%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO586+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 : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:18:13 PM UTC 2026
% Result : Theorem 130.33s 17.12s
% Output : Proof 130.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 74
% Number of leaves : 28
% Syntax : Number of formulae : 307 ( 199 unt; 0 def)
% Number of atoms : 482 ( 193 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 295 ( 120 ~; 114 |; 33 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-5 aty)
% Number of variables : 989 ( 88 sgn 400 !; 12 ?)
% 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(t206,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)],[t206]) ).
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]) ).
fof(f94,conjecture,
! [A,B,C,O,D,E,I,NWPNT1] :
( ( circle(I,A,B,E)
& coll(E,B,D)
& coll(E,A,C)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> perp(I,E,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL416048) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,O,D,E,I,NWPNT1] :
( ( circle(I,A,B,E)
& coll(E,B,D)
& coll(E,A,C)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> perp(I,E,C,D) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,O,D,E,I,NWPNT1] :
( ~ perp(I,E,C,D)
& circle(I,A,B,E)
& coll(E,B,D)
& coll(E,A,C)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ perp(sk26,sk25,sk22,sk24)
& circle(sk26,sk20,sk21,sk25)
& coll(sk25,sk21,sk24)
& coll(sk25,sk20,sk22)
& circle(sk23,sk20,sk24,sk27)
& 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,
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(h3,plain,
coll(sk20,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi115]) ).
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(h16,plain,
coll(sk20,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3]) ).
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(h42,plain,
coll(sk25,sk25,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h16,h16]) ).
cnf(c116,plain,
coll(sk25,sk21,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
coll(sk25,sk21,sk24) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h5,plain,
coll(sk24,sk24,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi116,hi116]) ).
cnf(h19,plain,
coll(sk25,sk25,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h5,h5]) ).
cnf(h101,plain,
coll(sk24,sk20,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h19,h42]) ).
cnf(h156,plain,
coll(sk24,sk25,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,h101]) ).
cnf(h409,plain,
coll(sk20,sk20,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h156,h156]) ).
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]) ).
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(h25,plain,
perp(sk20,sk26,sk11(sk20,sk21,sk25,sk26),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi7,h8]) ).
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(h62,plain,
para(sk20,sk26,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi8,h25,h8]) ).
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(h133,plain,
coll(sk20,sk26,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi66,h62]) ).
cnf(h386,plain,
coll(sk26,sk26,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h133,h133]) ).
cnf(h831,plain,
coll(sk20,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h386,h386]) ).
cnf(h2439,plain,
coll(sk26,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h831,h409]) ).
cnf(h3259,plain,
coll(sk26,sk20,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2439]) ).
fof(f90,axiom,
! [A,B,C,E,F] :
? [P] :
( ( coll(B,E,F)
& perp(A,C,C,B) )
=> ( perp(P,A,E,F)
& coll(P,E,F) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleX15) ).
fof(f90_nnf,plain,
! [A,B,C,E,F] :
? [P] :
( ( perp(P,A,E,F)
& coll(P,E,F) )
| ~ coll(B,E,F)
| ~ perp(A,C,C,B) ),
inference(nnf_transformation,[status(thm)],[f90]) ).
fof(f90_sk,plain,
! [A,C,B,E,F] :
( ( perp(sk16(A,B,C,E,F),A,E,F)
& coll(sk16(A,B,C,E,F),E,F) )
| ~ coll(B,E,F)
| ~ perp(A,C,C,B) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16])],[f90_nnf]) ).
cnf(c107,plain,
( perp(sk16(X0,X1,X2,X3,X4),X0,X3,X4)
| ~ coll(X1,X3,X4)
| ~ perp(X0,X2,X2,X1) ),
inference(cnf_transformation,[status(esa)],[f90_sk]) ).
cnf(hi107,axiom,
ifeq(perp(X0,X1,X1,X2),true,ifeq(coll(X2,X3,X4),true,perp(sk16(X0,X2,X1,X3,X4),X0,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c107]) ).
cnf(t122,plain,
perp(sk16(sk11(sk20,sk21,sk25,sk26),sk26,sk20,sk20,sk24),sk11(sk20,sk21,sk25,sk26),sk20,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi107,h8,h3259]) ).
cnf(t1104,plain,
perp(sk16(sk11(sk20,sk21,sk25,sk26),sk26,sk20,sk20,sk24),sk11(sk20,sk21,sk25,sk26),sk20,sk24) = true,
inference(orient,[status(thm)],[t122]) ).
