%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO618+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 : n013.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 83.94s 11.10s
% Output : Proof 83.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 27
% Syntax : Number of formulae : 240 ( 135 unt; 0 def)
% Number of atoms : 419 ( 129 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 298 ( 119 ~; 113 |; 39 &)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-4 aty)
% Number of variables : 804 ( 2 sgn 438 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f94,conjecture,
! [A,B,C,U,O,T] :
( ( coll(T,B,C)
& perp(A,O,A,T)
& circle(O,A,B,C)
& coll(U,B,C)
& eqangle(U,A,A,C,U,A,A,B) )
=> cong(T,A,T,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL618080) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,U,O,T] :
( ( coll(T,B,C)
& perp(A,O,A,T)
& circle(O,A,B,C)
& coll(U,B,C)
& eqangle(U,A,A,C,U,A,A,B) )
=> cong(T,A,T,U) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,U,O,T] :
( ~ cong(T,A,T,U)
& coll(T,B,C)
& perp(A,O,A,T)
& circle(O,A,B,C)
& coll(U,B,C)
& eqangle(U,A,A,C,U,A,A,B) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ cong(sk25,sk20,sk25,sk23)
& coll(sk25,sk21,sk22)
& perp(sk20,sk24,sk20,sk25)
& circle(sk24,sk20,sk21,sk22)
& coll(sk23,sk21,sk22)
& eqangle(sk23,sk20,sk20,sk22,sk23,sk20,sk20,sk21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25])],[f94_nnf]) ).
cnf(c118,plain,
~ cong(sk25,sk20,sk25,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(t21,plain,
cong(sk25,sk20,sk25,sk23) = false,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(t3041,plain,
cong(sk25,sk20,sk25,sk23) = false,
inference(orient,[status(thm)],[t21]) ).
fof(f75,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( cong(P,Q,U,V)
& eqratio(A,B,C,D,P,Q,U,V) )
=> cong(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD75) ).
fof(f75_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( cong(A,B,C,D)
| ~ cong(P,Q,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f75]) ).
fof(f75_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( cong(A,B,C,D)
| ~ cong(P,Q,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f75_nnf]) ).
cnf(c75,plain,
( cong(X0,X1,X2,X3)
| ~ cong(X4,X5,X6,X7)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f75_sk]) ).
cnf(t214,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(cong(X5,X6,X7,X8),true,cong(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c75]) ).
cnf(t366,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(cong(X5,X6,X7,X8),true,cong(X1,X2,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t214]) ).
fof(f28,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,C,D,P,Q,U,V)
=> eqratio(A,B,P,Q,C,D,U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD29) ).
fof(f28_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,P,Q,C,D,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,P,Q,C,D,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
( eqratio(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(t187,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,eqratio(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(t376,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,eqratio(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(orient,[status(thm)],[t187]) ).
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(c114,plain,
coll(sk23,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
coll(sk23,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h4,plain,
coll(sk22,sk22,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi114,hi114]) ).
cnf(h20,plain,
coll(sk23,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h4,h4]) ).
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(h65,plain,
coll(sk23,sk22,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi0,h20]) ).
cnf(c117,plain,
coll(sk25,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
coll(sk25,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h14,plain,
coll(sk22,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi117,hi117]) ).
cnf(h41,plain,
coll(sk23,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h4,h14]) ).
cnf(h129,plain,
coll(sk23,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi0,h41]) ).
cnf(h286,plain,
coll(sk25,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h129,h65]) ).
fof(f85,axiom,
! [A,B,C,H] :
? [P,Q] :
( ( perp(B,H,A,C)
& perp(A,H,B,C) )
=> ( perp(B,Q,C,A)
& coll(Q,C,A)
& perp(A,P,C,B)
& coll(P,C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleX10) ).
