%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO561+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 : n001.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 01:18:09 PM UTC 2026
% Result : Theorem 103.19s 13.98s
% Output : Proof 103.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 76
% Number of leaves : 32
% Syntax : Number of formulae : 312 ( 188 unt; 0 def)
% Number of atoms : 544 ( 184 equ)
% Maximal formula atoms : 14 ( 1 avg)
% Number of connectives : 373 ( 141 ~; 135 |; 65 &)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-8 aty)
% Number of functors : 14 ( 14 usr; 13 con; 0-4 aty)
% Number of variables : 1254 ( 128 sgn 531 !; 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(t238,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(t265,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)],[t238]) ).
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(t170,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(t268,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)],[t170]) ).
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(t167,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(t274,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)],[t167]) ).
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(t134,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)],[t134]) ).
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(t177,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(t287,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)],[t177]) ).
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(t121,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t294,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t121]) ).
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(t164,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)],[t164]) ).
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(t111,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)],[t111]) ).
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(t224,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)],[t224]) ).
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(t133,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(t276,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(orient,[status(thm)],[t133]) ).
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,P,Q,N,M,E,D,NWPNT1,NWPNT2] :
( ( coll(D,N,M)
& coll(D,A,B)
& coll(E,N,M)
& coll(E,A,C)
& circle(O,A,M,NWPNT2)
& coll(M,O,Q)
& circle(O,A,N,NWPNT1)
& coll(N,O,P)
& coll(Q,A,B)
& perp(Q,O,A,B)
& coll(P,A,C)
& perp(P,O,A,C)
& circle(O,A,B,C) )
=> eqangle(A,D,D,E,D,E,E,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL214022) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,O,P,Q,N,M,E,D,NWPNT1,NWPNT2] :
( ( coll(D,N,M)
& coll(D,A,B)
& coll(E,N,M)
& coll(E,A,C)
& circle(O,A,M,NWPNT2)
& coll(M,O,Q)
& circle(O,A,N,NWPNT1)
& coll(N,O,P)
& coll(Q,A,B)
& perp(Q,O,A,B)
& coll(P,A,C)
& perp(P,O,A,C)
& circle(O,A,B,C) )
=> eqangle(A,D,D,E,D,E,E,A) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,O,P,Q,N,M,E,D,NWPNT1,NWPNT2] :
( ~ eqangle(A,D,D,E,D,E,E,A)
& coll(D,N,M)
& coll(D,A,B)
& coll(E,N,M)
& coll(E,A,C)
& circle(O,A,M,NWPNT2)
& coll(M,O,Q)
& circle(O,A,N,NWPNT1)
& coll(N,O,P)
& coll(Q,A,B)
& perp(Q,O,A,B)
& coll(P,A,C)
& perp(P,O,A,C)
& circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ eqangle(sk20,sk29,sk29,sk28,sk29,sk28,sk28,sk20)
& coll(sk29,sk26,sk27)
& coll(sk29,sk20,sk21)
& coll(sk28,sk26,sk27)
& coll(sk28,sk20,sk22)
& circle(sk23,sk20,sk27,sk31)
& coll(sk27,sk23,sk25)
& circle(sk23,sk20,sk26,sk30)
& coll(sk26,sk23,sk24)
& coll(sk25,sk20,sk21)
& perp(sk25,sk23,sk20,sk21)
& coll(sk24,sk20,sk22)
& perp(sk24,sk23,sk20,sk22)
& 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(c114,plain,
perp(sk24,sk23,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
perp(sk24,sk23,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h1,plain,
perp(sk20,sk22,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi114]) ).
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(h36,plain,
para(sk20,sk22,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi8,h1,hi114]) ).
cnf(hi39,axiom,
ifeq(para(X0,X1,X2,X3),true,eqangle(X0,X1,X4,X5,X2,X3,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(h126,plain,
eqangle(sk20,sk22,V0,V1,sk20,sk22,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h36]) ).
