,true,eqangle(X1,X2,sk25,sk27,X1,X2,sk25,sk27),true),
inference(cp,[status(thm)],[t290,t7322]) ).
cnf(t29404,plain,
true = eqangle(X1,X2,sk25,sk27,X1,X2,sk25,sk27),
inference(step,[status(thm)],[t7328,t256]) ).
cnf(t12113,plain,
eqangle(X1,X2,sk25,sk27,X1,X2,sk25,sk27) = true,
inference(orient,[status(thm)],[t29404]) ).
cnf(t12115,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t296,t12113]) ).
cnf(t29405,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t12115,t256]) ).
cnf(t12137,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t29405]) ).
cnf(t12153,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,t12137]) ).
cnf(t31137,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)],[t12153,t256]) ).
cnf(t31138,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t31137,t12137]) ).
cnf(t31139,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t31138,t256]) ).
cnf(t26099,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t31139]) ).
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(t166,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)],[t166]) ).
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(t143,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)],[t143]) ).
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(t144,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)],[t144]) ).
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(t159,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)],[t159]) ).
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(t146,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)],[t146]) ).
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(c123,plain,
coll(sk29,sk22,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi123,negated_conjecture,
coll(sk29,sk22,sk24) = true,
inference(equality_encoding,[status(esa)],[c123]) ).
cnf(h20,plain,
coll(sk24,sk24,sk29) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi123,hi123]) ).
cnf(c121,plain,
coll(sk28,sk20,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi121,negated_conjecture,
coll(sk28,sk20,sk24) = true,
inference(equality_encoding,[status(esa)],[c121]) ).
cnf(h15,plain,
coll(sk24,sk24,sk28) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi121,hi121]) ).
cnf(h66,plain,
coll(sk28,sk29,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h15,h20]) ).
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(h170,plain,
coll(sk28,sk24,sk29) = true,
inference(hyper_resolution,[status(thm)],[hi0,h66]) ).
cnf(h576,plain,
coll(sk29,sk29,sk28) = true,
inference(hyper_resolution,[status(thm)],[hi2,h170,h170]) ).
cnf(c122,plain,
perp(sk29,sk25,sk22,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi122,negated_conjecture,
perp(sk29,sk25,sk22,sk24) = true,
inference(equality_encoding,[status(esa)],[c122]) ).
cnf(h18,plain,
perp(sk22,sk24,sk29,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi122]) ).
cnf(h62,plain,
para(sk29,sk25,sk29,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi122,h18]) ).
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(h164,plain,
eqangle(sk29,sk25,V0,V1,sk29,sk25,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h62]) ).
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(t31,plain,
cyclic(sk25,sk28,sk29,sk29) = true,
inference(hyper_resolution,[status(thm)],[hi42,h164,h576]) ).
cnf(t2740,plain,
cyclic(sk25,sk28,sk29,sk29) = true,
inference(orient,[status(thm)],[t31]) ).
cnf(t2741,plain,
true = ifeq(true,true,cyclic(sk25,sk29,sk28,sk29),true),
inference(cp,[status(thm)],[t346,t2740]) ).
cnf(t28839,plain,
true = cyclic(sk25,sk29,sk28,sk29),
inference(step,[status(thm)],[t2741,t256]) ).
cnf(t5087,plain,
cyclic(sk25,sk29,sk28,sk29) = true,
inference(orient,[status(thm)],[t28839]) ).
cnf(t5092,plain,
true = ifeq(true,true,eqangle(sk28,sk25,sk28,sk29,sk29,sk25,sk29,sk29),true),
inference(cp,[status(thm)],[t343,t5087]) ).
cnf(t29188,plain,
true = eqangle(sk28,sk25,sk28,sk29,sk29,sk25,sk29,sk29),
inference(step,[status(thm)],[t5092,t256]) ).
cnf(t9644,plain,
eqangle(sk28,sk25,sk28,sk29,sk29,sk25,sk29,sk29) = true,
inference(orient,[status(thm)],[t29188]) ).
cnf(t9660,plain,
true = ifeq(cyclic(sk25,sk29,sk28,sk25),true,ifeq(cyclic(sk25,sk29,sk28,sk29),true,ifeq(cyclic(sk25,sk29,sk28,sk29),true,ifeq(true,true,cong(sk25,sk29,sk25,sk29),true),true),true),true),
inference(cp,[status(thm)],[t341,t9644]) ).
