%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO569+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 : n014.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 01:18:10 PM UTC 2026
% Result : Theorem 131.94s 17.46s
% Output : Proof 131.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 72
% Number of leaves : 22
% Syntax : Number of formulae : 258 ( 174 unt; 0 def)
% Number of atoms : 418 ( 170 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 265 ( 105 ~; 99 |; 39 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-4 aty)
% Number of variables : 775 ( 78 sgn 316 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [A,B,C,D,O] :
( ( cong(O,A,O,D)
& cong(O,A,O,C)
& cong(O,A,O,B) )
=> cyclic(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD13) ).
fof(f12_nnf,plain,
! [A,B,C,D,O] :
( cyclic(A,B,C,D)
| ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [O,A,B,C,D] :
( cyclic(A,B,C,D)
| ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( cyclic(X0,X1,X2,X3)
| ~ cong(X4,X0,X4,X3)
| ~ cong(X4,X0,X4,X2)
| ~ cong(X4,X0,X4,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t232,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(cong(X1,X2,X1,X4),true,ifeq(cong(X1,X2,X1,X5),true,cyclic(X2,X3,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t273,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(cong(X1,X2,X1,X4),true,ifeq(cong(X1,X2,X1,X5),true,cyclic(X2,X3,X4,X5),true),true),true) = true,
inference(orient,[status(thm)],[t232]) ).
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(t94,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t336,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t94]) ).
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(t222,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X4,X3,X5),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(t333,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X4,X3,X5),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(orient,[status(thm)],[t222]) ).
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(t182,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t285,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(orient,[status(thm)],[t182]) ).
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(t104,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t292,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t104]) ).
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(t169,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(t271,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(orient,[status(thm)],[t169]) ).
fof(f73,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( para(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> para(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD73) ).
fof(f73_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
fof(f73_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f73_nnf]) ).
cnf(c73,plain,
( para(X0,X1,X2,X3)
| ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f73_sk]) ).
cnf(t202,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(t305,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t202]) ).
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(t175,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)],[t175]) ).
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(t172,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)],[t172]) ).
fof(f10,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD11) ).
fof(f10_nnf,plain,
! [A,B,M] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [M,B,A] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( midp(X2,X0,X1)
| ~ midp(X2,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(midp(X0,X1,X2),true,midp(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
fof(f94,conjecture,
! [A,B,C,O,C1,B1,P,Q] :
( ( coll(Q,A,B)
& coll(Q,O,B1)
& coll(P,A,C)
& coll(P,O,C1)
& midp(B1,C,A)
& midp(C1,B,A)
& circle(O,A,B,C) )
=> cyclic(Q,B,C,P) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL214031) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,O,C1,B1,P,Q] :
( ( coll(Q,A,B)
& coll(Q,O,B1)
& coll(P,A,C)
& coll(P,O,C1)
& midp(B1,C,A)
& midp(C1,B,A)
& circle(O,A,B,C) )
=> cyclic(Q,B,C,P) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,O,C1,B1,P,Q] :
( ~ cyclic(Q,B,C,P)
& coll(Q,A,B)
& coll(Q,O,B1)
& coll(P,A,C)
& coll(P,O,C1)
& midp(B1,C,A)
& midp(C1,B,A)
& circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ cyclic(sk27,sk21,sk22,sk26)
& coll(sk27,sk20,sk21)
& coll(sk27,sk23,sk25)
& coll(sk26,sk20,sk22)
& coll(sk26,sk23,sk24)
& midp(sk25,sk22,sk20)
& midp(sk24,sk21,sk20)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27])],[f94_nnf]) ).
cnf(c115,plain,
midp(sk25,sk22,sk20),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi115,negated_conjecture,
midp(sk25,sk22,sk20) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(h26,plain,
midp(sk25,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi115]) ).
cnf(c114,plain,
midp(sk24,sk21,sk20),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
midp(sk24,sk21,sk20) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h9,plain,
midp(sk24,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi114]) ).
fof(f44,axiom,
! [A,B,C,E,F] :
( ( midp(F,A,C)
& midp(E,A,B) )
=> para(E,F,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD44) ).
