%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO622+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 : n016.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 01:18:19 PM UTC 2026
% Result : Theorem 124.38s 16.50s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 90
% Number of leaves : 28
% Syntax : Number of formulae : 339 ( 231 unt; 0 def)
% Number of atoms : 515 ( 224 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 296 ( 120 ~; 114 |; 34 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-4 aty)
% Number of variables : 1022 ( 88 sgn 404 !; 7 ?)
% 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(f94,conjecture,
! [A,B,C,D,E,F,NWPNT1] :
( ( coll(F,A,D)
& perp(A,E,NWPNT1,F)
& midpoint(NWPNT1,A,E)
& coll(E,B,C)
& eqangle(E,A,A,C,E,A,A,B)
& circle(D,A,B,C) )
=> perp(E,F,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL8110985) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,NWPNT1] :
( ( coll(F,A,D)
& perp(A,E,NWPNT1,F)
& midpoint(NWPNT1,A,E)
& coll(E,B,C)
& eqangle(E,A,A,C,E,A,A,B)
& circle(D,A,B,C) )
=> perp(E,F,B,C) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F,NWPNT1] :
( ~ perp(E,F,B,C)
& coll(F,A,D)
& perp(A,E,NWPNT1,F)
& midpoint(NWPNT1,A,E)
& coll(E,B,C)
& eqangle(E,A,A,C,E,A,A,B)
& circle(D,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ perp(sk24,sk25,sk21,sk22)
& coll(sk25,sk20,sk23)
& perp(sk20,sk24,sk26,sk25)
& midpoint(sk26,sk20,sk24)
& coll(sk24,sk21,sk22)
& eqangle(sk24,sk20,sk20,sk22,sk24,sk20,sk20,sk21)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26])],[f94_nnf]) ).
cnf(c117,plain,
perp(sk20,sk24,sk26,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(t32,plain,
perp(sk20,sk24,sk26,sk25) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(t1069,plain,
perp(sk20,sk24,sk26,sk25) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(t1080,plain,
true = ifeq(eqangle(X1,X2,X3,X4,sk20,sk24,sk26,sk25),true,ifeq(true,true,perp(X1,X2,X3,X4),true),true),
inference(cp,[status(thm)],[t283,t1069]) ).
cnf(t22,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t22]) ).
cnf(t26069,plain,
true = ifeq(eqangle(X1,X2,X3,X4,sk20,sk24,sk26,sk25),true,perp(X1,X2,X3,X4),true),
inference(step,[status(thm)],[t1080,t256]) ).
cnf(t15074,plain,
ifeq(eqangle(X1,X2,X3,X4,sk20,sk24,sk26,sk25),true,perp(X1,X2,X3,X4),true) = true,
inference(orient,[status(thm)],[t26069]) ).
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(t174,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)],[t174]) ).
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(t171,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)],[t171]) ).
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(t137,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)],[t137]) ).
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(t181,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)],[t181]) ).
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(t117,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)],[t117]) ).
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(t168,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)],[t168]) ).
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(t105,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)],[t105]) ).
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(t221,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)],[t221]) ).
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(t136,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)],[t136]) ).
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(t173,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)],[t173]) ).
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(t114,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t334,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t114]) ).
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(t205,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)],[t205]) ).
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(c114,plain,
eqangle(sk24,sk20,sk20,sk22,sk24,sk20,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
eqangle(sk24,sk20,sk20,sk22,sk24,sk20,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h1,plain,
eqangle(sk24,sk20,sk24,sk20,sk20,sk22,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi20,hi114]) ).
cnf(hi18,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X2,X3,X0,X1,X6,X7,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h18,plain,
eqangle(sk24,sk20,sk24,sk20,sk20,sk21,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi18,h1]) ).
