%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO549+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 : n011.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 01:18:08 PM UTC 2026
% Result : Theorem 230.43s 60.85s
% Output : Proof 230.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 77
% Number of leaves : 25
% Syntax : Number of formulae : 293 ( 197 unt; 0 def)
% Number of atoms : 497 ( 189 equ)
% Maximal formula atoms : 17 ( 1 avg)
% Number of connectives : 315 ( 111 ~; 105 |; 74 &)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 18 ( 18 usr; 17 con; 0-4 aty)
% Number of variables : 959 ( 108 sgn 383 !; 16 ?)
% 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(t182,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)],[t182]) ).
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(t179,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)],[t179]) ).
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(t154,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)],[t154]) ).
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(t189,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)],[t189]) ).
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(t128,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)],[t128]) ).
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(t176,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)],[t176]) ).
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(t106,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)],[t106]) ).
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(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(t212,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)],[t212]) ).
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,D,O,C,P,F,P1,F2,F3,F1,L,M,NWPNT1,NWPNT2,NWPNT3] :
( ( coll(M,A,B)
& perp(M,P1,A,B)
& coll(L,A,B)
& perp(L,P,A,B)
& coll(F1,A,D)
& perp(F1,P,A,D)
& coll(F3,A,D)
& perp(F3,P1,A,D)
& coll(F2,A,C)
& perp(F2,P1,A,C)
& circle(O,A,P1,NWPNT3)
& coll(F,A,C)
& perp(F,P,A,C)
& circle(O,A,P,NWPNT2)
& circle(O,A,C,NWPNT1)
& circle(O,A,B,D) )
=> eqangle(F,L,L,F1,F2,M,M,F3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL012009) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,D,O,C,P,F,P1,F2,F3,F1,L,M,NWPNT1,NWPNT2,NWPNT3] :
( ( coll(M,A,B)
& perp(M,P1,A,B)
& coll(L,A,B)
& perp(L,P,A,B)
& coll(F1,A,D)
& perp(F1,P,A,D)
& coll(F3,A,D)
& perp(F3,P1,A,D)
& coll(F2,A,C)
& perp(F2,P1,A,C)
& circle(O,A,P1,NWPNT3)
& coll(F,A,C)
& perp(F,P,A,C)
& circle(O,A,P,NWPNT2)
& circle(O,A,C,NWPNT1)
& circle(O,A,B,D) )
=> eqangle(F,L,L,F1,F2,M,M,F3) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,D,O,C,P,F,P1,F2,F3,F1,L,M,NWPNT1,NWPNT2,NWPNT3] :
( ~ eqangle(F,L,L,F1,F2,M,M,F3)
& coll(M,A,B)
& perp(M,P1,A,B)
& coll(L,A,B)
& perp(L,P,A,B)
& coll(F1,A,D)
& perp(F1,P,A,D)
& coll(F3,A,D)
& perp(F3,P1,A,D)
& coll(F2,A,C)
& perp(F2,P1,A,C)
& circle(O,A,P1,NWPNT3)
& coll(F,A,C)
& perp(F,P,A,C)
& circle(O,A,P,NWPNT2)
& circle(O,A,C,NWPNT1)
& circle(O,A,B,D) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ eqangle(sk26,sk31,sk31,sk30,sk28,sk32,sk32,sk29)
& coll(sk32,sk20,sk21)
& perp(sk32,sk27,sk20,sk21)
& coll(sk31,sk20,sk21)
& perp(sk31,sk25,sk20,sk21)
& coll(sk30,sk20,sk22)
& perp(sk30,sk25,sk20,sk22)
& coll(sk29,sk20,sk22)
& perp(sk29,sk27,sk20,sk22)
& coll(sk28,sk20,sk24)
& perp(sk28,sk27,sk20,sk24)
& circle(sk23,sk20,sk27,sk35)
& coll(sk26,sk20,sk24)
& perp(sk26,sk25,sk20,sk24)
& circle(sk23,sk20,sk25,sk34)
& circle(sk23,sk20,sk24,sk33)
& 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,sk33,sk34,sk35])],[f94_nnf]) ).
