%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO602+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 01:18:16 PM UTC 2026
% Result : Theorem 122.47s 16.32s
% Output : Proof 122.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 74
% Number of leaves : 27
% Syntax : Number of formulae : 300 ( 196 unt; 0 def)
% Number of atoms : 495 ( 188 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 312 ( 117 ~; 111 |; 57 &)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 21 ( 21 usr; 18 con; 0-5 aty)
% Number of variables : 977 ( 88 sgn 409 !; 21 ?)
% 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(t190,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)],[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]) ).
fof(f94,conjecture,
! [A,B,E,F,D,M,E1,F1,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9] :
( ( circle(A,E,F1,NWPNT9)
& coll(F1,F,M)
& coll(E1,E,M)
& circle(A,E,E1,NWPNT8)
& circle(B,E,M,NWPNT7)
& coll(D,E,F)
& coll(D,A,B)
& circle(A,E,F,NWPNT6)
& circle(B,E,F,NWPNT5)
& circle(A,E,NWPNT3,NWPNT4)
& circle(B,E,NWPNT1,NWPNT2) )
=> perp(E1,F1,M,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL618064) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,E,F,D,M,E1,F1,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9] :
( ( circle(A,E,F1,NWPNT9)
& coll(F1,F,M)
& coll(E1,E,M)
& circle(A,E,E1,NWPNT8)
& circle(B,E,M,NWPNT7)
& coll(D,E,F)
& coll(D,A,B)
& circle(A,E,F,NWPNT6)
& circle(B,E,F,NWPNT5)
& circle(A,E,NWPNT3,NWPNT4)
& circle(B,E,NWPNT1,NWPNT2) )
=> perp(E1,F1,M,B) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,E,F,D,M,E1,F1,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9] :
( ~ perp(E1,F1,M,B)
& circle(A,E,F1,NWPNT9)
& coll(F1,F,M)
& coll(E1,E,M)
& circle(A,E,E1,NWPNT8)
& circle(B,E,M,NWPNT7)
& coll(D,E,F)
& coll(D,A,B)
& circle(A,E,F,NWPNT6)
& circle(B,E,F,NWPNT5)
& circle(A,E,NWPNT3,NWPNT4)
& circle(B,E,NWPNT1,NWPNT2) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ perp(sk26,sk27,sk25,sk21)
& circle(sk20,sk22,sk27,sk36)
& coll(sk27,sk23,sk25)
& coll(sk26,sk22,sk25)
& circle(sk20,sk22,sk26,sk35)
& circle(sk21,sk22,sk25,sk34)
& coll(sk24,sk22,sk23)
& coll(sk24,sk20,sk21)
& circle(sk20,sk22,sk23,sk33)
& circle(sk21,sk22,sk23,sk32)
& circle(sk20,sk22,sk30,sk31)
& circle(sk21,sk22,sk28,sk29) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29,sk30,sk31,sk32,sk33,sk34,sk35,sk36])],[f94_nnf]) ).
cnf(c121,plain,
coll(sk26,sk22,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi121,negated_conjecture,
coll(sk26,sk22,sk25) = true,
inference(equality_encoding,[status(esa)],[c121]) ).
cnf(h14,plain,
coll(sk26,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi121]) ).
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(h59,plain,
coll(sk22,sk22,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h14,h14]) ).
cnf(c118,plain,
coll(sk24,sk22,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi118,negated_conjecture,
coll(sk24,sk22,sk23) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(h9,plain,
coll(sk24,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi118]) ).
cnf(h45,plain,
coll(sk22,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h9,h9]) ).
cnf(h203,plain,
coll(sk24,sk26,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h45,h59]) ).
cnf(h652,plain,
coll(sk24,sk22,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi0,h203]) ).
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(h1369,plain,
coll(sk22,sk24,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi1,h652]) ).
cnf(c117,plain,
coll(sk24,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
coll(sk24,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h4,plain,
coll(sk21,sk21,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi117,hi117]) ).
cnf(h29,plain,
coll(sk24,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h4,h4]) ).
cnf(h8,plain,
coll(sk22,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi118]) ).
cnf(h44,plain,
coll(sk22,sk23,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi0,h8]) ).
cnf(h169,plain,
coll(sk24,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h44,h44]) ).
cnf(h465,plain,
coll(sk22,sk21,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h169,h29]) ).
cnf(h1104,plain,
coll(sk22,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,h465]) ).
cnf(h4837,plain,
coll(sk21,sk26,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h1104,h1369]) ).
cnf(h7298,plain,
coll(sk21,sk22,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi0,h4837]) ).