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(t44,plain,
eqangle(sk20,sk24,sk24,sk20,sk20,sk21,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi17,h18]) ).
cnf(t1649,plain,
eqangle(sk20,sk24,sk24,sk20,sk20,sk21,sk20,sk22) = true,
inference(orient,[status(thm)],[t44]) ).
cnf(t1652,plain,
true = ifeq(true,true,eqangle(sk24,sk20,sk20,sk24,sk20,sk22,sk20,sk21),true),
inference(cp,[status(thm)],[t290,t1649]) ).
cnf(t25177,plain,
true = eqangle(sk24,sk20,sk20,sk24,sk20,sk22,sk20,sk21),
inference(step,[status(thm)],[t1652,t256]) ).
cnf(t5014,plain,
eqangle(sk24,sk20,sk20,sk24,sk20,sk22,sk20,sk21) = true,
inference(orient,[status(thm)],[t25177]) ).
cnf(t5019,plain,
true = ifeq(true,true,ifeq(para(sk20,sk22,sk20,sk21),true,para(sk24,sk20,sk20,sk24),true),true),
inference(cp,[status(thm)],[t287,t5014]) ).
cnf(t25178,plain,
true = ifeq(para(sk20,sk22,sk20,sk21),true,para(sk24,sk20,sk20,sk24),true),
inference(step,[status(thm)],[t5019,t256]) ).
cnf(h3,plain,
eqangle(sk20,sk22,sk24,sk20,sk20,sk21,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi18,hi114]) ).
cnf(hi38,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X2,X3),true,para(X0,X1,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(t25,plain,
para(sk20,sk22,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi38,h3]) ).
cnf(t1907,plain,
para(sk20,sk22,sk20,sk21) = true,
inference(orient,[status(thm)],[t25]) ).
cnf(t25179,plain,
true = ifeq(true,true,para(sk24,sk20,sk20,sk24),true),
inference(step,[status(thm)],[t25178,t1907]) ).
cnf(t25180,plain,
true = para(sk24,sk20,sk20,sk24),
inference(step,[status(thm)],[t25179,t256]) ).
cnf(t5024,plain,
para(sk24,sk20,sk20,sk24) = true,
inference(orient,[status(thm)],[t25180]) ).
cnf(t5025,plain,
true = ifeq(true,true,para(sk24,sk20,sk24,sk20),true),
inference(cp,[status(thm)],[t334,t5024]) ).
cnf(t25181,plain,
true = para(sk24,sk20,sk24,sk20),
inference(step,[status(thm)],[t5025,t256]) ).
cnf(t5050,plain,
para(sk24,sk20,sk24,sk20) = true,
inference(orient,[status(thm)],[t25181]) ).
cnf(t5052,plain,
true = ifeq(true,true,eqangle(sk24,sk20,X1,X2,sk24,sk20,X1,X2),true),
inference(cp,[status(thm)],[t330,t5050]) ).
cnf(t25432,plain,
true = eqangle(sk24,sk20,X1,X2,sk24,sk20,X1,X2),
inference(step,[status(thm)],[t5052,t256]) ).
cnf(t8721,plain,
eqangle(sk24,sk20,X1,X2,sk24,sk20,X1,X2) = true,
inference(orient,[status(thm)],[t25432]) ).
cnf(t8727,plain,
true = ifeq(true,true,eqangle(X1,X2,sk24,sk20,X1,X2,sk24,sk20),true),
inference(cp,[status(thm)],[t290,t8721]) ).
cnf(t25737,plain,
true = eqangle(X1,X2,sk24,sk20,X1,X2,sk24,sk20),
inference(step,[status(thm)],[t8727,t256]) ).
cnf(t12307,plain,
eqangle(X1,X2,sk24,sk20,X1,X2,sk24,sk20) = true,
inference(orient,[status(thm)],[t25737]) ).
cnf(t12309,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t296,t12307]) ).
cnf(t25738,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t12309,t256]) ).
cnf(t12331,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t25738]) ).
cnf(t12347,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,t12331]) ).
cnf(t27093,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)],[t12347,t256]) ).
cnf(t27094,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t27093,t12331]) ).
cnf(t27095,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t27094,t256]) ).
cnf(t23871,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t27095]) ).
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(t159,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)],[t159]) ).