cnf(t1115,plain,
true = ifeq(eqangle(X1,X2,X3,X4,sk16(sk11(sk20,sk21,sk25,sk26),sk26,sk20,sk20,sk24),sk11(sk20,sk21,sk25,sk26),sk20,sk24),true,ifeq(true,true,perp(X1,X2,X3,X4),true),true),
inference(cp,[status(thm)],[t283,t1104]) ).
cnf(t28,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t28]) ).
cnf(t20338,plain,
true = ifeq(eqangle(X1,X2,X3,X4,sk16(sk11(sk20,sk21,sk25,sk26),sk26,sk20,sk20,sk24),sk11(sk20,sk21,sk25,sk26),sk20,sk24),true,perp(X1,X2,X3,X4),true),
inference(step,[status(thm)],[t1115,t256]) ).
cnf(t15395,plain,
ifeq(eqangle(X1,X2,X3,X4,sk16(sk11(sk20,sk21,sk25,sk26),sk26,sk20,sk20,sk24),sk11(sk20,sk21,sk25,sk26),sk20,sk24),true,perp(X1,X2,X3,X4),true) = true,
inference(orient,[status(thm)],[t20338]) ).
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(t153,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)],[t153]) ).
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(t150,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)],[t150]) ).
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(t112,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)],[t112]) ).
cnf(t160,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)],[t160]) ).
cnf(t81,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)],[t81]) ).
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(t147,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)],[t147]) ).
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(t111,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)],[t111]) ).
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(t152,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)],[t152]) ).
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(t106,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)],[t106]) ).
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(h9,plain,
perp(sk20,sk23,sk11(sk20,sk21,sk22,sk23),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi7,h0]) ).
cnf(h29,plain,
para(sk11(sk20,sk21,sk22,sk23),sk20,sk11(sk20,sk21,sk22,sk23),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,h0,h9]) ).
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(h69,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,h29]) ).
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(h167,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,h69]) ).
cnf(h68,plain,
coll(sk11(sk20,sk21,sk22,sk23),sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi66,h29]) ).
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(h521,plain,
cyclic(sk20,sk20,sk11(sk20,sk21,sk22,sk23),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h167,h68]) ).
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(t10,plain,
cong(sk20,sk20,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi43,h521,h521,h521,h167]) ).
cnf(t1798,plain,
cong(sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t1801,plain,
true = ifeq(true,true,eqangle(sk20,sk20,sk20,sk20,sk20,sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t322,t1798]) ).
cnf(t19349,plain,
true = eqangle(sk20,sk20,sk20,sk20,sk20,sk20,sk20,sk20),
inference(step,[status(thm)],[t1801,t256]) ).
cnf(t4528,plain,
eqangle(sk20,sk20,sk20,sk20,sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t19349]) ).
cnf(t4530,plain,
true = ifeq(true,true,para(sk20,sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t296,t4528]) ).
cnf(t19350,plain,
true = para(sk20,sk20,sk20,sk20),
inference(step,[status(thm)],[t4530,t256]) ).
cnf(t4551,plain,
para(sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t19350]) ).
cnf(t4553,plain,
true = ifeq(true,true,eqangle(sk20,sk20,X1,X2,sk20,sk20,X1,X2),true),
inference(cp,[status(thm)],[t330,t4551]) ).
cnf(t19637,plain,
true = eqangle(sk20,sk20,X1,X2,sk20,sk20,X1,X2),
inference(step,[status(thm)],[t4553,t256]) ).
cnf(t8785,plain,
eqangle(sk20,sk20,X1,X2,sk20,sk20,X1,X2) = true,
inference(orient,[status(thm)],[t19637]) ).
cnf(t8789,plain,
true = ifeq(true,true,eqangle(X1,X2,sk20,sk20,X1,X2,sk20,sk20),true),
inference(cp,[status(thm)],[t290,t8785]) ).
cnf(t19951,plain,
true = eqangle(X1,X2,sk20,sk20,X1,X2,sk20,sk20),
inference(step,[status(thm)],[t8789,t256]) ).
cnf(t12028,plain,
eqangle(X1,X2,sk20,sk20,X1,X2,sk20,sk20) = true,
inference(orient,[status(thm)],[t19951]) ).
cnf(t12029,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t296,t12028]) ).
cnf(t19952,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t12029,t256]) ).
cnf(t12051,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t19952]) ).
cnf(t12067,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,t12051]) ).
cnf(t20655,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)],[t12067,t256]) ).
cnf(t20656,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t20655,t12051]) ).
cnf(t20657,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t20656,t256]) ).
cnf(t18006,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t20657]) ).