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(hi18,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X2,X3,X0,X1,X6,X7,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t62,plain,
eqangle(X1,X2,sk20,sk22,X1,X2,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi18,h126]) ).
cnf(t1242,plain,
eqangle(X1,X2,sk20,sk22,X1,X2,sk20,sk22) = true,
inference(orient,[status(thm)],[t62]) ).
cnf(t1246,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t276,t1242]) ).
cnf(t46,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t46]) ).
cnf(t18759,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t1246,t256]) ).
cnf(t4921,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t18759]) ).
cnf(t4937,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,t4921]) ).
cnf(t20126,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)],[t4937,t256]) ).
cnf(t20127,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t20126,t4921]) ).
cnf(t20128,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t20127,t256]) ).
cnf(t17056,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t20128]) ).
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(t155,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)],[t155]) ).
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(t138,plain,
ifeq(coll(X1,X2,X3),true,ifeq(coll(X1,X2,X4),true,coll(X3,X4,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t260,plain,
ifeq(coll(X1,X2,X3),true,ifeq(coll(X1,X2,X4),true,coll(X3,X4,X1),true),true) = true,
inference(orient,[status(thm)],[t138]) ).
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(t107,plain,
ifeq(coll(X1,X2,X3),true,coll(X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t263,plain,
ifeq(coll(X1,X2,X3),true,coll(X1,X3,X2),true) = true,
inference(orient,[status(thm)],[t107]) ).
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD2) ).
fof(f1_nnf,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t108,plain,
ifeq(coll(X1,X2,X3),true,coll(X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t261,plain,
ifeq(coll(X1,X2,X3),true,coll(X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t108]) ).
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(t112,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)],[t112]) ).
cnf(t4922,plain,
true = ifeq(true,true,coll(X1,X2,X2),true),
inference(cp,[status(thm)],[t337,t4921]) ).
cnf(t18760,plain,
true = coll(X1,X2,X2),
inference(step,[status(thm)],[t4922,t256]) ).
cnf(t4947,plain,
coll(X1,X2,X2) = true,
inference(orient,[status(thm)],[t18760]) ).
cnf(t4949,plain,
true = ifeq(true,true,coll(X1,X2,X1),true),
inference(cp,[status(thm)],[t261,t4947]) ).
cnf(t18761,plain,
true = coll(X1,X2,X1),
inference(step,[status(thm)],[t4949,t256]) ).
cnf(t4991,plain,
coll(X1,X2,X1) = true,
inference(orient,[status(thm)],[t18761]) ).
cnf(t4994,plain,
true = ifeq(true,true,coll(X1,X1,X2),true),
inference(cp,[status(thm)],[t263,t4991]) ).
cnf(t18762,plain,
true = coll(X1,X1,X2),
inference(step,[status(thm)],[t4994,t256]) ).
cnf(t5023,plain,
coll(X1,X1,X2) = true,
inference(orient,[status(thm)],[t18762]) ).
cnf(t5026,plain,
true = ifeq(true,true,ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),true),
inference(cp,[status(thm)],[t260,t5023]) ).
cnf(t18763,plain,
true = ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t5026,t256]) ).
cnf(t18764,plain,
true = ifeq(true,true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t18763,t5023]) ).
cnf(t18765,plain,
true = coll(X3,X2,X1),
inference(step,[status(thm)],[t18764,t256]) ).
cnf(t5061,plain,
coll(X1,X2,X3) = true,
inference(orient,[status(thm)],[t18765]) ).
cnf(t18770,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(true,true,midp(X1,X2,X3),true),true) = true,
inference(step,[status(thm)],[t312,t5061]) ).
cnf(t18771,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(step,[status(thm)],[t18770,t256]) ).
cnf(t5065,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(rw,[status(thm)],[t18771]) ).
cnf(t17268,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t5065]) ).
fof(f75,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( cong(P,Q,U,V)
& eqratio(A,B,C,D,P,Q,U,V) )
=> cong(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD75) ).
fof(f75_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( cong(A,B,C,D)
| ~ cong(P,Q,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f75]) ).
fof(f75_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( cong(A,B,C,D)
| ~ cong(P,Q,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f75_nnf]) ).
cnf(c75,plain,
( cong(X0,X1,X2,X3)
| ~ cong(X4,X5,X6,X7)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f75_sk]) ).
cnf(t210,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(cong(X5,X6,X7,X8),true,cong(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c75]) ).
cnf(t366,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(cong(X5,X6,X7,X8),true,cong(X1,X2,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t210]) ).
fof(f28,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,C,D,P,Q,U,V)
=> eqratio(A,B,P,Q,C,D,U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD29) ).
fof(f28_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,P,Q,C,D,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,P,Q,C,D,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
( eqratio(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(t171,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,eqratio(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(t376,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,eqratio(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(orient,[status(thm)],[t171]) ).
cnf(hi0,axiom,
ifeq(coll(X0,X1,X2),true,coll(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(c122,plain,
coll(sk28,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi122,negated_conjecture,
coll(sk28,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c122]) ).
cnf(h21,plain,
coll(sk28,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi122]) ).