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(t106,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)],[t106]) ).
fof(f4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD5) ).
fof(f4_nnf,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t115,plain,
ifeq(para(X1,X2,X3,X4),true,para(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t331,plain,
ifeq(para(X1,X2,X3,X4),true,para(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t115]) ).
cnf(t172,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)],[t172]) ).
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(t131,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)],[t131]) ).
cnf(h26,plain,
para(sk20,sk22,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi38,h3]) ).
cnf(hi66,axiom,
ifeq(para(X0,X1,X0,X2),true,coll(X0,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(h79,plain,
coll(sk20,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi66,h26]) ).
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(h180,plain,
coll(sk21,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h79,h79]) ).
cnf(h389,plain,
coll(sk20,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h180,h180]) ).
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(c118,plain,
coll(sk25,sk20,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi118,negated_conjecture,
coll(sk25,sk20,sk23) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(h12,plain,
coll(sk25,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi118]) ).
cnf(h44,plain,
coll(sk20,sk20,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h12,h12]) ).
cnf(h119,plain,
coll(sk20,sk25,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,h44]) ).
cnf(h306,plain,
coll(sk20,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h119,h119]) ).
cnf(h697,plain,
coll(sk20,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h306,h389]) ).
cnf(hi19,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X4,X5,X6,X7,X0,X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(h2,plain,
eqangle(sk24,sk20,sk20,sk21,sk24,sk20,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi114]) ).
cnf(h22,plain,
eqangle(sk20,sk21,sk24,sk20,sk20,sk22,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi18,h2]) ).
cnf(h75,plain,
eqangle(sk21,sk20,sk24,sk20,sk20,sk22,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi17,h22]) ).
cnf(h205,plain,
para(sk21,sk20,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi38,h75]) ).
cnf(hi3,axiom,
ifeq(para(X0,X1,X2,X3),true,para(X0,X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h711,plain,
para(sk21,sk20,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi3,h205]) ).
cnf(h74,plain,
para(sk20,sk21,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi38,h22]) ).
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(h203,plain,
eqangle(sk20,sk21,V0,V1,sk20,sk22,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h74]) ).
cnf(h705,plain,
eqangle(sk20,sk21,sk20,sk22,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,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(c115,plain,
coll(sk24,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi115,negated_conjecture,
coll(sk24,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(h6,plain,
coll(sk21,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi115]) ).
cnf(h24,plain,
coll(sk22,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h6,h6]) ).
cnf(h52,plain,
coll(sk21,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h24,h24]) ).
fof(f51,axiom,
! [A,B,C,O,M] :
( ( eqangle(A,B,A,C,O,B,O,M)
& coll(M,B,C)
& circle(O,A,B,C) )
=> midp(M,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD51) ).
fof(f51_nnf,plain,
! [A,B,C,O,M] :
( midp(M,B,C)
| ~ eqangle(A,B,A,C,O,B,O,M)
| ~ coll(M,B,C)
| ~ circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f51]) ).
fof(f51_sk,plain,
! [O,A,B,C,M] :
( midp(M,B,C)
| ~ eqangle(A,B,A,C,O,B,O,M)
| ~ coll(M,B,C)
| ~ circle(O,A,B,C) ),
inference(skolemisation,[status(esa)],[f51_nnf]) ).
cnf(c51,plain,
( midp(X4,X1,X2)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X4)
| ~ coll(X4,X1,X2)
| ~ circle(X3,X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f51_sk]) ).
cnf(hi51,axiom,
ifeq(circle(X0,X1,X2,X3),true,ifeq(coll(X4,X2,X3),true,ifeq(eqangle(X1,X2,X1,X3,X0,X2,X0,X4),true,midp(X4,X2,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c51]) ).