fof(f85_nnf,plain,
! [A,B,C,H] :
? [P,Q] :
( ( perp(B,Q,C,A)
& coll(Q,C,A)
& perp(A,P,C,B)
& coll(P,C,B) )
| ~ perp(B,H,A,C)
| ~ perp(A,H,B,C) ),
inference(nnf_transformation,[status(thm)],[f85]) ).
fof(f85_sk,plain,
! [A,H,B,C] :
( ( perp(B,sk10(A,B,C,H),C,A)
& coll(sk10(A,B,C,H),C,A)
& perp(A,sk9(A,B,C,H),C,B)
& coll(sk9(A,B,C,H),C,B) )
| ~ perp(B,H,A,C)
| ~ perp(A,H,B,C) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9,sk10])],[f85_nnf]) ).
cnf(c98,plain,
( perp(X1,sk10(X0,X1,X2,X3),X2,X0)
| ~ perp(X1,X3,X0,X2)
| ~ perp(X0,X3,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f85_sk]) ).
cnf(hi98,axiom,
ifeq(perp(X0,X1,X2,X3),true,ifeq(perp(X2,X1,X0,X3),true,perp(X2,sk10(X0,X2,X3,X1),X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c98]) ).
cnf(c116,plain,
perp(sk20,sk24,sk20,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
perp(sk20,sk24,sk20,sk25) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h8,plain,
perp(sk20,sk10(sk20,sk20,sk25,sk24),sk25,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi98,hi116,hi116]) ).
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(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h38,plain,
perp(sk25,sk20,sk20,sk10(sk20,sk20,sk25,sk24)) = true,
inference(hyper_resolution,[status(thm)],[hi7,h8]) ).
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(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(h120,plain,
para(sk25,sk20,sk25,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,h38,h8]) ).
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(h361,plain,
coll(sk25,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi66,h120]) ).
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(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(c113,plain,
eqangle(sk23,sk20,sk20,sk22,sk23,sk20,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
eqangle(sk23,sk20,sk20,sk22,sk23,sk20,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h2,plain,
eqangle(sk20,sk22,sk23,sk20,sk20,sk21,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi18,hi113]) ).
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(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(h26,plain,
para(sk20,sk22,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi38,h2]) ).
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(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(h0,plain,
eqangle(sk23,sk20,sk23,sk20,sk20,sk22,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi20,hi113]) ).
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(h19,plain,
eqangle(sk20,sk23,sk23,sk20,sk20,sk22,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi17,h0]) ).
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(hi73,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,ifeq(para(X4,X5,X6,X7),true,para(X0,X1,X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(h89,plain,
para(sk20,sk23,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi73,h19,h26]) ).
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(hi3,axiom,
ifeq(para(X0,X1,X2,X3),true,para(X0,X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h261,plain,
para(sk20,sk23,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi3,h89]) ).
fof(f65,axiom,
! [A,B,C,D,O] :
( ( coll(O,B,D)
& coll(O,A,C)
& para(A,B,C,D) )
=> eqratio(O,A,A,C,O,B,B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD65) ).
fof(f65_nnf,plain,
! [A,B,C,D,O] :
( eqratio(O,A,A,C,O,B,B,D)
| ~ coll(O,B,D)
| ~ coll(O,A,C)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f65]) ).
fof(f65_sk,plain,
! [A,B,C,D,O] :
( eqratio(O,A,A,C,O,B,B,D)
| ~ coll(O,B,D)
| ~ coll(O,A,C)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f65_nnf]) ).
cnf(c65,plain,
( eqratio(X4,X0,X0,X2,X4,X1,X1,X3)
| ~ coll(X4,X1,X3)
| ~ coll(X4,X0,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
cnf(hi65,axiom,
ifeq(para(X0,X1,X2,X3),true,ifeq(coll(X4,X0,X2),true,ifeq(coll(X4,X1,X3),true,eqratio(X4,X0,X0,X2,X4,X1,X1,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c65]) ).
cnf(t83,plain,
eqratio(sk25,sk20,sk20,sk20,sk25,sk23,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi65,h261,h361,h286]) ).
