%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO558+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 : n013.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 149.14s 19.35s
% Output : Proof 149.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 72
% Number of leaves : 28
% Syntax : Number of formulae : 296 ( 188 unt; 0 def)
% Number of atoms : 501 ( 182 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 334 ( 129 ~; 123 |; 54 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-8 aty)
% Number of functors : 17 ( 17 usr; 13 con; 0-4 aty)
% Number of variables : 1065 ( 88 sgn 432 !; 18 ?)
% 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(t205,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)],[t205]) ).
fof(f86,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleX11) ).
fof(f86_nnf,plain,
! [A,B,C,O] :
? [P] :
( perp(P,A,A,O)
| ~ circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f86]) ).
fof(f86_sk,plain,
! [O,A,B,C] :
( perp(sk11(A,B,C,O),A,A,O)
| ~ circle(O,A,B,C) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f86_nnf]) ).
cnf(c99,plain,
( perp(sk11(X0,X1,X2,X3),X0,X0,X3)
| ~ circle(X3,X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f86_sk]) ).
cnf(hi99,axiom,
ifeq(circle(X0,X1,X2,X3),true,perp(sk11(X1,X2,X3,X0),X1,X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c99]) ).
fof(f94,conjecture,
! [A,C,K,O,N,B,G,O1,M,NWPNT1,NWPNT2,NWPNT3] :
( ( circle(O1,K,M,NWPNT3)
& circle(G,A,M,NWPNT2)
& circle(O1,K,N,B)
& circle(G,A,C,B)
& coll(B,C,N)
& coll(B,A,K)
& circle(O,A,N,NWPNT1)
& circle(O,A,C,K) )
=> perp(B,M,M,O) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL012018) ).
fof(f94_neg,negated_conjecture,
~ ! [A,C,K,O,N,B,G,O1,M,NWPNT1,NWPNT2,NWPNT3] :
( ( circle(O1,K,M,NWPNT3)
& circle(G,A,M,NWPNT2)
& circle(O1,K,N,B)
& circle(G,A,C,B)
& coll(B,C,N)
& coll(B,A,K)
& circle(O,A,N,NWPNT1)
& circle(O,A,C,K) )
=> perp(B,M,M,O) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,C,K,O,N,B,G,O1,M,NWPNT1,NWPNT2,NWPNT3] :
( ~ perp(B,M,M,O)
& circle(O1,K,M,NWPNT3)
& circle(G,A,M,NWPNT2)
& circle(O1,K,N,B)
& circle(G,A,C,B)
& coll(B,C,N)
& coll(B,A,K)
& circle(O,A,N,NWPNT1)
& circle(O,A,C,K) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ perp(sk25,sk28,sk28,sk23)
& circle(sk27,sk22,sk28,sk31)
& circle(sk26,sk20,sk28,sk30)
& circle(sk27,sk22,sk24,sk25)
& circle(sk26,sk20,sk21,sk25)
& coll(sk25,sk21,sk24)
& coll(sk25,sk20,sk22)
& circle(sk23,sk20,sk24,sk29)
& 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(c117,plain,
circle(sk26,sk20,sk21,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
circle(sk26,sk20,sk21,sk25) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h8,plain,
perp(sk11(sk20,sk21,sk25,sk26),sk20,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi99,hi117]) ).
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(h28,plain,
perp(sk20,sk26,sk11(sk20,sk21,sk25,sk26),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi7,h8]) ).