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(h8631,plain,
midp(sk21,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi51,hi113,h52,h705]) ).
fof(f45,axiom,
! [A,B,C,E,F] :
( ( coll(F,A,C)
& para(E,F,B,C)
& midp(E,A,B) )
=> midp(F,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD45) ).
fof(f45_nnf,plain,
! [A,B,C,E,F] :
( midp(F,A,C)
| ~ coll(F,A,C)
| ~ para(E,F,B,C)
| ~ midp(E,A,B) ),
inference(nnf_transformation,[status(thm)],[f45]) ).
fof(f45_sk,plain,
! [E,A,B,F,C] :
( midp(F,A,C)
| ~ coll(F,A,C)
| ~ para(E,F,B,C)
| ~ midp(E,A,B) ),
inference(skolemisation,[status(esa)],[f45_nnf]) ).
cnf(c45,plain,
( midp(X4,X0,X2)
| ~ coll(X4,X0,X2)
| ~ para(X3,X4,X1,X2)
| ~ midp(X3,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(hi45,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(para(X0,X3,X2,X4),true,ifeq(coll(X3,X1,X4),true,midp(X3,X1,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
cnf(t7,plain,
midp(sk20,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi45,h8631,h711,h697]) ).
cnf(t2625,plain,
midp(sk20,sk21,sk20) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t2628,plain,
true = ifeq(true,true,cong(sk20,sk21,sk20,sk20),true),
inference(cp,[status(thm)],[t363,t2625]) ).
cnf(t25126,plain,
true = cong(sk20,sk21,sk20,sk20),
inference(step,[status(thm)],[t2628,t256]) ).
cnf(t4082,plain,
cong(sk20,sk21,sk20,sk20) = true,
inference(orient,[status(thm)],[t25126]) ).
cnf(t4084,plain,
true = ifeq(true,true,eqangle(sk20,sk21,sk21,sk20,sk21,sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t322,t4082]) ).
cnf(t25337,plain,
true = eqangle(sk20,sk21,sk21,sk20,sk21,sk20,sk20,sk20),
inference(step,[status(thm)],[t4084,t256]) ).
cnf(t7804,plain,
eqangle(sk20,sk21,sk21,sk20,sk21,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t25337]) ).
cnf(t7806,plain,
true = ifeq(true,true,eqangle(sk21,sk20,sk21,sk20,sk21,sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t292,t7804]) ).
cnf(t25619,plain,
true = eqangle(sk21,sk20,sk21,sk20,sk21,sk20,sk20,sk20),
inference(step,[status(thm)],[t7806,t256]) ).
cnf(t10961,plain,
eqangle(sk21,sk20,sk21,sk20,sk21,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t25619]) ).
cnf(t10966,plain,
true = ifeq(true,true,ifeq(para(sk21,sk20,sk20,sk20),true,para(sk21,sk20,sk21,sk20),true),true),
inference(cp,[status(thm)],[t287,t10961]) ).
cnf(t25620,plain,
true = ifeq(para(sk21,sk20,sk20,sk20),true,para(sk21,sk20,sk21,sk20),true),
inference(step,[status(thm)],[t10966,t256]) ).
fof(f10,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD11) ).
fof(f10_nnf,plain,
! [A,B,M] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [M,B,A] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( midp(X2,X0,X1)
| ~ midp(X2,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t101,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t365,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X3,X2),true) = true,
inference(orient,[status(thm)],[t101]) ).
cnf(t2626,plain,
true = ifeq(true,true,midp(sk20,sk20,sk21),true),
inference(cp,[status(thm)],[t365,t2625]) ).
cnf(t25095,plain,
true = midp(sk20,sk20,sk21),
inference(step,[status(thm)],[t2626,t256]) ).
cnf(t3298,plain,
midp(sk20,sk20,sk21) = true,
inference(orient,[status(thm)],[t25095]) ).
cnf(t3299,plain,
true = ifeq(true,true,cong(sk20,sk20,sk20,sk21),true),
inference(cp,[status(thm)],[t363,t3298]) ).
cnf(t25128,plain,
true = cong(sk20,sk20,sk20,sk21),
inference(step,[status(thm)],[t3299,t256]) ).
cnf(t4159,plain,
cong(sk20,sk20,sk20,sk21) = true,
inference(orient,[status(thm)],[t25128]) ).