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(t135,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)],[t135]) ).
cnf(t252,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(t341,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(orient,[status(thm)],[t252]) ).
fof(f40,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('/export/starexec/sandbox/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(t110,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t343,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(orient,[status(thm)],[t110]) ).
cnf(h4,plain,
coll(sk25,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi115]) ).
cnf(h17,plain,
coll(sk20,sk20,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h4,h4]) ).
cnf(h134,plain,
eqangle(sk20,sk26,V0,V1,sk20,sk26,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h62]) ).
cnf(h397,plain,
cyclic(sk26,sk25,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h134,h17]) ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD15) ).
fof(f14_nnf,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,cyclic(X0,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t22,plain,
cyclic(sk26,sk20,sk25,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi14,h397]) ).
cnf(t2475,plain,
cyclic(sk26,sk20,sk25,sk20) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t2482,plain,
true = ifeq(true,true,eqangle(sk25,sk26,sk25,sk20,sk20,sk26,sk20,sk20),true),
inference(cp,[status(thm)],[t343,t2475]) ).
cnf(t19394,plain,
true = eqangle(sk25,sk26,sk25,sk20,sk20,sk26,sk20,sk20),
inference(step,[status(thm)],[t2482,t256]) ).
cnf(t5250,plain,
eqangle(sk25,sk26,sk25,sk20,sk20,sk26,sk20,sk20) = true,
inference(orient,[status(thm)],[t19394]) ).
cnf(t5266,plain,
true = ifeq(cyclic(sk26,sk20,sk25,sk26),true,ifeq(cyclic(sk26,sk20,sk25,sk20),true,ifeq(cyclic(sk26,sk20,sk25,sk20),true,ifeq(true,true,cong(sk26,sk20,sk26,sk20),true),true),true),true),
inference(cp,[status(thm)],[t341,t5250]) ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox/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(t77,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t344,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(orient,[status(thm)],[t77]) ).
cnf(t76,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t346,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(orient,[status(thm)],[t76]) ).
cnf(h2437,plain,
coll(sk25,sk26,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h17,h831]) ).
cnf(h3203,plain,
coll(sk25,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2437]) ).
cnf(h7248,plain,
coll(sk26,sk26,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h3203,h3203]) ).
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(h26,plain,
perp(sk11(sk20,sk21,sk25,sk26),sk20,sk26,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi6,h8]) ).
cnf(h64,plain,
para(sk20,sk26,sk26,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,h25,h26]) ).
cnf(h140,plain,
eqangle(sk20,sk26,V0,V1,sk26,sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h64]) ).
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(h438,plain,
eqangle(sk26,sk20,V0,V1,sk26,sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi17,h140]) ).
cnf(t16,plain,
cyclic(sk20,sk25,sk26,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi42,h438,h7248]) ).
cnf(t2418,plain,
cyclic(sk20,sk25,sk26,sk26) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(t2419,plain,
true = ifeq(true,true,cyclic(sk20,sk26,sk25,sk26),true),
inference(cp,[status(thm)],[t346,t2418]) ).
cnf(t19288,plain,
true = cyclic(sk20,sk26,sk25,sk26),
inference(step,[status(thm)],[t2419,t256]) ).
cnf(t3423,plain,
cyclic(sk20,sk26,sk25,sk26) = true,
inference(orient,[status(thm)],[t19288]) ).
cnf(t3426,plain,
true = ifeq(true,true,cyclic(sk26,sk20,sk25,sk26),true),
inference(cp,[status(thm)],[t344,t3423]) ).
cnf(t19308,plain,
true = cyclic(sk26,sk20,sk25,sk26),
inference(step,[status(thm)],[t3426,t256]) ).
cnf(t3779,plain,
cyclic(sk26,sk20,sk25,sk26) = true,
inference(orient,[status(thm)],[t19308]) ).