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(c119,plain,
circle(sk21,sk22,sk25,sk34),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi119,negated_conjecture,
circle(sk21,sk22,sk25,sk34) = true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(h10,plain,
perp(sk11(sk22,sk25,sk34,sk21),sk22,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi99,hi119]) ).
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(t109,plain,
perp(sk16(sk11(sk22,sk25,sk34,sk21),sk21,sk22,sk22,sk26),sk11(sk22,sk25,sk34,sk21),sk22,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi107,h10,h7298]) ).
cnf(t1156,plain,
perp(sk16(sk11(sk22,sk25,sk34,sk21),sk21,sk22,sk22,sk26),sk11(sk22,sk25,sk34,sk21),sk22,sk26) = true,
inference(orient,[status(thm)],[t109]) ).
cnf(t1167,plain,
true = ifeq(eqangle(X1,X2,X3,X4,sk16(sk11(sk22,sk25,sk34,sk21),sk21,sk22,sk22,sk26),sk11(sk22,sk25,sk34,sk21),sk22,sk26),true,ifeq(true,true,perp(X1,X2,X3,X4),true),true),
inference(cp,[status(thm)],[t283,t1156]) ).
cnf(t45,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t45]) ).
cnf(t29847,plain,
true = ifeq(eqangle(X1,X2,X3,X4,sk16(sk11(sk22,sk25,sk34,sk21),sk21,sk22,sk22,sk26),sk11(sk22,sk25,sk34,sk21),sk22,sk26),true,perp(X1,X2,X3,X4),true),
inference(step,[status(thm)],[t1167,t256]) ).
cnf(t23459,plain,
ifeq(eqangle(X1,X2,X3,X4,sk16(sk11(sk22,sk25,sk34,sk21),sk21,sk22,sk22,sk26),sk11(sk22,sk25,sk34,sk21),sk22,sk26),true,perp(X1,X2,X3,X4),true) = true,
inference(orient,[status(thm)],[t29847]) ).
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(t141,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)],[t141]) ).
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(t138,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)],[t138]) ).
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(t103,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)],[t103]) ).
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(t148,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)],[t148]) ).
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(t82,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)],[t82]) ).
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(t135,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)],[t135]) ).
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(t205,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)],[t205]) ).
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(t102,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)],[t102]) ).
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(t140,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)],[t140]) ).
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(t101,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)],[t101]) ).
cnf(h7,plain,
coll(sk23,sk23,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi118,hi118]) ).
cnf(h41,plain,
coll(sk24,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h7,h7]) ).
cnf(h162,plain,
coll(sk21,sk23,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h29,h41]) ).
cnf(h375,plain,
coll(sk21,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi0,h162]) ).
cnf(h947,plain,
coll(sk23,sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h375,h375]) ).
cnf(c122,plain,
coll(sk27,sk23,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi122,negated_conjecture,
coll(sk27,sk23,sk25) = true,
inference(equality_encoding,[status(esa)],[c122]) ).
cnf(h16,plain,
coll(sk23,sk27,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi122]) ).
cnf(h65,plain,
coll(sk25,sk25,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h16,h16]) ).
cnf(h211,plain,
coll(sk23,sk23,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h65,h65]) ).
cnf(h2930,plain,
coll(sk25,sk21,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h211,h947]) ).
cnf(h5804,plain,
coll(sk25,sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2930]) ).
cnf(h9096,plain,
coll(sk21,sk21,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h5804,h5804]) ).
cnf(c113,plain,
circle(sk21,sk22,sk28,sk29),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
circle(sk21,sk22,sk28,sk29) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h0,plain,
perp(sk11(sk22,sk28,sk29,sk21),sk22,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi99,hi113]) ).
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(h20,plain,
perp(sk11(sk22,sk28,sk29,sk21),sk22,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi6,h0]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h19,plain,
perp(sk22,sk21,sk11(sk22,sk28,sk29,sk21),sk22) = true,
inference(hyper_resolution,[status(thm)],[hi7,h0]) ).
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(h79,plain,
para(sk22,sk21,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi8,h19,h20]) ).
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(h260,plain,
eqangle(sk22,sk21,V0,V1,sk21,sk22,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h79]) ).