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(h2,plain,
perp(sk24,sk23,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi114]) ).
cnf(h38,plain,
para(sk20,sk22,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,h1,h2]) ).
fof(f65,axiom,
! [A,B,C,D,O] :
( ( coll(O,B,D)
& coll(O,A,C)
& para(A,B,C,D) )
=> eqratio(O,A,A,C,O,B,B,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD65) ).
fof(f65_nnf,plain,
! [A,B,C,D,O] :
( eqratio(O,A,A,C,O,B,B,D)
| ~ coll(O,B,D)
| ~ coll(O,A,C)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f65]) ).
fof(f65_sk,plain,
! [A,B,C,D,O] :
( eqratio(O,A,A,C,O,B,B,D)
| ~ coll(O,B,D)
| ~ coll(O,A,C)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f65_nnf]) ).
cnf(c65,plain,
( eqratio(X4,X0,X0,X2,X4,X1,X1,X3)
| ~ coll(X4,X1,X3)
| ~ coll(X4,X0,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
cnf(hi65,axiom,
ifeq(para(X0,X1,X2,X3),true,ifeq(coll(X4,X0,X2),true,ifeq(coll(X4,X1,X3),true,eqratio(X4,X0,X0,X2,X4,X1,X1,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c65]) ).
cnf(h138,plain,
eqratio(sk28,sk20,sk20,sk22,sk28,sk22,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi65,h38,hi122,h21]) ).
fof(f27,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,C,D,P,Q,U,V)
=> eqratio(P,Q,U,V,A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD28) ).
fof(f27_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(P,Q,U,V,A,B,C,D)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(P,Q,U,V,A,B,C,D)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
( eqratio(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(hi27,axiom,
ifeq(eqratio(X0,X1,X2,X3,X4,X5,X6,X7),true,eqratio(X4,X5,X6,X7,X0,X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(h461,plain,
eqratio(sk28,sk22,sk22,sk20,sk28,sk20,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi27,h138]) ).
fof(f29,axiom,
! [A,B,C,D,E,F,G,H,P,Q,U,V] :
( ( eqratio(P,Q,U,V,E,F,G,H)
& eqratio(A,B,C,D,P,Q,U,V) )
=> eqratio(A,B,C,D,E,F,G,H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD30) ).
fof(f29_nnf,plain,
! [A,B,C,D,E,F,G,H,P,Q,U,V] :
( eqratio(A,B,C,D,E,F,G,H)
| ~ eqratio(P,Q,U,V,E,F,G,H)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqratio(A,B,C,D,E,F,G,H)
| ~ eqratio(P,Q,U,V,E,F,G,H)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
( eqratio(X0,X1,X2,X3,X4,X5,X6,X7)
| ~ eqratio(X8,X9,X10,X11,X4,X5,X6,X7)
| ~ eqratio(X0,X1,X2,X3,X8,X9,X10,X11) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(hi29,axiom,
ifeq(eqratio(X0,X1,X2,X3,X4,X5,X6,X7),true,ifeq(eqratio(X4,X5,X6,X7,X8,X9,X10,X11),true,eqratio(X0,X1,X2,X3,X8,X9,X10,X11),true),true) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(t87,plain,
eqratio(sk28,sk20,sk20,sk22,sk28,sk20,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi29,h138,h461]) ).
cnf(t2944,plain,
eqratio(sk28,sk20,sk20,sk22,sk28,sk20,sk20,sk22) = true,
inference(orient,[status(thm)],[t87]) ).
cnf(t2945,plain,
true = ifeq(true,true,eqratio(sk28,sk20,sk28,sk20,sk20,sk22,sk20,sk22),true),
inference(cp,[status(thm)],[t376,t2944]) ).
cnf(t18991,plain,
true = eqratio(sk28,sk20,sk28,sk20,sk20,sk22,sk20,sk22),
inference(step,[status(thm)],[t2945,t256]) ).
