%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG021-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n005.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 02:38:12 PM UTC 2026
% Result : Unsatisfiable 2.55s 1.37s
% Output : CNFRefutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 36 unt; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 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 : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 54 ( 0 sgn 54 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_additive_identity) ).
fof(f9,axiom,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_additive_inverse) ).
fof(f10,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(reorient_equations,[],[f9]) ).
fof(f11,axiom,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',additive_inverse_additive_inverse) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',distribute2) ).
fof(f14,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).
fof(f15,axiom,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',associativity_for_addition) ).
fof(f18,axiom,
! [X2,X0,X1] : associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X1,X2)))),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',associator) ).
fof(f20,negated_conjecture,
associator(add(u,v),x,y) != add(associator(u,x,y),associator(v,x,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_linearised_form3) ).
fof(f21,plain,
add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))) != add(add(multiply(multiply(u,x),y),additive_inverse(multiply(u,multiply(x,y)))),add(multiply(multiply(v,x),y),additive_inverse(multiply(v,multiply(x,y))))),
inference(definition_unfolding,[],[f20,f18,f18,f18]) ).
tcf(c_66,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(cnf_transformation,[],[f2]) ).
tcf(c_70,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = additive_identity,
inference(cnf_transformation,[],[f10]) ).
tcf(c_71,plain,
! [X0: $i] : additive_inverse(additive_inverse(X0)) = X0,
inference(cnf_transformation,[],[f11]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(cnf_transformation,[],[f13]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[],[f14]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(cnf_transformation,[],[f15]) ).
tcf(c_78,negated_conjecture,
add(add(multiply(multiply(u,x),y),additive_inverse(multiply(u,multiply(x,y)))),add(multiply(multiply(v,x),y),additive_inverse(multiply(v,multiply(x,y))))) != add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))),
inference(cnf_transformation,[],[f21]) ).
tcf(c_90,negated_conjecture,
add(multiply(multiply(u,x),y),add(multiply(multiply(v,x),y),add(additive_inverse(multiply(u,multiply(x,y))),additive_inverse(multiply(v,multiply(x,y)))))) != add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))),
inference(theory_normalisation,[status(thm)],[c_78,c_75,c_74]) ).
tcf(c_117,plain,
add(additive_inverse(multiply(u,multiply(x,y))),add(additive_inverse(multiply(v,multiply(x,y))),multiply(add(multiply(u,x),multiply(v,x)),y))) != add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))),
inference(ac_demodulation,[status(thm)],[c_90,c_73,c_75,c_74]) ).
tcf(c_118,plain,
add(additive_inverse(multiply(u,multiply(x,y))),add(additive_inverse(multiply(v,multiply(x,y))),multiply(multiply(add(u,v),x),y))) != add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))),
inference(ac_demodulation,[status(thm)],[c_117,c_73,c_75,c_74]) ).
tcf(c_213,plain,
! [X0: $i,X1: $i,X2: $i] : add(X0,add(X1,X2)) = add(X1,add(X0,X2)),
inference(superposition,[status(thm)],[c_75,c_74]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,additive_inverse(X0))) = add(X1,additive_identity),
inference(superposition,[status(thm)],[c_70,c_213]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,additive_inverse(add(X0,X1)))) = additive_identity,
inference(superposition,[status(thm)],[c_75,c_70]) ).
tcf(c_271,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(demodulation,[status(thm)],[c_228,c_66]) ).
tcf(c_281,plain,
! [X0: $i,X1: $i] : add(additive_inverse(X0),add(X1,X0)) = X1,
inference(superposition,[status(thm)],[c_71,c_271]) ).
tcf(c_292,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(theory_normalisation,[status(thm)],[c_281,c_75,c_74]) ).
tcf(c_353,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(additive_inverse(X1),X0))) = add(X1,additive_identity),
inference(superposition,[status(thm)],[c_247,c_292]) ).
tcf(c_520,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(additive_inverse(X1),X0))) = X1,
inference(demodulation,[status(thm)],[c_353,c_66]) ).
tcf(c_525,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(X0,additive_inverse(X1)))) = X1,
inference(superposition,[status(thm)],[c_74,c_520]) ).
tcf(c_598,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(X0,X1))) = additive_inverse(X1),
inference(superposition,[status(thm)],[c_71,c_525]) ).