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(t145,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)],[t145]) ).
cnf(c120,plain,
perp(sk28,sk25,sk20,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi120,negated_conjecture,
perp(sk28,sk25,sk20,sk24) = true,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(h13,plain,
perp(sk20,sk24,sk28,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi120]) ).
cnf(h51,plain,
para(sk28,sk25,sk28,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi120,h13]) ).
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(hi66,axiom,
ifeq(para(X0,X1,X0,X2),true,coll(X0,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(h139,plain,
coll(sk28,sk25,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi66,h51]) ).
cnf(h451,plain,
coll(sk25,sk25,sk28) = true,
inference(hyper_resolution,[status(thm)],[hi2,h139,h139]) ).
cnf(h163,plain,
coll(sk29,sk25,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi66,h62]) ).
cnf(h540,plain,
coll(sk25,sk25,sk29) = true,
inference(hyper_resolution,[status(thm)],[hi2,h163,h163]) ).
cnf(h2065,plain,
coll(sk29,sk28,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h540,h451]) ).
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(h549,plain,
eqangle(sk29,sk25,sk29,sk25,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h164]) ).
cnf(t26,plain,
cyclic(sk25,sk25,sk29,sk28) = true,
inference(hyper_resolution,[status(thm)],[hi42,h549,h2065]) ).
cnf(t2647,plain,
cyclic(sk25,sk25,sk29,sk28) = true,
inference(orient,[status(thm)],[t26]) ).
cnf(t2648,plain,
true = ifeq(true,true,cyclic(sk25,sk29,sk25,sk28),true),
inference(cp,[status(thm)],[t346,t2647]) ).
cnf(t28830,plain,
true = cyclic(sk25,sk29,sk25,sk28),
inference(step,[status(thm)],[t2648,t256]) ).
cnf(t4928,plain,
cyclic(sk25,sk29,sk25,sk28) = true,
inference(orient,[status(thm)],[t28830]) ).
cnf(t4929,plain,
true = ifeq(true,true,cyclic(sk25,sk29,sk28,sk25),true),
inference(cp,[status(thm)],[t348,t4928]) ).
cnf(t28867,plain,
true = cyclic(sk25,sk29,sk28,sk25),
inference(step,[status(thm)],[t4929,t256]) ).
cnf(t5598,plain,
cyclic(sk25,sk29,sk28,sk25) = true,
inference(orient,[status(thm)],[t28867]) ).
cnf(t29189,plain,
true = ifeq(true,true,ifeq(cyclic(sk25,sk29,sk28,sk29),true,ifeq(cyclic(sk25,sk29,sk28,sk29),true,ifeq(true,true,cong(sk25,sk29,sk25,sk29),true),true),true),true),
inference(step,[status(thm)],[t9660,t5598]) ).
cnf(t29190,plain,
true = ifeq(cyclic(sk25,sk29,sk28,sk29),true,ifeq(cyclic(sk25,sk29,sk28,sk29),true,ifeq(true,true,cong(sk25,sk29,sk25,sk29),true),true),true),
inference(step,[status(thm)],[t29189,t256]) ).
cnf(t29191,plain,
true = ifeq(true,true,ifeq(cyclic(sk25,sk29,sk28,sk29),true,ifeq(true,true,cong(sk25,sk29,sk25,sk29),true),true),true),
inference(step,[status(thm)],[t29190,t5087]) ).
cnf(t29192,plain,
true = ifeq(cyclic(sk25,sk29,sk28,sk29),true,ifeq(true,true,cong(sk25,sk29,sk25,sk29),true),true),
inference(step,[status(thm)],[t29191,t256]) ).
cnf(t29193,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk25,sk29,sk25,sk29),true),true),
inference(step,[status(thm)],[t29192,t5087]) ).