cnf(t7157,plain,
eqratio(sk28,sk20,sk28,sk20,sk20,sk22,sk20,sk22) = true,
inference(orient,[status(thm)],[t18991]) ).
cnf(t7166,plain,
true = ifeq(true,true,ifeq(cong(sk20,sk22,sk20,sk22),true,cong(sk28,sk20,sk28,sk20),true),true),
inference(cp,[status(thm)],[t366,t7157]) ).
cnf(t18992,plain,
true = ifeq(cong(sk20,sk22,sk20,sk22),true,cong(sk28,sk20,sk28,sk20),true),
inference(step,[status(thm)],[t7166,t256]) ).
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(t113,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)],[t113]) ).
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(t114,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)],[t114]) ).
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(t249,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)],[t249]) ).
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(t132,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)],[t132]) ).
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(h88,plain,
coll(sk20,sk20,sk28) = true,
inference(hyper_resolution,[status(thm)],[hi2,h21,h21]) ).
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(h380,plain,
cyclic(sk22,sk28,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h126,h88]) ).
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(t33,plain,
cyclic(sk22,sk20,sk28,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi14,h380]) ).
cnf(t2587,plain,
cyclic(sk22,sk20,sk28,sk20) = true,
inference(orient,[status(thm)],[t33]) ).
cnf(t2594,plain,
true = ifeq(true,true,eqangle(sk28,sk22,sk28,sk20,sk20,sk22,sk20,sk20),true),
inference(cp,[status(thm)],[t343,t2587]) ).
cnf(t18952,plain,
true = eqangle(sk28,sk22,sk28,sk20,sk20,sk22,sk20,sk20),
inference(step,[status(thm)],[t2594,t256]) ).
cnf(t6743,plain,
eqangle(sk28,sk22,sk28,sk20,sk20,sk22,sk20,sk20) = true,
inference(orient,[status(thm)],[t18952]) ).
cnf(t6758,plain,
true = ifeq(cyclic(sk22,sk20,sk28,sk22),true,ifeq(cyclic(sk22,sk20,sk28,sk20),true,ifeq(cyclic(sk22,sk20,sk28,sk20),true,ifeq(true,true,cong(sk22,sk20,sk22,sk20),true),true),true),true),
inference(cp,[status(thm)],[t341,t6743]) ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD16) ).
fof(f15_nnf,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t117,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t344,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(orient,[status(thm)],[t117]) ).
cnf(t116,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)],[t116]) ).
cnf(h19,plain,
coll(sk22,sk22,sk28) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi122,hi122]) ).
cnf(h140,plain,
eqangle(sk20,sk22,V0,V1,sk22,sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h38]) ).
fof(f17,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(B,A,C,D,P,Q,U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD18) ).
fof(f17_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(B,A,C,D,P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(B,A,C,D,P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( eqangle(X1,X0,X2,X3,X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi17,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X1,X0,X2,X3,X4,X5,X6,X7),true) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(h470,plain,
eqangle(sk22,sk20,V0,V1,sk22,sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi17,h140]) ).
cnf(t29,plain,
cyclic(sk20,sk28,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi42,h470,h19]) ).
cnf(t2532,plain,
cyclic(sk20,sk28,sk22,sk22) = true,
inference(orient,[status(thm)],[t29]) ).
cnf(t2533,plain,
true = ifeq(true,true,cyclic(sk20,sk22,sk28,sk22),true),
inference(cp,[status(thm)],[t346,t2532]) ).
cnf(t18844,plain,
true = cyclic(sk20,sk22,sk28,sk22),
inference(step,[status(thm)],[t2533,t256]) ).
cnf(t5199,plain,
cyclic(sk20,sk22,sk28,sk22) = true,
inference(orient,[status(thm)],[t18844]) ).
cnf(t5202,plain,
true = ifeq(true,true,cyclic(sk22,sk20,sk28,sk22),true),
inference(cp,[status(thm)],[t344,t5199]) ).
cnf(t18872,plain,
true = cyclic(sk22,sk20,sk28,sk22),
inference(step,[status(thm)],[t5202,t256]) ).
cnf(t5627,plain,
cyclic(sk22,sk20,sk28,sk22) = true,
inference(orient,[status(thm)],[t18872]) ).