fof(f44_nnf,plain,
! [A,B,C,E,F] :
( para(E,F,B,C)
| ~ midp(F,A,C)
| ~ midp(E,A,B) ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [E,A,B,F,C] :
( para(E,F,B,C)
| ~ midp(F,A,C)
| ~ midp(E,A,B) ),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c44,plain,
( para(X3,X4,X1,X2)
| ~ midp(X4,X0,X2)
| ~ midp(X3,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(hi44,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(midp(X3,X1,X4),true,para(X0,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
cnf(h170,plain,
para(sk24,sk25,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi44,h9,h26]) ).
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(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(t38,plain,
eqangle(sk24,sk25,X1,X2,sk21,sk22,X1,X2) = true,
inference(hyper_resolution,[status(thm)],[hi39,h170]) ).
cnf(t1934,plain,
eqangle(sk24,sk25,X1,X2,sk21,sk22,X1,X2) = true,
inference(orient,[status(thm)],[t38]) ).
cnf(t1937,plain,
true = ifeq(true,true,eqangle(sk24,sk25,sk21,sk22,X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t312,t1934]) ).
cnf(t24,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t24]) ).
cnf(t16467,plain,
true = eqangle(sk24,sk25,sk21,sk22,X1,X2,X1,X2),
inference(step,[status(thm)],[t1937,t256]) ).
cnf(t5243,plain,
eqangle(sk24,sk25,sk21,sk22,X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t16467]) ).
cnf(t5248,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,sk24,sk25,sk21,sk22),true),
inference(cp,[status(thm)],[t306,t5243]) ).
cnf(t16599,plain,
true = eqangle(X1,X2,X1,X2,sk24,sk25,sk21,sk22),
inference(step,[status(thm)],[t5248,t256]) ).
cnf(t7214,plain,
eqangle(X1,X2,X1,X2,sk24,sk25,sk21,sk22) = true,
inference(orient,[status(thm)],[t16599]) ).
cnf(t7219,plain,
true = ifeq(true,true,ifeq(para(sk24,sk25,sk21,sk22),true,para(X1,X2,X1,X2),true),true),
inference(cp,[status(thm)],[t305,t7214]) ).
cnf(t16600,plain,
true = ifeq(para(sk24,sk25,sk21,sk22),true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t7219,t256]) ).
cnf(t33,plain,
para(sk24,sk25,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi44,h9,h26]) ).
cnf(t2832,plain,
para(sk24,sk25,sk21,sk22) = true,
inference(orient,[status(thm)],[t33]) ).
cnf(t16601,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t16600,t2832]) ).
cnf(t16602,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t16601,t256]) ).
cnf(t7224,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t16602]) ).
cnf(t7241,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,ifeq(para(X2,X3,X2,X3),true,midp(X1,X3,X3),true),true),true),
inference(cp,[status(thm)],[t333,t7224]) ).
cnf(t17491,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)],[t7241,t256]) ).
cnf(t17492,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t17491,t7224]) ).
cnf(t17493,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t17492,t256]) ).
cnf(t14920,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t17493]) ).
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(t160,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(t272,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(orient,[status(thm)],[t160]) ).
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(t357,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(orient,[status(thm)],[t253]) ).
fof(f40,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('/export/starexec/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(t139,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t359,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(orient,[status(thm)],[t139]) ).
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(t99,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t362,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(orient,[status(thm)],[t99]) ).
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(t100,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t360,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(orient,[status(thm)],[t100]) ).
cnf(hi68,axiom,
ifeq(midp(X0,X1,X2),true,cong(X0,X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(h165,plain,
cong(sk25,sk20,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi68,h26]) ).
cnf(hi12,axiom,
ifeq(cong(X0,X1,X0,X2),true,ifeq(cong(X0,X1,X0,X3),true,ifeq(cong(X0,X1,X0,X4),true,cyclic(X1,X2,X3,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t20,plain,
cyclic(sk20,sk22,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi12,h165,h165,h165]) ).