cnf(t19395,plain,
true = ifeq(true,true,ifeq(cyclic(sk26,sk20,sk25,sk20),true,ifeq(cyclic(sk26,sk20,sk25,sk20),true,ifeq(true,true,cong(sk26,sk20,sk26,sk20),true),true),true),true),
inference(step,[status(thm)],[t5266,t3779]) ).
cnf(t19396,plain,
true = ifeq(cyclic(sk26,sk20,sk25,sk20),true,ifeq(cyclic(sk26,sk20,sk25,sk20),true,ifeq(true,true,cong(sk26,sk20,sk26,sk20),true),true),true),
inference(step,[status(thm)],[t19395,t256]) ).
cnf(t19397,plain,
true = ifeq(true,true,ifeq(cyclic(sk26,sk20,sk25,sk20),true,ifeq(true,true,cong(sk26,sk20,sk26,sk20),true),true),true),
inference(step,[status(thm)],[t19396,t2475]) ).
cnf(t19398,plain,
true = ifeq(cyclic(sk26,sk20,sk25,sk20),true,ifeq(true,true,cong(sk26,sk20,sk26,sk20),true),true),
inference(step,[status(thm)],[t19397,t256]) ).
cnf(t19399,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk26,sk20,sk26,sk20),true),true),
inference(step,[status(thm)],[t19398,t2475]) ).
cnf(t19400,plain,
true = ifeq(true,true,cong(sk26,sk20,sk26,sk20),true),
inference(step,[status(thm)],[t19399,t256]) ).
cnf(t19401,plain,
true = cong(sk26,sk20,sk26,sk20),
inference(step,[status(thm)],[t19400,t256]) ).
cnf(t5267,plain,
cong(sk26,sk20,sk26,sk20) = true,
inference(orient,[status(thm)],[t19401]) ).
cnf(t5278,plain,
true = ifeq(true,true,ifeq(coll(sk26,sk20,sk20),true,midp(sk26,sk20,sk20),true),true),
inference(cp,[status(thm)],[t312,t5267]) ).
cnf(t19402,plain,
true = ifeq(coll(sk26,sk20,sk20),true,midp(sk26,sk20,sk20),true),
inference(step,[status(thm)],[t5278,t256]) ).
cnf(t71,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t337,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t71]) ).
cnf(t2423,plain,
true = ifeq(true,true,eqangle(sk26,sk20,sk26,sk25,sk26,sk20,sk26,sk25),true),
inference(cp,[status(thm)],[t343,t2418]) ).
cnf(t19375,plain,
true = eqangle(sk26,sk20,sk26,sk25,sk26,sk20,sk26,sk25),
inference(step,[status(thm)],[t2423,t256]) ).
cnf(t4907,plain,
eqangle(sk26,sk20,sk26,sk25,sk26,sk20,sk26,sk25) = true,
inference(orient,[status(thm)],[t19375]) ).
cnf(t4908,plain,
true = ifeq(true,true,para(sk26,sk20,sk26,sk20),true),
inference(cp,[status(thm)],[t296,t4907]) ).
cnf(t19376,plain,
true = para(sk26,sk20,sk26,sk20),
inference(step,[status(thm)],[t4908,t256]) ).
cnf(t4924,plain,
para(sk26,sk20,sk26,sk20) = true,
inference(orient,[status(thm)],[t19376]) ).
cnf(t4925,plain,
true = ifeq(true,true,coll(sk26,sk20,sk20),true),
inference(cp,[status(thm)],[t337,t4924]) ).
cnf(t19377,plain,
true = coll(sk26,sk20,sk20),
inference(step,[status(thm)],[t4925,t256]) ).
cnf(t4951,plain,
coll(sk26,sk20,sk20) = true,
inference(orient,[status(thm)],[t19377]) ).
cnf(t19403,plain,
true = ifeq(true,true,midp(sk26,sk20,sk20),true),
inference(step,[status(thm)],[t19402,t4951]) ).
cnf(t19404,plain,
true = midp(sk26,sk20,sk20),
inference(step,[status(thm)],[t19403,t256]) ).
cnf(t5308,plain,
midp(sk26,sk20,sk20) = true,
inference(orient,[status(thm)],[t19404]) ).
cnf(t18007,plain,
true = ifeq(true,true,midp(sk26,X1,X1),true),
inference(cp,[status(thm)],[t18006,t5308]) ).
cnf(t20658,plain,
true = midp(sk26,X1,X1),
inference(step,[status(thm)],[t18007,t256]) ).