cnf(t18953,plain,
true = ifeq(true,true,ifeq(cyclic(sk22,sk20,sk28,sk20),true,ifeq(cyclic(sk22,sk20,sk28,sk20),true,ifeq(true,true,cong(sk22,sk20,sk22,sk20),true),true),true),true),
inference(step,[status(thm)],[t6758,t5627]) ).
cnf(t18954,plain,
true = ifeq(cyclic(sk22,sk20,sk28,sk20),true,ifeq(cyclic(sk22,sk20,sk28,sk20),true,ifeq(true,true,cong(sk22,sk20,sk22,sk20),true),true),true),
inference(step,[status(thm)],[t18953,t256]) ).
cnf(t18955,plain,
true = ifeq(true,true,ifeq(cyclic(sk22,sk20,sk28,sk20),true,ifeq(true,true,cong(sk22,sk20,sk22,sk20),true),true),true),
inference(step,[status(thm)],[t18954,t2587]) ).
cnf(t18956,plain,
true = ifeq(cyclic(sk22,sk20,sk28,sk20),true,ifeq(true,true,cong(sk22,sk20,sk22,sk20),true),true),
inference(step,[status(thm)],[t18955,t256]) ).
cnf(t18957,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk22,sk20,sk22,sk20),true),true),
inference(step,[status(thm)],[t18956,t2587]) ).
cnf(t18958,plain,
true = ifeq(true,true,cong(sk22,sk20,sk22,sk20),true),
inference(step,[status(thm)],[t18957,t256]) ).
cnf(t18959,plain,
true = cong(sk22,sk20,sk22,sk20),
inference(step,[status(thm)],[t18958,t256]) ).
cnf(t6759,plain,
cong(sk22,sk20,sk22,sk20) = true,
inference(orient,[status(thm)],[t18959]) ).
cnf(t6762,plain,
true = ifeq(true,true,cong(sk22,sk20,sk20,sk22),true),
inference(cp,[status(thm)],[t308,t6759]) ).
cnf(t18960,plain,
true = cong(sk22,sk20,sk20,sk22),
inference(step,[status(thm)],[t6762,t256]) ).
cnf(t6790,plain,
cong(sk22,sk20,sk20,sk22) = true,
inference(orient,[status(thm)],[t18960]) ).
cnf(t6792,plain,
true = ifeq(true,true,cong(sk20,sk22,sk22,sk20),true),
inference(cp,[status(thm)],[t306,t6790]) ).
cnf(t18961,plain,
true = cong(sk20,sk22,sk22,sk20),
inference(step,[status(thm)],[t6792,t256]) ).
cnf(t6800,plain,
cong(sk20,sk22,sk22,sk20) = true,
inference(orient,[status(thm)],[t18961]) ).
cnf(t6802,plain,
true = ifeq(true,true,cong(sk20,sk22,sk20,sk22),true),
inference(cp,[status(thm)],[t308,t6800]) ).
cnf(t18962,plain,
true = cong(sk20,sk22,sk20,sk22),
inference(step,[status(thm)],[t6802,t256]) ).
cnf(t6809,plain,
cong(sk20,sk22,sk20,sk22) = true,
inference(orient,[status(thm)],[t18962]) ).
cnf(t18993,plain,
true = ifeq(true,true,cong(sk28,sk20,sk28,sk20),true),
inference(step,[status(thm)],[t18992,t6809]) ).
cnf(t18994,plain,
true = cong(sk28,sk20,sk28,sk20),
inference(step,[status(thm)],[t18993,t256]) ).
cnf(t7167,plain,
cong(sk28,sk20,sk28,sk20) = true,
inference(orient,[status(thm)],[t18994]) ).
cnf(t17270,plain,
true = ifeq(true,true,midp(sk28,sk20,sk20),true),
inference(cp,[status(thm)],[t17268,t7167]) ).
cnf(t20183,plain,
true = midp(sk28,sk20,sk20),
inference(step,[status(thm)],[t17270,t256]) ).
cnf(t17299,plain,
midp(sk28,sk20,sk20) = true,
inference(orient,[status(thm)],[t20183]) ).
cnf(t17300,plain,
true = ifeq(true,true,midp(sk28,X1,X1),true),
inference(cp,[status(thm)],[t17056,t17299]) ).
cnf(t20193,plain,
true = midp(sk28,X1,X1),
inference(step,[status(thm)],[t17300,t256]) ).