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]) ).
cnf(h69,plain,
perp(sk20,sk26,sk20,sk11(sk20,sk21,sk25,sk26)) = true,
inference(hyper_resolution,[status(thm)],[hi6,h28]) ).
fof(f85,axiom,
! [A,B,C,H] :
? [P,Q] :
( ( perp(B,H,A,C)
& perp(A,H,B,C) )
=> ( perp(B,Q,C,A)
& coll(Q,C,A)
& perp(A,P,C,B)
& coll(P,C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleX10) ).
fof(f85_nnf,plain,
! [A,B,C,H] :
? [P,Q] :
( ( perp(B,Q,C,A)
& coll(Q,C,A)
& perp(A,P,C,B)
& coll(P,C,B) )
| ~ perp(B,H,A,C)
| ~ perp(A,H,B,C) ),
inference(nnf_transformation,[status(thm)],[f85]) ).
fof(f85_sk,plain,
! [A,H,B,C] :
( ( perp(B,sk10(A,B,C,H),C,A)
& coll(sk10(A,B,C,H),C,A)
& perp(A,sk9(A,B,C,H),C,B)
& coll(sk9(A,B,C,H),C,B) )
| ~ perp(B,H,A,C)
| ~ perp(A,H,B,C) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9,sk10])],[f85_nnf]) ).
cnf(c96,plain,
( perp(X0,sk9(X0,X1,X2,X3),X2,X1)
| ~ perp(X1,X3,X0,X2)
| ~ perp(X0,X3,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f85_sk]) ).
cnf(hi96,axiom,
ifeq(perp(X0,X1,X2,X3),true,ifeq(perp(X2,X1,X0,X3),true,perp(X0,sk9(X0,X2,X3,X1),X3,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c96]) ).
cnf(h161,plain,
perp(sk20,sk9(sk20,sk20,sk11(sk20,sk21,sk25,sk26),sk26),sk11(sk20,sk21,sk25,sk26),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi96,h69,h69]) ).
cnf(h505,plain,
perp(sk11(sk20,sk21,sk25,sk26),sk20,sk20,sk9(sk20,sk20,sk11(sk20,sk21,sk25,sk26),sk26)) = true,
inference(hyper_resolution,[status(thm)],[hi7,h161]) ).
cnf(c119,plain,
circle(sk26,sk20,sk28,sk30),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi119,negated_conjecture,
circle(sk26,sk20,sk28,sk30) = true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(h10,plain,
perp(sk11(sk20,sk28,sk30,sk26),sk20,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi99,hi119]) ).
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(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(h66,plain,
para(sk11(sk20,sk28,sk30,sk26),sk20,sk11(sk20,sk21,sk25,sk26),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,h10,h28]) ).
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(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(h152,plain,
eqangle(sk11(sk20,sk28,sk30,sk26),sk20,V0,V1,sk11(sk20,sk21,sk25,sk26),sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h66]) ).
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(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(h435,plain,
eqangle(sk20,sk11(sk20,sk28,sk30,sk26),V0,V1,sk11(sk20,sk21,sk25,sk26),sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi17,h152]) ).
cnf(hi74,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,ifeq(perp(X4,X5,X6,X7),true,perp(X0,X1,X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c74]) ).
cnf(t141,plain,
perp(sk20,sk11(sk20,sk28,sk30,sk26),sk20,sk9(sk20,sk20,sk11(sk20,sk21,sk25,sk26),sk26)) = true,
inference(hyper_resolution,[status(thm)],[hi74,h435,h505]) ).
cnf(t1034,plain,
perp(sk20,sk11(sk20,sk28,sk30,sk26),sk20,sk9(sk20,sk20,sk11(sk20,sk21,sk25,sk26),sk26)) = true,
inference(orient,[status(thm)],[t141]) ).
cnf(t1045,plain,
true = ifeq(eqangle(X1,X2,X3,X4,sk20,sk11(sk20,sk28,sk30,sk26),sk20,sk9(sk20,sk20,sk11(sk20,sk21,sk25,sk26),sk26)),true,ifeq(true,true,perp(X1,X2,X3,X4),true),true),
inference(cp,[status(thm)],[t283,t1034]) ).
cnf(t40,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t40]) ).
cnf(t18574,plain,
true = ifeq(eqangle(X1,X2,X3,X4,sk20,sk11(sk20,sk28,sk30,sk26),sk20,sk9(sk20,sk20,sk11(sk20,sk21,sk25,sk26),sk26)),true,perp(X1,X2,X3,X4),true),
inference(step,[status(thm)],[t1045,t256]) ).
cnf(t14616,plain,
ifeq(eqangle(X1,X2,X3,X4,sk20,sk11(sk20,sk28,sk30,sk26),sk20,sk9(sk20,sk20,sk11(sk20,sk21,sk25,sk26),sk26)),true,perp(X1,X2,X3,X4),true) = true,
inference(orient,[status(thm)],[t18574]) ).