cnf(c116,plain,
perp(sk26,sk25,sk20,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
perp(sk26,sk25,sk20,sk24) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h3,plain,
perp(sk20,sk24,sk26,sk25) = 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(h45,plain,
perp(sk20,sk24,sk25,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi6,h3]) ).
cnf(c119,plain,
perp(sk28,sk27,sk20,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi119,negated_conjecture,
perp(sk28,sk27,sk20,sk24) = true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(h9,plain,
perp(sk20,sk24,sk28,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi119]) ).
cnf(h56,plain,
perp(sk20,sk24,sk27,sk28) = true,
inference(hyper_resolution,[status(thm)],[hi6,h9]) ).
cnf(h173,plain,
perp(sk27,sk28,sk20,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi7,h56]) ).
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(t40,plain,
para(sk27,sk28,sk25,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi8,h173,h45]) ).
cnf(t1993,plain,
para(sk27,sk28,sk25,sk26) = true,
inference(orient,[status(thm)],[t40]) ).
cnf(t1998,plain,
true = ifeq(true,true,eqangle(sk27,sk28,X1,X2,sk25,sk26,X1,X2),true),
inference(cp,[status(thm)],[t330,t1993]) ).
cnf(t35,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t35]) ).
cnf(t43949,plain,
true = eqangle(sk27,sk28,X1,X2,sk25,sk26,X1,X2),
inference(step,[status(thm)],[t1998,t256]) ).
cnf(t8124,plain,
eqangle(sk27,sk28,X1,X2,sk25,sk26,X1,X2) = true,
inference(orient,[status(thm)],[t43949]) ).
cnf(t8125,plain,
true = ifeq(true,true,eqangle(sk27,sk28,sk25,sk26,X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t294,t8124]) ).
cnf(t44605,plain,
true = eqangle(sk27,sk28,sk25,sk26,X1,X2,X1,X2),
inference(step,[status(thm)],[t8125,t256]) ).
cnf(t16522,plain,
eqangle(sk27,sk28,sk25,sk26,X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t44605]) ).
cnf(t16527,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,sk27,sk28,sk25,sk26),true),
inference(cp,[status(thm)],[t288,t16522]) ).
cnf(t45417,plain,
true = eqangle(X1,X2,X1,X2,sk27,sk28,sk25,sk26),
inference(step,[status(thm)],[t16527,t256]) ).
cnf(t24981,plain,
eqangle(X1,X2,X1,X2,sk27,sk28,sk25,sk26) = true,
inference(orient,[status(thm)],[t45417]) ).
cnf(t24986,plain,
true = ifeq(true,true,ifeq(para(sk27,sk28,sk25,sk26),true,para(X1,X2,X1,X2),true),true),
inference(cp,[status(thm)],[t287,t24981]) ).
cnf(t45418,plain,
true = ifeq(para(sk27,sk28,sk25,sk26),true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t24986,t256]) ).
cnf(t45419,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t45418,t1993]) ).
cnf(t45420,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t45419,t256]) ).
cnf(t24991,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t45420]) ).
cnf(t25007,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,t24991]) ).
cnf(t47194,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)],[t25007,t256]) ).
cnf(t47195,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t47194,t24991]) ).
cnf(t47196,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t47195,t256]) ).
cnf(t41025,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t47196]) ).
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(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(t120,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)],[t120]) ).
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(t121,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)],[t121]) ).
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(t152,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)],[t152]) ).
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(t123,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)],[t123]) ).
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(c124,plain,
coll(sk30,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi124,negated_conjecture,
coll(sk30,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c124]) ).
cnf(h23,plain,
coll(sk30,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi124]) ).