cnf(t17495,plain,
midp(sk28,X1,X1) = true,
inference(orient,[status(thm)],[t20193]) ).
cnf(t17496,plain,
true = ifeq(true,true,cong(sk28,X1,sk28,X1),true),
inference(cp,[status(thm)],[t363,t17495]) ).
cnf(t20197,plain,
true = cong(sk28,X1,sk28,X1),
inference(step,[status(thm)],[t17496,t256]) ).
cnf(t17575,plain,
cong(sk28,X1,sk28,X1) = true,
inference(orient,[status(thm)],[t20197]) ).
cnf(t17586,plain,
true = ifeq(true,true,ifeq(cong(sk28,X1,sk28,X1),true,perp(sk28,sk28,X2,X1),true),true),
inference(cp,[status(thm)],[t311,t17575]) ).
cnf(t20202,plain,
true = ifeq(cong(sk28,X1,sk28,X1),true,perp(sk28,sk28,X2,X1),true),
inference(step,[status(thm)],[t17586,t256]) ).
cnf(t20203,plain,
true = ifeq(true,true,perp(sk28,sk28,X2,X1),true),
inference(step,[status(thm)],[t20202,t17575]) ).
cnf(t20204,plain,
true = perp(sk28,sk28,X2,X1),
inference(step,[status(thm)],[t20203,t256]) ).
cnf(t17723,plain,
perp(sk28,sk28,X1,X2) = true,
inference(orient,[status(thm)],[t20204]) ).
cnf(t17724,plain,
true = ifeq(true,true,perp(X1,X2,sk28,sk28),true),
inference(cp,[status(thm)],[t294,t17723]) ).
cnf(t20218,plain,
true = perp(X1,X2,sk28,sk28),
inference(step,[status(thm)],[t17724,t256]) ).
cnf(t17935,plain,
perp(X1,X2,sk28,sk28) = true,
inference(orient,[status(thm)],[t20218]) ).
cnf(t17941,plain,
true = ifeq(true,true,ifeq(perp(sk28,sk28,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t287,t17935]) ).
cnf(t20232,plain,
true = ifeq(perp(sk28,sk28,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t17941,t256]) ).
cnf(t20233,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t20232,t17723]) ).
cnf(t20234,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t20233,t256]) ).
cnf(t18243,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t20234]) ).
cnf(t20235,plain,
ifeq(true,true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(step,[status(thm)],[t330,t18243]) ).
cnf(t20236,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(step,[status(thm)],[t20235,t256]) ).
cnf(t18244,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(rw,[status(thm)],[t20236]) ).
cnf(t18528,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4) = true,
inference(orient,[status(thm)],[t18244]) ).
cnf(t18531,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true),
inference(cp,[status(thm)],[t274,t18528]) ).
cnf(t20280,plain,
true = eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(step,[status(thm)],[t18531,t256]) ).
cnf(t18559,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6) = true,
inference(orient,[status(thm)],[t20280]) ).
cnf(t18561,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,X3,X4,X5,X6),true),
inference(cp,[status(thm)],[t268,t18559]) ).
cnf(t20284,plain,
true = eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(step,[status(thm)],[t18561,t256]) ).
cnf(t18596,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6) = true,
inference(orient,[status(thm)],[t20284]) ).
cnf(t18604,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)],[t265,t18596]) ).
cnf(t20323,plain,
true = ifeq(true,true,ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),true),
inference(step,[status(thm)],[t18604,t18559]) ).
cnf(t20324,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),
inference(step,[status(thm)],[t20323,t256]) ).
cnf(t20325,plain,
true = eqangle(X1,X2,X3,X4,X7,X8,X9,X10),
inference(step,[status(thm)],[t20324,t256]) ).
cnf(t18696,plain,
eqangle(X1,X2,X3,X4,X5,X6,X7,X8) = true,
inference(orient,[status(thm)],[t20325]) ).
cnf(c126,plain,
~ eqangle(sk20,sk29,sk29,sk28,sk29,sk28,sk28,sk20),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
eqangle(sk20,sk29,sk29,sk28,sk29,sk28,sk28,sk20) != true,
inference(equality_encoding,[status(esa)],[c126]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t18696]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO561+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 12:29:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 103.19/13.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 103.19/13.98 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------