%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP777+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.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 01:35:23 PM UTC 2026
% Result : Theorem 207.35s 33.95s
% Output : CNFRefutation 207.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 89 ( 89 unt; 0 def)
% Number of atoms : 89 ( 88 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 166 ( 0 sgn 165 !; 1 ?; 127 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : difference(X1,product(X1,X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
fof(f2,axiom,
! [X0,X1] : product(X1,difference(X1,X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
fof(f3,axiom,
! [X0,X1] : quotient(product(X1,X0),X0) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
fof(f4,axiom,
! [X0,X1] : product(quotient(X1,X0),X0) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
fof(f5,axiom,
! [X0,X1,X2,X3] : product(product(X3,X2),product(X1,X0)) = product(product(X3,X1),product(X2,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
fof(f6,axiom,
! [X0] : product(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
fof(f7,axiom,
! [X0,X1] : product(product(product(X1,X0),X0),product(X0,product(X0,X1))) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).
fof(f8,axiom,
! [X0,X1,X2] : bigC(X2,X1,X0) = product(product(X2,X1),product(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos08) ).
fof(f9,axiom,
product(product(a,c),product(c,b)) = product(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).
fof(f10,conjecture,
! [X0] : bigC(a,b,X0) = bigC(c,c,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f11,negated_conjecture,
~ ! [X0] : bigC(a,b,X0) = bigC(c,c,X0),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,plain,
? [X0] : bigC(a,b,X0) != bigC(c,c,X0),
inference(ennf_transformation,[],[f11]) ).
fof(f13,plain,
bigC(a,b,sK0) != bigC(c,c,sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f12]) ).
fof(f14,plain,
! [X0,X1] : difference(X1,product(X1,X0)) = X0,
inference(cnf_transformation,[],[f1]) ).
fof(f15,plain,
! [X0,X1] : product(X1,difference(X1,X0)) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f16,plain,
! [X0,X1] : quotient(product(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f3]) ).
fof(f17,plain,
! [X0,X1] : product(quotient(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f4]) ).
fof(f18,plain,
! [X2,X3,X0,X1] : product(product(X3,X2),product(X1,X0)) = product(product(X3,X1),product(X2,X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f19,plain,
! [X0] : product(X0,X0) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f20,plain,
! [X0,X1] : product(product(product(X1,X0),X0),product(X0,product(X0,X1))) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f21,plain,
! [X2,X0,X1] : bigC(X2,X1,X0) = product(product(X2,X1),product(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f22,plain,
product(product(a,c),product(c,b)) = product(a,b),
inference(cnf_transformation,[],[f9]) ).
fof(f23,plain,
bigC(a,b,sK0) != bigC(c,c,sK0),
inference(cnf_transformation,[],[f13]) ).
fof(f24,plain,
product(product(a,b),product(sK0,a)) != product(product(c,c),product(sK0,c)),
inference(definition_unfolding,[],[f23,f21,f21]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : difference(X0,product(X0,X1)) = X1,
inference(cnf_transformation,[],[f14]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : product(X0,difference(X0,X1)) = X1,
inference(cnf_transformation,[],[f15]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : quotient(product(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f16]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : product(quotient(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f17]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : product(product(X0,X1),product(X2,X3)) = product(product(X0,X2),product(X1,X3)),
inference(cnf_transformation,[],[f18]) ).
tcf(c_54,plain,
! [X0: $i] : product(X0,X0) = X0,
inference(cnf_transformation,[],[f19]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : product(product(product(X0,X1),X1),product(X1,product(X1,X0))) = X1,
inference(cnf_transformation,[],[f20]) ).
tcf(c_56,plain,
product(product(a,c),product(c,b)) = product(a,b),
inference(cnf_transformation,[],[f22]) ).
tcf(c_57,negated_conjecture,
product(product(a,b),product(sK0,a)) != product(product(c,c),product(sK0,c)),
inference(cnf_transformation,[],[f24]) ).
tcf(c_83,plain,
product(product(a,b),product(sK0,a)) != product(c,product(sK0,c)),
inference(demodulation,[status(thm)],[c_57,c_54]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i] : quotient(X0,difference(X1,X0)) = X1,
inference(superposition,[status(thm)],[c_50,c_51]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i] : difference(quotient(X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c_52,c_49]) ).
tcf(c_159,plain,
difference(product(a,c),product(a,b)) = product(c,b),
inference(superposition,[status(thm)],[c_56,c_49]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i] : quotient(X0,product(X0,product(X0,X1))) = product(product(X1,X0),X0),
inference(superposition,[status(thm)],[c_55,c_51]) ).
tcf(c_258,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : product(product(X0,X1),product(difference(X0,X2),X3)) = product(X2,product(X1,X3)),
inference(superposition,[status(thm)],[c_50,c_53]) ).