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(h86,plain,
coll(sk20,sk20,sk30) = true,
inference(hyper_resolution,[status(thm)],[hi2,h23,h23]) ).
cnf(c117,plain,
coll(sk26,sk20,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
coll(sk26,sk20,sk24) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h7,plain,
coll(sk26,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi117]) ).
cnf(h50,plain,
coll(sk20,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h7,h7]) ).
cnf(h233,plain,
coll(sk26,sk30,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h50,h86]) ).
cnf(h817,plain,
coll(sk26,sk20,sk30) = true,
inference(hyper_resolution,[status(thm)],[hi0,h233]) ).
cnf(h3900,plain,
coll(sk30,sk30,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h817,h817]) ).
cnf(c123,plain,
perp(sk30,sk25,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi123,negated_conjecture,
perp(sk30,sk25,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c123]) ).
cnf(h19,plain,
perp(sk20,sk22,sk30,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi123]) ).
cnf(h77,plain,
para(sk30,sk25,sk30,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi123,h19]) ).
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(h218,plain,
eqangle(sk30,sk25,V0,V1,sk30,sk25,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h77]) ).
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(t20,plain,
cyclic(sk25,sk26,sk30,sk30) = true,
inference(hyper_resolution,[status(thm)],[hi42,h218,h3900]) ).
cnf(t2716,plain,
cyclic(sk25,sk26,sk30,sk30) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(t2717,plain,
true = ifeq(true,true,cyclic(sk25,sk30,sk26,sk30),true),
inference(cp,[status(thm)],[t346,t2716]) ).
cnf(t43756,plain,
true = cyclic(sk25,sk30,sk26,sk30),
inference(step,[status(thm)],[t2717,t256]) ).
cnf(t4898,plain,
cyclic(sk25,sk30,sk26,sk30) = true,
inference(orient,[status(thm)],[t43756]) ).
cnf(t4903,plain,
true = ifeq(true,true,eqangle(sk26,sk25,sk26,sk30,sk30,sk25,sk30,sk30),true),
inference(cp,[status(thm)],[t343,t4898]) ).
cnf(t44231,plain,
true = eqangle(sk26,sk25,sk26,sk30,sk30,sk25,sk30,sk30),
inference(step,[status(thm)],[t4903,t256]) ).
cnf(t13125,plain,
eqangle(sk26,sk25,sk26,sk30,sk30,sk25,sk30,sk30) = true,
inference(orient,[status(thm)],[t44231]) ).
cnf(t13141,plain,
true = ifeq(cyclic(sk25,sk30,sk26,sk25),true,ifeq(cyclic(sk25,sk30,sk26,sk30),true,ifeq(cyclic(sk25,sk30,sk26,sk30),true,ifeq(true,true,cong(sk25,sk30,sk25,sk30),true),true),true),true),
inference(cp,[status(thm)],[t341,t13125]) ).
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(t122,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)],[t122]) ).
cnf(h43,plain,
para(sk26,sk25,sk26,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi116,h3]) ).
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(h138,plain,
coll(sk26,sk25,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi66,h43]) ).
cnf(h380,plain,
coll(sk25,sk25,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h138,h138]) ).
cnf(h217,plain,
coll(sk30,sk25,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi66,h77]) ).
cnf(h770,plain,
coll(sk25,sk25,sk30) = true,
inference(hyper_resolution,[status(thm)],[hi2,h217,h217]) ).
cnf(h3118,plain,
coll(sk30,sk26,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h770,h380]) ).
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(h784,plain,
eqangle(sk30,sk25,sk30,sk25,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h218]) ).
cnf(t19,plain,
cyclic(sk25,sk25,sk30,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi42,h784,h3118]) ).
cnf(t2661,plain,
cyclic(sk25,sk25,sk30,sk26) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t2662,plain,
true = ifeq(true,true,cyclic(sk25,sk30,sk25,sk26),true),
inference(cp,[status(thm)],[t346,t2661]) ).
cnf(t43751,plain,
true = cyclic(sk25,sk30,sk25,sk26),
inference(step,[status(thm)],[t2662,t256]) ).
cnf(t4809,plain,
cyclic(sk25,sk30,sk25,sk26) = true,
inference(orient,[status(thm)],[t43751]) ).