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(h956,plain,
eqangle(sk21,sk22,V0,V1,sk21,sk22,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi17,h260]) ).
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(t40,plain,
cyclic(sk22,sk25,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi42,h956,h9096]) ).
cnf(t2424,plain,
cyclic(sk22,sk25,sk21,sk21) = true,
inference(orient,[status(thm)],[t40]) ).
cnf(t2429,plain,
true = ifeq(true,true,eqangle(sk21,sk22,sk21,sk25,sk21,sk22,sk21,sk25),true),
inference(cp,[status(thm)],[t343,t2424]) ).
cnf(t28104,plain,
true = eqangle(sk21,sk22,sk21,sk25,sk21,sk22,sk21,sk25),
inference(step,[status(thm)],[t2429,t256]) ).
cnf(t5114,plain,
eqangle(sk21,sk22,sk21,sk25,sk21,sk22,sk21,sk25) = true,
inference(orient,[status(thm)],[t28104]) ).
cnf(t5115,plain,
true = ifeq(true,true,para(sk21,sk22,sk21,sk22),true),
inference(cp,[status(thm)],[t296,t5114]) ).
cnf(t28105,plain,
true = para(sk21,sk22,sk21,sk22),
inference(step,[status(thm)],[t5115,t256]) ).
cnf(t5131,plain,
para(sk21,sk22,sk21,sk22) = true,
inference(orient,[status(thm)],[t28105]) ).
cnf(t5135,plain,
true = ifeq(true,true,eqangle(sk21,sk22,X1,X2,sk21,sk22,X1,X2),true),
inference(cp,[status(thm)],[t312,t5131]) ).
cnf(t28405,plain,
true = eqangle(sk21,sk22,X1,X2,sk21,sk22,X1,X2),
inference(step,[status(thm)],[t5135,t256]) ).
cnf(t9718,plain,
eqangle(sk21,sk22,X1,X2,sk21,sk22,X1,X2) = true,
inference(orient,[status(thm)],[t28405]) ).
cnf(t9723,plain,
true = ifeq(true,true,eqangle(X1,X2,sk21,sk22,X1,X2,sk21,sk22),true),
inference(cp,[status(thm)],[t290,t9718]) ).
cnf(t28754,plain,
true = eqangle(X1,X2,sk21,sk22,X1,X2,sk21,sk22),
inference(step,[status(thm)],[t9723,t256]) ).
cnf(t13421,plain,
eqangle(X1,X2,sk21,sk22,X1,X2,sk21,sk22) = true,
inference(orient,[status(thm)],[t28754]) ).
cnf(t13423,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t296,t13421]) ).
cnf(t28755,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t13423,t256]) ).
cnf(t13445,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t28755]) ).
cnf(t13461,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,t13445]) ).
cnf(t30287,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)],[t13461,t256]) ).
cnf(t30288,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t30287,t13445]) ).
cnf(t30289,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t30288,t256]) ).
cnf(t26878,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t30289]) ).
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(t126,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)],[t126]) ).
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(t253,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(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)],[t253]) ).
cnf(h13,plain,
coll(sk22,sk26,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi121]) ).
cnf(h57,plain,
coll(sk25,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h13,h13]) ).
cnf(h191,plain,
coll(sk22,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h57,h57]) ).
cnf(h77,plain,
para(sk22,sk21,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi8,h19,h0]) ).
cnf(h254,plain,
eqangle(sk22,sk21,V0,V1,sk22,sk21,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h77]) ).
cnf(h911,plain,
cyclic(sk21,sk25,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi42,h254,h191]) ).
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(t35,plain,
cyclic(sk21,sk22,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi14,h911]) ).
cnf(t2557,plain,
cyclic(sk21,sk22,sk25,sk22) = true,
inference(orient,[status(thm)],[t35]) ).
cnf(t2564,plain,
true = ifeq(true,true,eqangle(sk25,sk21,sk25,sk22,sk22,sk21,sk22,sk22),true),
inference(cp,[status(thm)],[t343,t2557]) ).
cnf(t28123,plain,
true = eqangle(sk25,sk21,sk25,sk22,sk22,sk21,sk22,sk22),
inference(step,[status(thm)],[t2564,t256]) ).
cnf(t5457,plain,
eqangle(sk25,sk21,sk25,sk22,sk22,sk21,sk22,sk22) = true,
inference(orient,[status(thm)],[t28123]) ).
cnf(t5473,plain,
true = ifeq(cyclic(sk21,sk22,sk25,sk21),true,ifeq(cyclic(sk21,sk22,sk25,sk22),true,ifeq(cyclic(sk21,sk22,sk25,sk22),true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),true),true),
inference(cp,[status(thm)],[t341,t5457]) ).