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(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(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)],[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/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(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(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)],[t167]) ).
cnf(t132,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)],[t132]) ).
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(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)],[t177]) ).
cnf(t85,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)],[t85]) ).
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(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/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(t70,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)],[t70]) ).
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(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(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)],[t222]) ).
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(t131,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)],[t131]) ).
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(t169,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)],[t169]) ).
fof(f46,axiom,
! [A,B,O] :
( cong(O,A,O,B)
=> eqangle(O,A,A,B,A,B,O,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD46) ).
fof(f46_nnf,plain,
! [A,B,O] :
( eqangle(O,A,A,B,A,B,O,B)
| ~ cong(O,A,O,B) ),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
! [O,A,B] :
( eqangle(O,A,A,B,A,B,O,B)
| ~ cong(O,A,O,B) ),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c46,plain,
( eqangle(X2,X0,X0,X1,X0,X1,X2,X1)
| ~ cong(X2,X0,X2,X1) ),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(t126,plain,
ifeq(cong(X1,X2,X1,X3),true,eqangle(X1,X2,X2,X3,X2,X3,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t322,plain,
ifeq(cong(X1,X2,X1,X3),true,eqangle(X1,X2,X2,X3,X2,X3,X1,X3),true) = true,
inference(orient,[status(thm)],[t126]) ).
cnf(c113,plain,
circle(sk23,sk20,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
circle(sk23,sk20,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h0,plain,
perp(sk11(sk20,sk21,sk22,sk23),sk20,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi99,hi113]) ).
cnf(h12,plain,
perp(sk20,sk23,sk11(sk20,sk21,sk22,sk23),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi7,h0]) ).
cnf(h38,plain,
para(sk11(sk20,sk21,sk22,sk23),sk20,sk11(sk20,sk21,sk22,sk23),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,h0,h12]) ).
cnf(h93,plain,
eqangle(sk11(sk20,sk21,sk22,sk23),sk20,V0,V1,sk11(sk20,sk21,sk22,sk23),sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h38]) ).
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(h257,plain,
eqangle(sk11(sk20,sk21,sk22,sk23),sk20,sk11(sk20,sk21,sk22,sk23),sk20,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h93]) ).
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(hi66,axiom,
ifeq(para(X0,X1,X0,X2),true,coll(X0,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(h92,plain,
coll(sk11(sk20,sk21,sk22,sk23),sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi66,h38]) ).
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(h1025,plain,
cyclic(sk20,sk20,sk11(sk20,sk21,sk22,sk23),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h257,h92]) ).
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(t28,plain,
cong(sk20,sk20,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi43,h1025,h1025,h1025,h257]) ).
cnf(t1771,plain,
cong(sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t28]) ).
cnf(t1774,plain,
true = ifeq(true,true,eqangle(sk20,sk20,sk20,sk20,sk20,sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t322,t1771]) ).
cnf(t17604,plain,
true = eqangle(sk20,sk20,sk20,sk20,sk20,sk20,sk20,sk20),
inference(step,[status(thm)],[t1774,t256]) ).
cnf(t4216,plain,
eqangle(sk20,sk20,sk20,sk20,sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t17604]) ).
cnf(t4218,plain,
true = ifeq(true,true,para(sk20,sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t296,t4216]) ).
cnf(t17605,plain,
true = para(sk20,sk20,sk20,sk20),
inference(step,[status(thm)],[t4218,t256]) ).
cnf(t4239,plain,
para(sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t17605]) ).
cnf(t4241,plain,
true = ifeq(true,true,eqangle(sk20,sk20,X1,X2,sk20,sk20,X1,X2),true),
inference(cp,[status(thm)],[t330,t4239]) ).
