%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO617+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 : n014.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 01:18:18 PM UTC 2026
% Result : Theorem 224.96s 32.92s
% Output : Proof 224.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 80
% Number of leaves : 25
% Syntax : Number of formulae : 276 ( 180 unt; 0 def)
% Number of atoms : 432 ( 174 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 264 ( 108 ~; 102 |; 29 &)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 951 ( 108 sgn 363 !; 6 ?)
% 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(t242,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)],[t242]) ).
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(t186,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)],[t186]) ).
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(t183,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)],[t183]) ).
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(t148,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)],[t148]) ).
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(t193,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)],[t193]) ).
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(t127,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)],[t127]) ).
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(t180,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)],[t180]) ).
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(t112,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)],[t112]) ).
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(t228,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)],[t228]) ).
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(t147,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)],[t147]) ).
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(t185,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)],[t185]) ).
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,D,E,F] :
( ( coll(F,A,B)
& perp(F,C,A,B)
& coll(E,A,B)
& eqangle(E,C,C,B,E,C,C,A)
& circle(D,A,B,C) )
=> eqangle(F,C,C,E,E,C,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL618079) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F] :
( ( coll(F,A,B)
& perp(F,C,A,B)
& coll(E,A,B)
& eqangle(E,C,C,B,E,C,C,A)
& circle(D,A,B,C) )
=> eqangle(F,C,C,E,E,C,C,D) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F] :
( ~ eqangle(F,C,C,E,E,C,C,D)
& coll(F,A,B)
& perp(F,C,A,B)
& coll(E,A,B)
& eqangle(E,C,C,B,E,C,C,A)
& circle(D,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ eqangle(sk25,sk22,sk22,sk24,sk24,sk22,sk22,sk23)
& coll(sk25,sk20,sk21)
& perp(sk25,sk22,sk20,sk21)
& coll(sk24,sk20,sk21)
& eqangle(sk24,sk22,sk22,sk21,sk24,sk22,sk22,sk20)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25])],[f94_nnf]) ).
cnf(c116,plain,
perp(sk25,sk22,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
perp(sk25,sk22,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h8,plain,
perp(sk20,sk21,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi116]) ).
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(h35,plain,
perp(sk20,sk21,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi6,h8]) ).
cnf(h98,plain,
perp(sk22,sk25,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi7,h35]) ).
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(t31,plain,
para(sk22,sk25,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi8,h98,h35]) ).
cnf(t1898,plain,
para(sk22,sk25,sk22,sk25) = true,
inference(orient,[status(thm)],[t31]) ).
cnf(t1902,plain,
true = ifeq(true,true,eqangle(sk22,sk25,X1,X2,sk22,sk25,X1,X2),true),
inference(cp,[status(thm)],[t312,t1898]) ).
cnf(t28,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t28]) ).
cnf(t37800,plain,
true = eqangle(sk22,sk25,X1,X2,sk22,sk25,X1,X2),
inference(step,[status(thm)],[t1902,t256]) ).
cnf(t7477,plain,
eqangle(sk22,sk25,X1,X2,sk22,sk25,X1,X2) = true,
inference(orient,[status(thm)],[t37800]) ).
cnf(t7483,plain,
true = ifeq(true,true,eqangle(X1,X2,sk22,sk25,X1,X2,sk22,sk25),true),
inference(cp,[status(thm)],[t290,t7477]) ).
cnf(t38363,plain,
true = eqangle(X1,X2,sk22,sk25,X1,X2,sk22,sk25),
inference(step,[status(thm)],[t7483,t256]) ).
cnf(t14576,plain,
eqangle(X1,X2,sk22,sk25,X1,X2,sk22,sk25) = true,
inference(orient,[status(thm)],[t38363]) ).
cnf(t14578,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t296,t14576]) ).
cnf(t38364,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t14578,t256]) ).
cnf(t14601,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t38364]) ).
cnf(t14617,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,t14601]) ).
cnf(t40840,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)],[t14617,t256]) ).
cnf(t40841,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t40840,t14601]) ).
cnf(t40842,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t40841,t256]) ).
cnf(t35659,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t40842]) ).
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(t171,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)],[t171]) ).
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(t119,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t323,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t119]) ).
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(t120,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)],[t120]) ).
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]) ).
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(t146,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)],[t146]) ).
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(c115,plain,
coll(sk24,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi115,negated_conjecture,
coll(sk24,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(h5,plain,
coll(sk21,sk21,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi115,hi115]) ).
cnf(c117,plain,
coll(sk25,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
coll(sk25,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h10,plain,
coll(sk21,sk21,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi117,hi117]) ).
cnf(h38,plain,
coll(sk25,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h10,h5]) ).
