%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO548+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 : n007.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 01:18:07 PM UTC 2026
% Result : Theorem 120.91s 15.96s
% Output : Proof 120.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 88
% Number of leaves : 25
% Syntax : Number of formulae : 271 ( 175 unt; 0 def)
% Number of atoms : 467 ( 169 equ)
% Maximal formula atoms : 14 ( 1 avg)
% Number of connectives : 310 ( 114 ~; 108 |; 63 &)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 15 ( 15 usr; 14 con; 0-4 aty)
% Number of variables : 1072 ( 128 sgn 404 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( ( eqangle(P,Q,U,V,E,F,G,H)
& eqangle(A,B,C,D,P,Q,U,V) )
=> eqangle(A,B,C,D,E,F,G,H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD22) ).
fof(f21_nnf,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(t240,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(eqangle(X5,X6,X7,X8,X9,X10,X11,X12),true,eqangle(X1,X2,X3,X4,X9,X10,X11,X12),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t286,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(eqangle(X5,X6,X7,X8,X9,X10,X11,X12),true,eqangle(X1,X2,X3,X4,X9,X10,X11,X12),true),true) = true,
inference(orient,[status(thm)],[t240]) ).
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(t175,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X5,X6,X7,X8,X1,X2,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(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)],[t175]) ).
fof(f20,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(A,B,P,Q,C,D,U,V) ),
file('/export/starexec/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(t172,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(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)],[t172]) ).
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(t151,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)],[t151]) ).
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(t182,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(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)],[t182]) ).
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(t133,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)],[t133]) ).
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(t169,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(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)],[t169]) ).
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(t123,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)],[t123]) ).
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(t226,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)],[t226]) ).
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(t150,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)],[t150]) ).
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(t174,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)],[t174]) ).
fof(f3,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD4) ).
fof(f3_nnf,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t130,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t316,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t130]) ).
fof(f73,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( para(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> para(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD73) ).
fof(f73_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
fof(f73_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f73_nnf]) ).
cnf(c73,plain,
( para(X0,X1,X2,X3)
| ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f73_sk]) ).
cnf(t210,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(t287,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t210]) ).
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(t173,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X2,X1,X3,X4,X5,X6,X7,X8),true) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t292,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X2,X1,X3,X4,X5,X6,X7,X8),true) = true,
inference(orient,[status(thm)],[t173]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
fof(f94,conjecture,
! [A,B,C,O,P,G,F,P1,G1,F1,K,NWPNT1,NWPNT2] :
( ( coll(K,G,F)
& coll(K,G1,F1)
& coll(F1,A,C)
& perp(F1,P1,A,C)
& coll(G1,A,B)
& perp(G1,P1,A,B)
& circle(O,A,P1,NWPNT2)
& coll(F,A,C)
& perp(F,P,A,C)
& coll(G,A,B)
& perp(G,P,A,B)
& circle(O,A,P,NWPNT1)
& circle(O,A,B,C) )
=> eqangle(P,A,A,P1,F1,K,K,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL012008) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,O,P,G,F,P1,G1,F1,K,NWPNT1,NWPNT2] :
( ( coll(K,G,F)
& coll(K,G1,F1)
& coll(F1,A,C)
& perp(F1,P1,A,C)
& coll(G1,A,B)
& perp(G1,P1,A,B)
& circle(O,A,P1,NWPNT2)
& coll(F,A,C)
& perp(F,P,A,C)
& coll(G,A,B)
& perp(G,P,A,B)
& circle(O,A,P,NWPNT1)
& circle(O,A,B,C) )
=> eqangle(P,A,A,P1,F1,K,K,F) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,O,P,G,F,P1,G1,F1,K,NWPNT1,NWPNT2] :
( ~ eqangle(P,A,A,P1,F1,K,K,F)
& coll(K,G,F)
& coll(K,G1,F1)
& coll(F1,A,C)
& perp(F1,P1,A,C)
& coll(G1,A,B)
& perp(G1,P1,A,B)
& circle(O,A,P1,NWPNT2)
& coll(F,A,C)
& perp(F,P,A,C)
& coll(G,A,B)
& perp(G,P,A,B)
& circle(O,A,P,NWPNT1)
& circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ eqangle(sk24,sk20,sk20,sk27,sk29,sk30,sk30,sk26)
& coll(sk30,sk25,sk26)
& coll(sk30,sk28,sk29)
& coll(sk29,sk20,sk22)
& perp(sk29,sk27,sk20,sk22)
& coll(sk28,sk20,sk21)
& perp(sk28,sk27,sk20,sk21)
& circle(sk23,sk20,sk27,sk32)
& coll(sk26,sk20,sk22)
& perp(sk26,sk24,sk20,sk22)
& coll(sk25,sk20,sk21)
& perp(sk25,sk24,sk20,sk21)
& circle(sk23,sk20,sk24,sk31)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29,sk30,sk31,sk32])],[f94_nnf]) ).
