%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO556+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 01:18:09 PM UTC 2026
% Result : Theorem 276.59s 36.16s
% Output : Proof 276.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 75
% Number of leaves : 31
% Syntax : Number of formulae : 352 ( 232 unt; 0 def)
% Number of atoms : 592 ( 224 equ)
% Maximal formula atoms : 16 ( 1 avg)
% Number of connectives : 381 ( 141 ~; 135 |; 74 &)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 13 ( 13 usr; 12 con; 0-4 aty)
% Number of variables : 1231 ( 88 sgn 517 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f74,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( perp(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> perp(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD74) ).
fof(f74_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( perp(A,B,C,D)
| ~ perp(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f74]) ).
fof(f74_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( perp(A,B,C,D)
| ~ perp(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f74_nnf]) ).
cnf(c74,plain,
( perp(X0,X1,X2,X3)
| ~ perp(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f74_sk]) ).
cnf(t213,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(perp(X5,X6,X7,X8),true,perp(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c74]) ).
cnf(t283,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(perp(X5,X6,X7,X8),true,perp(X1,X2,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t213]) ).
fof(f6,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('/export/starexec/sandbox/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]) ).
fof(f94,conjecture,
! [A,B,O,M,P,Q,D,C,T,K,S] :
( ( coll(S,P,K)
& coll(S,Q,T)
& coll(K,B,O)
& perp(K,P,B,O)
& coll(T,A,O)
& perp(T,Q,A,O)
& coll(C,B,O)
& perp(C,A,B,O)
& coll(D,A,O)
& perp(D,B,A,O)
& coll(Q,B,O)
& perp(Q,M,B,O)
& coll(P,A,O)
& perp(P,M,A,O)
& coll(M,A,B) )
=> perp(O,S,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL012016) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,O,M,P,Q,D,C,T,K,S] :
( ( coll(S,P,K)
& coll(S,Q,T)
& coll(K,B,O)
& perp(K,P,B,O)
& coll(T,A,O)
& perp(T,Q,A,O)
& coll(C,B,O)
& perp(C,A,B,O)
& coll(D,A,O)
& perp(D,B,A,O)
& coll(Q,B,O)
& perp(Q,M,B,O)
& coll(P,A,O)
& perp(P,M,A,O)
& coll(M,A,B) )
=> perp(O,S,P,Q) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,O,M,P,Q,D,C,T,K,S] :
( ~ perp(O,S,P,Q)
& coll(S,P,K)
& coll(S,Q,T)
& coll(K,B,O)
& perp(K,P,B,O)
& coll(T,A,O)
& perp(T,Q,A,O)
& coll(C,B,O)
& perp(C,A,B,O)
& coll(D,A,O)
& perp(D,B,A,O)
& coll(Q,B,O)
& perp(Q,M,B,O)
& coll(P,A,O)
& perp(P,M,A,O)
& coll(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ perp(sk22,sk30,sk24,sk25)
& coll(sk30,sk24,sk29)
& coll(sk30,sk25,sk28)
& coll(sk29,sk21,sk22)
& perp(sk29,sk24,sk21,sk22)
& coll(sk28,sk20,sk22)
& perp(sk28,sk25,sk20,sk22)
& coll(sk27,sk21,sk22)
& perp(sk27,sk20,sk21,sk22)
& coll(sk26,sk20,sk22)
& perp(sk26,sk21,sk20,sk22)
& coll(sk25,sk21,sk22)
& perp(sk25,sk23,sk21,sk22)
& coll(sk24,sk20,sk22)
& perp(sk24,sk23,sk20,sk22)
& coll(sk23,sk20,sk21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29,sk30])],[f94_nnf]) ).
cnf(c124,plain,
perp(sk29,sk24,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi124,negated_conjecture,
perp(sk29,sk24,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c124]) ).
cnf(h29,plain,
perp(sk29,sk24,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi124]) ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD8) ).
fof(f7_nnf,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t79,plain,
perp(sk22,sk21,sk29,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi7,h29]) ).
cnf(t1345,plain,
perp(sk22,sk21,sk29,sk24) = true,
inference(orient,[status(thm)],[t79]) ).
cnf(t1356,plain,
true = ifeq(eqangle(X1,X2,X3,X4,sk22,sk21,sk29,sk24),true,ifeq(true,true,perp(X1,X2,X3,X4),true),true),
inference(cp,[status(thm)],[t283,t1345]) ).