cnf(t2769,plain,
eqratio(sk25,sk20,sk20,sk20,sk25,sk23,sk23,sk23) = true,
inference(orient,[status(thm)],[t83]) ).
cnf(t2770,plain,
true = ifeq(true,true,eqratio(sk25,sk20,sk25,sk23,sk20,sk20,sk23,sk23),true),
inference(cp,[status(thm)],[t376,t2769]) ).
cnf(t37,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t37]) ).
cnf(t11858,plain,
true = eqratio(sk25,sk20,sk25,sk23,sk20,sk20,sk23,sk23),
inference(step,[status(thm)],[t2770,t256]) ).
cnf(t11398,plain,
eqratio(sk25,sk20,sk25,sk23,sk20,sk20,sk23,sk23) = true,
inference(orient,[status(thm)],[t11858]) ).
cnf(t11408,plain,
true = ifeq(true,true,ifeq(cong(sk20,sk20,sk23,sk23),true,cong(sk25,sk20,sk25,sk23),true),true),
inference(cp,[status(thm)],[t366,t11398]) ).
cnf(t11859,plain,
true = ifeq(cong(sk20,sk20,sk23,sk23),true,cong(sk25,sk20,sk25,sk23),true),
inference(step,[status(thm)],[t11408,t256]) ).
fof(f43,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD43) ).
fof(f43_nnf,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c43,plain,
( cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(t253,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(t341,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(orient,[status(thm)],[t253]) ).
cnf(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(t312,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]) ).
cnf(h282,plain,
coll(sk25,sk25,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h129,h129]) ).
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(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(h362,plain,
eqangle(sk25,sk20,V0,V1,sk25,sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h120]) ).
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(h2311,plain,
cyclic(sk20,sk23,sk25,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi42,h362,h282]) ).
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(hi40,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,eqangle(X2,X0,X2,X1,X3,X0,X3,X1),true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t76,plain,
eqangle(sk25,sk20,sk25,sk23,sk25,sk20,sk25,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi40,h2311]) ).
cnf(t1823,plain,
eqangle(sk25,sk20,sk25,sk23,sk25,sk20,sk25,sk23) = true,
inference(orient,[status(thm)],[t76]) ).
cnf(t1827,plain,
true = ifeq(true,true,eqangle(sk25,sk20,sk25,sk20,sk25,sk23,sk25,sk23),true),
inference(cp,[status(thm)],[t312,t1823]) ).
cnf(t11672,plain,
true = eqangle(sk25,sk20,sk25,sk20,sk25,sk23,sk25,sk23),
inference(step,[status(thm)],[t1827,t256]) ).
cnf(t8116,plain,
eqangle(sk25,sk20,sk25,sk20,sk25,sk23,sk25,sk23) = true,
inference(orient,[status(thm)],[t11672]) ).
cnf(t8126,plain,
true = ifeq(cyclic(sk20,sk20,sk25,sk23),true,ifeq(cyclic(sk20,sk20,sk25,sk23),true,ifeq(cyclic(sk20,sk20,sk25,sk25),true,ifeq(true,true,cong(sk20,sk20,sk23,sk23),true),true),true),true),
inference(cp,[status(thm)],[t341,t8116]) ).
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(t141,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)],[t141]) ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD16) ).
fof(f15_nnf,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t142,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t344,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(orient,[status(thm)],[t142]) ).
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(t140,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)],[t140]) ).
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(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(h1,plain,
eqangle(sk23,sk20,sk20,sk21,sk23,sk20,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi113]) ).