cnf(t3089,plain,
cyclic(sk20,sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(t3090,plain,
true = ifeq(true,true,cyclic(sk22,sk20,sk22,sk22),true),
inference(cp,[status(thm)],[t360,t3089]) ).
cnf(t16446,plain,
true = cyclic(sk22,sk20,sk22,sk22),
inference(step,[status(thm)],[t3090,t256]) ).
cnf(t4873,plain,
cyclic(sk22,sk20,sk22,sk22) = true,
inference(orient,[status(thm)],[t16446]) ).
cnf(t4874,plain,
true = ifeq(true,true,cyclic(sk22,sk22,sk20,sk22),true),
inference(cp,[status(thm)],[t362,t4873]) ).
cnf(t16454,plain,
true = cyclic(sk22,sk22,sk20,sk22),
inference(step,[status(thm)],[t4874,t256]) ).
cnf(t5027,plain,
cyclic(sk22,sk22,sk20,sk22) = true,
inference(orient,[status(thm)],[t16454]) ).
cnf(t5030,plain,
true = ifeq(true,true,eqangle(sk20,sk22,sk20,sk22,sk22,sk22,sk22,sk22),true),
inference(cp,[status(thm)],[t359,t5027]) ).
cnf(t16584,plain,
true = eqangle(sk20,sk22,sk20,sk22,sk22,sk22,sk22,sk22),
inference(step,[status(thm)],[t5030,t256]) ).
cnf(t7095,plain,
eqangle(sk20,sk22,sk20,sk22,sk22,sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t16584]) ).
cnf(t7108,plain,
true = ifeq(cyclic(sk22,sk22,sk20,sk22),true,ifeq(cyclic(sk22,sk22,sk20,sk22),true,ifeq(cyclic(sk22,sk22,sk20,sk22),true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),true),true),
inference(cp,[status(thm)],[t357,t7095]) ).
cnf(t16585,plain,
true = ifeq(true,true,ifeq(cyclic(sk22,sk22,sk20,sk22),true,ifeq(cyclic(sk22,sk22,sk20,sk22),true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),true),true),
inference(step,[status(thm)],[t7108,t5027]) ).
cnf(t16586,plain,
true = ifeq(cyclic(sk22,sk22,sk20,sk22),true,ifeq(cyclic(sk22,sk22,sk20,sk22),true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),true),
inference(step,[status(thm)],[t16585,t256]) ).
cnf(t16587,plain,
true = ifeq(true,true,ifeq(cyclic(sk22,sk22,sk20,sk22),true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),true),
inference(step,[status(thm)],[t16586,t5027]) ).
cnf(t16588,plain,
true = ifeq(cyclic(sk22,sk22,sk20,sk22),true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),
inference(step,[status(thm)],[t16587,t256]) ).
cnf(t16589,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),
inference(step,[status(thm)],[t16588,t5027]) ).
cnf(t16590,plain,
true = ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),
inference(step,[status(thm)],[t16589,t256]) ).
cnf(t16591,plain,
true = cong(sk22,sk22,sk22,sk22),
inference(step,[status(thm)],[t16590,t256]) ).
cnf(t7109,plain,
cong(sk22,sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t16591]) ).
cnf(t7119,plain,
true = ifeq(true,true,ifeq(coll(sk22,sk22,sk22),true,midp(sk22,sk22,sk22),true),true),
inference(cp,[status(thm)],[t272,t7109]) ).
cnf(t16592,plain,
true = ifeq(coll(sk22,sk22,sk22),true,midp(sk22,sk22,sk22),true),
inference(step,[status(thm)],[t7119,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(t95,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t353,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t95]) ).