tcf(c_262,plain,
! [X0: $i,X1: $i,X2: $i] : product(product(X0,X1),product(X0,X2)) = product(X0,product(X1,X2)),
inference(superposition,[status(thm)],[c_54,c_53]) ).
tcf(c_264,plain,
! [X0: $i,X1: $i] : product(product(product(a,c),X0),product(product(c,b),X1)) = product(product(a,b),product(X0,X1)),
inference(superposition,[status(thm)],[c_56,c_53]) ).
tcf(c_266,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : product(product(X0,quotient(X1,X2)),product(X3,X2)) = product(product(X0,X3),X1),
inference(superposition,[status(thm)],[c_52,c_53]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i,X2: $i] : product(product(X0,X1),product(X2,X1)) = product(product(X0,X2),X1),
inference(superposition,[status(thm)],[c_54,c_53]) ).
tcf(c_576,plain,
! [X0: $i,X1: $i,X2: $i] : product(X0,product(difference(X0,X1),X2)) = product(X1,product(X0,X2)),
inference(superposition,[status(thm)],[c_50,c_262]) ).
tcf(c_583,plain,
! [X0: $i,X1: $i,X2: $i] : product(X0,product(X1,difference(X0,X2))) = product(product(X0,X1),X2),
inference(superposition,[status(thm)],[c_50,c_262]) ).
tcf(c_587,plain,
! [X0: $i,X1: $i] : product(product(X0,X1),X0) = product(X0,product(X1,X0)),
inference(superposition,[status(thm)],[c_54,c_262]) ).
tcf(c_597,plain,
! [X0: $i,X1: $i,X2: $i] : difference(product(X0,X1),product(X0,product(X1,X2))) = product(X0,X2),
inference(superposition,[status(thm)],[c_262,c_49]) ).
tcf(c_751,plain,
! [X0: $i,X1: $i] : quotient(product(X0,product(X1,X0)),X0) = product(X0,X1),
inference(superposition,[status(thm)],[c_587,c_51]) ).
tcf(c_1067,plain,
! [X0: $i,X1: $i] : product(X0,quotient(X1,X0)) = quotient(product(X0,X1),X0),
inference(superposition,[status(thm)],[c_52,c_751]) ).
tcf(c_1131,plain,
! [X0: $i,X1: $i] : product(X0,quotient(difference(X0,X1),X0)) = quotient(X1,X0),
inference(superposition,[status(thm)],[c_50,c_1067]) ).
tcf(c_1142,plain,
! [X0: $i,X1: $i] : difference(product(X0,quotient(X1,X0)),product(X0,X1)) = X0,
inference(superposition,[status(thm)],[c_1067,c_149]) ).
tcf(c_1179,plain,
! [X0: $i,X1: $i] : product(product(quotient(difference(X0,X1),X0),X0),X0) = quotient(X0,product(X0,quotient(X1,X0))),
inference(superposition,[status(thm)],[c_1131,c_184]) ).
tcf(c_1183,plain,
! [X0: $i,X1: $i] : difference(X0,quotient(X1,X0)) = quotient(difference(X0,X1),X0),
inference(superposition,[status(thm)],[c_1131,c_49]) ).
tcf(c_1190,plain,
! [X0: $i,X1: $i] : quotient(X0,product(X0,quotient(X1,X0))) = product(difference(X0,X1),X0),
inference(demodulation,[status(thm)],[c_1179,c_52]) ).
tcf(c_1252,plain,
! [X0: $i,X1: $i] : difference(product(X0,quotient(X1,X0)),quotient(product(X0,X1),product(X0,quotient(X1,X0)))) = quotient(X0,product(X0,quotient(X1,X0))),
inference(superposition,[status(thm)],[c_1142,c_1183]) ).
tcf(c_1253,plain,
! [X0: $i,X1: $i] : difference(difference(X0,quotient(X1,X0)),difference(X0,X1)) = X0,
inference(superposition,[status(thm)],[c_1183,c_149]) ).
tcf(c_1254,plain,
! [X0: $i,X1: $i] : product(difference(X0,quotient(X1,X0)),X0) = difference(X0,X1),
inference(superposition,[status(thm)],[c_1183,c_52]) ).
tcf(c_1256,plain,
! [X0: $i,X1: $i] : difference(product(X0,quotient(X1,X0)),quotient(product(X0,X1),product(X0,quotient(X1,X0)))) = product(difference(X0,X1),X0),
inference(demodulation,[status(thm)],[c_1252,c_1190]) ).