cnf(t4161,plain,
true = ifeq(true,true,eqangle(sk20,sk20,sk20,sk21,sk20,sk21,sk20,sk21),true),
inference(cp,[status(thm)],[t322,t4159]) ).
cnf(t25339,plain,
true = eqangle(sk20,sk20,sk20,sk21,sk20,sk21,sk20,sk21),
inference(step,[status(thm)],[t4161,t256]) ).
cnf(t7830,plain,
eqangle(sk20,sk20,sk20,sk21,sk20,sk21,sk20,sk21) = true,
inference(orient,[status(thm)],[t25339]) ).
cnf(t7831,plain,
true = ifeq(true,true,para(sk20,sk20,sk20,sk21),true),
inference(cp,[status(thm)],[t296,t7830]) ).
cnf(t25340,plain,
true = para(sk20,sk20,sk20,sk21),
inference(step,[status(thm)],[t7831,t256]) ).
cnf(t7846,plain,
para(sk20,sk20,sk20,sk21) = true,
inference(orient,[status(thm)],[t25340]) ).
cnf(t7847,plain,
true = ifeq(true,true,para(sk20,sk20,sk21,sk20),true),
inference(cp,[status(thm)],[t334,t7846]) ).
cnf(t25341,plain,
true = para(sk20,sk20,sk21,sk20),
inference(step,[status(thm)],[t7847,t256]) ).
cnf(t7873,plain,
para(sk20,sk20,sk21,sk20) = true,
inference(orient,[status(thm)],[t25341]) ).
cnf(t7874,plain,
true = ifeq(true,true,para(sk21,sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t331,t7873]) ).
cnf(t25343,plain,
true = para(sk21,sk20,sk20,sk20),
inference(step,[status(thm)],[t7874,t256]) ).
cnf(t7923,plain,
para(sk21,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t25343]) ).
cnf(t25621,plain,
true = ifeq(true,true,para(sk21,sk20,sk21,sk20),true),
inference(step,[status(thm)],[t25620,t7923]) ).
cnf(t25622,plain,
true = para(sk21,sk20,sk21,sk20),
inference(step,[status(thm)],[t25621,t256]) ).
cnf(t10974,plain,
para(sk21,sk20,sk21,sk20) = true,
inference(orient,[status(thm)],[t25622]) ).
cnf(t10975,plain,
true = ifeq(true,true,para(sk21,sk20,sk20,sk21),true),
inference(cp,[status(thm)],[t334,t10974]) ).
cnf(t25623,plain,
true = para(sk21,sk20,sk20,sk21),
inference(step,[status(thm)],[t10975,t256]) ).
cnf(t10999,plain,
para(sk21,sk20,sk20,sk21) = true,
inference(orient,[status(thm)],[t25623]) ).
cnf(t11000,plain,
true = ifeq(true,true,para(sk20,sk21,sk21,sk20),true),
inference(cp,[status(thm)],[t331,t10999]) ).
cnf(t25624,plain,
true = para(sk20,sk21,sk21,sk20),
inference(step,[status(thm)],[t11000,t256]) ).
cnf(t11023,plain,
para(sk20,sk21,sk21,sk20) = true,
inference(orient,[status(thm)],[t25624]) ).
cnf(t11024,plain,
true = ifeq(true,true,para(sk20,sk21,sk20,sk21),true),
inference(cp,[status(thm)],[t334,t11023]) ).
cnf(t25625,plain,
true = para(sk20,sk21,sk20,sk21),
inference(step,[status(thm)],[t11024,t256]) ).
cnf(t11046,plain,
para(sk20,sk21,sk20,sk21) = true,
inference(orient,[status(thm)],[t25625]) ).
cnf(t11047,plain,
true = ifeq(true,true,coll(sk20,sk21,sk21),true),
inference(cp,[status(thm)],[t337,t11046]) ).
cnf(t25626,plain,
true = coll(sk20,sk21,sk21),
inference(step,[status(thm)],[t11047,t256]) ).
cnf(t11070,plain,
coll(sk20,sk21,sk21) = true,
inference(orient,[status(thm)],[t25626]) ).
cnf(t11077,plain,
true = ifeq(cong(sk20,sk21,sk20,sk21),true,ifeq(true,true,midp(sk20,sk21,sk21),true),true),
inference(cp,[status(thm)],[t312,t11070]) ).
fof(f22,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD23) ).
fof(f22_nnf,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( cong(X0,X1,X3,X2)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t109,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t308,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t109]) ).