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(t140,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)],[t140]) ).
cnf(t4876,plain,
true = ifeq(true,true,eqangle(sk22,sk22,sk22,sk20,sk22,sk22,sk22,sk20),true),
inference(cp,[status(thm)],[t359,t4873]) ).
cnf(t16566,plain,
true = eqangle(sk22,sk22,sk22,sk20,sk22,sk22,sk22,sk20),
inference(step,[status(thm)],[t4876,t256]) ).
cnf(t6909,plain,
eqangle(sk22,sk22,sk22,sk20,sk22,sk22,sk22,sk20) = true,
inference(orient,[status(thm)],[t16566]) ).
cnf(t6911,plain,
true = ifeq(true,true,para(sk22,sk22,sk22,sk22),true),
inference(cp,[status(thm)],[t314,t6909]) ).
cnf(t16567,plain,
true = para(sk22,sk22,sk22,sk22),
inference(step,[status(thm)],[t6911,t256]) ).
cnf(t6923,plain,
para(sk22,sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t16567]) ).
cnf(t6924,plain,
true = ifeq(true,true,coll(sk22,sk22,sk22),true),
inference(cp,[status(thm)],[t353,t6923]) ).
cnf(t16568,plain,
true = coll(sk22,sk22,sk22),
inference(step,[status(thm)],[t6924,t256]) ).
cnf(t6943,plain,
coll(sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t16568]) ).
cnf(t16593,plain,
true = ifeq(true,true,midp(sk22,sk22,sk22),true),
inference(step,[status(thm)],[t16592,t6943]) ).
cnf(t16594,plain,
true = midp(sk22,sk22,sk22),
inference(step,[status(thm)],[t16593,t256]) ).
cnf(t7147,plain,
midp(sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t16594]) ).
cnf(t14921,plain,
true = ifeq(true,true,midp(sk22,X1,X1),true),
inference(cp,[status(thm)],[t14920,t7147]) ).
cnf(t17494,plain,
true = midp(sk22,X1,X1),
inference(step,[status(thm)],[t14921,t256]) ).
cnf(t14926,plain,
midp(sk22,X1,X1) = true,
inference(orient,[status(thm)],[t17494]) ).
cnf(t14927,plain,
true = ifeq(true,true,cong(sk22,X1,sk22,X1),true),
inference(cp,[status(thm)],[t336,t14926]) ).
cnf(t17497,plain,
true = cong(sk22,X1,sk22,X1),
inference(step,[status(thm)],[t14927,t256]) ).
cnf(t14986,plain,
cong(sk22,X1,sk22,X1) = true,
inference(orient,[status(thm)],[t17497]) ).
cnf(t14998,plain,
true = ifeq(true,true,ifeq(cong(sk22,X1,sk22,X1),true,perp(sk22,sk22,X2,X1),true),true),
inference(cp,[status(thm)],[t271,t14986]) ).
cnf(t17501,plain,
true = ifeq(cong(sk22,X1,sk22,X1),true,perp(sk22,sk22,X2,X1),true),
inference(step,[status(thm)],[t14998,t256]) ).
cnf(t17502,plain,
true = ifeq(true,true,perp(sk22,sk22,X2,X1),true),
inference(step,[status(thm)],[t17501,t14986]) ).
cnf(t17503,plain,
true = perp(sk22,sk22,X2,X1),
inference(step,[status(thm)],[t17502,t256]) ).
cnf(t15108,plain,
perp(sk22,sk22,X1,X2) = true,
inference(orient,[status(thm)],[t17503]) ).
cnf(t15109,plain,
true = ifeq(true,true,perp(X1,X2,sk22,sk22),true),
inference(cp,[status(thm)],[t292,t15108]) ).
cnf(t17513,plain,
true = perp(X1,X2,sk22,sk22),
inference(step,[status(thm)],[t15109,t256]) ).
cnf(t15260,plain,
perp(X1,X2,sk22,sk22) = true,
inference(orient,[status(thm)],[t17513]) ).
cnf(t15267,plain,
true = ifeq(true,true,ifeq(perp(sk22,sk22,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t285,t15260]) ).
cnf(t17519,plain,
true = ifeq(perp(sk22,sk22,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t15267,t256]) ).
cnf(t17520,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t17519,t15108]) ).
cnf(t17521,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t17520,t256]) ).
cnf(t15410,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t17521]) ).
cnf(t17533,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(step,[status(thm)],[t333,t15410]) ).
cnf(t17534,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t17533,t256]) ).
cnf(t17535,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t17534,t15410]) ).