tcf(c_1292,plain,
! [X0: $i,X1: $i] : difference(difference(product(X0,quotient(X1,X0)),quotient(product(X0,X1),product(X0,quotient(X1,X0)))),X0) = product(X0,quotient(X1,X0)),
inference(superposition,[status(thm)],[c_1142,c_1253]) ).
tcf(c_1299,plain,
! [X0: $i,X1: $i] : difference(product(difference(X0,X1),X0),X0) = product(X0,quotient(X1,X0)),
inference(demodulation,[status(thm)],[c_1292,c_1256]) ).
tcf(c_1388,plain,
! [X0: $i,X1: $i] : product(difference(X0,X1),X0) = difference(X0,product(X1,X0)),
inference(superposition,[status(thm)],[c_51,c_1254]) ).
tcf(c_1431,plain,
! [X0: $i,X1: $i] : quotient(product(X0,X1),product(difference(X1,X0),X1)) = X1,
inference(superposition,[status(thm)],[c_1388,c_144]) ).
tcf(c_1454,plain,
! [X0: $i,X1: $i] : product(difference(product(difference(X0,X1),X0),X0),product(difference(X0,X1),X0)) = difference(product(difference(X0,X1),X0),product(X1,X0)),
inference(superposition,[status(thm)],[c_1431,c_1254]) ).
tcf(c_1461,plain,
! [X0: $i,X1: $i] : difference(product(difference(X0,X1),X0),product(X1,X0)) = X1,
inference(demodulation,[status(thm)],[c_1454,c_50,c_54,c_266,c_1299]) ).
tcf(c_1493,plain,
! [X0: $i,X1: $i] : difference(product(difference(X0,quotient(X1,X0)),X0),X1) = quotient(X1,X0),
inference(superposition,[status(thm)],[c_52,c_1461]) ).
tcf(c_1506,plain,
! [X0: $i,X1: $i] : product(product(difference(X0,X1),X0),X1) = product(X1,X0),
inference(superposition,[status(thm)],[c_1461,c_50]) ).
tcf(c_1509,plain,
! [X0: $i,X1: $i] : product(difference(X0,X1),X0) = quotient(product(X1,X0),X1),
inference(superposition,[status(thm)],[c_1461,c_144]) ).
tcf(c_1510,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X1),X1) = quotient(X1,X0),
inference(demodulation,[status(thm)],[c_1493,c_1254]) ).
tcf(c_1856,plain,
! [X0: $i,X1: $i] : difference(X0,product(X1,X0)) = quotient(product(X1,X0),X1),
inference(superposition,[status(thm)],[c_49,c_1510]) ).
tcf(c_1870,plain,
! [X0: $i,X1: $i] : product(difference(X0,X1),quotient(X1,X0)) = X1,
inference(superposition,[status(thm)],[c_1510,c_50]) ).
tcf(c_2208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : product(product(difference(X0,X1),X2),product(X0,X3)) = product(quotient(product(X1,X0),X1),product(X2,X3)),
inference(superposition,[status(thm)],[c_1509,c_53]) ).
tcf(c_2240,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : product(product(difference(X0,X1),X2),product(X0,X3)) = product(product(X1,quotient(X0,X1)),product(X2,X3)),
inference(demodulation,[status(thm)],[c_2208,c_1067]) ).
tcf(c_3698,plain,
! [X0: $i,X1: $i,X2: $i] : quotient(product(product(X0,X1),X2),product(X1,X2)) = product(X0,X2),
inference(superposition,[status(thm)],[c_269,c_51]) ).
tcf(c_9625,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,product(product(X0,X1),X2)) = product(X1,difference(X0,X2)),
inference(superposition,[status(thm)],[c_583,c_49]) ).
tcf(c_10665,plain,
! [X0: $i,X1: $i,X2: $i] : difference(product(X0,X1),product(X0,X2)) = product(X0,difference(X1,X2)),
inference(superposition,[status(thm)],[c_50,c_597]) ).
tcf(c_10742,plain,
product(a,difference(c,b)) = product(c,b),
inference(demodulation,[status(thm)],[c_159,c_10665]) ).
tcf(c_11106,plain,
difference(a,product(c,b)) = difference(c,b),
inference(superposition,[status(thm)],[c_10742,c_49]) ).
tcf(c_11199,plain,
product(product(difference(c,b),a),product(c,b)) = product(product(c,b),a),
inference(superposition,[status(thm)],[c_11106,c_1506]) ).
tcf(c_11213,plain,
product(product(c,b),a) = product(product(b,a),c),
inference(demodulation,[status(thm)],[c_11199,c_266,c_2240]) ).
tcf(c_11352,plain,
quotient(product(product(c,b),a),product(b,a)) = difference(c,product(product(c,b),a)),
inference(superposition,[status(thm)],[c_11213,c_1856]) ).