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(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(h22,plain,
eqangle(sk23,sk20,sk20,sk22,sk23,sk20,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi21,hi113,h1]) ).
cnf(h77,plain,
para(sk23,sk20,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi38,h22]) ).
cnf(h232,plain,
coll(sk23,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi66,h77]) ).
cnf(h609,plain,
coll(sk20,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h232,h232]) ).
cnf(h12,plain,
perp(sk20,sk25,sk20,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi116]) ).
cnf(h58,plain,
para(sk20,sk25,sk20,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi8,h12,hi116]) ).
cnf(h183,plain,
eqangle(sk20,sk25,V0,V1,sk20,sk25,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h58]) ).
cnf(h1508,plain,
cyclic(sk25,sk23,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h183,h609]) ).
cnf(hi14,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,cyclic(X0,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t32,plain,
cyclic(sk25,sk20,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi14,h1508]) ).
cnf(t2473,plain,
cyclic(sk25,sk20,sk23,sk20) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(t2474,plain,
true = ifeq(true,true,cyclic(sk25,sk20,sk20,sk23),true),
inference(cp,[status(thm)],[t348,t2473]) ).
cnf(t11450,plain,
true = cyclic(sk25,sk20,sk20,sk23),
inference(step,[status(thm)],[t2474,t256]) ).
cnf(t3959,plain,
cyclic(sk25,sk20,sk20,sk23) = true,
inference(orient,[status(thm)],[t11450]) ).
cnf(t3960,plain,
true = ifeq(true,true,cyclic(sk20,sk25,sk20,sk23),true),
inference(cp,[status(thm)],[t344,t3959]) ).
cnf(t11470,plain,
true = cyclic(sk20,sk25,sk20,sk23),
inference(step,[status(thm)],[t3960,t256]) ).
cnf(t4335,plain,
cyclic(sk20,sk25,sk20,sk23) = true,
inference(orient,[status(thm)],[t11470]) ).
cnf(t4336,plain,
true = ifeq(true,true,cyclic(sk20,sk20,sk25,sk23),true),
inference(cp,[status(thm)],[t346,t4335]) ).
cnf(t11492,plain,
true = cyclic(sk20,sk20,sk25,sk23),
inference(step,[status(thm)],[t4336,t256]) ).
cnf(t4744,plain,
cyclic(sk20,sk20,sk25,sk23) = true,
inference(orient,[status(thm)],[t11492]) ).
cnf(t11673,plain,
true = ifeq(true,true,ifeq(cyclic(sk20,sk20,sk25,sk23),true,ifeq(cyclic(sk20,sk20,sk25,sk25),true,ifeq(true,true,cong(sk20,sk20,sk23,sk23),true),true),true),true),
inference(step,[status(thm)],[t8126,t4744]) ).
cnf(t11674,plain,
true = ifeq(cyclic(sk20,sk20,sk25,sk23),true,ifeq(cyclic(sk20,sk20,sk25,sk25),true,ifeq(true,true,cong(sk20,sk20,sk23,sk23),true),true),true),
inference(step,[status(thm)],[t11673,t256]) ).
cnf(t11675,plain,
true = ifeq(true,true,ifeq(cyclic(sk20,sk20,sk25,sk25),true,ifeq(true,true,cong(sk20,sk20,sk23,sk23),true),true),true),
inference(step,[status(thm)],[t11674,t4744]) ).
cnf(t11676,plain,
true = ifeq(cyclic(sk20,sk20,sk25,sk25),true,ifeq(true,true,cong(sk20,sk20,sk23,sk23),true),true),
inference(step,[status(thm)],[t11675,t256]) ).
cnf(c97,plain,
( coll(sk10(X0,X1,X2,X3),X2,X0)
| ~ perp(X1,X3,X0,X2)
| ~ perp(X0,X3,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f85_sk]) ).
cnf(hi97,axiom,
ifeq(perp(X0,X1,X2,X3),true,ifeq(perp(X2,X1,X0,X3),true,coll(sk10(X0,X2,X3,X1),X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c97]) ).
cnf(h9,plain,
coll(sk10(sk20,sk20,sk25,sk24),sk25,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi97,hi116,hi116]) ).