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(h100,plain,
coll(sk25,sk21,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi0,h38]) ).
cnf(h256,plain,
coll(sk24,sk24,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h100,h100]) ).
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(c114,plain,
eqangle(sk24,sk22,sk22,sk21,sk24,sk22,sk22,sk20),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
eqangle(sk24,sk22,sk22,sk21,sk24,sk22,sk22,sk20) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h2,plain,
eqangle(sk24,sk22,sk22,sk20,sk24,sk22,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi114]) ).
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(h20,plain,
eqangle(sk24,sk22,sk22,sk21,sk24,sk22,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi21,hi114,h2]) ).
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(h66,plain,
para(sk24,sk22,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi38,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(h194,plain,
eqangle(sk24,sk22,V0,V1,sk24,sk22,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h66]) ).
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(h992,plain,
cyclic(sk22,sk25,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi42,h194,h256]) ).
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(t18,plain,
cyclic(sk22,sk24,sk25,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi14,h992]) ).
cnf(t2630,plain,
cyclic(sk22,sk24,sk25,sk24) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(t2635,plain,
true = ifeq(true,true,eqangle(sk25,sk22,sk25,sk24,sk24,sk22,sk24,sk24),true),
inference(cp,[status(thm)],[t343,t2630]) ).
cnf(t37843,plain,
true = eqangle(sk25,sk22,sk25,sk24,sk24,sk22,sk24,sk24),
inference(step,[status(thm)],[t2635,t256]) ).
cnf(t8035,plain,
eqangle(sk25,sk22,sk25,sk24,sk24,sk22,sk24,sk24) = true,
inference(orient,[status(thm)],[t37843]) ).
cnf(t8051,plain,
true = ifeq(cyclic(sk22,sk24,sk25,sk22),true,ifeq(cyclic(sk22,sk24,sk25,sk24),true,ifeq(cyclic(sk22,sk24,sk25,sk24),true,ifeq(true,true,cong(sk22,sk24,sk22,sk24),true),true),true),true),
inference(cp,[status(thm)],[t341,t8035]) ).
fof(f13,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD14) ).
fof(f13_nnf,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t121,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t348,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t121]) ).
cnf(t122,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)],[t122]) ).
fof(f66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD66) ).
fof(f66_nnf,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f66]) ).
fof(f66_sk,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f66_nnf]) ).
cnf(c66,plain,
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f66_sk]) ).
cnf(hi66,axiom,
ifeq(para(X0,X1,X0,X2),true,coll(X0,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(h193,plain,
coll(sk24,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi66,h66]) ).
cnf(h594,plain,
coll(sk22,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h193,h193]) ).
cnf(h33,plain,
para(sk25,sk22,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi116,h8]) ).
cnf(h94,plain,
coll(sk25,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi66,h33]) ).
cnf(h229,plain,
coll(sk22,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h94,h94]) ).
cnf(h1133,plain,
coll(sk25,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h229,h594]) ).
cnf(h95,plain,
eqangle(sk25,sk22,V0,V1,sk25,sk22,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h33]) ).
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(h283,plain,
eqangle(sk25,sk22,sk25,sk22,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h95]) ).
cnf(t15,plain,
cyclic(sk22,sk22,sk25,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi42,h283,h1133]) ).
cnf(t2502,plain,
cyclic(sk22,sk22,sk25,sk24) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(t2503,plain,
true = ifeq(true,true,cyclic(sk22,sk22,sk24,sk25),true),
inference(cp,[status(thm)],[t348,t2502]) ).
cnf(t37602,plain,
true = cyclic(sk22,sk22,sk24,sk25),
inference(step,[status(thm)],[t2503,t256]) ).
cnf(t4081,plain,
cyclic(sk22,sk22,sk24,sk25) = true,
inference(orient,[status(thm)],[t37602]) ).
cnf(t4082,plain,
true = ifeq(true,true,cyclic(sk22,sk24,sk22,sk25),true),
inference(cp,[status(thm)],[t346,t4081]) ).
cnf(t37632,plain,
true = cyclic(sk22,sk24,sk22,sk25),
inference(step,[status(thm)],[t4082,t256]) ).
cnf(t4624,plain,
cyclic(sk22,sk24,sk22,sk25) = true,
inference(orient,[status(thm)],[t37632]) ).
cnf(t4625,plain,
true = ifeq(true,true,cyclic(sk22,sk24,sk25,sk22),true),
inference(cp,[status(thm)],[t348,t4624]) ).
cnf(t37673,plain,
true = cyclic(sk22,sk24,sk25,sk22),
inference(step,[status(thm)],[t4625,t256]) ).