cnf(t50,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t50]) ).
cnf(t51349,plain,
true = ifeq(eqangle(X1,X2,X3,X4,sk22,sk21,sk29,sk24),true,perp(X1,X2,X3,X4),true),
inference(step,[status(thm)],[t1356,t256]) ).
cnf(t43165,plain,
ifeq(eqangle(X1,X2,X3,X4,sk22,sk21,sk29,sk24),true,perp(X1,X2,X3,X4),true) = true,
inference(orient,[status(thm)],[t51349]) ).
fof(f19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(P,Q,U,V,A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD20) ).
fof(f19_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t186,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)],[t186]) ).
fof(f20,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(A,B,P,Q,C,D,U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD21) ).
fof(f20_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,P,Q,C,D,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,P,Q,C,D,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t183,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)],[t183]) ).
fof(f39,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD40) ).
fof(f39_nnf,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(t166,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(t312,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(orient,[status(thm)],[t166]) ).
fof(f8,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD9) ).
fof(f8_nnf,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t193,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)],[t193]) ).
cnf(t157,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)],[t157]) ).
fof(f56,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD56) ).
fof(f56_nnf,plain,
! [A,B,P,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [A,P,B,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c56,plain,
( perp(X0,X1,X2,X3)
| ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(t180,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(t326,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)],[t180]) ).
fof(f68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD68) ).
fof(f68_nnf,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f68]) ).
fof(f68_sk,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(skolemisation,[status(esa)],[f68_nnf]) ).
cnf(c68,plain,
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f68_sk]) ).
cnf(t145,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)],[t145]) ).
fof(f64,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD64) ).
fof(f64_nnf,plain,
! [A,B,C,D,M] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f64]) ).
fof(f64_sk,plain,
! [M,A,B,C,D] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f64_nnf]) ).
cnf(c64,plain,
( midp(X4,X2,X3)
| ~ para(X0,X3,X1,X2)
| ~ para(X0,X2,X1,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(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/sandbox/benchmark/theBenchmark.p',ruleD39) ).
fof(f38_nnf,plain,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
| ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [A,B,P,Q,C,D] :
( para(A,B,C,D)
| ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c38,plain,
( para(X0,X1,X2,X3)
| ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(t165,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)],[t165]) ).
fof(f18,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(C,D,A,B,U,V,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD19) ).
fof(f18_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t185,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)],[t185]) ).
fof(f3,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD4) ).
fof(f3_nnf,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t154,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t316,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t154]) ).
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/sandbox/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(t212,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(t287,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)],[t212]) ).
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/sandbox/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(t184,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X2,X1,X3,X4,X5,X6,X7,X8),true) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t292,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X2,X1,X3,X4,X5,X6,X7,X8),true) = true,
inference(orient,[status(thm)],[t184]) ).
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(h3,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(c122,plain,
perp(sk28,sk25,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi122,negated_conjecture,
perp(sk28,sk25,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c122]) ).
cnf(h47,plain,
para(sk28,sk25,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi122,h3]) ).
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(h173,plain,
eqangle(sk28,sk25,V0,V1,sk24,sk23,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h47]) ).
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(h488,plain,
eqangle(sk25,sk28,V0,V1,sk24,sk23,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi17,h173]) ).
cnf(h50,plain,
para(sk20,sk22,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi8,h3,hi114]) ).
cnf(h183,plain,
eqangle(sk20,sk22,V0,V1,sk20,sk22,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h50]) ).
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(h534,plain,
eqangle(sk20,sk22,sk20,sk22,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h183]) ).
fof(f21,axiom,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( ( eqangle(P,Q,U,V,E,F,G,H)
& eqangle(A,B,C,D,P,Q,U,V) )
=> eqangle(A,B,C,D,E,F,G,H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD22) ).
fof(f21_nnf,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi21,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,ifeq(eqangle(X4,X5,X6,X7,X8,X9,X10,X11),true,eqangle(X0,X1,X2,X3,X8,X9,X10,X11),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t94,plain,
eqangle(sk20,sk22,sk20,sk22,sk24,sk23,sk25,sk28) = true,
inference(hyper_resolution,[status(thm)],[hi21,h534,h488]) ).
cnf(t1883,plain,
eqangle(sk20,sk22,sk20,sk22,sk24,sk23,sk25,sk28) = true,
inference(orient,[status(thm)],[t94]) ).