cnf(c117,plain,
perp(sk26,sk24,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
perp(sk26,sk24,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h7,plain,
perp(sk20,sk22,sk26,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi117]) ).
cnf(hi8,axiom,
ifeq(perp(X0,X1,X2,X3),true,ifeq(perp(X2,X3,X4,X5),true,para(X0,X1,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(c122,plain,
perp(sk29,sk27,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi122,negated_conjecture,
perp(sk29,sk27,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c122]) ).
cnf(h45,plain,
para(sk29,sk27,sk26,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi122,h7]) ).
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(h138,plain,
eqangle(sk29,sk27,V0,V1,sk26,sk24,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h45]) ).
cnf(c115,plain,
perp(sk25,sk24,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi115,negated_conjecture,
perp(sk25,sk24,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(h2,plain,
perp(sk20,sk21,sk25,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi115]) ).
cnf(h37,plain,
para(sk20,sk21,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi8,h2,hi115]) ).
cnf(h118,plain,
eqangle(sk20,sk21,V0,V1,sk20,sk21,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h37]) ).
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(h349,plain,
eqangle(sk20,sk21,sk20,sk21,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h118]) ).
cnf(hi21,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,ifeq(eqangle(X4,X5,X6,X7,X8,X9,X10,X11),true,eqangle(X0,X1,X2,X3,X8,X9,X10,X11),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t61,plain,
eqangle(sk20,sk21,sk20,sk21,sk26,sk24,sk29,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi21,h349,h138]) ).
cnf(t1698,plain,
eqangle(sk20,sk21,sk20,sk21,sk26,sk24,sk29,sk27) = true,
inference(orient,[status(thm)],[t61]) ).
cnf(t1701,plain,
true = ifeq(true,true,eqangle(sk21,sk20,sk20,sk21,sk26,sk24,sk29,sk27),true),
inference(cp,[status(thm)],[t292,t1698]) ).
cnf(t30,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t30]) ).
cnf(t26017,plain,
true = eqangle(sk21,sk20,sk20,sk21,sk26,sk24,sk29,sk27),
inference(step,[status(thm)],[t1701,t256]) ).
cnf(t5357,plain,
eqangle(sk21,sk20,sk20,sk21,sk26,sk24,sk29,sk27) = true,
inference(orient,[status(thm)],[t26017]) ).
cnf(t5362,plain,
true = ifeq(true,true,ifeq(para(sk26,sk24,sk29,sk27),true,para(sk21,sk20,sk20,sk21),true),true),
inference(cp,[status(thm)],[t287,t5357]) ).
cnf(t26018,plain,
true = ifeq(para(sk26,sk24,sk29,sk27),true,para(sk21,sk20,sk20,sk21),true),
inference(step,[status(thm)],[t5362,t256]) ).
cnf(h18,plain,
perp(sk20,sk22,sk29,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi122]) ).
cnf(t34,plain,
para(sk26,sk24,sk29,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi117,h18]) ).
cnf(t2058,plain,
para(sk26,sk24,sk29,sk27) = true,
inference(orient,[status(thm)],[t34]) ).
cnf(t26019,plain,
true = ifeq(true,true,para(sk21,sk20,sk20,sk21),true),
inference(step,[status(thm)],[t26018,t2058]) ).
cnf(t26020,plain,
true = para(sk21,sk20,sk20,sk21),
inference(step,[status(thm)],[t26019,t256]) ).
cnf(t5368,plain,
para(sk21,sk20,sk20,sk21) = true,
inference(orient,[status(thm)],[t26020]) ).