cnf(t5397,plain,
cyclic(sk22,sk24,sk25,sk22) = true,
inference(orient,[status(thm)],[t37673]) ).
cnf(t37844,plain,
true = ifeq(true,true,ifeq(cyclic(sk22,sk24,sk25,sk24),true,ifeq(cyclic(sk22,sk24,sk25,sk24),true,ifeq(true,true,cong(sk22,sk24,sk22,sk24),true),true),true),true),
inference(step,[status(thm)],[t8051,t5397]) ).
cnf(t37845,plain,
true = ifeq(cyclic(sk22,sk24,sk25,sk24),true,ifeq(cyclic(sk22,sk24,sk25,sk24),true,ifeq(true,true,cong(sk22,sk24,sk22,sk24),true),true),true),
inference(step,[status(thm)],[t37844,t256]) ).
cnf(t37846,plain,
true = ifeq(true,true,ifeq(cyclic(sk22,sk24,sk25,sk24),true,ifeq(true,true,cong(sk22,sk24,sk22,sk24),true),true),true),
inference(step,[status(thm)],[t37845,t2630]) ).
cnf(t37847,plain,
true = ifeq(cyclic(sk22,sk24,sk25,sk24),true,ifeq(true,true,cong(sk22,sk24,sk22,sk24),true),true),
inference(step,[status(thm)],[t37846,t256]) ).
cnf(t37848,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk22,sk24,sk22,sk24),true),true),
inference(step,[status(thm)],[t37847,t2630]) ).
cnf(t37849,plain,
true = ifeq(true,true,cong(sk22,sk24,sk22,sk24),true),
inference(step,[status(thm)],[t37848,t256]) ).
cnf(t37850,plain,
true = cong(sk22,sk24,sk22,sk24),
inference(step,[status(thm)],[t37849,t256]) ).
cnf(t8052,plain,
cong(sk22,sk24,sk22,sk24) = true,
inference(orient,[status(thm)],[t37850]) ).
cnf(t8055,plain,
true = ifeq(true,true,cong(sk22,sk24,sk24,sk22),true),
inference(cp,[status(thm)],[t323,t8052]) ).
cnf(t37854,plain,
true = cong(sk22,sk24,sk24,sk22),
inference(step,[status(thm)],[t8055,t256]) ).
cnf(t8120,plain,
cong(sk22,sk24,sk24,sk22) = true,
inference(orient,[status(thm)],[t37854]) ).
cnf(t8122,plain,
true = ifeq(true,true,cong(sk24,sk22,sk22,sk24),true),
inference(cp,[status(thm)],[t321,t8120]) ).
cnf(t37855,plain,
true = cong(sk24,sk22,sk22,sk24),
inference(step,[status(thm)],[t8122,t256]) ).
cnf(t8130,plain,
cong(sk24,sk22,sk22,sk24) = true,
inference(orient,[status(thm)],[t37855]) ).
cnf(t8132,plain,
true = ifeq(true,true,cong(sk24,sk22,sk24,sk22),true),
inference(cp,[status(thm)],[t323,t8130]) ).
cnf(t37856,plain,
true = cong(sk24,sk22,sk24,sk22),
inference(step,[status(thm)],[t8132,t256]) ).
cnf(t8140,plain,
cong(sk24,sk22,sk24,sk22) = true,
inference(orient,[status(thm)],[t37856]) ).
cnf(t8149,plain,
true = ifeq(true,true,ifeq(coll(sk24,sk22,sk22),true,midp(sk24,sk22,sk22),true),true),
inference(cp,[status(thm)],[t327,t8140]) ).
cnf(t37857,plain,
true = ifeq(coll(sk24,sk22,sk22),true,midp(sk24,sk22,sk22),true),
inference(step,[status(thm)],[t8149,t256]) ).
cnf(t113,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)],[t113]) ).
cnf(t34,plain,
para(sk24,sk22,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi38,h20]) ).
cnf(t2209,plain,
para(sk24,sk22,sk24,sk22) = true,
inference(orient,[status(thm)],[t34]) ).
cnf(t2210,plain,
true = ifeq(true,true,coll(sk24,sk22,sk22),true),
inference(cp,[status(thm)],[t319,t2209]) ).
cnf(t37575,plain,
true = coll(sk24,sk22,sk22),
inference(step,[status(thm)],[t2210,t256]) ).
cnf(t3350,plain,
coll(sk24,sk22,sk22) = true,
inference(orient,[status(thm)],[t37575]) ).
cnf(t37858,plain,
true = ifeq(true,true,midp(sk24,sk22,sk22),true),
inference(step,[status(thm)],[t37857,t3350]) ).