cnf(t4810,plain,
true = ifeq(true,true,cyclic(sk25,sk30,sk26,sk25),true),
inference(cp,[status(thm)],[t348,t4809]) ).
cnf(t43804,plain,
true = cyclic(sk25,sk30,sk26,sk25),
inference(step,[status(thm)],[t4810,t256]) ).
cnf(t5849,plain,
cyclic(sk25,sk30,sk26,sk25) = true,
inference(orient,[status(thm)],[t43804]) ).
cnf(t44232,plain,
true = ifeq(true,true,ifeq(cyclic(sk25,sk30,sk26,sk30),true,ifeq(cyclic(sk25,sk30,sk26,sk30),true,ifeq(true,true,cong(sk25,sk30,sk25,sk30),true),true),true),true),
inference(step,[status(thm)],[t13141,t5849]) ).
cnf(t44233,plain,
true = ifeq(cyclic(sk25,sk30,sk26,sk30),true,ifeq(cyclic(sk25,sk30,sk26,sk30),true,ifeq(true,true,cong(sk25,sk30,sk25,sk30),true),true),true),
inference(step,[status(thm)],[t44232,t256]) ).
cnf(t44234,plain,
true = ifeq(true,true,ifeq(cyclic(sk25,sk30,sk26,sk30),true,ifeq(true,true,cong(sk25,sk30,sk25,sk30),true),true),true),
inference(step,[status(thm)],[t44233,t4898]) ).
cnf(t44235,plain,
true = ifeq(cyclic(sk25,sk30,sk26,sk30),true,ifeq(true,true,cong(sk25,sk30,sk25,sk30),true),true),
inference(step,[status(thm)],[t44234,t256]) ).
cnf(t44236,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk25,sk30,sk25,sk30),true),true),
inference(step,[status(thm)],[t44235,t4898]) ).
cnf(t44237,plain,
true = ifeq(true,true,cong(sk25,sk30,sk25,sk30),true),
inference(step,[status(thm)],[t44236,t256]) ).
cnf(t44238,plain,
true = cong(sk25,sk30,sk25,sk30),
inference(step,[status(thm)],[t44237,t256]) ).
cnf(t13142,plain,
cong(sk25,sk30,sk25,sk30) = true,
inference(orient,[status(thm)],[t44238]) ).
cnf(t13145,plain,
true = ifeq(true,true,cong(sk25,sk30,sk30,sk25),true),
inference(cp,[status(thm)],[t308,t13142]) ).
cnf(t44242,plain,
true = cong(sk25,sk30,sk30,sk25),
inference(step,[status(thm)],[t13145,t256]) ).
cnf(t13210,plain,
cong(sk25,sk30,sk30,sk25) = true,
inference(orient,[status(thm)],[t44242]) ).
cnf(t13212,plain,
true = ifeq(true,true,cong(sk30,sk25,sk25,sk30),true),
inference(cp,[status(thm)],[t306,t13210]) ).
cnf(t44243,plain,
true = cong(sk30,sk25,sk25,sk30),
inference(step,[status(thm)],[t13212,t256]) ).
cnf(t13220,plain,
cong(sk30,sk25,sk25,sk30) = true,
inference(orient,[status(thm)],[t44243]) ).
cnf(t13222,plain,
true = ifeq(true,true,cong(sk30,sk25,sk30,sk25),true),
inference(cp,[status(thm)],[t308,t13220]) ).
cnf(t44244,plain,
true = cong(sk30,sk25,sk30,sk25),
inference(step,[status(thm)],[t13222,t256]) ).
cnf(t13229,plain,
cong(sk30,sk25,sk30,sk25) = true,
inference(orient,[status(thm)],[t44244]) ).
cnf(t13238,plain,
true = ifeq(true,true,ifeq(coll(sk30,sk25,sk25),true,midp(sk30,sk25,sk25),true),true),
inference(cp,[status(thm)],[t312,t13229]) ).
cnf(t44245,plain,
true = ifeq(coll(sk30,sk25,sk25),true,midp(sk30,sk25,sk25),true),
inference(step,[status(thm)],[t13238,t256]) ).
cnf(t107,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)],[t107]) ).