cnf(t17804,plain,
true = eqangle(sk20,sk20,X1,X2,sk20,sk20,X1,X2),
inference(step,[status(thm)],[t4241,t256]) ).
cnf(t7136,plain,
eqangle(sk20,sk20,X1,X2,sk20,sk20,X1,X2) = true,
inference(orient,[status(thm)],[t17804]) ).
cnf(t7140,plain,
true = ifeq(true,true,eqangle(X1,X2,sk20,sk20,X1,X2,sk20,sk20),true),
inference(cp,[status(thm)],[t290,t7136]) ).
cnf(t18071,plain,
true = eqangle(X1,X2,sk20,sk20,X1,X2,sk20,sk20),
inference(step,[status(thm)],[t7140,t256]) ).
cnf(t10342,plain,
eqangle(X1,X2,sk20,sk20,X1,X2,sk20,sk20) = true,
inference(orient,[status(thm)],[t18071]) ).
cnf(t10343,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t296,t10342]) ).
cnf(t18072,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t10343,t256]) ).
cnf(t10365,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t18072]) ).
cnf(t10381,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,t10365]) ).
cnf(t18795,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)],[t10381,t256]) ).
cnf(t18796,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t18795,t10365]) ).
cnf(t18797,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t18796,t256]) ).
cnf(t16429,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t18797]) ).
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(t154,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)],[t154]) ).
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(t206,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)],[t206]) ).
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(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(h39,plain,
para(sk20,sk23,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi8,h12,h0]) ).
cnf(h95,plain,
coll(sk20,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi66,h39]) ).
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(h182,plain,
coll(sk23,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi1,h95]) ).
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(c115,plain,
coll(sk25,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi115,negated_conjecture,
coll(sk25,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(h4,plain,
coll(sk25,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi115]) ).
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(h20,plain,
coll(sk20,sk20,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h4,h4]) ).
cnf(h181,plain,
coll(sk23,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h95,h95]) ).
cnf(h460,plain,
coll(sk20,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h181,h181]) ).
cnf(h872,plain,
coll(sk23,sk25,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h460,h20]) ).
cnf(h2456,plain,
coll(sk23,sk20,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi0,h872]) ).
cnf(h3673,plain,
coll(sk25,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h2456,h182]) ).
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(h258,plain,
eqangle(V0,V1,sk11(sk20,sk21,sk22,sk23),sk20,V0,V1,sk11(sk20,sk21,sk22,sk23),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi18,h93]) ).
cnf(hi38,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X2,X3),true,para(X0,X1,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(h1057,plain,
para(V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi38,h258]) ).
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(t60,plain,
eqratio(sk25,sk23,sk23,sk23,sk25,sk23,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi65,h1057,h3673,h3673]) ).
cnf(t2802,plain,
eqratio(sk25,sk23,sk23,sk23,sk25,sk23,sk23,sk23) = true,
inference(orient,[status(thm)],[t60]) ).
cnf(t2803,plain,
true = ifeq(true,true,eqratio(sk25,sk23,sk25,sk23,sk23,sk23,sk23,sk23),true),
inference(cp,[status(thm)],[t376,t2802]) ).
cnf(t17729,plain,
true = eqratio(sk25,sk23,sk25,sk23,sk23,sk23,sk23,sk23),
inference(step,[status(thm)],[t2803,t256]) ).
cnf(t6118,plain,
eqratio(sk25,sk23,sk25,sk23,sk23,sk23,sk23,sk23) = true,
inference(orient,[status(thm)],[t17729]) ).
cnf(t6127,plain,
true = ifeq(true,true,ifeq(cong(sk23,sk23,sk23,sk23),true,cong(sk25,sk23,sk25,sk23),true),true),
inference(cp,[status(thm)],[t366,t6118]) ).
cnf(t17730,plain,
true = ifeq(cong(sk23,sk23,sk23,sk23),true,cong(sk25,sk23,sk25,sk23),true),
inference(step,[status(thm)],[t6127,t256]) ).