cnf(t1886,plain,
true = ifeq(true,true,eqangle(sk22,sk20,sk20,sk22,sk24,sk23,sk25,sk28),true),
inference(cp,[status(thm)],[t292,t1883]) ).
cnf(t47966,plain,
true = eqangle(sk22,sk20,sk20,sk22,sk24,sk23,sk25,sk28),
inference(step,[status(thm)],[t1886,t256]) ).
cnf(t7925,plain,
eqangle(sk22,sk20,sk20,sk22,sk24,sk23,sk25,sk28) = true,
inference(orient,[status(thm)],[t47966]) ).
cnf(t7932,plain,
true = ifeq(true,true,ifeq(para(sk24,sk23,sk25,sk28),true,para(sk22,sk20,sk20,sk22),true),true),
inference(cp,[status(thm)],[t287,t7925]) ).
cnf(t47967,plain,
true = ifeq(para(sk24,sk23,sk25,sk28),true,para(sk22,sk20,sk20,sk22),true),
inference(step,[status(thm)],[t7932,t256]) ).
cnf(h23,plain,
perp(sk20,sk22,sk28,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi122]) ).
cnf(h115,plain,
para(sk24,sk23,sk28,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi114,h23]) ).
cnf(hi3,axiom,
ifeq(para(X0,X1,X2,X3),true,para(X0,X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t55,plain,
para(sk24,sk23,sk25,sk28) = true,
inference(hyper_resolution,[status(thm)],[hi3,h115]) ).
cnf(t2084,plain,
para(sk24,sk23,sk25,sk28) = true,
inference(orient,[status(thm)],[t55]) ).
cnf(t47968,plain,
true = ifeq(true,true,para(sk22,sk20,sk20,sk22),true),
inference(step,[status(thm)],[t47967,t2084]) ).
cnf(t47969,plain,
true = para(sk22,sk20,sk20,sk22),
inference(step,[status(thm)],[t47968,t256]) ).
cnf(t7937,plain,
para(sk22,sk20,sk20,sk22) = true,
inference(orient,[status(thm)],[t47969]) ).
cnf(t7938,plain,
true = ifeq(true,true,para(sk22,sk20,sk22,sk20),true),
inference(cp,[status(thm)],[t316,t7937]) ).
cnf(t47970,plain,
true = para(sk22,sk20,sk22,sk20),
inference(step,[status(thm)],[t7938,t256]) ).
cnf(t7962,plain,
para(sk22,sk20,sk22,sk20) = true,
inference(orient,[status(thm)],[t47970]) ).
cnf(t7964,plain,
true = ifeq(true,true,eqangle(sk22,sk20,X1,X2,sk22,sk20,X1,X2),true),
inference(cp,[status(thm)],[t312,t7962]) ).
cnf(t48604,plain,
true = eqangle(sk22,sk20,X1,X2,sk22,sk20,X1,X2),
inference(step,[status(thm)],[t7964,t256]) ).
cnf(t17613,plain,
eqangle(sk22,sk20,X1,X2,sk22,sk20,X1,X2) = true,
inference(orient,[status(thm)],[t48604]) ).
cnf(t17618,plain,
true = ifeq(true,true,eqangle(X1,X2,sk22,sk20,X1,X2,sk22,sk20),true),
inference(cp,[status(thm)],[t290,t17613]) ).
cnf(t49252,plain,
true = eqangle(X1,X2,sk22,sk20,X1,X2,sk22,sk20),
inference(step,[status(thm)],[t17618,t256]) ).
cnf(t24326,plain,
eqangle(X1,X2,sk22,sk20,X1,X2,sk22,sk20) = true,
inference(orient,[status(thm)],[t49252]) ).
cnf(t24328,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t296,t24326]) ).
cnf(t49253,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t24328,t256]) ).
cnf(t24350,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t49253]) ).
cnf(t24366,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,t24350]) ).
cnf(t51560,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)],[t24366,t256]) ).
cnf(t51561,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t51560,t24350]) ).
cnf(t51562,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t51561,t256]) ).
cnf(t45009,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t51562]) ).
fof(f67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD67) ).
fof(f67_nnf,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f67]) ).
fof(f67_sk,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f67_nnf]) ).
cnf(c67,plain,
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f67_sk]) ).
cnf(t171,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(t327,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)],[t171]) ).
fof(f22,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD23) ).
fof(f22_nnf,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( cong(X0,X1,X3,X2)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t149,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t323,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t149]) ).