cnf(t29194,plain,
true = ifeq(true,true,cong(sk25,sk29,sk25,sk29),true),
inference(step,[status(thm)],[t29193,t256]) ).
cnf(t29195,plain,
true = cong(sk25,sk29,sk25,sk29),
inference(step,[status(thm)],[t29194,t256]) ).
cnf(t9661,plain,
cong(sk25,sk29,sk25,sk29) = true,
inference(orient,[status(thm)],[t29195]) ).
cnf(t9664,plain,
true = ifeq(true,true,cong(sk25,sk29,sk29,sk25),true),
inference(cp,[status(thm)],[t308,t9661]) ).
cnf(t29199,plain,
true = cong(sk25,sk29,sk29,sk25),
inference(step,[status(thm)],[t9664,t256]) ).
cnf(t9729,plain,
cong(sk25,sk29,sk29,sk25) = true,
inference(orient,[status(thm)],[t29199]) ).
cnf(t9731,plain,
true = ifeq(true,true,cong(sk29,sk25,sk25,sk29),true),
inference(cp,[status(thm)],[t306,t9729]) ).
cnf(t29200,plain,
true = cong(sk29,sk25,sk25,sk29),
inference(step,[status(thm)],[t9731,t256]) ).
cnf(t9739,plain,
cong(sk29,sk25,sk25,sk29) = true,
inference(orient,[status(thm)],[t29200]) ).
cnf(t9741,plain,
true = ifeq(true,true,cong(sk29,sk25,sk29,sk25),true),
inference(cp,[status(thm)],[t308,t9739]) ).
cnf(t29201,plain,
true = cong(sk29,sk25,sk29,sk25),
inference(step,[status(thm)],[t9741,t256]) ).
cnf(t9748,plain,
cong(sk29,sk25,sk29,sk25) = true,
inference(orient,[status(thm)],[t29201]) ).
cnf(t9757,plain,
true = ifeq(true,true,ifeq(coll(sk29,sk25,sk25),true,midp(sk29,sk25,sk25),true),true),
inference(cp,[status(thm)],[t312,t9748]) ).
cnf(t29202,plain,
true = ifeq(coll(sk29,sk25,sk25),true,midp(sk29,sk25,sk25),true),
inference(step,[status(thm)],[t9757,t256]) ).
cnf(t130,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)],[t130]) ).
cnf(t49,plain,
para(sk29,sk25,sk29,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi122,h18]) ).
cnf(t2414,plain,
para(sk29,sk25,sk29,sk25) = true,
inference(orient,[status(thm)],[t49]) ).
cnf(t2415,plain,
true = ifeq(true,true,coll(sk29,sk25,sk25),true),
inference(cp,[status(thm)],[t337,t2414]) ).
cnf(t28778,plain,
true = coll(sk29,sk25,sk25),
inference(step,[status(thm)],[t2415,t256]) ).
cnf(t3583,plain,
coll(sk29,sk25,sk25) = true,
inference(orient,[status(thm)],[t28778]) ).
cnf(t29203,plain,
true = ifeq(true,true,midp(sk29,sk25,sk25),true),
inference(step,[status(thm)],[t29202,t3583]) ).
cnf(t29204,plain,
true = midp(sk29,sk25,sk25),
inference(step,[status(thm)],[t29203,t256]) ).
cnf(t9787,plain,
midp(sk29,sk25,sk25) = true,
inference(orient,[status(thm)],[t29204]) ).
cnf(t26100,plain,
true = ifeq(true,true,midp(sk29,X1,X1),true),
inference(cp,[status(thm)],[t26099,t9787]) ).
cnf(t31140,plain,
true = midp(sk29,X1,X1),
inference(step,[status(thm)],[t26100,t256]) ).
cnf(t26114,plain,
midp(sk29,X1,X1) = true,
inference(orient,[status(thm)],[t31140]) ).
cnf(t26115,plain,
true = ifeq(true,true,cong(sk29,X1,sk29,X1),true),
inference(cp,[status(thm)],[t363,t26114]) ).