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(t110,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t306,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t110]) ).
cnf(hi64,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(para(X1,X3,X2,X4),true,ifeq(para(X1,X4,X2,X3),true,midp(X0,X3,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(t8,plain,
midp(sk21,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi64,h8631,h711,h711]) ).
cnf(t2657,plain,
midp(sk21,sk20,sk20) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t2658,plain,
true = ifeq(true,true,cong(sk21,sk20,sk21,sk20),true),
inference(cp,[status(thm)],[t363,t2657]) ).
cnf(t25127,plain,
true = cong(sk21,sk20,sk21,sk20),
inference(step,[status(thm)],[t2658,t256]) ).
cnf(t4118,plain,
cong(sk21,sk20,sk21,sk20) = true,
inference(orient,[status(thm)],[t25127]) ).
cnf(t4121,plain,
true = ifeq(true,true,cong(sk21,sk20,sk20,sk21),true),
inference(cp,[status(thm)],[t308,t4118]) ).
cnf(t25142,plain,
true = cong(sk21,sk20,sk20,sk21),
inference(step,[status(thm)],[t4121,t256]) ).
cnf(t4433,plain,
cong(sk21,sk20,sk20,sk21) = true,
inference(orient,[status(thm)],[t25142]) ).
cnf(t4435,plain,
true = ifeq(true,true,cong(sk20,sk21,sk21,sk20),true),
inference(cp,[status(thm)],[t306,t4433]) ).
cnf(t25156,plain,
true = cong(sk20,sk21,sk21,sk20),
inference(step,[status(thm)],[t4435,t256]) ).
cnf(t4667,plain,
cong(sk20,sk21,sk21,sk20) = true,
inference(orient,[status(thm)],[t25156]) ).
cnf(t4669,plain,
true = ifeq(true,true,cong(sk20,sk21,sk20,sk21),true),
inference(cp,[status(thm)],[t308,t4667]) ).
cnf(t25165,plain,
true = cong(sk20,sk21,sk20,sk21),
inference(step,[status(thm)],[t4669,t256]) ).
cnf(t4814,plain,
cong(sk20,sk21,sk20,sk21) = true,
inference(orient,[status(thm)],[t25165]) ).
cnf(t25628,plain,
true = ifeq(true,true,ifeq(true,true,midp(sk20,sk21,sk21),true),true),
inference(step,[status(thm)],[t11077,t4814]) ).
cnf(t25629,plain,
true = ifeq(true,true,midp(sk20,sk21,sk21),true),
inference(step,[status(thm)],[t25628,t256]) ).
cnf(t25630,plain,
true = midp(sk20,sk21,sk21),
inference(step,[status(thm)],[t25629,t256]) ).
cnf(t11131,plain,
midp(sk20,sk21,sk21) = true,
inference(orient,[status(thm)],[t25630]) ).
cnf(t23876,plain,
true = ifeq(true,true,midp(sk20,X1,X1),true),
inference(cp,[status(thm)],[t23871,t11131]) ).
cnf(t27096,plain,
true = midp(sk20,X1,X1),
inference(step,[status(thm)],[t23876,t256]) ).
cnf(t23880,plain,
midp(sk20,X1,X1) = true,
inference(orient,[status(thm)],[t27096]) ).
cnf(t23881,plain,
true = ifeq(true,true,cong(sk20,X1,sk20,X1),true),
inference(cp,[status(thm)],[t363,t23880]) ).