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/sandbox/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(t214,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)],[t214]) ).
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/sandbox/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(t190,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,eqratio(X5,X6,X7,X8,X1,X2,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(t370,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,eqratio(X5,X6,X7,X8,X1,X2,X3,X4),true) = true,
inference(orient,[status(thm)],[t190]) ).
fof(f0,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox/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(c117,plain,
coll(sk25,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
coll(sk25,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h12,plain,
coll(sk25,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi117]) ).
cnf(c116,plain,
perp(sk25,sk23,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
perp(sk25,sk23,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h9,plain,
perp(sk25,sk23,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi116]) ).
cnf(h8,plain,
perp(sk21,sk22,sk25,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi116]) ).
cnf(h63,plain,
para(sk21,sk22,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi8,h8,h9]) ).
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/sandbox/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(h245,plain,
eqratio(sk25,sk21,sk21,sk22,sk25,sk22,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi65,h63,hi117,h12]) ).
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/sandbox/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(hi28,axiom,
ifeq(eqratio(X0,X1,X2,X3,X4,X5,X6,X7),true,eqratio(X0,X1,X4,X5,X2,X3,X6,X7),true) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(t121,plain,
eqratio(sk25,sk21,sk25,sk22,sk21,sk22,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi28,h245]) ).
cnf(t3007,plain,
eqratio(sk25,sk21,sk25,sk22,sk21,sk22,sk22,sk21) = true,
inference(orient,[status(thm)],[t121]) ).
cnf(t3014,plain,
true = ifeq(true,true,eqratio(sk21,sk22,sk22,sk21,sk25,sk21,sk25,sk22),true),
inference(cp,[status(thm)],[t370,t3007]) ).
cnf(t48220,plain,
true = eqratio(sk21,sk22,sk22,sk21,sk25,sk21,sk25,sk22),
inference(step,[status(thm)],[t3014,t256]) ).
cnf(t12008,plain,
eqratio(sk21,sk22,sk22,sk21,sk25,sk21,sk25,sk22) = true,
inference(orient,[status(thm)],[t48220]) ).
cnf(t12016,plain,
true = ifeq(true,true,ifeq(cong(sk25,sk21,sk25,sk22),true,cong(sk21,sk22,sk22,sk21),true),true),
inference(cp,[status(thm)],[t366,t12008]) ).
cnf(t48221,plain,
true = ifeq(cong(sk25,sk21,sk25,sk22),true,cong(sk21,sk22,sk22,sk21),true),
inference(step,[status(thm)],[t12016,t256]) ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD24) ).
fof(f23_nnf,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( cong(X2,X3,X0,X1)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(t150,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t321,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t150]) ).
cnf(t187,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)],[t187]) ).
fof(f2,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD3) ).
fof(f2_nnf,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(coll(X0,X1,X2),true,ifeq(coll(X0,X1,X3),true,coll(X2,X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(c113,plain,
coll(sk23,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
coll(sk23,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h0,plain,
coll(sk21,sk21,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi113,hi113]) ).
cnf(h40,plain,
coll(sk21,sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0]) ).
cnf(h154,plain,
coll(sk21,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h40,h40]) ).
cnf(h71,plain,
coll(sk21,sk21,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h12,h12]) ).
cnf(h413,plain,
coll(sk25,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h71,h154]) ).
cnf(h10,plain,
coll(sk22,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi117,hi117]) ).
cnf(h68,plain,
coll(sk22,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi0,h10]) ).
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD2) ).
fof(f1_nnf,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(coll(X0,X1,X2),true,coll(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h251,plain,
coll(sk25,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi1,h68]) ).
cnf(h64,plain,
perp(sk22,sk21,sk25,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi7,h9]) ).
cnf(h248,plain,
para(sk22,sk21,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi8,h64,h9]) ).
cnf(t124,plain,
eqratio(sk25,sk22,sk22,sk22,sk25,sk21,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi65,h248,h251,h413]) ).
cnf(t2949,plain,
eqratio(sk25,sk22,sk22,sk22,sk25,sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t124]) ).
cnf(t2950,plain,
true = ifeq(true,true,eqratio(sk25,sk22,sk25,sk21,sk22,sk22,sk21,sk21),true),
inference(cp,[status(thm)],[t376,t2949]) ).
cnf(t48183,plain,
true = eqratio(sk25,sk22,sk25,sk21,sk22,sk22,sk21,sk21),
inference(step,[status(thm)],[t2950,t256]) ).