cnf(t5369,plain,
true = ifeq(true,true,para(sk21,sk20,sk21,sk20),true),
inference(cp,[status(thm)],[t316,t5368]) ).
cnf(t26021,plain,
true = para(sk21,sk20,sk21,sk20),
inference(step,[status(thm)],[t5369,t256]) ).
cnf(t5394,plain,
para(sk21,sk20,sk21,sk20) = true,
inference(orient,[status(thm)],[t26021]) ).
cnf(t5396,plain,
true = ifeq(true,true,eqangle(sk21,sk20,X1,X2,sk21,sk20,X1,X2),true),
inference(cp,[status(thm)],[t312,t5394]) ).
cnf(t26357,plain,
true = eqangle(sk21,sk20,X1,X2,sk21,sk20,X1,X2),
inference(step,[status(thm)],[t5396,t256]) ).
cnf(t10257,plain,
eqangle(sk21,sk20,X1,X2,sk21,sk20,X1,X2) = true,
inference(orient,[status(thm)],[t26357]) ).
cnf(t10262,plain,
true = ifeq(true,true,eqangle(X1,X2,sk21,sk20,X1,X2,sk21,sk20),true),
inference(cp,[status(thm)],[t290,t10257]) ).
cnf(t26678,plain,
true = eqangle(X1,X2,sk21,sk20,X1,X2,sk21,sk20),
inference(step,[status(thm)],[t10262,t256]) ).
cnf(t13602,plain,
eqangle(X1,X2,sk21,sk20,X1,X2,sk21,sk20) = true,
inference(orient,[status(thm)],[t26678]) ).
cnf(t13604,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t296,t13602]) ).
cnf(t26679,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t13604,t256]) ).
cnf(t13626,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t26679]) ).
cnf(t13642,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,t13626]) ).
cnf(t27626,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)],[t13642,t256]) ).
cnf(t27627,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t27626,t13626]) ).
cnf(t27628,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t27627,t256]) ).
cnf(t22023,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t27628]) ).
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(t156,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)],[t156]) ).
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(t155,plain,
ifeq(coll(X1,X2,X3),true,ifeq(coll(X1,X2,X4),true,coll(X3,X4,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t260,plain,
ifeq(coll(X1,X2,X3),true,ifeq(coll(X1,X2,X4),true,coll(X3,X4,X1),true),true) = true,
inference(orient,[status(thm)],[t155]) ).
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(t116,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)],[t116]) ).
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(t117,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)],[t117]) ).
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(t124,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)],[t124]) ).
cnf(t13627,plain,
true = ifeq(true,true,coll(X1,X2,X2),true),
inference(cp,[status(thm)],[t319,t13626]) ).
cnf(t26680,plain,
true = coll(X1,X2,X2),
inference(step,[status(thm)],[t13627,t256]) ).
cnf(t13652,plain,
coll(X1,X2,X2) = true,
inference(orient,[status(thm)],[t26680]) ).
cnf(t13654,plain,
true = ifeq(true,true,coll(X1,X2,X1),true),
inference(cp,[status(thm)],[t261,t13652]) ).
cnf(t26681,plain,
true = coll(X1,X2,X1),
inference(step,[status(thm)],[t13654,t256]) ).
cnf(t13695,plain,
coll(X1,X2,X1) = true,
inference(orient,[status(thm)],[t26681]) ).
cnf(t13698,plain,
true = ifeq(true,true,coll(X1,X1,X2),true),
inference(cp,[status(thm)],[t263,t13695]) ).
cnf(t26682,plain,
true = coll(X1,X1,X2),
inference(step,[status(thm)],[t13698,t256]) ).
cnf(t13727,plain,
coll(X1,X1,X2) = true,
inference(orient,[status(thm)],[t26682]) ).
cnf(t13730,plain,
true = ifeq(true,true,ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),true),
inference(cp,[status(thm)],[t260,t13727]) ).
cnf(t26683,plain,
true = ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t13730,t256]) ).
cnf(t26684,plain,
true = ifeq(true,true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t26683,t13727]) ).
cnf(t26685,plain,
true = coll(X3,X2,X1),
inference(step,[status(thm)],[t26684,t256]) ).
cnf(t13763,plain,
coll(X1,X2,X3) = true,
inference(orient,[status(thm)],[t26685]) ).