cnf(t31145,plain,
true = cong(sk29,X1,sk29,X1),
inference(step,[status(thm)],[t26115,t256]) ).
cnf(t26214,plain,
cong(sk29,X1,sk29,X1) = true,
inference(orient,[status(thm)],[t31145]) ).
cnf(t26225,plain,
true = ifeq(true,true,ifeq(cong(sk29,X1,sk29,X1),true,perp(sk29,sk29,X2,X1),true),true),
inference(cp,[status(thm)],[t311,t26214]) ).
cnf(t31151,plain,
true = ifeq(cong(sk29,X1,sk29,X1),true,perp(sk29,sk29,X2,X1),true),
inference(step,[status(thm)],[t26225,t256]) ).
cnf(t31152,plain,
true = ifeq(true,true,perp(sk29,sk29,X2,X1),true),
inference(step,[status(thm)],[t31151,t26214]) ).
cnf(t31153,plain,
true = perp(sk29,sk29,X2,X1),
inference(step,[status(thm)],[t31152,t256]) ).
cnf(t26392,plain,
perp(sk29,sk29,X1,X2) = true,
inference(orient,[status(thm)],[t31153]) ).
cnf(t26398,plain,
true = ifeq(true,true,perp(X1,X2,sk29,sk29),true),
inference(cp,[status(thm)],[t274,t26392]) ).
cnf(t31173,plain,
true = perp(X1,X2,sk29,sk29),
inference(step,[status(thm)],[t26398,t256]) ).
cnf(t26713,plain,
perp(X1,X2,sk29,sk29) = true,
inference(orient,[status(thm)],[t31173]) ).
cnf(t26729,plain,
true = ifeq(true,true,ifeq(perp(sk29,sk29,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t26713]) ).
cnf(t31197,plain,
true = ifeq(perp(sk29,sk29,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t26729,t256]) ).
cnf(t31198,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t31197,t26392]) ).
cnf(t31199,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t31198,t256]) ).
cnf(t27198,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t31199]) ).
cnf(t31210,plain,
ifeq(true,true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(step,[status(thm)],[t330,t27198]) ).
cnf(t31211,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(step,[status(thm)],[t31210,t256]) ).
cnf(t27206,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(rw,[status(thm)],[t31211]) ).
cnf(t28019,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4) = true,
inference(orient,[status(thm)],[t27206]) ).
cnf(t28022,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true),
inference(cp,[status(thm)],[t294,t28019]) ).
cnf(t31321,plain,
true = eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(step,[status(thm)],[t28022,t256]) ).
cnf(t28167,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6) = true,
inference(orient,[status(thm)],[t31321]) ).
cnf(t28169,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,X3,X4,X5,X6),true),
inference(cp,[status(thm)],[t288,t28167]) ).
cnf(t31351,plain,
true = eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(step,[status(thm)],[t28169,t256]) ).
cnf(t28564,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6) = true,
inference(orient,[status(thm)],[t31351]) ).
cnf(t28574,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,t28564]) ).
cnf(t31408,plain,
true = ifeq(true,true,ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),true),
inference(step,[status(thm)],[t28574,t28167]) ).
cnf(t31409,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),
inference(step,[status(thm)],[t31408,t256]) ).
cnf(t31410,plain,
true = eqangle(X1,X2,X3,X4,X7,X8,X9,X10),
inference(step,[status(thm)],[t31409,t256]) ).
cnf(t28758,plain,
eqangle(X1,X2,X3,X4,X5,X6,X7,X8) = true,
inference(orient,[status(thm)],[t31410]) ).
cnf(c124,plain,
~ eqangle(sk25,sk27,sk27,sk28,sk25,sk26,sk26,sk29),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
eqangle(sk25,sk27,sk27,sk28,sk25,sk26,sk26,sk29) != true,
inference(equality_encoding,[status(esa)],[c124]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t28758]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO584+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/5.37 % Computer : n019.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Wed Sep 23 12:28:43 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 158.87/26.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 158.87/26.22 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------