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(t153,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)],[t153]) ).
cnf(c120,plain,
coll(sk28,sk20,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi120,negated_conjecture,
coll(sk28,sk20,sk24) = true,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(h13,plain,
coll(sk28,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi120]) ).
cnf(h63,plain,
coll(sk20,sk20,sk28) = true,
inference(hyper_resolution,[status(thm)],[hi2,h13,h13]) ).
cnf(h232,plain,
coll(sk28,sk30,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h63,h86]) ).
cnf(h816,plain,
coll(sk28,sk20,sk30) = true,
inference(hyper_resolution,[status(thm)],[hi0,h232]) ).
cnf(h3872,plain,
coll(sk30,sk30,sk28) = true,
inference(hyper_resolution,[status(thm)],[hi2,h816,h816]) ).
cnf(t22,plain,
cyclic(sk25,sk28,sk30,sk30) = true,
inference(hyper_resolution,[status(thm)],[hi42,h218,h3872]) ).
cnf(t2697,plain,
cyclic(sk25,sk28,sk30,sk30) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t2702,plain,
true = ifeq(true,true,eqangle(sk30,sk25,sk30,sk28,sk30,sk25,sk30,sk28),true),
inference(cp,[status(thm)],[t343,t2697]) ).
cnf(t44074,plain,
true = eqangle(sk30,sk25,sk30,sk28,sk30,sk25,sk30,sk28),
inference(step,[status(thm)],[t2702,t256]) ).
cnf(t9974,plain,
eqangle(sk30,sk25,sk30,sk28,sk30,sk25,sk30,sk28) = true,
inference(orient,[status(thm)],[t44074]) ).
cnf(t9975,plain,
true = ifeq(true,true,para(sk30,sk25,sk30,sk25),true),
inference(cp,[status(thm)],[t296,t9974]) ).
cnf(t44075,plain,
true = para(sk30,sk25,sk30,sk25),
inference(step,[status(thm)],[t9975,t256]) ).
cnf(t9989,plain,
para(sk30,sk25,sk30,sk25) = true,
inference(orient,[status(thm)],[t44075]) ).
cnf(t9990,plain,
true = ifeq(true,true,coll(sk30,sk25,sk25),true),
inference(cp,[status(thm)],[t337,t9989]) ).
cnf(t44076,plain,
true = coll(sk30,sk25,sk25),
inference(step,[status(thm)],[t9990,t256]) ).
cnf(t10015,plain,
coll(sk30,sk25,sk25) = true,
inference(orient,[status(thm)],[t44076]) ).
cnf(t44246,plain,
true = ifeq(true,true,midp(sk30,sk25,sk25),true),
inference(step,[status(thm)],[t44245,t10015]) ).
cnf(t44247,plain,
true = midp(sk30,sk25,sk25),
inference(step,[status(thm)],[t44246,t256]) ).
cnf(t13268,plain,
midp(sk30,sk25,sk25) = true,
inference(orient,[status(thm)],[t44247]) ).
cnf(t41026,plain,
true = ifeq(true,true,midp(sk30,X1,X1),true),
inference(cp,[status(thm)],[t41025,t13268]) ).
cnf(t47197,plain,
true = midp(sk30,X1,X1),
inference(step,[status(thm)],[t41026,t256]) ).
cnf(t41034,plain,
midp(sk30,X1,X1) = true,
inference(orient,[status(thm)],[t47197]) ).
cnf(t41035,plain,
true = ifeq(true,true,cong(sk30,X1,sk30,X1),true),
inference(cp,[status(thm)],[t363,t41034]) ).
cnf(t47202,plain,
true = cong(sk30,X1,sk30,X1),
inference(step,[status(thm)],[t41035,t256]) ).