cnf(t11516,plain,
eqratio(sk25,sk22,sk25,sk21,sk22,sk22,sk21,sk21) = true,
inference(orient,[status(thm)],[t48183]) ).
cnf(t11526,plain,
true = ifeq(true,true,ifeq(cong(sk22,sk22,sk21,sk21),true,cong(sk25,sk22,sk25,sk21),true),true),
inference(cp,[status(thm)],[t366,t11516]) ).
cnf(t48184,plain,
true = ifeq(cong(sk22,sk22,sk21,sk21),true,cong(sk25,sk22,sk25,sk21),true),
inference(step,[status(thm)],[t11526,t256]) ).
cnf(h61,plain,
para(sk21,sk22,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi8,h8,hi116]) ).
cnf(h222,plain,
eqangle(sk21,sk22,V0,V1,sk21,sk22,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h61]) ).
cnf(h841,plain,
eqangle(sk21,sk22,sk21,sk22,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h222]) ).
cnf(h11,plain,
coll(sk21,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi117]) ).
cnf(h69,plain,
coll(sk22,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h11,h11]) ).
cnf(h252,plain,
coll(sk21,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h69,h69]) ).
fof(f42,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD42b) ).
fof(f42_nnf,plain,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [P,A,B,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c42,plain,
( cyclic(X0,X1,X2,X3)
| ~ coll(X2,X3,X1)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi42,axiom,
ifeq(eqangle(X0,X1,X0,X2,X3,X1,X3,X2),true,ifeq(coll(X0,X3,X2),true,cyclic(X1,X2,X0,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c42]) ).
cnf(h833,plain,
cyclic(sk22,sk22,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi42,h222,h252]) ).
fof(f43,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD43) ).
fof(f43_nnf,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c43,plain,
( cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(hi43,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,ifeq(cyclic(X0,X1,X2,X4),true,ifeq(cyclic(X0,X1,X2,X5),true,ifeq(eqangle(X2,X0,X2,X1,X5,X3,X5,X4),true,cong(X0,X1,X3,X4),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(t32,plain,
cong(sk22,sk22,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi43,h833,h833,h833,h841]) ).
cnf(t2573,plain,
cong(sk22,sk22,sk21,sk21) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(t48185,plain,
true = ifeq(true,true,cong(sk25,sk22,sk25,sk21),true),
inference(step,[status(thm)],[t48184,t2573]) ).
cnf(t48186,plain,
true = cong(sk25,sk22,sk25,sk21),
inference(step,[status(thm)],[t48185,t256]) ).
cnf(t11527,plain,
cong(sk25,sk22,sk25,sk21) = true,
inference(orient,[status(thm)],[t48186]) ).
cnf(t11532,plain,
true = ifeq(true,true,cong(sk25,sk21,sk25,sk22),true),
inference(cp,[status(thm)],[t321,t11527]) ).
cnf(t48192,plain,
true = cong(sk25,sk21,sk25,sk22),
inference(step,[status(thm)],[t11532,t256]) ).
cnf(t11634,plain,
cong(sk25,sk21,sk25,sk22) = true,
inference(orient,[status(thm)],[t48192]) ).
cnf(t48222,plain,
true = ifeq(true,true,cong(sk21,sk22,sk22,sk21),true),
inference(step,[status(thm)],[t48221,t11634]) ).
cnf(t48223,plain,
true = cong(sk21,sk22,sk22,sk21),
inference(step,[status(thm)],[t48222,t256]) ).
cnf(t12017,plain,
cong(sk21,sk22,sk22,sk21) = true,
inference(orient,[status(thm)],[t48223]) ).
cnf(t12019,plain,
true = ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),
inference(cp,[status(thm)],[t323,t12017]) ).
cnf(t48224,plain,
true = cong(sk21,sk22,sk21,sk22),
inference(step,[status(thm)],[t12019,t256]) ).
cnf(t12028,plain,
cong(sk21,sk22,sk21,sk22) = true,
inference(orient,[status(thm)],[t48224]) ).
cnf(t12037,plain,
true = ifeq(true,true,ifeq(coll(sk21,sk22,sk22),true,midp(sk21,sk22,sk22),true),true),
inference(cp,[status(thm)],[t327,t12028]) ).
cnf(t48225,plain,
true = ifeq(coll(sk21,sk22,sk22),true,midp(sk21,sk22,sk22),true),
inference(step,[status(thm)],[t12037,t256]) ).
fof(f66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD66) ).
fof(f66_nnf,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f66]) ).
fof(f66_sk,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f66_nnf]) ).
cnf(c66,plain,
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f66_sk]) ).
cnf(t146,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t319,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t146]) ).