cnf(t17536,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(step,[status(thm)],[t17535,t256]) ).
cnf(t15417,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(rw,[status(thm)],[t17536]) ).
cnf(t16162,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(orient,[status(thm)],[t15417]) ).
cnf(h6,plain,
cong(sk24,sk21,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi68,hi114]) ).
cnf(h79,plain,
cyclic(sk21,sk20,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi12,h6,h6,h6]) ).
fof(f16,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,E)
& cyclic(A,B,C,D) )
=> cyclic(B,C,D,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD17) ).
fof(f16_nnf,plain,
! [A,B,C,D,E] :
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A,B,C,D,E] :
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,ifeq(cyclic(X0,X1,X2,X4),true,cyclic(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t16,plain,
cyclic(sk20,sk20,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi16,h79,h79]) ).
cnf(t3026,plain,
cyclic(sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(t3027,plain,
true = ifeq(true,true,eqangle(sk20,sk20,sk20,sk20,sk20,sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t359,t3026]) ).
cnf(t16481,plain,
true = eqangle(sk20,sk20,sk20,sk20,sk20,sk20,sk20,sk20),
inference(step,[status(thm)],[t3027,t256]) ).
cnf(t5435,plain,
eqangle(sk20,sk20,sk20,sk20,sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t16481]) ).
cnf(t5457,plain,
true = ifeq(cyclic(sk20,sk20,sk20,sk20),true,ifeq(cyclic(sk20,sk20,sk20,sk20),true,ifeq(cyclic(sk20,sk20,sk20,sk20),true,ifeq(true,true,cong(sk20,sk20,sk20,sk20),true),true),true),true),
inference(cp,[status(thm)],[t357,t5435]) ).
cnf(t16484,plain,
true = ifeq(true,true,ifeq(cyclic(sk20,sk20,sk20,sk20),true,ifeq(cyclic(sk20,sk20,sk20,sk20),true,ifeq(true,true,cong(sk20,sk20,sk20,sk20),true),true),true),true),
inference(step,[status(thm)],[t5457,t3026]) ).
cnf(t16485,plain,
true = ifeq(cyclic(sk20,sk20,sk20,sk20),true,ifeq(cyclic(sk20,sk20,sk20,sk20),true,ifeq(true,true,cong(sk20,sk20,sk20,sk20),true),true),true),
inference(step,[status(thm)],[t16484,t256]) ).
cnf(t16486,plain,
true = ifeq(true,true,ifeq(cyclic(sk20,sk20,sk20,sk20),true,ifeq(true,true,cong(sk20,sk20,sk20,sk20),true),true),true),
inference(step,[status(thm)],[t16485,t3026]) ).
cnf(t16487,plain,
true = ifeq(cyclic(sk20,sk20,sk20,sk20),true,ifeq(true,true,cong(sk20,sk20,sk20,sk20),true),true),
inference(step,[status(thm)],[t16486,t256]) ).
cnf(t16488,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk20,sk20,sk20,sk20),true),true),
inference(step,[status(thm)],[t16487,t3026]) ).
cnf(t16489,plain,
true = ifeq(true,true,cong(sk20,sk20,sk20,sk20),true),
inference(step,[status(thm)],[t16488,t256]) ).
cnf(t16490,plain,
true = cong(sk20,sk20,sk20,sk20),
inference(step,[status(thm)],[t16489,t256]) ).
cnf(t5506,plain,
cong(sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t16490]) ).
cnf(t5516,plain,
true = ifeq(true,true,ifeq(coll(sk20,sk20,sk20),true,midp(sk20,sk20,sk20),true),true),
inference(cp,[status(thm)],[t272,t5506]) ).
cnf(t16491,plain,
true = ifeq(coll(sk20,sk20,sk20),true,midp(sk20,sk20,sk20),true),
inference(step,[status(thm)],[t5516,t256]) ).
cnf(t5437,plain,
true = ifeq(true,true,para(sk20,sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t314,t5435]) ).
cnf(t16482,plain,
true = para(sk20,sk20,sk20,sk20),
inference(step,[status(thm)],[t5437,t256]) ).