cnf(t26690,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(true,true,midp(X1,X2,X3),true),true) = true,
inference(step,[status(thm)],[t327,t13763]) ).
cnf(t26691,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(step,[status(thm)],[t26690,t256]) ).
cnf(t13767,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(rw,[status(thm)],[t26691]) ).
cnf(t22535,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t13767]) ).
fof(f24,axiom,
! [A,B,C,D,E,F] :
( ( cong(C,D,E,F)
& cong(A,B,C,D) )
=> cong(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD25) ).
fof(f24_nnf,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( cong(X0,X1,X4,X5)
| ~ cong(X2,X3,X4,X5)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(t170,plain,
ifeq(cong(X1,X2,X3,X4),true,ifeq(cong(X3,X4,X5,X6),true,cong(X1,X2,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t320,plain,
ifeq(cong(X1,X2,X3,X4),true,ifeq(cong(X3,X4,X5,X6),true,cong(X1,X2,X5,X6),true),true) = true,
inference(orient,[status(thm)],[t170]) ).
cnf(h47,plain,
para(sk20,sk22,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi8,h7,hi117]) ).
cnf(h144,plain,
eqangle(sk20,sk22,V0,V1,sk20,sk22,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h47]) ).
cnf(h488,plain,
eqangle(sk20,sk22,sk20,sk22,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h144]) ).
cnf(hi1,axiom,
ifeq(coll(X0,X1,X2),true,coll(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(c118,plain,
coll(sk26,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi118,negated_conjecture,
coll(sk26,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(h10,plain,
coll(sk20,sk26,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi118]) ).
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(h53,plain,
coll(sk22,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h10,h10]) ).
cnf(h162,plain,
coll(sk20,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h53,h53]) ).
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(h501,plain,
cyclic(sk22,sk22,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h144,h162]) ).
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(t15,plain,
cong(sk22,sk22,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi43,h501,h501,h501,h488]) ).
cnf(t2422,plain,
cong(sk22,sk22,sk20,sk20) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(t2429,plain,
true = ifeq(true,true,ifeq(cong(sk20,sk20,X1,X2),true,cong(sk22,sk22,X1,X2),true),true),
inference(cp,[status(thm)],[t320,t2422]) ).
cnf(t27844,plain,
true = ifeq(cong(sk20,sk20,X1,X2),true,cong(sk22,sk22,X1,X2),true),
inference(step,[status(thm)],[t2429,t256]) ).
cnf(t23392,plain,
ifeq(cong(sk20,sk20,X1,X2),true,cong(sk22,sk22,X1,X2),true) = true,
inference(orient,[status(thm)],[t27844]) ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD24) ).
fof(f23_nnf,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( cong(X2,X3,X0,X1)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(t126,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t321,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t126]) ).
cnf(t2424,plain,
true = ifeq(true,true,cong(sk20,sk20,sk22,sk22),true),
inference(cp,[status(thm)],[t321,t2422]) ).
cnf(t25949,plain,
true = cong(sk20,sk20,sk22,sk22),
inference(step,[status(thm)],[t2424,t256]) ).
cnf(t4115,plain,
cong(sk20,sk20,sk22,sk22) = true,
inference(orient,[status(thm)],[t25949]) ).
cnf(t23393,plain,
true = ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),
inference(cp,[status(thm)],[t23392,t4115]) ).
cnf(t27845,plain,
true = cong(sk22,sk22,sk22,sk22),
inference(step,[status(thm)],[t23393,t256]) ).
cnf(t23396,plain,
cong(sk22,sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t27845]) ).
cnf(t23397,plain,
true = ifeq(true,true,midp(sk22,sk22,sk22),true),
inference(cp,[status(thm)],[t22535,t23396]) ).
cnf(t27846,plain,
true = midp(sk22,sk22,sk22),
inference(step,[status(thm)],[t23397,t256]) ).
cnf(t23422,plain,
midp(sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t27846]) ).
cnf(t23423,plain,
true = ifeq(true,true,midp(sk22,X1,X1),true),
inference(cp,[status(thm)],[t22023,t23422]) ).
cnf(t27847,plain,
true = midp(sk22,X1,X1),
inference(step,[status(thm)],[t23423,t256]) ).
cnf(t23441,plain,
midp(sk22,X1,X1) = true,
inference(orient,[status(thm)],[t27847]) ).