cnf(t18011,plain,
midp(sk26,X1,X1) = true,
inference(orient,[status(thm)],[t20658]) ).
cnf(t18012,plain,
true = ifeq(true,true,cong(sk26,X1,sk26,X1),true),
inference(cp,[status(thm)],[t363,t18011]) ).
cnf(t20661,plain,
true = cong(sk26,X1,sk26,X1),
inference(step,[status(thm)],[t18012,t256]) ).
cnf(t18071,plain,
cong(sk26,X1,sk26,X1) = true,
inference(orient,[status(thm)],[t20661]) ).
cnf(t18082,plain,
true = ifeq(true,true,ifeq(cong(sk26,X1,sk26,X1),true,perp(sk26,sk26,X2,X1),true),true),
inference(cp,[status(thm)],[t311,t18071]) ).
cnf(t20665,plain,
true = ifeq(cong(sk26,X1,sk26,X1),true,perp(sk26,sk26,X2,X1),true),
inference(step,[status(thm)],[t18082,t256]) ).
cnf(t20666,plain,
true = ifeq(true,true,perp(sk26,sk26,X2,X1),true),
inference(step,[status(thm)],[t20665,t18071]) ).
cnf(t20667,plain,
true = perp(sk26,sk26,X2,X1),
inference(step,[status(thm)],[t20666,t256]) ).
cnf(t18189,plain,
perp(sk26,sk26,X1,X2) = true,
inference(orient,[status(thm)],[t20667]) ).
cnf(t18190,plain,
true = ifeq(true,true,perp(X1,X2,sk26,sk26),true),
inference(cp,[status(thm)],[t274,t18189]) ).
cnf(t20678,plain,
true = perp(X1,X2,sk26,sk26),
inference(step,[status(thm)],[t18190,t256]) ).
cnf(t18349,plain,
perp(X1,X2,sk26,sk26) = true,
inference(orient,[status(thm)],[t20678]) ).
cnf(t18357,plain,
true = ifeq(true,true,ifeq(perp(sk26,sk26,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t18349]) ).
cnf(t20687,plain,
true = ifeq(perp(sk26,sk26,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t18357,t256]) ).
cnf(t20688,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t20687,t18189]) ).
cnf(t20689,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t20688,t256]) ).
cnf(t18550,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t20689]) ).
cnf(t20690,plain,
ifeq(true,true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(step,[status(thm)],[t330,t18550]) ).
cnf(t20691,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(step,[status(thm)],[t20690,t256]) ).
cnf(t18551,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(rw,[status(thm)],[t20691]) ).
cnf(t18986,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4) = true,
inference(orient,[status(thm)],[t18551]) ).
cnf(t18989,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true),
inference(cp,[status(thm)],[t294,t18986]) ).
cnf(t20763,plain,
true = eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(step,[status(thm)],[t18989,t256]) ).
cnf(t19086,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6) = true,
inference(orient,[status(thm)],[t20763]) ).
cnf(t19088,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,X3,X4,X5,X6),true),
inference(cp,[status(thm)],[t288,t19086]) ).
cnf(t20777,plain,
true = eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(step,[status(thm)],[t19088,t256]) ).
cnf(t19202,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6) = true,
inference(orient,[status(thm)],[t20777]) ).
cnf(t19212,plain,
true = ifeq(true,true,perp(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t15395,t19202]) ).
cnf(t20778,plain,
true = perp(X1,X2,X1,X2),
inference(step,[status(thm)],[t19212,t256]) ).
cnf(t19214,plain,
perp(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t20778]) ).
cnf(t19220,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,t19214]) ).
cnf(t20780,plain,
true = ifeq(true,true,ifeq(true,true,perp(X1,X2,X3,X4),true),true),
inference(step,[status(thm)],[t19220,t19086]) ).
cnf(t20781,plain,
true = ifeq(true,true,perp(X1,X2,X3,X4),true),
inference(step,[status(thm)],[t20780,t256]) ).
cnf(t20782,plain,
true = perp(X1,X2,X3,X4),
inference(step,[status(thm)],[t20781,t256]) ).
cnf(t19255,plain,
perp(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t20782]) ).
cnf(c118,plain,
~ perp(sk26,sk25,sk22,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
perp(sk26,sk25,sk22,sk24) != true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t19255]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO586+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 12:34:19 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 130.33/17.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 130.33/17.12 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------