cnf(h96,plain,
eqangle(sk20,sk23,V0,V1,sk20,sk23,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h39]) ).
cnf(h271,plain,
eqangle(sk20,sk23,sk20,sk23,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h96]) ).
cnf(h1105,plain,
cyclic(sk23,sk23,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi42,h271,h95]) ).
cnf(t30,plain,
cong(sk23,sk23,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi43,h1105,h1105,h1105,h271]) ).
cnf(t1833,plain,
cong(sk23,sk23,sk23,sk23) = true,
inference(orient,[status(thm)],[t30]) ).
cnf(t17731,plain,
true = ifeq(true,true,cong(sk25,sk23,sk25,sk23),true),
inference(step,[status(thm)],[t17730,t1833]) ).
cnf(t17732,plain,
true = cong(sk25,sk23,sk25,sk23),
inference(step,[status(thm)],[t17731,t256]) ).
cnf(t6128,plain,
cong(sk25,sk23,sk25,sk23) = true,
inference(orient,[status(thm)],[t17732]) ).
cnf(t6139,plain,
true = ifeq(true,true,ifeq(coll(sk25,sk23,sk23),true,midp(sk25,sk23,sk23),true),true),
inference(cp,[status(thm)],[t312,t6128]) ).
cnf(t17733,plain,
true = ifeq(coll(sk25,sk23,sk23),true,midp(sk25,sk23,sk23),true),
inference(step,[status(thm)],[t6139,t256]) ).
cnf(t67,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)],[t67]) ).
cnf(t66,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)],[t66]) ).
cnf(h870,plain,
coll(sk25,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h20,h460]) ).
cnf(h2406,plain,
coll(sk25,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi0,h870]) ).
cnf(t10,plain,
coll(sk23,sk23,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h2406,h2406]) ).
cnf(t472,plain,
coll(sk23,sk23,sk25) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t475,plain,
true = ifeq(true,true,coll(sk23,sk25,sk23),true),
inference(cp,[status(thm)],[t263,t472]) ).
cnf(t17564,plain,
true = coll(sk23,sk25,sk23),
inference(step,[status(thm)],[t475,t256]) ).
cnf(t3136,plain,
coll(sk23,sk25,sk23) = true,
inference(orient,[status(thm)],[t17564]) ).
cnf(t3139,plain,
true = ifeq(true,true,coll(sk25,sk23,sk23),true),
inference(cp,[status(thm)],[t261,t3136]) ).
cnf(t17577,plain,
true = coll(sk25,sk23,sk23),
inference(step,[status(thm)],[t3139,t256]) ).
cnf(t3545,plain,
coll(sk25,sk23,sk23) = true,
inference(orient,[status(thm)],[t17577]) ).
cnf(t17734,plain,
true = ifeq(true,true,midp(sk25,sk23,sk23),true),
inference(step,[status(thm)],[t17733,t3545]) ).
cnf(t17735,plain,
true = midp(sk25,sk23,sk23),
inference(step,[status(thm)],[t17734,t256]) ).
cnf(t6169,plain,
midp(sk25,sk23,sk23) = true,
inference(orient,[status(thm)],[t17735]) ).
cnf(t16430,plain,
true = ifeq(true,true,midp(sk25,X1,X1),true),
inference(cp,[status(thm)],[t16429,t6169]) ).
cnf(t18798,plain,
true = midp(sk25,X1,X1),
inference(step,[status(thm)],[t16430,t256]) ).
cnf(t16436,plain,
midp(sk25,X1,X1) = true,
inference(orient,[status(thm)],[t18798]) ).
cnf(t16437,plain,
true = ifeq(true,true,cong(sk25,X1,sk25,X1),true),
inference(cp,[status(thm)],[t363,t16436]) ).
cnf(t18801,plain,
true = cong(sk25,X1,sk25,X1),
inference(step,[status(thm)],[t16437,t256]) ).