cnf(t23442,plain,
true = ifeq(true,true,cong(sk22,X1,sk22,X1),true),
inference(cp,[status(thm)],[t363,t23441]) ).
cnf(t27849,plain,
true = cong(sk22,X1,sk22,X1),
inference(step,[status(thm)],[t23442,t256]) ).
cnf(t23471,plain,
cong(sk22,X1,sk22,X1) = true,
inference(orient,[status(thm)],[t27849]) ).
cnf(t23482,plain,
true = ifeq(true,true,ifeq(cong(sk22,X1,sk22,X1),true,perp(sk22,sk22,X2,X1),true),true),
inference(cp,[status(thm)],[t326,t23471]) ).
cnf(t27852,plain,
true = ifeq(cong(sk22,X1,sk22,X1),true,perp(sk22,sk22,X2,X1),true),
inference(step,[status(thm)],[t23482,t256]) ).
cnf(t27853,plain,
true = ifeq(true,true,perp(sk22,sk22,X2,X1),true),
inference(step,[status(thm)],[t27852,t23471]) ).
cnf(t27854,plain,
true = perp(sk22,sk22,X2,X1),
inference(step,[status(thm)],[t27853,t256]) ).
cnf(t23537,plain,
perp(sk22,sk22,X1,X2) = true,
inference(orient,[status(thm)],[t27854]) ).
cnf(t23561,plain,
true = ifeq(true,true,perp(X1,X2,sk22,sk22),true),
inference(cp,[status(thm)],[t274,t23537]) ).
cnf(t27866,plain,
true = perp(X1,X2,sk22,sk22),
inference(step,[status(thm)],[t23561,t256]) ).
cnf(t23760,plain,
perp(X1,X2,sk22,sk22) = true,
inference(orient,[status(thm)],[t27866]) ).
cnf(t23793,plain,
true = ifeq(true,true,ifeq(perp(sk22,sk22,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t23760]) ).
cnf(t27908,plain,
true = ifeq(perp(sk22,sk22,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t23793,t256]) ).
cnf(t27909,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t27908,t23537]) ).
cnf(t27910,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t27909,t256]) ).
cnf(t24090,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t27910]) ).
cnf(t27995,plain,
ifeq(true,true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(step,[status(thm)],[t312,t24090]) ).
cnf(t27996,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(step,[status(thm)],[t27995,t256]) ).
cnf(t24154,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(rw,[status(thm)],[t27996]) ).
cnf(t25495,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4) = true,
inference(orient,[status(thm)],[t24154]) ).
cnf(t25498,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true),
inference(cp,[status(thm)],[t294,t25495]) ).
cnf(t28128,plain,
true = eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(step,[status(thm)],[t25498,t256]) ).
cnf(t25629,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6) = true,
inference(orient,[status(thm)],[t28128]) ).
cnf(t25631,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,X3,X4,X5,X6),true),
inference(cp,[status(thm)],[t288,t25629]) ).
cnf(t28138,plain,
true = eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(step,[status(thm)],[t25631,t256]) ).
cnf(t25719,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6) = true,
inference(orient,[status(thm)],[t28138]) ).
cnf(t25728,plain,
true = ifeq(eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true,ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),true),
inference(cp,[status(thm)],[t286,t25719]) ).
cnf(t28190,plain,
true = ifeq(true,true,ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),true),
inference(step,[status(thm)],[t25728,t25629]) ).
cnf(t28191,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),
inference(step,[status(thm)],[t28190,t256]) ).
cnf(t28192,plain,
true = eqangle(X1,X2,X3,X4,X7,X8,X9,X10),
inference(step,[status(thm)],[t28191,t256]) ).
cnf(t25910,plain,
eqangle(X1,X2,X3,X4,X5,X6,X7,X8) = true,
inference(orient,[status(thm)],[t28192]) ).
cnf(c126,plain,
~ eqangle(sk24,sk20,sk20,sk27,sk29,sk30,sk30,sk26),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
eqangle(sk24,sk20,sk20,sk27,sk29,sk30,sk30,sk26) != true,
inference(equality_encoding,[status(esa)],[c126]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t25910]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO548+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 : n007.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 12:20:08 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 120.91/15.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 120.91/15.96 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------