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(t78,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)],[t78]) ).
cnf(t77,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)],[t77]) ).
cnf(t2425,plain,
true = ifeq(true,true,cyclic(sk22,sk21,sk25,sk21),true),
inference(cp,[status(thm)],[t346,t2424]) ).
cnf(t28045,plain,
true = cyclic(sk22,sk21,sk25,sk21),
inference(step,[status(thm)],[t2425,t256]) ).
cnf(t4031,plain,
cyclic(sk22,sk21,sk25,sk21) = true,
inference(orient,[status(thm)],[t28045]) ).
cnf(t4034,plain,
true = ifeq(true,true,cyclic(sk21,sk22,sk25,sk21),true),
inference(cp,[status(thm)],[t344,t4031]) ).
cnf(t28066,plain,
true = cyclic(sk21,sk22,sk25,sk21),
inference(step,[status(thm)],[t4034,t256]) ).
cnf(t4402,plain,
cyclic(sk21,sk22,sk25,sk21) = true,
inference(orient,[status(thm)],[t28066]) ).
cnf(t28124,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk22,sk25,sk22),true,ifeq(cyclic(sk21,sk22,sk25,sk22),true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),true),true),
inference(step,[status(thm)],[t5473,t4402]) ).
cnf(t28125,plain,
true = ifeq(cyclic(sk21,sk22,sk25,sk22),true,ifeq(cyclic(sk21,sk22,sk25,sk22),true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),true),
inference(step,[status(thm)],[t28124,t256]) ).
cnf(t28126,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk22,sk25,sk22),true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),true),
inference(step,[status(thm)],[t28125,t2557]) ).
cnf(t28127,plain,
true = ifeq(cyclic(sk21,sk22,sk25,sk22),true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),
inference(step,[status(thm)],[t28126,t256]) ).
cnf(t28128,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),
inference(step,[status(thm)],[t28127,t2557]) ).
cnf(t28129,plain,
true = ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),
inference(step,[status(thm)],[t28128,t256]) ).
cnf(t28130,plain,
true = cong(sk21,sk22,sk21,sk22),
inference(step,[status(thm)],[t28129,t256]) ).
cnf(t5474,plain,
cong(sk21,sk22,sk21,sk22) = true,
inference(orient,[status(thm)],[t28130]) ).
cnf(t5485,plain,
true = ifeq(true,true,ifeq(coll(sk21,sk22,sk22),true,midp(sk21,sk22,sk22),true),true),
inference(cp,[status(thm)],[t327,t5474]) ).
cnf(t28131,plain,
true = ifeq(coll(sk21,sk22,sk22),true,midp(sk21,sk22,sk22),true),
inference(step,[status(thm)],[t5485,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(t71,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)],[t71]) ).
cnf(t5132,plain,
true = ifeq(true,true,coll(sk21,sk22,sk22),true),
inference(cp,[status(thm)],[t319,t5131]) ).
cnf(t28106,plain,
true = coll(sk21,sk22,sk22),
inference(step,[status(thm)],[t5132,t256]) ).
cnf(t5158,plain,
coll(sk21,sk22,sk22) = true,
inference(orient,[status(thm)],[t28106]) ).
cnf(t28132,plain,
true = ifeq(true,true,midp(sk21,sk22,sk22),true),
inference(step,[status(thm)],[t28131,t5158]) ).
cnf(t28133,plain,
true = midp(sk21,sk22,sk22),
inference(step,[status(thm)],[t28132,t256]) ).
cnf(t5515,plain,
midp(sk21,sk22,sk22) = true,
inference(orient,[status(thm)],[t28133]) ).
cnf(t26879,plain,
true = ifeq(true,true,midp(sk21,X1,X1),true),
inference(cp,[status(thm)],[t26878,t5515]) ).
cnf(t30290,plain,
true = midp(sk21,X1,X1),
inference(step,[status(thm)],[t26879,t256]) ).