cnf(t27098,plain,
true = cong(sk20,X1,sk20,X1),
inference(step,[status(thm)],[t23881,t256]) ).
cnf(t23920,plain,
cong(sk20,X1,sk20,X1) = true,
inference(orient,[status(thm)],[t27098]) ).
cnf(t23931,plain,
true = ifeq(true,true,ifeq(cong(sk20,X1,sk20,X1),true,perp(sk20,sk20,X2,X1),true),true),
inference(cp,[status(thm)],[t311,t23920]) ).
cnf(t27101,plain,
true = ifeq(cong(sk20,X1,sk20,X1),true,perp(sk20,sk20,X2,X1),true),
inference(step,[status(thm)],[t23931,t256]) ).
cnf(t27102,plain,
true = ifeq(true,true,perp(sk20,sk20,X2,X1),true),
inference(step,[status(thm)],[t27101,t23920]) ).
cnf(t27103,plain,
true = perp(sk20,sk20,X2,X1),
inference(step,[status(thm)],[t27102,t256]) ).
cnf(t24008,plain,
perp(sk20,sk20,X1,X2) = true,
inference(orient,[status(thm)],[t27103]) ).
cnf(t24011,plain,
true = ifeq(true,true,perp(X1,X2,sk20,sk20),true),
inference(cp,[status(thm)],[t274,t24008]) ).
cnf(t27110,plain,
true = perp(X1,X2,sk20,sk20),
inference(step,[status(thm)],[t24011,t256]) ).
cnf(t24133,plain,
perp(X1,X2,sk20,sk20) = true,
inference(orient,[status(thm)],[t27110]) ).
cnf(t24144,plain,
true = ifeq(true,true,ifeq(perp(sk20,sk20,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t24133]) ).
cnf(t27118,plain,
true = ifeq(perp(sk20,sk20,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t24144,t256]) ).
cnf(t27119,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t27118,t24008]) ).
cnf(t27120,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t27119,t256]) ).
cnf(t24300,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t27120]) ).
cnf(t27125,plain,
ifeq(true,true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(step,[status(thm)],[t330,t24300]) ).
cnf(t27126,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(step,[status(thm)],[t27125,t256]) ).
cnf(t24304,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(rw,[status(thm)],[t27126]) ).
cnf(t24641,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4) = true,
inference(orient,[status(thm)],[t24304]) ).
cnf(t24644,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true),
inference(cp,[status(thm)],[t294,t24641]) ).
cnf(t27190,plain,
true = eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(step,[status(thm)],[t24644,t256]) ).
cnf(t24714,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6) = true,
inference(orient,[status(thm)],[t27190]) ).
cnf(t24716,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,X3,X4,X5,X6),true),
inference(cp,[status(thm)],[t288,t24714]) ).
cnf(t27208,plain,
true = eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(step,[status(thm)],[t24716,t256]) ).
cnf(t25006,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6) = true,
inference(orient,[status(thm)],[t27208]) ).
cnf(t25007,plain,
true = ifeq(true,true,perp(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t15074,t25006]) ).
cnf(t27209,plain,
true = perp(X1,X2,X1,X2),
inference(step,[status(thm)],[t25007,t256]) ).
cnf(t25019,plain,
perp(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t27209]) ).
cnf(t25025,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,t25019]) ).
cnf(t27211,plain,
true = ifeq(true,true,ifeq(true,true,perp(X1,X2,X3,X4),true),true),
inference(step,[status(thm)],[t25025,t24714]) ).
cnf(t27212,plain,
true = ifeq(true,true,perp(X1,X2,X3,X4),true),
inference(step,[status(thm)],[t27211,t256]) ).
cnf(t27213,plain,
true = perp(X1,X2,X3,X4),
inference(step,[status(thm)],[t27212,t256]) ).
cnf(t25062,plain,
perp(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t27213]) ).
cnf(c119,plain,
~ perp(sk24,sk25,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
perp(sk24,sk25,sk21,sk22) != true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t25062]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO622+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 12:39:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 124.38/16.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 124.38/16.50 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------