tcf(c_716,plain,
! [X0: $i,X1: $i] : additive_inverse(add(additive_inverse(X0),X1)) = add(X0,additive_inverse(X1)),
inference(superposition,[status(thm)],[c_598,c_292]) ).
tcf(c_793,plain,
! [X0: $i,X1: $i] : add(additive_inverse(X0),additive_inverse(X1)) = additive_inverse(add(X0,X1)),
inference(superposition,[status(thm)],[c_71,c_716]) ).
tcf(c_945,plain,
! [X0: $i,X1: $i,X2: $i] : add(additive_inverse(X0),add(additive_inverse(X1),X2)) = add(additive_inverse(add(X0,X1)),X2),
inference(superposition,[status(thm)],[c_793,c_75]) ).
tcf(c_966,plain,
add(additive_inverse(add(multiply(u,multiply(x,y)),multiply(v,multiply(x,y)))),multiply(multiply(add(u,v),x),y)) != add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))),
inference(demodulation,[status(thm)],[c_118,c_945]) ).
tcf(c_967,plain,
add(multiply(multiply(add(u,v),x),y),additive_inverse(add(multiply(u,multiply(x,y)),multiply(v,multiply(x,y))))) != add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))),
inference(theory_normalisation,[status(thm)],[c_966,c_75,c_74]) ).
tcf(c_968,plain,
$false,
inference(ground_joinability,[status(thm)],[c_967,c_73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG021-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.56 % Computer : n005.cluster.edu
% 0.12/0.56 % Model : x86_64 x86_64
% 0.12/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.56 % Memory : 8046.5625MB
% 0.12/0.56 % OS : Linux 6.8.0-71-generic
% 0.12/0.56 % CPULimit : 300
% 0.12/0.56 % WCLimit : 300
% 0.12/0.56 % DateTime : Thu Sep 24 07:47:03 UTC 2026
% 0.12/0.56 % CPUTime :
% 0.12/0.56 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.60 Running UEQ theorem proving
% 0.12/0.60 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.61
% 0.12/0.61 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.61
% 0.12/0.61 % Detected problem language: tptp
% 0.12/0.62 % Proving...
% 2.55/1.37 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.55/1.37 % SZS status Started for theBenchmark.p
% 2.55/1.37 % SZS status Unsatisfiable for theBenchmark.p
% 2.55/1.37
% 2.55/1.37 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.55/1.37
% 2.55/1.37 % ------ iProver source info
% 2.55/1.37
% 2.55/1.37 % git: date: 2026-07-19 20:42:38 +0200
% 2.55/1.37 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.55/1.37 % git: non_committed_changes: false
% 2.55/1.37
% 2.55/1.37 % ------ Parsing...% successful
% 2.55/1.37
% 2.55/1.37
% 2.55/1.37 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.55/1.37
% 2.55/1.37 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.55/1.37
% 2.55/1.37 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.55/1.37
% 2.55/1.37 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.55/1.37 % ------ Proving...
% 2.55/1.37 % ------ Problem Properties
% 2.55/1.37
% 2.55/1.37 %
% 2.55/1.37 % clauses 13
% 2.55/1.37 % conjectures 0
% 2.55/1.37 % EPR 0
% 2.55/1.37 % Horn 13
% 2.55/1.37 % unary 13
% 2.55/1.37 % binary 0
% 2.55/1.37 % lits 13
% 2.55/1.37 % lits eq 13
% 2.55/1.37 % fd_pure 0
% 2.55/1.37 % fd_pseudo 0
% 2.55/1.37 % fd_cond 0
% 2.55/1.37 % fd_pseudo_cond 0
% 2.55/1.37 % AC symbols 1
% 2.55/1.37
% 2.55/1.37 % ------ Input Options Time Limit: Unbounded
% 2.55/1.37
% 2.55/1.37
% 2.55/1.37 % ------
% 2.55/1.37 % Current options:
% 2.55/1.37 % ------
% 2.55/1.37
% 2.55/1.37
% 2.55/1.37 %
% 2.55/1.37
% 2.55/1.37 % ------ Proving...
% 2.55/1.37 %
% 2.55/1.37
% 2.55/1.37 % SZS status Unsatisfiable for theBenchmark.p
% 2.55/1.37
% 2.55/1.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.55/1.37
% 2.55/1.37
%------------------------------------------------------------------------------