cnf(t26881,plain,
midp(sk21,X1,X1) = true,
inference(orient,[status(thm)],[t30290]) ).
cnf(t26882,plain,
true = ifeq(true,true,cong(sk21,X1,sk21,X1),true),
inference(cp,[status(thm)],[t363,t26881]) ).
cnf(t30292,plain,
true = cong(sk21,X1,sk21,X1),
inference(step,[status(thm)],[t26882,t256]) ).
cnf(t26921,plain,
cong(sk21,X1,sk21,X1) = true,
inference(orient,[status(thm)],[t30292]) ).
cnf(t26932,plain,
true = ifeq(true,true,ifeq(cong(sk21,X1,sk21,X1),true,perp(sk21,sk21,X2,X1),true),true),
inference(cp,[status(thm)],[t326,t26921]) ).
cnf(t30296,plain,
true = ifeq(cong(sk21,X1,sk21,X1),true,perp(sk21,sk21,X2,X1),true),
inference(step,[status(thm)],[t26932,t256]) ).
cnf(t30297,plain,
true = ifeq(true,true,perp(sk21,sk21,X2,X1),true),
inference(step,[status(thm)],[t30296,t26921]) ).
cnf(t30298,plain,
true = perp(sk21,sk21,X2,X1),
inference(step,[status(thm)],[t30297,t256]) ).
cnf(t27030,plain,
perp(sk21,sk21,X1,X2) = true,
inference(orient,[status(thm)],[t30298]) ).
cnf(t27031,plain,
true = ifeq(true,true,perp(X1,X2,sk21,sk21),true),
inference(cp,[status(thm)],[t274,t27030]) ).
cnf(t30304,plain,
true = perp(X1,X2,sk21,sk21),
inference(step,[status(thm)],[t27031,t256]) ).
cnf(t27140,plain,
perp(X1,X2,sk21,sk21) = true,
inference(orient,[status(thm)],[t30304]) ).
cnf(t27148,plain,
true = ifeq(true,true,ifeq(perp(sk21,sk21,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t27140]) ).
cnf(t30312,plain,
true = ifeq(perp(sk21,sk21,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t27148,t256]) ).
cnf(t30313,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t30312,t27030]) ).
cnf(t30314,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t30313,t256]) ).
cnf(t27311,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t30314]) ).
cnf(t30315,plain,
ifeq(true,true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(step,[status(thm)],[t312,t27311]) ).
cnf(t30316,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(step,[status(thm)],[t30315,t256]) ).
cnf(t27312,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(rw,[status(thm)],[t30316]) ).
cnf(t27753,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4) = true,
inference(orient,[status(thm)],[t27312]) ).
cnf(t27756,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true),
inference(cp,[status(thm)],[t294,t27753]) ).
cnf(t30388,plain,
true = eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(step,[status(thm)],[t27756,t256]) ).
cnf(t27844,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6) = true,
inference(orient,[status(thm)],[t30388]) ).
cnf(t27846,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,X3,X4,X5,X6),true),
inference(cp,[status(thm)],[t288,t27844]) ).
cnf(t30398,plain,
true = eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(step,[status(thm)],[t27846,t256]) ).
cnf(t27934,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6) = true,
inference(orient,[status(thm)],[t30398]) ).
cnf(t27944,plain,
true = ifeq(true,true,perp(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t23459,t27934]) ).
cnf(t30399,plain,
true = perp(X1,X2,X1,X2),
inference(step,[status(thm)],[t27944,t256]) ).
cnf(t27947,plain,
perp(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t30399]) ).
cnf(t27953,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,t27947]) ).
cnf(t30401,plain,
true = ifeq(true,true,ifeq(true,true,perp(X1,X2,X3,X4),true),true),
inference(step,[status(thm)],[t27953,t27844]) ).
cnf(t30402,plain,
true = ifeq(true,true,perp(X1,X2,X3,X4),true),
inference(step,[status(thm)],[t30401,t256]) ).
cnf(t30403,plain,
true = perp(X1,X2,X3,X4),
inference(step,[status(thm)],[t30402,t256]) ).
cnf(t27990,plain,
perp(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t30403]) ).
cnf(c124,plain,
~ perp(sk26,sk27,sk25,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
perp(sk26,sk27,sk25,sk21) != true,
inference(equality_encoding,[status(esa)],[c124]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t27990]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO602+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 12:37:05 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 122.47/16.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 122.47/16.32 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------