cnf(t5458,plain,
para(sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t16482]) ).
cnf(t5459,plain,
true = ifeq(true,true,coll(sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t353,t5458]) ).
cnf(t16483,plain,
true = coll(sk20,sk20,sk20),
inference(step,[status(thm)],[t5459,t256]) ).
cnf(t5479,plain,
coll(sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t16483]) ).
cnf(t16492,plain,
true = ifeq(true,true,midp(sk20,sk20,sk20),true),
inference(step,[status(thm)],[t16491,t5479]) ).
cnf(t16493,plain,
true = midp(sk20,sk20,sk20),
inference(step,[status(thm)],[t16492,t256]) ).
cnf(t5544,plain,
midp(sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t16493]) ).
cnf(t14923,plain,
true = ifeq(true,true,midp(sk20,X1,X1),true),
inference(cp,[status(thm)],[t14920,t5544]) ).
cnf(t17496,plain,
true = midp(sk20,X1,X1),
inference(step,[status(thm)],[t14923,t256]) ).
cnf(t14966,plain,
midp(sk20,X1,X1) = true,
inference(orient,[status(thm)],[t17496]) ).
cnf(t16165,plain,
true = ifeq(true,true,midp(sk20,X1,X2),true),
inference(cp,[status(thm)],[t16162,t14966]) ).
cnf(t17620,plain,
true = midp(sk20,X1,X2),
inference(step,[status(thm)],[t16165,t256]) ).
cnf(t16184,plain,
midp(sk20,X1,X2) = true,
inference(orient,[status(thm)],[t17620]) ).
cnf(t16185,plain,
true = ifeq(true,true,cong(sk20,X1,sk20,X2),true),
inference(cp,[status(thm)],[t336,t16184]) ).
cnf(t17625,plain,
true = cong(sk20,X1,sk20,X2),
inference(step,[status(thm)],[t16185,t256]) ).
cnf(t16233,plain,
cong(sk20,X1,sk20,X2) = true,
inference(orient,[status(thm)],[t17625]) ).
cnf(t16251,plain,
true = ifeq(true,true,ifeq(cong(sk20,X1,sk20,X2),true,ifeq(cong(sk20,X1,sk20,X3),true,cyclic(X1,X4,X2,X3),true),true),true),
inference(cp,[status(thm)],[t273,t16233]) ).
cnf(t17634,plain,
true = ifeq(cong(sk20,X1,sk20,X2),true,ifeq(cong(sk20,X1,sk20,X3),true,cyclic(X1,X4,X2,X3),true),true),
inference(step,[status(thm)],[t16251,t256]) ).
cnf(t17635,plain,
true = ifeq(true,true,ifeq(cong(sk20,X1,sk20,X3),true,cyclic(X1,X4,X2,X3),true),true),
inference(step,[status(thm)],[t17634,t16233]) ).
cnf(t17636,plain,
true = ifeq(cong(sk20,X1,sk20,X3),true,cyclic(X1,X4,X2,X3),true),
inference(step,[status(thm)],[t17635,t256]) ).
cnf(t17637,plain,
true = ifeq(true,true,cyclic(X1,X4,X2,X3),true),
inference(step,[status(thm)],[t17636,t16233]) ).
cnf(t17638,plain,
true = cyclic(X1,X4,X2,X3),
inference(step,[status(thm)],[t17637,t256]) ).
cnf(t16392,plain,
cyclic(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t17638]) ).
cnf(c120,plain,
~ cyclic(sk27,sk21,sk22,sk26),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
cyclic(sk27,sk21,sk22,sk26) != true,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t16392]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO569+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.58 % Computer : n014.cluster.edu
% 0.09/0.58 % Model : x86_64 x86_64
% 0.09/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.58 % Memory : 8046.5625MB
% 0.09/0.58 % OS : Linux 6.8.0-71-generic
% 0.09/0.58 % CPULimit : 300
% 0.09/0.58 % WCLimit : 300
% 0.09/0.58 % DateTime : Wed Sep 23 12:25:20 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.58 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 131.94/17.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 131.94/17.46 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------