cnf(t16496,plain,
cong(sk25,X1,sk25,X1) = true,
inference(orient,[status(thm)],[t18801]) ).
cnf(t16507,plain,
true = ifeq(true,true,ifeq(cong(sk25,X1,sk25,X1),true,perp(sk25,sk25,X2,X1),true),true),
inference(cp,[status(thm)],[t311,t16496]) ).
cnf(t18805,plain,
true = ifeq(cong(sk25,X1,sk25,X1),true,perp(sk25,sk25,X2,X1),true),
inference(step,[status(thm)],[t16507,t256]) ).
cnf(t18806,plain,
true = ifeq(true,true,perp(sk25,sk25,X2,X1),true),
inference(step,[status(thm)],[t18805,t16496]) ).
cnf(t18807,plain,
true = perp(sk25,sk25,X2,X1),
inference(step,[status(thm)],[t18806,t256]) ).
cnf(t16614,plain,
perp(sk25,sk25,X1,X2) = true,
inference(orient,[status(thm)],[t18807]) ).
cnf(t16615,plain,
true = ifeq(true,true,perp(X1,X2,sk25,sk25),true),
inference(cp,[status(thm)],[t274,t16614]) ).
cnf(t18820,plain,
true = perp(X1,X2,sk25,sk25),
inference(step,[status(thm)],[t16615,t256]) ).
cnf(t16792,plain,
perp(X1,X2,sk25,sk25) = true,
inference(orient,[status(thm)],[t18820]) ).
cnf(t16800,plain,
true = ifeq(true,true,ifeq(perp(sk25,sk25,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t16792]) ).
cnf(t18826,plain,
true = ifeq(perp(sk25,sk25,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t16800,t256]) ).
cnf(t18827,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t18826,t16614]) ).
cnf(t18828,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t18827,t256]) ).
cnf(t16948,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t18828]) ).
cnf(t18829,plain,
ifeq(true,true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(step,[status(thm)],[t330,t16948]) ).
cnf(t18830,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(step,[status(thm)],[t18829,t256]) ).
cnf(t16949,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(rw,[status(thm)],[t18830]) ).
cnf(t17286,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4) = true,
inference(orient,[status(thm)],[t16949]) ).
cnf(t17289,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true),
inference(cp,[status(thm)],[t294,t17286]) ).
cnf(t18894,plain,
true = eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(step,[status(thm)],[t17289,t256]) ).
cnf(t17369,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6) = true,
inference(orient,[status(thm)],[t18894]) ).
cnf(t17371,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,X3,X4,X5,X6),true),
inference(cp,[status(thm)],[t288,t17369]) ).
cnf(t18909,plain,
true = eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(step,[status(thm)],[t17371,t256]) ).
cnf(t17489,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6) = true,
inference(orient,[status(thm)],[t18909]) ).
cnf(t17499,plain,
true = ifeq(true,true,perp(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t14616,t17489]) ).
cnf(t18910,plain,
true = perp(X1,X2,X1,X2),
inference(step,[status(thm)],[t17499,t256]) ).
cnf(t17501,plain,
perp(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t18910]) ).
cnf(t17507,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,t17501]) ).
cnf(t18912,plain,
true = ifeq(true,true,ifeq(true,true,perp(X1,X2,X3,X4),true),true),
inference(step,[status(thm)],[t17507,t17369]) ).
cnf(t18913,plain,
true = ifeq(true,true,perp(X1,X2,X3,X4),true),
inference(step,[status(thm)],[t18912,t256]) ).
cnf(t18914,plain,
true = perp(X1,X2,X3,X4),
inference(step,[status(thm)],[t18913,t256]) ).
cnf(t17543,plain,
perp(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t18914]) ).
cnf(c121,plain,
~ perp(sk25,sk28,sk28,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
perp(sk25,sk28,sk28,sk23) != true,
inference(equality_encoding,[status(esa)],[c121]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t17543]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO558+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n013.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 12:23:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 149.14/19.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 149.14/19.35 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------