cnf(t37859,plain,
true = midp(sk24,sk22,sk22),
inference(step,[status(thm)],[t37858,t256]) ).
cnf(t8179,plain,
midp(sk24,sk22,sk22) = true,
inference(orient,[status(thm)],[t37859]) ).
cnf(t35660,plain,
true = ifeq(true,true,midp(sk24,X1,X1),true),
inference(cp,[status(thm)],[t35659,t8179]) ).
cnf(t40843,plain,
true = midp(sk24,X1,X1),
inference(step,[status(thm)],[t35660,t256]) ).
cnf(t35668,plain,
midp(sk24,X1,X1) = true,
inference(orient,[status(thm)],[t40843]) ).
cnf(t35669,plain,
true = ifeq(true,true,cong(sk24,X1,sk24,X1),true),
inference(cp,[status(thm)],[t363,t35668]) ).
cnf(t40846,plain,
true = cong(sk24,X1,sk24,X1),
inference(step,[status(thm)],[t35669,t256]) ).
cnf(t35728,plain,
cong(sk24,X1,sk24,X1) = true,
inference(orient,[status(thm)],[t40846]) ).
cnf(t35739,plain,
true = ifeq(true,true,ifeq(cong(sk24,X1,sk24,X1),true,perp(sk24,sk24,X2,X1),true),true),
inference(cp,[status(thm)],[t326,t35728]) ).
cnf(t40850,plain,
true = ifeq(cong(sk24,X1,sk24,X1),true,perp(sk24,sk24,X2,X1),true),
inference(step,[status(thm)],[t35739,t256]) ).
cnf(t40851,plain,
true = ifeq(true,true,perp(sk24,sk24,X2,X1),true),
inference(step,[status(thm)],[t40850,t35728]) ).
cnf(t40852,plain,
true = perp(sk24,sk24,X2,X1),
inference(step,[status(thm)],[t40851,t256]) ).
cnf(t35846,plain,
perp(sk24,sk24,X1,X2) = true,
inference(orient,[status(thm)],[t40852]) ).
cnf(t35849,plain,
true = ifeq(true,true,perp(X1,X2,sk24,sk24),true),
inference(cp,[status(thm)],[t274,t35846]) ).
cnf(t40863,plain,
true = perp(X1,X2,sk24,sk24),
inference(step,[status(thm)],[t35849,t256]) ).
cnf(t36083,plain,
perp(X1,X2,sk24,sk24) = true,
inference(orient,[status(thm)],[t40863]) ).
cnf(t36094,plain,
true = ifeq(true,true,ifeq(perp(sk24,sk24,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t36083]) ).
cnf(t40880,plain,
true = ifeq(perp(sk24,sk24,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t36094,t256]) ).
cnf(t40881,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t40880,t35846]) ).
cnf(t40882,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t40881,t256]) ).
cnf(t36419,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t40882]) ).
cnf(t40887,plain,
ifeq(true,true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(step,[status(thm)],[t312,t36419]) ).
cnf(t40888,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(step,[status(thm)],[t40887,t256]) ).
cnf(t36423,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(rw,[status(thm)],[t40888]) ).
cnf(t37161,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4) = true,
inference(orient,[status(thm)],[t36423]) ).
cnf(t37164,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true),
inference(cp,[status(thm)],[t294,t37161]) ).
cnf(t40987,plain,
true = eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(step,[status(thm)],[t37164,t256]) ).
cnf(t37278,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6) = true,
inference(orient,[status(thm)],[t40987]) ).
cnf(t37280,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,X3,X4,X5,X6),true),
inference(cp,[status(thm)],[t288,t37278]) ).
cnf(t41001,plain,
true = eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(step,[status(thm)],[t37280,t256]) ).
cnf(t37401,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6) = true,
inference(orient,[status(thm)],[t41001]) ).
cnf(t37409,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,t37401]) ).
cnf(t41056,plain,
true = ifeq(true,true,ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),true),
inference(step,[status(thm)],[t37409,t37278]) ).
cnf(t41057,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),
inference(step,[status(thm)],[t41056,t256]) ).
cnf(t41058,plain,
true = eqangle(X1,X2,X3,X4,X7,X8,X9,X10),
inference(step,[status(thm)],[t41057,t256]) ).
cnf(t37563,plain,
eqangle(X1,X2,X3,X4,X5,X6,X7,X8) = true,
inference(orient,[status(thm)],[t41058]) ).
cnf(c118,plain,
~ eqangle(sk25,sk22,sk22,sk24,sk24,sk22,sk22,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
eqangle(sk25,sk22,sk22,sk24,sk24,sk22,sk22,sk23) != true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t37563]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO617+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 12:34:05 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 224.96/32.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 224.96/32.92 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------