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(h487,plain,
eqangle(V0,V1,sk28,sk25,V0,V1,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi18,h173]) ).
cnf(h246,plain,
eqangle(sk21,sk22,V0,V1,sk22,sk21,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h63]) ).
cnf(t102,plain,
eqangle(sk21,sk22,sk28,sk25,sk22,sk21,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi21,h246,h487]) ).
cnf(t1987,plain,
eqangle(sk21,sk22,sk28,sk25,sk22,sk21,sk24,sk23) = true,
inference(orient,[status(thm)],[t102]) ).
cnf(t1988,plain,
true = ifeq(true,true,eqangle(sk21,sk22,sk22,sk21,sk28,sk25,sk24,sk23),true),
inference(cp,[status(thm)],[t294,t1987]) ).
cnf(t47998,plain,
true = eqangle(sk21,sk22,sk22,sk21,sk28,sk25,sk24,sk23),
inference(step,[status(thm)],[t1988,t256]) ).
cnf(t8400,plain,
eqangle(sk21,sk22,sk22,sk21,sk28,sk25,sk24,sk23) = true,
inference(orient,[status(thm)],[t47998]) ).
cnf(t8407,plain,
true = ifeq(true,true,ifeq(para(sk28,sk25,sk24,sk23),true,para(sk21,sk22,sk22,sk21),true),true),
inference(cp,[status(thm)],[t287,t8400]) ).
cnf(t47999,plain,
true = ifeq(para(sk28,sk25,sk24,sk23),true,para(sk21,sk22,sk22,sk21),true),
inference(step,[status(thm)],[t8407,t256]) ).
cnf(t65,plain,
para(sk28,sk25,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi122,h3]) ).
cnf(t2424,plain,
para(sk28,sk25,sk24,sk23) = true,
inference(orient,[status(thm)],[t65]) ).
cnf(t48000,plain,
true = ifeq(true,true,para(sk21,sk22,sk22,sk21),true),
inference(step,[status(thm)],[t47999,t2424]) ).
cnf(t48001,plain,
true = para(sk21,sk22,sk22,sk21),
inference(step,[status(thm)],[t48000,t256]) ).
cnf(t8412,plain,
para(sk21,sk22,sk22,sk21) = true,
inference(orient,[status(thm)],[t48001]) ).
cnf(t8413,plain,
true = ifeq(true,true,para(sk21,sk22,sk21,sk22),true),
inference(cp,[status(thm)],[t316,t8412]) ).
cnf(t48002,plain,
true = para(sk21,sk22,sk21,sk22),
inference(step,[status(thm)],[t8413,t256]) ).
cnf(t8437,plain,
para(sk21,sk22,sk21,sk22) = true,
inference(orient,[status(thm)],[t48002]) ).
cnf(t8438,plain,
true = ifeq(true,true,coll(sk21,sk22,sk22),true),
inference(cp,[status(thm)],[t319,t8437]) ).
cnf(t48003,plain,
true = coll(sk21,sk22,sk22),
inference(step,[status(thm)],[t8438,t256]) ).
cnf(t8461,plain,
coll(sk21,sk22,sk22) = true,
inference(orient,[status(thm)],[t48003]) ).
cnf(t48226,plain,
true = ifeq(true,true,midp(sk21,sk22,sk22),true),
inference(step,[status(thm)],[t48225,t8461]) ).
cnf(t48227,plain,
true = midp(sk21,sk22,sk22),
inference(step,[status(thm)],[t48226,t256]) ).
cnf(t12067,plain,
midp(sk21,sk22,sk22) = true,
inference(orient,[status(thm)],[t48227]) ).
cnf(t45010,plain,
true = ifeq(true,true,midp(sk21,X1,X1),true),
inference(cp,[status(thm)],[t45009,t12067]) ).
cnf(t51563,plain,
true = midp(sk21,X1,X1),
inference(step,[status(thm)],[t45010,t256]) ).
cnf(t45015,plain,
midp(sk21,X1,X1) = true,
inference(orient,[status(thm)],[t51563]) ).