cnf(t41139,plain,
cong(sk30,X1,sk30,X1) = true,
inference(orient,[status(thm)],[t47202]) ).
cnf(t41150,plain,
true = ifeq(true,true,ifeq(cong(sk30,X1,sk30,X1),true,perp(sk30,sk30,X2,X1),true),true),
inference(cp,[status(thm)],[t311,t41139]) ).
cnf(t47208,plain,
true = ifeq(cong(sk30,X1,sk30,X1),true,perp(sk30,sk30,X2,X1),true),
inference(step,[status(thm)],[t41150,t256]) ).
cnf(t47209,plain,
true = ifeq(true,true,perp(sk30,sk30,X2,X1),true),
inference(step,[status(thm)],[t47208,t41139]) ).
cnf(t47210,plain,
true = perp(sk30,sk30,X2,X1),
inference(step,[status(thm)],[t47209,t256]) ).
cnf(t41317,plain,
perp(sk30,sk30,X1,X2) = true,
inference(orient,[status(thm)],[t47210]) ).
cnf(t41324,plain,
true = ifeq(true,true,perp(X1,X2,sk30,sk30),true),
inference(cp,[status(thm)],[t274,t41317]) ).
cnf(t47232,plain,
true = perp(X1,X2,sk30,sk30),
inference(step,[status(thm)],[t41324,t256]) ).
cnf(t41664,plain,
perp(X1,X2,sk30,sk30) = true,
inference(orient,[status(thm)],[t47232]) ).
cnf(t41681,plain,
true = ifeq(true,true,ifeq(perp(sk30,sk30,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t41664]) ).
cnf(t47259,plain,
true = ifeq(perp(sk30,sk30,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t41681,t256]) ).
cnf(t47260,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t47259,t41317]) ).
cnf(t47261,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t47260,t256]) ).
cnf(t42196,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t47261]) ).
cnf(t47274,plain,
ifeq(true,true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(step,[status(thm)],[t330,t42196]) ).
cnf(t47275,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(step,[status(thm)],[t47274,t256]) ).
cnf(t42206,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(rw,[status(thm)],[t47275]) ).
cnf(t43021,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4) = true,
inference(orient,[status(thm)],[t42206]) ).
cnf(t43024,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true),
inference(cp,[status(thm)],[t294,t43021]) ).
cnf(t47387,plain,
true = eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(step,[status(thm)],[t43024,t256]) ).
cnf(t43169,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6) = true,
inference(orient,[status(thm)],[t47387]) ).
cnf(t43171,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,X3,X4,X5,X6),true),
inference(cp,[status(thm)],[t288,t43169]) ).
cnf(t47413,plain,
true = eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(step,[status(thm)],[t43171,t256]) ).
cnf(t43458,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6) = true,
inference(orient,[status(thm)],[t47413]) ).
cnf(t43468,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,t43458]) ).
cnf(t47472,plain,
true = ifeq(true,true,ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),true),
inference(step,[status(thm)],[t43468,t43169]) ).
cnf(t47473,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),
inference(step,[status(thm)],[t47472,t256]) ).
cnf(t47474,plain,
true = eqangle(X1,X2,X3,X4,X7,X8,X9,X10),
inference(step,[status(thm)],[t47473,t256]) ).
cnf(t43678,plain,
eqangle(X1,X2,X3,X4,X5,X6,X7,X8) = true,
inference(orient,[status(thm)],[t47474]) ).
cnf(c129,plain,
~ eqangle(sk26,sk31,sk31,sk30,sk28,sk32,sk32,sk29),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
eqangle(sk26,sk31,sk31,sk30,sk28,sk32,sk32,sk29) != true,
inference(equality_encoding,[status(esa)],[c129]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t43678]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO549+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/30.65 % CPULimit : 300
% 0.07/30.65 % WCLimit : 300
% 0.07/30.65 % DateTime : Wed Sep 23 12:23:25 UTC 2026
% 0.07/30.65 % CPUTime :
% 0.07/30.65 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 230.43/60.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 230.43/60.85 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------