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(h45,plain,
coll(sk25,sk10(sk20,sk20,sk25,sk24),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi1,h9]) ).
cnf(h138,plain,
coll(sk20,sk20,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h45,h45]) ).
cnf(t35,plain,
cyclic(sk25,sk25,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h183,h138]) ).
cnf(t2510,plain,
cyclic(sk25,sk25,sk20,sk20) = true,
inference(orient,[status(thm)],[t35]) ).
cnf(t2511,plain,
true = ifeq(true,true,cyclic(sk25,sk20,sk25,sk20),true),
inference(cp,[status(thm)],[t346,t2510]) ).
cnf(t11453,plain,
true = cyclic(sk25,sk20,sk25,sk20),
inference(step,[status(thm)],[t2511,t256]) ).
cnf(t4013,plain,
cyclic(sk25,sk20,sk25,sk20) = true,
inference(orient,[status(thm)],[t11453]) ).
cnf(t4014,plain,
true = ifeq(true,true,cyclic(sk25,sk20,sk20,sk25),true),
inference(cp,[status(thm)],[t348,t4013]) ).
cnf(t11473,plain,
true = cyclic(sk25,sk20,sk20,sk25),
inference(step,[status(thm)],[t4014,t256]) ).
cnf(t4387,plain,
cyclic(sk25,sk20,sk20,sk25) = true,
inference(orient,[status(thm)],[t11473]) ).
cnf(t4388,plain,
true = ifeq(true,true,cyclic(sk20,sk25,sk20,sk25),true),
inference(cp,[status(thm)],[t344,t4387]) ).
cnf(t11494,plain,
true = cyclic(sk20,sk25,sk20,sk25),
inference(step,[status(thm)],[t4388,t256]) ).
cnf(t4778,plain,
cyclic(sk20,sk25,sk20,sk25) = true,
inference(orient,[status(thm)],[t11494]) ).
cnf(t4779,plain,
true = ifeq(true,true,cyclic(sk20,sk20,sk25,sk25),true),
inference(cp,[status(thm)],[t346,t4778]) ).
cnf(t11507,plain,
true = cyclic(sk20,sk20,sk25,sk25),
inference(step,[status(thm)],[t4779,t256]) ).
cnf(t5002,plain,
cyclic(sk20,sk20,sk25,sk25) = true,
inference(orient,[status(thm)],[t11507]) ).
cnf(t11677,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk20,sk20,sk23,sk23),true),true),
inference(step,[status(thm)],[t11676,t5002]) ).
cnf(t11678,plain,
true = ifeq(true,true,cong(sk20,sk20,sk23,sk23),true),
inference(step,[status(thm)],[t11677,t256]) ).
cnf(t11679,plain,
true = cong(sk20,sk20,sk23,sk23),
inference(step,[status(thm)],[t11678,t256]) ).
cnf(t8127,plain,
cong(sk20,sk20,sk23,sk23) = true,
inference(orient,[status(thm)],[t11679]) ).
cnf(t11860,plain,
true = ifeq(true,true,cong(sk25,sk20,sk25,sk23),true),
inference(step,[status(thm)],[t11859,t8127]) ).
cnf(t11861,plain,
true = cong(sk25,sk20,sk25,sk23),
inference(step,[status(thm)],[t11860,t256]) ).
cnf(t11862,plain,
true = false,
inference(step,[status(thm)],[t11861,t3041]) ).
cnf(t11409,plain,
false = true,
inference(orient,[status(thm)],[t11862]) ).
cnf(t11863,plain,
cong(sk25,sk20,sk25,sk23) = true,
inference(step,[status(thm)],[t3041,t11409]) ).
cnf(t11410,plain,
cong(sk25,sk20,sk25,sk23) = true,
inference(orient,[status(thm)],[t11863]) ).
cnf(goal_0,negated_conjecture,
cong(sk25,sk20,sk25,sk23) != true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t11410]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO618+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.38 % Computer : n013.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Wed Sep 23 12:34:00 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 83.94/11.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 83.94/11.10 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------