cnf(t45016,plain,
true = ifeq(true,true,cong(sk21,X1,sk21,X1),true),
inference(cp,[status(thm)],[t363,t45015]) ).
cnf(t51567,plain,
true = cong(sk21,X1,sk21,X1),
inference(step,[status(thm)],[t45016,t256]) ).
cnf(t45099,plain,
cong(sk21,X1,sk21,X1) = true,
inference(orient,[status(thm)],[t51567]) ).
cnf(t45110,plain,
true = ifeq(true,true,ifeq(cong(sk21,X1,sk21,X1),true,perp(sk21,sk21,X2,X1),true),true),
inference(cp,[status(thm)],[t326,t45099]) ).
cnf(t51572,plain,
true = ifeq(cong(sk21,X1,sk21,X1),true,perp(sk21,sk21,X2,X1),true),
inference(step,[status(thm)],[t45110,t256]) ).
cnf(t51573,plain,
true = ifeq(true,true,perp(sk21,sk21,X2,X1),true),
inference(step,[status(thm)],[t51572,t45099]) ).
cnf(t51574,plain,
true = perp(sk21,sk21,X2,X1),
inference(step,[status(thm)],[t51573,t256]) ).
cnf(t45247,plain,
perp(sk21,sk21,X1,X2) = true,
inference(orient,[status(thm)],[t51574]) ).
cnf(t45256,plain,
true = ifeq(true,true,perp(X1,X2,sk21,sk21),true),
inference(cp,[status(thm)],[t274,t45247]) ).
cnf(t51592,plain,
true = perp(X1,X2,sk21,sk21),
inference(step,[status(thm)],[t45256,t256]) ).
cnf(t45559,plain,
perp(X1,X2,sk21,sk21) = true,
inference(orient,[status(thm)],[t51592]) ).
cnf(t45579,plain,
true = ifeq(true,true,ifeq(perp(sk21,sk21,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t45559]) ).
cnf(t51623,plain,
true = ifeq(perp(sk21,sk21,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t45579,t256]) ).
cnf(t51624,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t51623,t45247]) ).
cnf(t51625,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t51624,t256]) ).
cnf(t46122,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t51625]) ).
cnf(t51642,plain,
ifeq(true,true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(step,[status(thm)],[t312,t46122]) ).
cnf(t51643,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(step,[status(thm)],[t51642,t256]) ).
cnf(t46135,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(rw,[status(thm)],[t51643]) ).
cnf(t47109,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4) = true,
inference(orient,[status(thm)],[t46135]) ).
cnf(t47112,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true),
inference(cp,[status(thm)],[t294,t47109]) ).
cnf(t51760,plain,
true = eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(step,[status(thm)],[t47112,t256]) ).
cnf(t47262,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6) = true,
inference(orient,[status(thm)],[t51760]) ).
cnf(t47264,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,X3,X4,X5,X6),true),
inference(cp,[status(thm)],[t288,t47262]) ).
cnf(t51786,plain,
true = eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(step,[status(thm)],[t47264,t256]) ).
cnf(t47656,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6) = true,
inference(orient,[status(thm)],[t51786]) ).
cnf(t47657,plain,
true = ifeq(true,true,perp(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t43165,t47656]) ).
cnf(t51787,plain,
true = perp(X1,X2,X1,X2),
inference(step,[status(thm)],[t47657,t256]) ).
cnf(t47671,plain,
perp(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t51787]) ).
cnf(t47678,plain,
true = ifeq(eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true,ifeq(true,true,perp(X1,X2,X3,X4),true),true),
inference(cp,[status(thm)],[t283,t47671]) ).
cnf(t51789,plain,
true = ifeq(true,true,ifeq(true,true,perp(X1,X2,X3,X4),true),true),
inference(step,[status(thm)],[t47678,t47262]) ).
cnf(t51790,plain,
true = ifeq(true,true,perp(X1,X2,X3,X4),true),
inference(step,[status(thm)],[t51789,t256]) ).
cnf(t51791,plain,
true = perp(X1,X2,X3,X4),
inference(step,[status(thm)],[t51790,t256]) ).
cnf(t47720,plain,
perp(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t51791]) ).
cnf(c128,plain,
~ perp(sk22,sk30,sk24,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
perp(sk22,sk30,sk24,sk25) != true,
inference(equality_encoding,[status(esa)],[c128]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t47720]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO556+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 12:23:34 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 276.59/36.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 276.59/36.16 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------