tcf(c_11359,plain,
product(b,difference(c,a)) = product(c,a),
inference(demodulation,[status(thm)],[c_11352,c_3698,c_9625]) ).
tcf(c_11538,plain,
product(product(c,b),a) = product(c,product(c,a)),
inference(superposition,[status(thm)],[c_11359,c_583]) ).
tcf(c_11912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : product(X0,product(difference(difference(X1,X0),X2),X3)) = product(X2,product(quotient(X0,X1),X3)),
inference(superposition,[status(thm)],[c_1870,c_258]) ).
tcf(c_11928,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : product(product(X0,X1),product(X2,product(difference(X0,X3),X4))) = product(X3,product(X1,product(difference(difference(X0,X3),X2),X4))),
inference(superposition,[status(thm)],[c_576,c_258]) ).
tcf(c_11973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : product(product(product(X0,X1),X2),product(X3,product(X1,X4))) = product(product(X0,X1),product(X2,product(difference(X0,X3),X4))),
inference(superposition,[status(thm)],[c_258,c_262]) ).
tcf(c_17089,plain,
! [X0: $i] : product(product(product(a,c),X0),product(c,product(c,a))) = product(product(a,b),product(X0,a)),
inference(superposition,[status(thm)],[c_11538,c_264]) ).
tcf(c_17139,plain,
! [X0: $i] : product(product(a,b),product(X0,a)) = product(c,product(X0,c)),
inference(demodulation,[status(thm)],[c_17089,c_52,c_11973,c_11912,c_11928]) ).
tcf(c_17165,plain,
product(c,product(sK0,c)) != product(c,product(sK0,c)),
inference(demodulation,[status(thm)],[c_83,c_17139]) ).
tcf(c_17166,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_17165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP777+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/5.52 % Computer : n012.cluster.edu
% 0.04/5.52 % Model : x86_64 x86_64
% 0.04/5.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/5.52 % Memory : 8046.5625MB
% 0.04/5.52 % OS : Linux 6.8.0-71-generic
% 0.04/5.52 % CPULimit : 300
% 0.04/5.52 % WCLimit : 300
% 0.04/5.52 % DateTime : Wed Sep 23 16:01:12 UTC 2026
% 0.04/5.53 % CPUTime :
% 0.04/5.53 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/5.55 Running first-order theorem proving
% 0.04/5.55 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/5.56
% 0.04/5.56 % ======== iProver multi-core TPTP/SMT =========
% 0.04/5.56
% 0.04/5.56 % Detected problem language: tptp
% 0.04/5.56 % Proving...
% 207.35/33.95 % SZS status Started for theBenchmark.p
% 207.35/33.95 % SZS status Theorem for theBenchmark.p
% 207.35/33.95
% 207.35/33.95 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 207.35/33.95
% 207.35/33.95 % ------ iProver source info
% 207.35/33.95
% 207.35/33.95 % git: date: 2026-07-19 20:42:38 +0200
% 207.35/33.95 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 207.35/33.95 % git: non_committed_changes: false
% 207.35/33.95
% 207.35/33.95 % ------ Parsing...
% 207.35/33.95 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 207.35/33.95
% 207.35/33.95 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 207.35/33.95
% 207.35/33.95 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 207.35/33.95
% 207.35/33.95 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 207.35/33.95 % ------ Proving...
% 207.35/33.95 % ------ Problem Properties
% 207.35/33.95
% 207.35/33.95 %
% 207.35/33.95 % clauses 9
% 207.35/33.95 % conjectures 0
% 207.35/33.95 % EPR 0
% 207.35/33.95 % Horn 9
% 207.35/33.95 % unary 9
% 207.35/33.95 % binary 0
% 207.35/33.95 % lits 9
% 207.35/33.95 % lits eq 9
% 207.35/33.95 % fd_pure 0
% 207.35/33.95 % fd_pseudo 0
% 207.35/33.95 % fd_cond 0
% 207.35/33.95 % fd_pseudo_cond 0
% 207.35/33.95 % AC symbols 0
% 207.35/33.95
% 207.35/33.95 % ------ Input Options Time Limit: Unbounded
% 207.35/33.95
% 207.35/33.95
% 207.35/33.95 % ------
% 207.35/33.95 % Current options:
% 207.35/33.95 % ------
% 207.35/33.95
% 207.35/33.95
% 207.35/33.95 %
% 207.35/33.95
% 207.35/33.95 % ------ Proving...
% 207.35/33.95 %
% 207.35/33.95
% 207.35/33.95 % SZS status Theorem for theBenchmark.p
% 207.35/33.95
% 207.35/33.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 207.35/33.95
% 207.35/33.95
%------------------------------------------------------------------------------